1 university of calgary long-term flexural performance of prestressed-nsm-cfrp

University of Calgary

PRISM: University of Calgary's Digital Repository

Graduate Studies The Vault: Electronic Theses and Dissertations

2013-11-07

Long-Term Flexural Performance of

Prestressed-NSM-CFRP Strengthened RC Beams

Yadollahi Omran, Hamid

Yadollahi Omran, H. (2013). Long-Term Flexural Performance of Prestressed-NSM-CFRP

Strengthened RC Beams (Unpublished doctoral thesis). University of Calgary, Calgary, AB.

doi:10.11575/PRISM/26783

http://hdl.handle.net/11023/1159

doctoral thesis

University of Calgary graduate students retain copyright ownership and moral rights for their

thesis. You may use this material in any way that is permitted by the Copyright Act or through

licensing that has been assigned to the document. For uses that are not allowable under

copyright legislation or licensing, you are required to seek permission.

Downloaded from PRISM: https://prism.ucalgary.ca

1

UNIVERSITY OF CALGARY

Long-Term Flexural Performance of Prestressed-NSM-CFRP Strengthened RC Beams

by

Hamid Yadollahi Omran

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF CIVIL ENGINEERING

CALGARY, ALBERTA

November, 2013

© Hamid Yadollahi Omran 2013

Harmonica

Rectangle

iii

Abstract

The use of prestressed Fibre Reinforced Polymer (FRP) for strengthening

structural members requires gaining further knowledge about the long-term behaviour of

these members. In this research, the long-term flexural performance of the prestressed

Near-Surface Mounted (NSM) Carbon Fibre Reinforced Polymer (CFRP) strengthened

Reinforced Concrete (RC) beams subjected to accelerated environmental exposure and

sustained load condition was studied. The static behaviour of the exposed and unexposed

beams was predicted numerically and analytically, and the predicted results were

compared with the experimental ones. The prestressing system used for tensioning the

NSM CFRP reinforcements was modified. The prestress loss in the NSM CFRP

reinforcements was studied. Deformability and ductility of the prestressed NSM CFRP

strengthened RC beams were studied in detail. Furthermore, the effects of the different

parameters on the flexural behaviour of the NSM CFRP strengthened RC beams and on

the pullout capacity of the anchorage system used for prestressing were investigated

numerically. The findings showed the significant effect of the applied exposure on the

flexural performance of the beams, and furthermore, the high reliability of the developed

numerical and analytical models for simulation of the static flexural behaviour of the

exposed and unexposed beams. The results of this research lead to an understanding of

the long-term flexural behave iour of the RC beams strengthened using prestressed NSM

CFRP reinforcements and pursue the evolution of this strengthening system to be used in

practical projects with sufficient confidence.

iv

Preface

In a country like Canada, deterioration of reinforced concrete (RC) bridges and

buildings due to severe weather conditions combined with aging and overloading causes

significant economical and social problems. Repairing damaged structures using proper

technique is vital to halt the losses of cost and time. The main advantages of FRP

materials such as excellent corrosion resistance, low density, and high tensile strength in

comparison with the conventional strengthening materials made FRP one of the most

commonly applied strengthening materials within past fifteen years. Among different

types of the strengthening systems developed for RC beams, prestressed Near-Surface-

Mounted (NSM) Carbon Fibre Reinforced Polymer (CFRP) is one of the latest techniques

for strengthening of concrete members.

This thesis consists of three parts: experimental study, finite element (FE)

analysis, and analytical investigation in which the long-term flexural performance of the

NSM CFRP strengthened RC beams was investigated. The experimental study consisted

of two phases and an additional investigation for the modification of the prestressing

system. The flexural performance of the prestressed NSM CFRP strengthened RC beams

subjected to freeze-thaw cycles was investigated in phase I, which consisted of nine

large-scale (5.15 m long with rectangular section 200×400 mm) beams: one un-

strengthened control RC beam, four strengthened RC beams using CFRP strips, and four

strengthened beams using CFRP rebars. CFRP rebar and strips with similar axial stiffness

were used for strengthening. The strengthened beams were prestressed to 0, 20, 40, and

v

60% of the ultimate CFRP tensile strain reported by the manufacturer. After

strengthening, all nine beams were initially loaded up to 1.2 times the analytical cracking

load for each beam, and then placed inside an environmental testing facility chamber,

exposed to 500 freeze-thaw cycles where each cycle was programmed between -34oC to

+34oC with period of 8 hrs and a relative humidity of 75% for temperatures above +20

oC.

The flexural performance of the prestressed NSM CFRP strengthened RC beams

subjected to combined freeze-thaw cycles and sustained load was investigated in phase II,

which consisted of five RC beams: one un-strengthened control beam and four beams

similar to the beams strengthened with CFRP strips in phase I. The beams in phase II

were subjected to the exposure similar to that of phase I (except that the relative humidity

of 75% for temperatures above +20oC was replaced with water spray, 18 L/min for a time

period of 10 min, at temperature +20oC, to increase the severity of the applied exposure)

while each beam was being subjected to a sustained load equal to 62 kN (47% of

analytical ultimate load of the non-prestressed NSM-CFRP strengthened RC beam). After

being subjected to exposure and loading, all beams in phases I and II were tested to

failure under four-point bending configuration and static monotonic loading. The tests

results revealed that the flexural performance of the beams tested in phase II was

significantly affected by the applied exposure and sustained loading while the exposure

had insignificant effects on the flexural performance of the beams tested in phase I.

Furthermore, an experimental investigation was performed on the modification of the

prestressing system used for NSM CFRP strengthening in phases I and II, to avoid

cracking at the location of the brackets during prestressing. The temporary steel brackets

vi

were modified to be capable of changing the eccentricity for prestressing (the location of

the jacks). To investigate the performance of the modified prestressing system, the

prestressing using the modified system was applied to three concrete specimens

(200×400×1500 mm) to a load equivalent to 93% of the CFRP ultimate strength reported

by the manufacturer, for three different eccentricities. The results showed the modified

system performed appropriately so that the cracking at location of the brackets can be

avoided during prestressing.

The FE analysis consisted of four parts performed using finite element software,

ANSYS. In part I, a nonlinear 3D FE model was developed to simulate the behaviour of

RC beams strengthened with prestressed NSM-CFRP strips. The model considered the

debonding at the concrete-epoxy interface. The FE model was compared and validated

with experimental test results reported by Gaafar (2007). In part II, a parametric study

was performed on the RC beams strengthened with prestressed NSM-CFRP strips by

developing a simplified 3D nonlinear FE model to decrease the solution time for doing

the parametric study. Then, the model was used to analyze twenty-three beams to assess

the effects of the prestressing level in NSM-CFRP strips, the tensile steel reinforcement

ratio, and the concrete compressive strength. In part III, a 3D FE model was developed to

simulate the behaviour of the end-steel anchor used for the prestressed NSM-CFRP

reinforcement. The CFRP-epoxy and epoxy-anchor interfaces were modeled by assigning

Coulomb friction model. Then, fourteen models were analyzed to investigate the effects

of bond cohesion, anchor length, anchor width, and anchor height on the interfacial stress

distributions and anchorage capacity. In part IV, the post-exposure load-deflection

vii

responses of the five beams tested in phase II of the experimental program were predicted

by developing a nonlinear 3D FE model similar to part I (FE modeling of unexposed

beams).

The analytical investigation consisted of two sections. In section I, after a brief

review on the available deformability or ductility indices, three deformability indices

were modified to be applicable for NSM-CFRP strengthened RC beams. Afterwards,

results of eighteen large-scale RC beams strengthened with prestressed and non-

prestressed NSM-CFRP strips and rebars were employed to evaluate their ductility and

deformability based on the modified models and the conventional indices. Furthermore,

the limits of the design Code (CAN/CSA-S6-06, 2011) for ductility and deformability of

the beams were used and new limits were proposed and validated for different models. In

section II, the load-deflection responses of the nine tested beams in phase I of the

experimental program were predicted analytically by developing a code in Mathematica

software. The code has the capabilities of assigning the actual concrete stress-strain curve

based on Loov's equation, elasto-plastic behaviour for compression and tension steel,

linear behaviour for FRP, and different prestressed CFRP length along the length of the

beam. Perfect bond is assumed in the analytical model. The mid-span deflection at each

applied load (moment) is calculated using integration of curvatures along the length of

the beam.

viii

Acknowledgements

I would like to express my greatest gratitude to the supervisor of this research, Dr.

Raafat El-Hacha who offered invaluable assistance, support, and guidance during this

PhD journey.

Thanks to the Intelligent Sensing for Innovative Structures Network (ISIS

Canada) and the University of Calgary through the URGC for partially financially

supporting this research. The in-kind support from Lafarge Canada for supplying the

Concrete, Sika Canada for providing the epoxy materials, and Hughes Brothers for

providing the CFRP reinforcements used in this project. Thanks to civil engineering lab

technicians at the University of Calgary: Terry Quinn, Dan Tilleman, Don Anson, Mirsad

Berbic, and Daniel Larson for endless help in progress of this project, and making

friendly environment in the lab. Many thanks to my friends and fellow graduate students,

in particular, Fadi Oudah, Khaled Abdelrahman, Donna Chen, Pouya Zangeneh, Khoa

Tran, Rashid Popal, Mohamadreza Seraji, Maryam Taghbostani, and Mona Amiri for

sharing thoughts, their supports, and all loving memories. Special thanks to Dr. Gerd

Birkle who provided me the opportunity to work during last two years of my education

that without his support it could have been tough. At the end, I would like to express my

gratitude and love to my beloved family and relatives for their support and endless love

during my studies.

To each one of you who has helped me on this journey:

“May the wind always be on your back and the sun upon your face”

ix

Dedication

With respect and love to:

My parents, Eyni & Leili, my brother, Saeid, and my sisters, Sara & Fariba, who have

made the happiest moments of my life whenever I have passed at home in the bosom of

my family

My uncle Ebrahim, who bravely fought against liver cancer for two years just after I

embarked upon this PhD journey and finally…, with all loving memories

My dearest grandparents

x

Table of Contents

Approval Page ..................................................................................................................... ii

Abstract .............................................................................................................................. iii Preface................................................................................................................................ iv Acknowledgements .......................................................................................................... viii Dedication .......................................................................................................................... ix Table of Contents .................................................................................................................x

List of Tables ................................................................................................................. xviii List of Figures and Illustrations ...................................................................................... xxii

List of Nomenclature and Symbols................................................................................xxxv

List of Abbreviations ......................................................................................................... xl

CHAPTER ONE: GENERAL INTRODUCTION ..............................................................1 1.1 Introduction ................................................................................................................1

1.2 The Most Important Reasons for Strengthening of Structures ..................................2 1.3 Methods for Upgrading the RC Members .................................................................3

1.4 Statement of the Problem ...........................................................................................3 1.4.1 Performance of Strengthened Beam with Prestressed NSM-FRP .....................3 1.4.2 Effects of Freeze-Thaw Exposure .....................................................................4

1.4.3 Effects of Sustained Load Combined with Freeze-Thaw Exposure ..................5

1.4.4 FE Analysis of the Prestressed NSM-FRP Strengthened RC Beams ................5 1.4.5 Analytical Model of the Exposed Prestressed NSM-FRP Strengthened RC

Beams .................................................................................................................6

1.4.6 Anchorage for Prestressed NSM-FRP Strengthening Method ..........................7 1.4.7 Modification of NSM-FRP Prestressing System ...............................................7

1.4.8 Deformability and Ductility of the Prestressed FRP Strengthened RC

Beams .................................................................................................................8

1.5 Research Objectives ...................................................................................................9 1.5.1 Principal Objectives ...........................................................................................9 1.5.2 Secondary Objectives ......................................................................................10

1.6 Scope of Work .........................................................................................................10 1.7 Thesis Layout ...........................................................................................................14

CHAPTER TWO: LITERATURE REVIEW ....................................................................15 2.1 Introduction ..............................................................................................................15

2.2 History of Engineering Materials ............................................................................15 2.3 Fibre Reinforced Polymer ........................................................................................16

2.3.1 Fibres ...............................................................................................................18 2.3.1.1 Carbon ....................................................................................................19 2.3.1.2 Glass .......................................................................................................20 2.3.1.3 Aramid ...................................................................................................21

xi

2.3.2 Matrices ...........................................................................................................21 2.3.3 FRP Composite ................................................................................................24

2.4 Strengthening Concrete Structures Using FRP Materials ........................................26 2.4.1 Externally Bonded Strengthening Method ......................................................27

2.4.2 Near-Surface Mounted Strengthening Method ...............................................27 2.5 History of NSM Method ..........................................................................................30 2.6 Material Used for NSM ...........................................................................................31

2.6.1 Reinforcements ................................................................................................31 2.6.2 Groove Filler ...................................................................................................32

2.7 Comparison between NSM-FRP and EB-FRP Technique ......................................33 2.8 Background of the Topic .........................................................................................34

2.9 Prestressed NSM-FRP Strengthened RC Beam .......................................................35

2.10 Environmental Exposure ........................................................................................47 2.10.1 Effect of Freeze-Thaw Exposure on Concrete ..............................................47 2.10.2 Effect of Freeze-Thaw Exposure on Steel Rebar ..........................................49

2.10.3 Effect of Freeze-Thaw Exposure on CFRP Reinforcement ..........................50 2.10.4 Effect of Freeze-Thaw Exposure on Epoxy Adhesive ..................................52

2.10.5 Effect of Sustained Loading on Concrete ......................................................53 2.10.6 Effect of Sustained Loading on FRP and Adhesive ......................................54 2.10.7 Synergistic Effect of Sustained Load and Freeze-Thaw Exposure ...............55

2.10.8 Effect of Environmental Exposure on FRP-Strengthened RC Beam ............56

2.11 FE Modeling of FRP-Strengthened RC Beams .....................................................64 2.12 Research Gaps ........................................................................................................73 2.13 Summary ................................................................................................................76

CHAPTER THREE: EXPERIMENTAL PROGRAM ......................................................77 3.1 Introduction ..............................................................................................................77

3.2 Test Matrix ...............................................................................................................77 3.3 RC Beam Specimens ...............................................................................................81

3.3.1 Design ..............................................................................................................81 3.3.2 Details of Beams ..............................................................................................84 3.3.3 Manufacturer Material Properties ....................................................................87

3.3.3.1 Steel Reinforcements .............................................................................87 3.3.3.2 Concrete .................................................................................................87

3.3.3.3 CFRP Reinforcements ...........................................................................87 3.3.3.4 Epoxy Adhesives ...................................................................................87

3.3.3.5 Anchor Bolts ..........................................................................................88 3.3.4 Fabrication .......................................................................................................88 3.3.5 Instrumentation ................................................................................................89

3.4 Prestressed NSM FRP Strengthening System .........................................................91 3.5 Initial Loading after Strengthening ..........................................................................91 3.6 Freeze-Thaw Cycling Exposure ...............................................................................92 3.7 Sustained Loading ....................................................................................................97

xii

3.8 Testing Procedure ..................................................................................................107 3.9 Summary ................................................................................................................108

CHAPTER FOUR: EXPERIMENTAL RESULTS AND DISCUSSION ......................109 4.1 Introduction ............................................................................................................109

4.2 Phase I: Prestressed NSM-CFRP Strengthened RC Beams under Freeze-Thaw

Exposure ..............................................................................................................110 4.2.1 Test Beams and Material Properties ..............................................................110

4.2.1.1 Steel Reinforcements ...........................................................................110

4.2.1.2 Concrete ...............................................................................................111 4.2.1.3 CFRP Reinforcements .........................................................................112

4.2.1.4 Epoxy Adhesives .................................................................................112 4.2.1.5 Anchor Bolts ........................................................................................112

4.2.2 Load-Deflection Response ............................................................................112 4.2.2.1 Pre-Cracking Behaviour ......................................................................116 4.2.2.2 Post-Cracking Behaviour .....................................................................118

4.2.2.3 Failure Mode and Cracking Pattern .....................................................120 4.2.3 Load-Strain Response ....................................................................................131

4.2.4 Strain Profile along the CFRP Strips or Rebar ..............................................140 4.2.5 Strain Distribution at Mid-span .....................................................................144

4.3 Effects of CFRP Geometry: Rebar versus Strips ...................................................149

4.4 Calculation of Optimum and Beneficial Prestressing Levels ................................152

4.5 Effects of Freeze-Thaw Cycling Exposure ............................................................156 4.5.1 Material Properties of the Unexposed Beams ...............................................156


4.5.1.2 CFRP Reinforcements .........................................................................156 4.5.1.3 Concrete ...............................................................................................157


4.5.2 Error Analysis ................................................................................................157 4.5.3 Load-Deflection Response ............................................................................161

4.5.3.1 Beams Strengthened with CFRP Strips ...............................................161 4.5.3.2 Beams Strengthened with CFRP Rebar ...............................................165 4.5.3.3 Beams Strengthened with CFRP Rebar versus Strips .........................170

4.5.4 Effects of Prestressing ...................................................................................173 4.6 Deformability and Ductility of NSM CFRP Strengthened RC Beams ..................178

4.6.1 Existing Ductility and Deformability Models ...............................................181 4.6.1.1 Displacement Ductility Index ..............................................................181 4.6.1.2 Curvature Ductility Index ....................................................................182 4.6.1.3 Rotational Ductility Index ...................................................................182 4.6.1.4 Deformability Factor ............................................................................183 4.6.1.5 Naaman and Jeong (1995) Index .........................................................183 4.6.1.6 Abdelrahman Index ..............................................................................184

xiii

4.6.1.7 CHBDC Deformability Factor .............................................................185 4.6.1.8 Zou Index .............................................................................................186 4.6.1.9 Rashid Index ........................................................................................187

4.6.2 Modification of the Deformability Models for FRP Strengthened RC

Beams .............................................................................................................189 4.6.2.1 Modified Deformability Factor ............................................................189 4.6.2.2 Modified CHBDC Deformability Index ..............................................190 4.6.2.3 Modified Zou Index .............................................................................191

4.6.3 Deformability of NSM-CFRP Strengthened RC Beam .................................192

4.6.3.1 Considered Beams ...............................................................................192 4.6.3.2 Deformability Analysis and Discussions .............................................194

4.7 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under Combined

Sustained Load and Freeze-Thaw Exposure ........................................................206 4.7.1 Test Beams and Material Properties ..............................................................206


4.7.1.2 Concrete ...............................................................................................207 4.7.1.3 CFRP Strips .........................................................................................208


4.7.2 Results from Sustained Load and Freeze-Thaw Exposure ............................208

4.7.3 Load-Deflection Response ............................................................................223

4.7.4 Load-Strain Response ....................................................................................236 4.7.5 Strain Profile along the CFRP Strips .............................................................243 4.7.6 Strain Distribution at Mid-span .....................................................................246

4.8 Combined Effects of Freeze-Thaw Cycling Exposure and Sustained Load ..........248 4.8.1 Material Properties of the Compared Beams .................................................249

4.8.2 Error Analysis ................................................................................................249 4.8.3 Load-Deflection Response ............................................................................250

4.9 Prestress Losses in Phases I & II ...........................................................................256 4.10 Modification of Temporary and Fixed Brackets of the Anchorage System for

Prestressing ..........................................................................................................265 4.10.1 Modified Prestressing System and Material Properties ...............................269

4.10.1.1 Concrete .............................................................................................271

4.10.1.2 Steel Reinforcements .........................................................................271

4.10.1.3 Dywidag Thread-Bar and Nuts ..........................................................271

4.10.1.4 Steel Bolts ..........................................................................................271 4.10.2 Testing Procedure ........................................................................................272 4.10.3 Results and Discussion ................................................................................273

4.11 Summary ..............................................................................................................277

CHAPTER FIVE: NUMERICAL AND ANALYTICAL SIMULATIONS ...................279 5.1 Introduction ............................................................................................................279

xiv

5.2 Finite Element Modeling of RC Beams Strengthened with Prestressed NSM-

FRP ......................................................................................................................280 5.2.1 Experimental Program Overview and Material Properties ...........................280


5.2.1.2 Concrete ...............................................................................................283 5.2.1.3 CFRP Strips .........................................................................................283 5.2.1.4 Epoxy Adhesives .................................................................................283 5.2.1.5 Anchor Bolts ........................................................................................283

5.2.2 Description of Finite Element Model ............................................................284

5.2.3 Modeling of Materials ...................................................................................285 5.2.3.1 Concrete ...............................................................................................285


5.2.3.3 CFRP Strips .........................................................................................295 5.2.3.4 Epoxy Adhesives .................................................................................296 5.2.3.5 End Anchor and Loading and Supporting Steel Plates ........................298

5.2.3.6 Bolts at End Anchors ...........................................................................298 5.2.4 Debonding Model ..........................................................................................299

5.2.4.1 Identification of Shear Stress-Slip Model ............................................304 5.2.4.2 Identification of Normal Tension Stress-Gap Model ..........................306

5.2.5 Modeling of Prestressing ...............................................................................307

5.2.6 Mesh Sensitivity Analysis .............................................................................308

5.2.7 Nonlinear Analysis ........................................................................................316 5.2.8 FE Results, Validation, and Discussion ........................................................318

5.2.8.1 Load-Deflection Curve ........................................................................318

5.2.8.2 Strain Profiles and Distributions ..........................................................324 5.2.8.3 Debonding aspects ...............................................................................329

5.3 Parametric Study on RC Beams Strengthened with Prestressed NSM-FRP .........332 5.3.1 Modeled Beams .............................................................................................332

5.3.2 Description of FE Model ...............................................................................334 5.3.3 Modeling of Materials ...................................................................................335

5.3.3.1 Concrete ...............................................................................................335 5.3.3.2 Steel Reinforcements ...........................................................................337 5.3.3.3 CFRP Strips .........................................................................................337

5.3.3.4 Epoxy Adhesive ...................................................................................337

5.3.3.5 Bolts at Steel End Anchor ....................................................................338

5.3.3.6 Steel End Anchor and Loading and Supporting Steel Plates ...............338 5.3.3.7 Bond at Concrete-Epoxy Interface ......................................................338 5.3.3.8 Modeling of Prestressing .....................................................................339

5.3.4 Nonlinear Solution .........................................................................................339 5.3.5 Validation of the Model .................................................................................340

5.3.6 Parametric Study ...........................................................................................343 5.3.6.1 Effects of Prestressing Level in the NSM CFRP .................................343 5.3.6.2 Effects of Tension Steel Reinforcement ..............................................357

xv

5.3.6.3 Effects of Concrete Compressive Strength ..........................................363 5.4 FE Modeling of Steel End Anchor and Parametric Study .....................................364

5.4.1 Description of the FE Model .........................................................................365 5.4.2 Modeling of Materials ...................................................................................367

5.4.2.1 Steel End Anchor .................................................................................367 5.4.2.2 CFRP Strip ...........................................................................................368 5.4.2.3 Epoxy Adhesive ...................................................................................368 5.4.2.4 Anchor Bolt ..........................................................................................369 5.4.2.5 Bond .....................................................................................................369

5.4.3 Mesh Sensitivity Analysis .............................................................................370 5.4.4 Nonlinear Analysis ........................................................................................374

5.4.5 Numerical Results and Discussion ................................................................378

5.4.5.1 Effects of Bond Cohesion ....................................................................378 5.4.5.2 Effects of Anchorage Length ...............................................................381 5.4.5.3 Effects of Adhesive Width ...................................................................385

5.4.5.4 Effects of Adhesive Height ..................................................................390 5.5 Analytical Modeling of RC Beams Strengthened With Prestressed NSM-CFRP

Reinforcements Subjected to Freeze-Thaw Exposure .........................................395 5.5.1 Experimental Program Overview ..................................................................396 5.5.2 Description of Algorithm ..............................................................................397

5.5.2.1 Concepts for Calculation of Deflection at an Arbitrary Load Level ...397

5.5.3 Modeling of Materials ...................................................................................402 5.5.3.1 Concrete of Exposed Beam ..................................................................402 5.5.3.2 Steel Reinforcement .............................................................................403

5.5.3.3 CFRP Strip or Rebar ............................................................................404 5.5.4 Nonlinear Analysis ........................................................................................404

5.5.5 Analytical Results and Discussion ................................................................406 5.5.5.1 Load-Deflection Curve ........................................................................406

5.6 FE Modeling of RC Beams Strengthened with Prestressed NSM-CFRP

Reinforcement Subjected to Freeze-Thaw Exposure and Sustained Load ..........413 5.6.1 Experimental Program Overview ..................................................................413 5.6.2 Description of finite element model ..............................................................413 5.6.3 Debonding Model of Exposed Beams ...........................................................414

5.6.3.1 Bond-Slip Model for Exposed Beams .................................................414

5.6.3.2 Normal Tension Stress-Gap Model for Exposed Beams .....................415

5.6.4 Modeling of Prestressing ...............................................................................415 5.6.5 Modeling of Materials ...................................................................................416

5.6.5.1 Concrete of Exposed Beams ................................................................416 5.6.5.2 Steel Reinforcement .............................................................................418 5.6.5.3 CFRP Strip ...........................................................................................419

5.6.5.4 Epoxy Adhesive, Loading Plate, Steel Anchors, and Steel Bolts ........420 5.6.6 Nonlinear Analysis ........................................................................................420 5.6.7 Numerical Results and Discussion ................................................................421

xvi

5.7 Summary ................................................................................................................425

CHAPTER SIX: CONCLUSIONS AND RECOMMENDATIONS ..............................427 6.1 Introduction ............................................................................................................427 6.2 Conclusions ............................................................................................................428

6.2.1 Experimental Test Results .............................................................................428 6.2.1.1 Phase I: Experimental Study on RC Beams Strengthened with

Prestressed NSM-CFRP Strips and Rebar Subjected to Freeze-Thaw

Exposure................................................................................................428

6.2.1.2 Deformability and Ductility of NSM CFRP Strengthened RC Beams 431 6.2.1.3 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under

Combined Sustained Load and Freeze-Thaw Exposure .......................432 6.2.1.4 Prestress Losses in Prestressed NSM CFRP Strips and Rebar ............435

6.2.1.5 Modification of the NSM CFRP Prestressing System .........................435 6.2.2 Numerical and Analytical Simulations ..........................................................436

6.2.2.1 Finite Element Modeling of RC Beams Strengthened with

Prestressed NSM-FRP...........................................................................436 6.2.2.2 Parametric Study on RC Beams Strengthened with Prestressed

NSM-FRP..............................................................................................437 6.2.2.3 FE Modeling of Steel End Anchor and Parametric Study ...................438 6.2.2.4 Analytical Modeling of RC Beams Strengthened With Prestressed

NSM-CFRP Reinforcements Subjected to Freeze-Thaw Exposure .....439

6.2.2.5 FE Modeling of RC Beams Strengthened with Prestressed NSM-

CFRP Reinforcement Subjected to Freeze-Thaw Exposure and

Sustained Load ......................................................................................440

6.3 Recommendations ..................................................................................................441

REFERENCES ................................................................................................................443

LIST OF TO DATE PUBLICATIONS FROM THE RESEARCH PRESENTED IN

THIS PHD THESIS ................................................................................................467

APPENDIX A: BEAM DESIGN.....................................................................................470 A.1 Introduction ...........................................................................................................470

A.2 Design Concepts, Source Code, and Results ........................................................470

APPENDIX B: FABRICATION OF BEAMS ................................................................477 B.1 Introduction ...........................................................................................................477 B.2 Fabrication of Formwork ......................................................................................477 B.3 Steel Cage ..............................................................................................................478

B.4 Casting Concrete ...................................................................................................479 B.5 Strengthening Procedure .......................................................................................480

B.5.1 General Steps ................................................................................................480

B.5.2 Preparation of CFRP Strips or Rebar ............................................................483

xvii

B.5.3 Steel Bolts for End Anchors and Temporary Brackets .................................484 B.5.4 Mechanical Anchors .....................................................................................485 B.5.5 Temporary Brackets ......................................................................................486 B.5.6 Cutting Grooves ............................................................................................487

B.5.7 Drilling Holes for Bolts ................................................................................488 B.5.8 Prestressing System for NSM CFRP ............................................................489

APPENDIX C: ANCILLARY TEST RESULTS ............................................................491 C.1 Introduction ...........................................................................................................491

C.2 Concrete ................................................................................................................491 C.3 CFRP Strip and Rebar ...........................................................................................495

C.4 Steel Reinforcements ............................................................................................498

APPENDIX D: ANSYS LOGS .......................................................................................501

D.1 Introduction ...........................................................................................................501 D.2 ANSYS Logs for BS-P2-R ...................................................................................501

D.2.1 BS-P2-R.mntr ...............................................................................................501

D.2.2 BS-P2-R.BSC ...............................................................................................505 D.2.3 BS-P2-R.stat .................................................................................................505

D.2.4 BS-P2-R.s01 .................................................................................................506 D.2.5 BS-P2-R.s02 .................................................................................................507 D.2.6 BS-P2-R.s03 .................................................................................................508

D.2.7 BS-P2-R.s04 .................................................................................................509

D.2.8 BS-P2-R.s05 .................................................................................................511 D.2.9 BS-P2-R.s06 .................................................................................................512 D.2.10 BS-P2-R.s07 ...............................................................................................513

APPENDIX E: DEVELOPED COMPUTATIONAL SOURCE CODE IN

MATHEMATICA...................................................................................................516

E.1 Introduction ...........................................................................................................516 E.2 Calculation of the Exposed Concrete Stress-Strain Curve ....................................516

E.3 Computational Source Code ..................................................................................517

xviii

List of Tables

Table ‎2-1: Some application of polymer composites (Sheikh-Ahmad, 2008). ................. 18

Table ‎2-2: Tensile properties of typical carbon fibres (Akovali, 2001). .......................... 20

Table ‎2-3: Typical properties of different glass fibres (Akovali, 2001). .......................... 20

Table ‎2-4: Properties of some aramid fibres (Akovali, 2001). ......................................... 21

Table ‎2-5: Mechanical and thermal properties of matrix materials at room

temperature (Sheikh-Ahmad, 2008). ......................................................................... 23

Table ‎2-6: Some aspects of epoxy and polyester thermosets (Akovali, 2001). ................ 24

Table ‎2-7: Environmental considerations for different FRP materials (NCHRP, 2004). . 25

Table ‎2-8: Typical properties of FRP bars (ISIS Design Manual No.3, 2007). ............... 26

Table ‎2-9: Aspects of EB and NSM strengthening methods (Täljsten et al., 2003). ........ 34

Table ‎2-10: Summary of existing experimental work on flexural strengthening using

NSM-FRP reinforcements. ....................................................................................... 39


NSM-FRP reinforcements (Cont’d). ......................................................................... 40













xix

Table ‎2-11: Thermal expansion coefficient of concrete in different temperature

(Oldershaw, 2008). .................................................................................................... 49

Table ‎2-12: Summary of some existing research on freeze-thaw exposure (study of

the considered cycles). .............................................................................................. 62

Table 2-12: Summary of some existing research on freeze-thaw exposure (study of

the considered cycles) (Cont’d). ............................................................................... 63

Table ‎3-1: Test matrix. ...................................................................................................... 79

Table ‎3-2: Summary of the specimens used for modification of the brackets.................. 81

Table ‎3-3: Summary of designed specimens. ................................................................... 83

Table ‎3-4: Properties of CFRP strip and rebar recommended by the manufacturer

(Hughes Brothers, 2010a and b). .............................................................................. 87

Table ‎3-5: Properties of epoxy adhesives reported by the manufacturer (Sika, 2010a

and b). ....................................................................................................................... 88

Table ‎3-6: Summary of initial loading and obtained experimental and theoretical

cracking loads. .......................................................................................................... 92

Table ‎3-7: Environmental chamber schedule for one freeze-thaw cycle. ......................... 96

Table ‎4-1: CFRP material properties obtained from tension tests. ................................. 112

Table ‎4-2: Summary of the test results of the beams subjected to freeze-thaw

exposure (phase I). .................................................................................................. 115

Table ‎4-3: Strain in CFRP strips or rebar, extreme compression fibre of concrete,

compression steel, and tension steel at mid-span at different stages. ..................... 139

Table ‎4-4: Strain in extreme compression fibre of concrete, compression steel, tension

steel, and CFRP strips or rebar at mid-span. ........................................................... 149

Table ‎4-5: CFRP material properties for unexposed beams. .......................................... 156

Table ‎4-6: Uncertainty in comparison of the exposed and unexposed beams based on

material properties. ................................................................................................. 160

Table ‎4-7: Summary of the test results for strengthened beam using CFRP strips. ....... 163

Table ‎4-8: Summary of the test results for strengthened beam using CFRP rebars. ...... 169

xx

Table ‎4-9: Summary of existing ductility and deformability indices. ............................ 188

Table ‎4-10: Results of the beams (load-deflection). ....................................................... 193

Table ‎4-11: Results of the beams (moment-curvature). .................................................. 194

Table ‎4-12: Ductility or deformability indices of beams. ............................................... 196

Table ‎4-13: CFRP material properties obtained from tension tests. ............................... 208

Table ‎4-14: Debonded length of the beams shown in Figure ‎4-67. ................................ 217

Table ‎4-15: Summary of the test results for phase II (beams subjected to combined

sustained load and freeze-thaw exposure). ............................................................. 227


compression steel, and tension steel at mid-span at different stages. ..................... 243

Table ‎4-17: Strain in extreme compression fibre of concrete, compression steel,

tension steel, and CFRP strip or rebar at mid-span section. ................................... 248

Table ‎4-18: Uncertainty in comparison of sets BS-FS and BS-F based on material

properties. ................................................................................................................ 250

Table ‎4-19: Summary of the test results for strengthened beam using CFRP strips

(phases I & II). ........................................................................................................ 253

Table ‎4-20: Modification of the prestressing system test results. ................................... 274

Table ‎5-1: Mesh sensitivity models. ............................................................................... 311

Table ‎5-2: Summary of load-steps assigned for nonlinear analysis. .............................. 317

Table ‎5-3: Summary of the results. ................................................................................. 323

Table ‎5-4: Properties of the modeled beams. .................................................................. 333

Table ‎5-5: Summary of load-steps assigned for nonlinear analysis. .............................. 339

Table ‎5-6: Comparison between numerical and experimental results of beam BS-58-

0.75-40. ................................................................................................................... 343

Table ‎5-7: Summary of the results for the effects of prestressing. ................................. 346

Table ‎5-8: Summary of the results for the effects of tension steel ratio. ........................ 357

xxi

Table ‎5-9: Summary of the results for the effects of concrete compressive strength. .... 364

Table ‎5-10: Summary of the modeled steel end anchors. ............................................... 366

Table ‎5-11: Summary of FE results, cohesion effects. ................................................... 380

Table ‎5-12: Summary of FE results, anchor length effects. ........................................... 384

Table ‎5-13: Summary of FE results, adhesive width effects. ......................................... 387

Table ‎5-14: Summary of FE results, adhesive height effects. ........................................ 392

Table ‎5-15: Summary of the results for BS-F set. .......................................................... 410

Table ‎5-16: Summary of the results for BR-F set. .......................................................... 412

Table ‎5-17: Summary of load-steps assigned for nonlinear analysis. ............................ 421

Table ‎5-18: Summary of the results. ............................................................................... 423

Table A-1: Summary of designed specimens. ................................................................ 476

Table B-1: Groove and CFRP strips/rebar lengths. ........................................................ 484

Table C-1: Concrete compression test results. ................................................................ 494

Table C-2: Properties of the CFRP materials obtained from tension tests. .................... 497

xxii

List of Figures and Illustrations

Figure ‎2-1: The evolution of materials for civil engineering (Ashby, 1987). ................... 16

Figure ‎2-2: Typical stress-strain curves of the different fibres and common steel

reinforcements (ACI 440R, 2007). ........................................................................... 19

Figure ‎2-3: Different types of FRP composites (Sireg, 2011). ......................................... 25

Figure ‎2-4: Typical stress-strain curves for matrix, fibres, and resulted FRP composite

(ISIS Design Manual No.3, 2007). ........................................................................... 26

Figure ‎2-5: Schematic of flexural strengthening using FRP: (a) EB FRP, (b) NSM-

FRP strips, and (c) NSM-FRP rebars. ....................................................................... 28

Figure ‎2-6: Some field applications of NSM-FRP based strengthening........................... 29

Figure ‎2-7: Different shapes of FRP reinforcements for NSM strengthening (De

Lorenzis and Teng, 2007). ........................................................................................ 32

Figure ‎2-8: Damage done to the concrete cylinder after 500 cycles of freeze-thaw

(tested in this research). ............................................................................................ 48

Figure ‎2-9: Concept of residual stresses in composite at high and low temperatures

(Dutta, 1989). ............................................................................................................ 51

Figure ‎2-10: Applied exposure on the FRP specimens (Micelli, 2004). .......................... 52

Figure ‎2-11: Creep strain-time relationship for concrete under uni-axial stress (Bisby,

2006). ........................................................................................................................ 54

Figure ‎3-1: Geometry of the beams and test setup. .......................................................... 85

Figure ‎3-2: Details of the beams. ...................................................................................... 86

Figure ‎3-3: Beams instrumentation: (a) elevation and (b) cross-section at mid-span

location. ..................................................................................................................... 90

Figure ‎3-4: Maximum mean daily temperature (CAN/CSA-S6-06, 2011). ..................... 93

Figure ‎3-5: Minimum mean daily temperature (CAN/CSA-S6-06, 2011). ...................... 93

Figure ‎3-6: Annual mean relative humidity (CAN/CSA-S6-06, 2011). ........................... 94

Figure ‎3-7: Three typical freeze-thaw cycles.................................................................... 96

xxiii

Figure ‎3-8: Plan view of chamber floor equipped for sustained loading. ......................... 99

Figure ‎3-9: Plan view of sustained loading..................................................................... 100

Figure ‎3-10: Side view of sustained loading. .................................................................. 101

Figure ‎3-11: Cross view of sustained loading. ................................................................ 102

Figure ‎3-12: Sustained load setup in the environmental chamber. ................................. 103

Figure ‎3-13: Applying Sustained load in the chamber. .................................................. 104

Figure ‎3-14: Beams under sustained load and after 500 freeze-thaw cycles. ................. 105

Figure ‎3-15: Beams under sustained load and after 500 freeze-thaw cycles. ................. 106

Figure ‎3-16: Test setup. .................................................................................................. 107

Figure ‎4-1: Load-deflection curves of the beams subjected to freeze-thaw exposure

(phase I). ................................................................................................................. 114

Figure ‎4-2: Interaction between temporary brackets and beam due to prestressing. ...... 117

Figure ‎4-3: Photos of beam B0-F at failure. ................................................................... 123

Figure ‎4-4: Photos of beam BS-NP-F at failure.............................................................. 124

Figure ‎4-5: Photos of beam BR-NP-F at failure. ............................................................ 125

Figure ‎4-6: Photos of beam BS-P1-F at failure. ............................................................. 126

Figure ‎4-7: Photos of beam BR-P1-F at failure. ............................................................. 127

Figure ‎4-8: Photos of beam BS-P2-F at failure. ............................................................. 128

Figure ‎4-9: Photos of beam BR-P2-F at failure. ............................................................. 129

Figure ‎4-10: Photos of beam BS-P3-F at failure. ........................................................... 130

Figure ‎4-11: Photos of beam BR-P3-F at failure. ........................................................... 131

Figure ‎4-12: Load-strain curves: BS-NP-F vs BR-NP-F. ............................................... 135

Figure ‎4-13: Load-strain curves: BS-P1-F vs BR-P1-F. ................................................. 135


xxiv


Figure ‎4-16: Load-CFRP strain curves for all beams. .................................................... 137

Figure ‎4-17: Load-concrete strain curves for all beams. ................................................ 137

Figure ‎4-18: Load-tension steel strain curves for all beams. .......................................... 138

Figure ‎4-19: Load-compression steel strain curves for all beams. ................................. 138

Figure ‎4-20: Local buckling of compression steel bars at mid-span of beam B0-F. ...... 139

Figure ‎4-21: Strain profile along the length of the CFRP strips or rebar at cracking. .... 142

Figure ‎4-22: Strain profile along the length of the CFRP strips or rebar at yielding. .... 143

Figure ‎4-23: Strain profile along the length of the CFRP strips or rebar at ultimate. .... 143

Figure ‎4-24: Strain distribution at mid-span at cracking. ............................................... 146

Figure ‎4-25: Strain distribution at mid-span at yielding. ................................................ 147

Figure ‎4-26: Strain distribution at mid-span at ultimate. ................................................ 148

Figure ‎4-27: Damage done to the prestressed NSM CFRP strengthened beams at

failure (bottom view) (Cont’d). ............................................................................... 151

Figure ‎4-28: Effects of prestressing on energy absorption and calculation of optimum

prestressing level ..................................................................................................... 153

Figure ‎4-29: Schematic for the concept of improvement in energy absorption. ............ 155

Figure ‎4-30: Calculation of the beneficial prestressing level. ........................................ 155

Figure ‎4-31: Comparison between exposed and unexposed RC beams strengthened

using CFRP strips. .................................................................................................. 162

Figure ‎4-32: Comparison between exposed and unexposed beams strengthened with

CFRP rebars. ........................................................................................................... 168

Figure ‎4-33: Comparison between exposed and unexposed beams. ............................... 172

Figure ‎4-34: Effects of prestressing on cracking load w.r.t non-prestressed NSM

CFRP strengthened beam in each set. ..................................................................... 173

xxv

Figure ‎4-35: Effects of prestressing on yield load w.r.t non-prestressed NSM CFRP

strengthened beam in each set. ................................................................................ 174

Figure ‎4-36: Effects of prestressing on ultimate load w.r.t non-prestressed

strengthened beam in each set. ................................................................................ 175

Figure ‎4-37: Effects of prestressing on deflection at ultimate load w.r.t non-

prestressed NSM CFRP strengthened beam in each set. ........................................ 177

Figure ‎4-38: Effects of prestressing on the energy absorption of the exposed and

unexposed NSM CFRP strengthened RC beams. ................................................... 178

Figure ‎4-39: Total, elastic, and inelastic energies (Retrieved from Naaman and Jeong,

1995). ...................................................................................................................... 184

Figure ‎4-40: Equivalent deflection, Δ1, and failure deflection, Δu (Retrieved from

Abdelrahman et al., 1995). ...................................................................................... 185

Figure ‎4-41: Idealized tri-linear slope load-deflection response. ................................... 190

Figure ‎4-42: Idealized tri-linear slope moment-curvature response. .............................. 191

Figure ‎4-43: Deformability and ductility models applied to the unexposed beams. ...... 197

Figure ‎4-44: Deformability and ductility models applied to the exposed beams. .......... 198

Figure ‎4-45: Comparison between the original and the modified deformability models

applied to the unexposed beams.............................................................................. 200

Figure ‎4-46: Comparison between the original and the modified deformability models

applied to the exposed beams.................................................................................. 201

Figure ‎4-47: Verification of proposed limit for curvature ductility index (µ). ............. 203

Figure ‎4-48: Verification of proposed limit for displacement ductility index (µD). ....... 203

Figure ‎4-49: Verification of proposed limit for modified J factor (Jm). ......................... 204

Figure ‎4-50: Verification of proposed limit for modified Zou index (Zm). .................... 204

Figure ‎4-51: Verification of proposed limit for modified deformability factor (µEm). ... 205

Figure ‎4-52: Load-deflection history for beam B0-FS. .................................................. 210

Figure ‎4-53: Load-deflection history for beam BS-NP-FS. ............................................ 211

xxvi

Figure ‎4-54: Load-deflection history for beam BS-P1-FS. ............................................ 211



Figure ‎4-57: Sustained load history for beam B0-F........................................................ 213

Figure ‎4-58: Sustained load history for beam BS-NP-FS. .............................................. 213

Figure ‎4-59: Sustained load history for beam BS-P1-FS. .............................................. 213



Figure ‎4-62: Deflection history for beam B0-FS. ........................................................... 214

Figure ‎4-63: Deflection history for beam BS-NP-FS. .................................................... 215

Figure ‎4-64: Deflection history for beam BS-P1-FS. ..................................................... 215



Figure ‎4-67: Debonding occurred at concrete-epoxy interface due to freeze-thaw

exposure and sustained load. ................................................................................... 217

Figure ‎4-68: Images of beam B0-FS after exposure. ...................................................... 218

Figure ‎4-69: Images of beam BS-NP-FS after exposure. ............................................... 219

Figure ‎4-70: images of beam BS-P1-FS after exposure. ................................................ 220

Figure ‎4-71: Images of beam BS-P2-FS after exposure. ................................................ 221

Figure ‎4-72: Images of beam BS-P3-FS after exposure. ................................................ 222

Figure ‎4-73: Load-deflection curves of the beams subjected to combined sustained

load and freeze-thaw exposure (phase II, set BS-FS, including permanent

deflection after sustained load and freeze-thaw exposure). .................................... 225

Figure ‎4-74: Load-deflection curves of the beams subjected to combined sustained

load and freeze-thaw exposure (phase II, set BS-FS). ............................................ 226

xxvii

Figure ‎4-75: Photos of beam B0-FS at failure. ............................................................... 228

Figure ‎4-76: Photos of beam BS-NP-FS at failure. ........................................................ 229

Figure ‎4-77: Photos of beam BS-P1-FS at failure. ......................................................... 230



Figure ‎4-80: Load-strain curves for BS-NP-FS. ............................................................. 239

Figure ‎4-81: Load-strain curves for BS-P1-FS. .............................................................. 239



Figure ‎4-84: Load-CFRP strain for all beams................................................................. 241

Figure ‎4-85: Load-concrete strain in extreme compression fibre for all beams. ............ 241

Figure ‎4-86: Load-tension steel strain curves for all beams. .......................................... 242

Figure ‎4-87: Load-compression steel strain curves for all beams. ................................. 242

Figure ‎4-88: Gap between bolt and jacking end anchor causing future prestress loss. .. 244

Figure ‎4-89: Strain profile along the length of the NSM CFRP strip at yielding. .......... 245

Figure ‎4-90: Strain profile along the length of the NSM CFRP strip at ultimate. .......... 246

Figure ‎4-91: Strain distribution at mid-span at yielding. ................................................ 247

Figure ‎4-92: Strain distribution at mid-span at ultimate. ................................................ 248

Figure ‎4-93: Comparison between exposed beams tested in phase I and II (freeze-

thaw exposure versus combined sustained load and freeze-thaw exposure). ......... 252

Figure ‎4-94: Effects of exposure on the energy absorption of the prestressed NSM

CFRP strengthened RC beams. ............................................................................... 255

Figure ‎4-95: Losses in prestressed NSM CFRP strip or rebar: BS-P1-F and BR-P1-F. 258


xxviii


Figure ‎4-98: Losses in NSM CFRP strip (BS sets) at room temperature. ...................... 259

Figure ‎4-99: CFRP Strain fluctuation in beam BS-NP-F under freeze-thaw exposure. . 262

Figure ‎4-100: CFRP Strain fluctuation in beam BS-P1-F under freeze-thaw exposure. 262



Figure ‎4-103: CFRP Strain fluctuation in beam BR-NP-F under freeze-thaw

exposure. ................................................................................................................. 264

Figure ‎4-104: CFRP Strain fluctuation in beam BR-P1-F under freeze-thaw exposure. 264

Figure ‎4-105: CFRP Strain fluctuation in beam BR-P2-F under freeze-thaw exposure. 265

Figure ‎4-106: Prestressing system developed by Gaafar (2007). ................................... 266

Figure ‎4-108: Cracks at the locations of steel brackets at high prestress level. .............. 267

Figure ‎4-109: Interaction between temporary steel brackets and beam. ........................ 268

Figure ‎4-110: Modified prestressing system applied to the specimens. ......................... 270

Figure ‎4-111: Applied test steps: low, medium, and high eccentricities. ....................... 273

Figure ‎4-112: Damage done to the specimens after three steps of test. .......................... 275

Figure ‎5-1: Details of the modeled beams. ..................................................................... 281

Figure ‎5-2: Stress-strain curves of steel bars. ................................................................. 282

Figure ‎5-3: Quarter of the beam to be modeled. ............................................................. 284

Figure ‎5-4: Geometry of Solid65 element (SAS, 2009). ................................................ 286

Figure ‎5-5: Concrete constitutive model in compression under flexural loading. .......... 289

Figure ‎5-6: Concrete constitutive model in tension (Retrieved from SAS, 2009).......... 292

Figure ‎5-7: Different approaches for modeling of reinforcement (Tavarez, 2001). ....... 293

Figure ‎5-8: Geometry of Link8 element (SAS, 2009). ................................................... 295

xxix

Figure ‎5-9: Geometry of Solid45 element (SAS, 2009). ................................................ 296

Figure ‎5-10: Strain-strain curve assigned to CFRP strip elements. ................................ 296

Figure ‎5-11: Strain-strain curve assigned to epoxy elements, Sikadur® 330. ................. 297

Figure ‎5-12: Strain-strain curve assigned to epoxy elements, Sikadur® 30. ................... 297

Figure ‎5-13: Geometry of Beam4 element (SAS, 2009). ............................................... 299

Figure ‎5-14: Geometry of elements for concrete-epoxy interface (SAS, 2009). ............ 301

Figure ‎5-15: Bilinear shear stress-slip model. ................................................................ 302

Figure ‎5-16: Bilinear normal tension stress-gap model. ................................................. 302

Figure ‎5-17: Mesh sensitivity models. ............................................................................ 312

Figure ‎5-18: Mesh sensitivity at 20 kN........................................................................... 313

Figure ‎5-19: The meshed beam (quarter of the tested beam). ........................................ 314

Figure ‎5-20: Cross-section of the beam. ......................................................................... 314

Figure ‎5-21: Steel reinforcements. .................................................................................. 315

Figure ‎5-22: Mesh at the end groove. ............................................................................. 315

Figure ‎5-23: Contact around the groove. ........................................................................ 315

Figure ‎5-24: End-steel anchor. ........................................................................................ 316

Figure ‎5-25: Comparison between FE and experimental results for B0-R and BS-NP-

R. ............................................................................................................................. 321

Figure ‎5-26: Comparison between FE and experimental results for BS-P1-R. .............. 321



Figure ‎5-29: Comparison between experimental and numerical strain profile along the

CFRP strip for beam BS-NP-R. .............................................................................. 325


CFRP strip for beam BS-P1-R. ............................................................................... 325

xxx





Figure ‎5-33: Comparison between experimental and numerical strain distribution

across the depth at mid-span for beam BS-NP-R. .................................................. 327


across the depth at mid-span for beam BS-P1-R. ................................................... 327





Figure ‎5-37: Debonding Parameter (dm) contour at the concrete-epoxy interface in the

model: (a) BS-NP-R at initiation of debonding (load = 130.4 kN, deflection =

80.14 mm) and (b) BS-NP-R at ultimate. ............................................................... 330

Figure ‎5-38: Debonding Parameter (dm) contour at the concrete-epoxy interface in the

model: (a) BS-P2-R at initiation of debonding (load = 140.4 kN, deflection =

68.32 mm) and (b) BS-P2-R at ultimate. ................................................................ 331

Figure ‎5-39: Simplified concrete compressive stress-strain curves. ............................... 336

Figure ‎5-40: Meshed beam. ............................................................................................ 340

Figure ‎5-41: Comparison between experimental and numerical load-deflection curves

of beam BS-58-0.75-40. .......................................................................................... 341


length of CFRP strips of beam BS-58-0.75-40. ...................................................... 342

Figure ‎5-43: Load-deflection curves of the modeled beams-effects of prestressing

level on set BS-0.75-40. .......................................................................................... 344


level on set BS-1.25-40. .......................................................................................... 344


level on set BS-1.75-40. .......................................................................................... 345

xxxi


level on set BS-2.25-40. .......................................................................................... 345

Figure ‎5-47: Effects of prestressing on negative camber. ............................................... 347

Figure ‎5-48: Effects of prestressing on cracking load. ................................................... 348

Figure ‎5-49: Effects of prestressing on yield load. ......................................................... 349

Figure ‎5-50: Effects of prestressing on ultimate load. .................................................... 350

Figure ‎5-51: Effects of prestressing on ultimate deflection. ........................................... 351

Figure ‎5-52: Effects of prestressing on ductility index. .................................................. 353

Figure ‎5-53: Effects of prestressing on energy absorption. ............................................ 353

Figure ‎5-54: Determination of optimum prestressing level for set BS-0.75................... 355




Figure ‎5-58: Effects of tension steel ratio on negative camber. ..................................... 359

Figure ‎5-59: Effects of tension steel ratio on cracking load. .......................................... 360

Figure ‎5-60: Effects of tension steel ratio on yield load. ................................................ 360

Figure ‎5-61: Effects of tension steel ratio on ultimate load. ........................................... 361

Figure ‎5-62: Effects of tension steel ratio on ultimate deflection. .................................. 361

Figure ‎5-63: Effects of tension steel ratio on ductility index.......................................... 362

Figure ‎5-64: Effects of tension steel ratio on energy absorption. ................................... 362

Figure ‎5-65: Effects of concrete compressive strength on the load-deflection curve. .... 363

Figure ‎5-66: Anchorage system for prestressed NSM-CFRP strengthening. ................. 365

Figure ‎5-67: Details of the modeled end anchors and abbreviation of dimensions. ....... 367

Figure ‎5-68: Stress-strain curve of anchor steel (Emam, 2007). .................................... 368

xxxii

Figure ‎5-69: Stress-strain curve for anchor bolts (Hilti Inc)........................................... 369

Figure ‎5-70: Anchorage model with 1509 elements developed for sensitivity analysis. 372




Figure ‎5-74: Mesh sensitivity (at 100 kN). ..................................................................... 374

Figure ‎5-75: Meshed anchor (steel tube length = 250 mm). ........................................... 376

Figure ‎5-76: Assigned constraints to the anchor model.................................................. 377

Figure ‎5-77: Effects of cohesion value (5-20 MPa) on load-displacement curves. ........ 378

Figure ‎5-78: Effects of cohesion value (5-20 MPa) on shear stress at CFRP-epoxy

vertical interface at 50 kN. ...................................................................................... 379

Figure ‎5-79: Effects of cohesion value (5-20 MPa) on shear stress at steel-epoxy


Figure ‎5-80: Developed FE models for the effects of anchorage length. ....................... 382

Figure ‎5-81: Effects of bond length (150-450 mm) on load-displacement curves. ........ 383

Figure ‎5-82: Effects of bond length (150-450 mm) on shear stress at CFRP-epoxy


Figure ‎5-83: Effects of bond length (150-450 mm) on shear stress at steel-epoxy


Figure ‎5-84: Developed FE models for the effects of adhesive width. .......................... 386

Figure ‎5-85: Effects of adhesive width (Wa=3.5-10.5 mm) on load-displacement

curves. ..................................................................................................................... 387

Figure ‎5-86: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at steel-

epoxy horizontal interface at 50 kN. ....................................................................... 388


epoxy vertical interface at 50 kN. ........................................................................... 388

xxxiii

Figure ‎5-88: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at CFRP-




Figure ‎5-90: Developed FE models for the effects of adhesive height. .......................... 391

Figure ‎5-91: Effects of adhesive height (Ha=1.5-7.5 mm) on load-displacement

curves. ..................................................................................................................... 392

Figure ‎5-92: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at steel-




Figure ‎5-94: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at CFRP-




Figure ‎5-96: Finding the integration limits for Equation 5-29 using moment diagram. 400

Figure ‎5-97: Strain and stress distribution on a prestressed NSM-CFRP strengthened

section. .................................................................................................................... 406

Figure ‎5-98: Comparison between experimental and analytical load-deflection

responses for BS-F set. ........................................................................................... 409

Figure ‎5-99: Comparison between experimental and analytical load-deflection

responses for BR-F set. ........................................................................................... 411

Figure ‎5-100: Simulation of the beams with exposed concrete materials. ..................... 417

Figure ‎5-101: Stress-strain curves of the steel bars for exposed beams in phase II. ...... 419

Figure ‎5-102: Stress-strain curves assigned to the CFRP strip elements........................ 420

Figure ‎5-103: Comparison between experimental and numerical load-deflection

curves. ..................................................................................................................... 422

Figure B-1: Fabrication of formwork. ............................................................................ 477

xxxiv

Figure B-2: Fabrication of the steel cage and placement in the formwork. .................... 479

Figure B-3: Fabrication of RC beams. ............................................................................ 480

Figure B-4: Attaching the CFRP reinforcements to the end anchors. ............................ 485

Figure B-5: Prestressing system developed by Gaafar (2007). ....................................... 486

Figure B-7: Cutting the groove. ...................................................................................... 488

Figure B-8: Groove preparation. ..................................................................................... 488

Figure B-9: Prestessed NSM strengthening. ................................................................... 490

Figure C-1: Concrete compression test and type of failure ............................................ 493

Figure C-2: Typical stress-strain curves of concrete (from batch#1 at 28 days) ............ 493

Figure C-2: Tension tests on CFRP strips and rebars. .................................................... 495

Figure C-3: Stress-strain relation of CFRP strip from batch #1. .................................... 496

Figure C-4: Stress-strain relation of CFRP rebar from batch #2. ................................... 496

Figure C-5: Stress-strain relation of CFRP strip from batch #3. .................................... 497

Figure C-6: Stress-strain curve of 15M steel bars in batch #1. ....................................... 499



xxxv

List of Nomenclature and Symbols

Symbol Definition

Ab

Abdelrahman deformability index

Ac area of concrete, mm2

Afrp area of FRP, mm2

Asc area of compression steel reinforcement, mm2

Ash area of one leg of the stirrup, mm2

Ast area of tension steel reinforcement, mm2

b width of RC beam, mm

b′ width of the stirrup (between centre lines of the bar), mm

b″ width of confined core measured to outside of the stirrup, mm

c depth of the neutral axis, mm

C cohesion, MPa

Cc compressive force carried by concrete, kN

Cs force in compression steel rebars, kN

d′ depth of the stirrup (between centre lines of the bar), mm

d″ depth of confined core measured to outside of the stirrup, mm

db bar diameter, mm

df depth to the centroid of the CFRP strips or rebars, mm

dm debonding parameter

dsc depth to the centroid of the top steel rebars, mm

dst depth to the centroid of the bottom steel rebars, mm

db bolt diameter, mm

dh hole diameter, mm

Ec modulus of elasticity of concrete, MPa

Ec exposed modulus of elasticity of concrete after exposure, MPa

Ec unexposed modulus of elasticity of concrete before exposure, MPa

Eel elastic part of the total energy, kN.mm

Efrp modulus of elasticity of FRP, GPa

Es area under load-deflection curve at service, kN.mm

Esc modulus of elasticity of compression steel reinforcement, GPa

Est modulus of elasticity of tension steel reinforcement, GPa

Etot total energy absorption, kN.mm

Eu area under load-deflection curve up to peak load, kN.mm

EI(x) flexural stiffness as a function of distance x, N.mm2

f′c concrete compressive strength, MPa

fc28 concrete compressive strength at 28 days, MPa

fc concrete compressive stress, MPa

fc exposed concrete compressive strength after exposure, MPa

xxxvi

fc unexposed concrete compressive strength before exposure, MPa

ffrpu ultimate tensile strength of FRP, MPa

fr tensile strength of concrete, MPa

fyc yield stress of compression steel, MPa

fyt yield stress of tension steel, MPa

Gcn total values of normal fracture energies, N/mm

Gct total values of shear fracture energies, N/mm

Gfo the base value of fracture energy, N/mm

h height of RC beam, mm

hf height of the CFRP strip, mm

Ha height of adhesive, mm

Ht height of anchor tube, mm

Igt moment of inertia of the gross transformed section, mm4

Igt-st the moment of inertia of the gross transformed strengthened section, mm4

Igt-un moment of inertia of the gross transformed un-strengthened section, mm4

J J deformability factor

Jm modified J factor

Kn contact normal stiffness, N/mm3

Kt contact shear stiffness, N/mm3

Lp distance from the support to the point load, mm

Lf length of CFRP strips, mm

Lo un-strengthened length of the beam at one side, mm

Lp length of anchor plate, mm

Lt length of anchor tube, mm

M moment, kN.m

Mapplied applied moment on the beam, kN.m

Mc moment corresponding to maximum concrete compressive strain of 0.001,

kN.m

Mcr moment at cracking, kN.m

Mu moment at ultimate state, kN.m

M(x) applied moment as a function of distance x, kN.m

Mp(x) moment due to prestressing as a function of distance x, kN.m

N number of freeze-thaw cycles

p contact pressure, MPa

Papplied applied load to each beam after strengthening for cracking, kN

Pcn cracking load of non-prestressed strengthened beam, kN

Pcr cracking load, kN

Pcr-exp. experimental cracking load, kN

Pcr-theo. theoretical cracking load, kN

Pcr-theo. sw. theoretical cracking load by considering the effect of self-weight, kN

Pu0 ultimate load of un-strengthened control beam, kN

xxxvii

Pu ultimate load, kN

Pun ultimate load of non-prestressed strengthened beam, kN

Py0 yielding load of un-strengthened control beam, kN

Py yielding load, kN

Pyn yielding load of non-prestressed strengthened beam, kN

R Rashid index

s percentage of uncertainty

sc uncertainty due to axial stiffness of the concrete material

scu uncertainty due to strength of the concrete material

sfrp uncertainty due to axial stiffness of the CFRP material

sfrpu uncertainty due to strength of the CFRP material

ssc uncertainty due to axial stiffness of the compression steel

sst uncertainty due to axial stiffness of the tension steel reinforcements

ssty uncertainty due to strength of the tension steel reinforcements

Ssh spacing of stirrups, mm

tf thickness of CFRP strip, mm

Tf force in CFRP strip or rebar, kN

Ts force in bottom steel rebars, kN

Tf thickness of CFRP strips, mm

Tt thickness of anchor tube, mm

un contact gap, mm

ūn contact gap at the maximum contact normal tension stress, mm

unc contact gap at the completion of debonding, mm

ut contact slip, mm

ūt contact slip at the maximum contact shear stress, mm

utc

contact slip at the completion of debonding, mm

Wa adhesive width, mm

Wf width of CFRP strips, mm

Wp width of anchor plate, mm

Wt width of anchor tube, mm

x distance from the support, mm

xcr distance from the support to a point where the applied moment is equal to

the cracking moment of the section, mm

xcr-st distance from the support to a point where the applied moment is equal to

the cracking moment capacity of the strengthened section, mm

xcr-un distance from the support to a point where the applied moment is equal to

the cracking moment capacity of the un-strengthened section, mm

y vertical distance from the neutral axis, mm

ӯCc distance between neutral axis and point of action of the resultant

compressive force on concrete, mm

Z Zou index

xxxviii

Zm modified Zou index

αfrp coefficient of thermal expansion of the CFRP, 1/oC

γ aspect ratio of the interface failure plane

Δ deflection, mm

Δcr deflection at cracking load, mm

Δcrush deflection at the initiation of concrete cover crushing, mm

Δl equivalent uncracked deflection at peak load, mm

Δo initial camber due to prestressing, mm

Δoe effective camber at seven days after prestressing, mm

Δop permanent deflection after initial loading, or sustained loading, mm

Δu deflection at ultimate load, mm

Δy deflection at yielding load, mm

ɛ Strain

ɛ0 strain at maximum concrete compressive strength

0 exposed concrete strain at peak stress after exposure

0 unexposed concrete strain at peak stress before exposure

ɛ50c confined concrete strain on the descending branch at 0.5f′c

ɛ50u unconfined concrete strain on the descending branch at 0.5f′c ɛc concrete strain

ɛc@u concrete strain at extreme compression fibre at ultimate load

cc concrete strain at extreme compression fibre

f strain in CFRP rebar or strip

ɛfrp@u maximum CFRP strain at ultimate load

ɛfrpu ultimate tensile strain of CFRP reinforcement

ɛl strain at the end of the linear part up to 0.3f′c

ɛp target prestrain value in CFRP reinforcement

pe effective prestrain in CFRP rebar or strips at seven days after prestressing

ɛsc strain in compression steel

ɛst strain in tension steel

yc yield strain of compression steel

yt yield strain of tension steel

u rotation at peak load, rad

y rotation at yielding, rad

μ friction coefficient

µD displacement ductility index

µE deformability factor

µEm modified deformability factor

µN-J Naaman and Jeong index

µ rotation ductility index

µ curvature ductility index

xxxix

oC degree Celcius

σ axial stress, MPa

σmax maximum normal tensile stress of contact, MPa

σn contact normal stress, MPa

τ shear strength, MPa

τt contact shear stress, MPa

τmax maximum shear stress of contact, MPa

Φ area under P-Δ curve, kN.mm

φ curvature, rad/mm

c curvature corresponding to maximum concrete compressive strain of 0.001,

rad/mm

cr mid-span curvature at cracking, rad/mm

o curvature due to prestressing, rad/mm

oe effective curvature seven days after prestressing, rad/mm

u mid-span curvature at peak load, rad/mm

y mid-span curvature at yielding, rad/mm

(x) curvature at distance x, rad/mm

xl

List of Abbreviations

Abbreviation Definition

AFRP

aramid fibre reinforced polymer

CC concrete crushing

CCS concrete cover spalling

CFRP carbon fibre reinforced polymer

DB debonding

EB

FE

externally bonded

finite element

FM failure mode

FR FRP rupture

FRP fibre reinforced polymer

GFRP glass fibre reinforced polymer

HSS hollow structural steel,

LSC linear strain conversion

NSM near-surface mounted

RC reinforced concrete

SG strain gauge

SRLS self-reacting loading system

TC thermocouple

UV ultra-violet

1

Chapter One: General Introduction

1.1 Introduction

In a country like Canada which experiences an annual mean relative humidity of

50-90% (CAN/CSA–S6–06, 2011) and an average freeze-thaw frequency of 39 cycles

per year (Fraser, 1959), deterioration of reinforced concrete (RC) members of bridges and

buildings due to severe weather conditions is a common problem. In most cases, this

deterioration is accompanied by aging, cyclic/fatigue loads, and overloading causing

serious economic and social problems. Canada has over 80,000 bridges of which about

50% are over 35 years old and close to their 50 years design life (Ramcharitar, 2004). In

the United States, the Federal Highway Administration (FHWA) data in the National

Bridge Inventory (NBI) show almost 40% of the 650,000 highway bridges are

structurally deficient or functionally obsolete (Yanev, 2005). The annual rehabilitation

and replacement cost of bridges in Canada is $0.7 billion (Mirza and Haider, 2003) while

this value is $7 billion in the United States (Yanev, 2005). Just in the province of Alberta,

Canada, there are over 1500 reinforced concrete bridges built during mid-part of the 20th

century (Sayed-Ahmed et al., 2004). Most of them are short span (8-12 m) and simply

supported. Over the years, many of these bridges have shown signs of degradation due to

severe environmental conditions. Identification of proper upgrading methods for

damaged structures is vital to overcome the problems. Among the different types of

strengthening techniques developed for RC girders/beams, the prestressed Near-Surface

Mounted (NSM) Carbon Fibre Reinforced Polymer (CFRP) method is one of the latest.

The CFRP material has the advantages of excellent corrosion resistance, high tensile

2

strength, and low density in comparison with conventional steel reinforcement, which is

being replaced in some cases by FRP within past fifteen years. In the NSM method, the

strengthening reinforcement is mounted in a groove made in the concrete cover and is

bonded with epoxy adhesive/cement mortar. These main advantages of the NSM-CFRP

method include reduced debonding possibility and better resistance against fire in

comparison with Externally Bonded (EB)-FRP method. The effectiveness of the

prestressed NSM strengthening technique has been proved through conducting laboratory

projects (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Badawi and Soudki,

2009); However, in these researches, prestressing of the NSM-CFRP reinforcements was

performed against both ends of the RC beam or against an independent steel reaction

frame that made the proposed prestressed NSM method unsuitable for field application.

In the research described here, the CFRP strips/rebars were prestressed using an

innovative anchorage system, developed by Gaafar (2007), that consists of two steel

anchors bonded to the end of the CFRP strips/rebar using epoxy and a movable bracket

temporarily mounted on the beam. Overall, this project mainly focuses on the effects of

prestressing level, freeze-thaw exposure, and sustained and static loading to cover the

gaps in this field and to provide a better understanding of the effectiveness of the NSM

strengthening technique to be employed in practical projects with confidence.

1.2 The Most Important Reasons for Strengthening of Structures

Strengthening of damaged/deficient structures is categorized based on the

following main reasons:

Respond to change in performance level or increase in applied load

3

Upgrade to meet new Standards and Codes criteria

Correct an error in design and construction

Repair environmental damages due to severe weather condition, earthquake,

corrosion etc

Correct architectural difficulties and practical problems

1.3 Methods for Upgrading the RC Members

To satisfy the demands mentioned above, upgrading a structure or a member of a

structure can be performed according to one of the following methods:

Steel jacketing

Concrete covering with reinforcement

Post-tensioned cables

Fibre Reinforcement Polymer (FRP) strengthening

1.4 Statement of the Problem

The research significance of the study reported in this thesis is built upon on the

gaps that exisist in the filed of understanding the long-term performamnce of RC

structures strengthened using FRP materials.

1.4.1 Performance of Strengthened Beam with Prestressed NSM-FRP

Recently application of prestressed NSM-FRP has become an interesting topic for

researchers (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Gaafar, 2007;

Badawi and Soudki, 2009). In fact, strengthening using prestressed NSM-FRP can

4

improve the performance of a beam with respect to a non-prestressed strengthened beam

in terms of serviceability, crack development propagation and load-carrying capacity.

Different issues including applying the prestressing; instantaneous and long-term

prestressing losses, effect of prestressing on the bond behaviour; energy absorption;

ductility; deformability; cracking, yielding, and ultimate loads; CFRP geometry for

strengthening need to be addressed in detail to enhance the understanding of prestressed

NSM-FRP strengthened beam to be confidently implemented in practical projects.

1.4.2 Effects of Freeze-Thaw Exposure

Deterioration of concrete/strengthened concrete members due to long-term

exposure including freeze-thaw cycling exposure is well documented (Toutanji and

Gómez, 1997; Frigione et al., 2006; Tan et al., 2009; El-Hacha et al., 2010) but, the long-

term performance of the NSM-FRP strengthened RC beams is rarely studied (Derias,

2008; Mitchell, 2010). In this context, the long-term behaviour of the prestressed NSM-

FRP strengthened RC beams subjected to freeze-thaw cycling exposure has never been

examined. The freeze-thaw exposure probably has its major effect on the concrete and

bond of the strengthened RC beams resulting in a reduced load-carrying capacity. These

issues need to be studied in detail by experimental investigations of prestressed NSM-

FRP strengthened RC beams subjected to freeze-thaw cycling exposure and comparing

the results with those from similar beams without any environmental exposure.

5

1.4.3 Effects of Sustained Load Combined with Freeze-Thaw Exposure

To pursue the study on the long-term performance of the prestressed NSM-CFRP

strengthened beams, the combined effects of freeze-thaw cycling exposure and sustained

load, which have never been examined on these types of strengthened RC beams, are

investigated. Sustained load causes creep and cracks in the beams and under freeze-thaw

exposure along with humidity or moisture may cause major damage to the strengthened

beams. In this context, the performance of the prestressed NSM-FRP strengthened RC

beams under the combined effects of sustained load and freeze-thaw exposure are studied

in detail in terms of damage due to exposure, load-deflection response, ductility, energy

absorption, and mode of failure in comparison with the results of the similar beams

subjected to the freeze-thaw cycles.

1.4.4 FE Analysis of the Prestressed NSM-FRP Strengthened RC Beams

Numerical and analytical investigations of FRP strengthening methods have been

pursued parallel to the experiments and practical applications. Many researchers

simulated the behaviour of Externally Bonded (EB) FRP strengthened RC flexural

members using 2D or 3D FE models, considering perfect bond between interfaces due to

the fact that debonding failure was not observed in tests (Kachlakev et al., 2001;

Chansawat, 2003; Jia, 2003; Supaviriyakit et al., 2004; Chansawat et al., 2006; Camata

et al., 2007; Nour et al., 2007; Rafi et al., 2007); however, a few researchers considered

debonding effects in the FE modeling of EB strengthened RC beams of which most are in

2D (Buyle-Bodin et al., 2002; Kishi et al., 2005; Pham and Al-Mahaidi, 2005; Coronado

and Lopez, 2006). On the other hand, FE modeling of NSM-FRP strengthened RC beams

6

is rarely carried out (Kang et al., 2005; Omran and El-Hacha, 2010a; Soliman et al.,

2010). In the NSM strengthened RC beam, the debonding occurs at the concrete-epoxy

interface which is the weakest interface, and the main reason for a/the shortage of

research in this field is identification of appropriate bond behaviour that can be

reasonably applicable to the NSM technique. Therefore, developing a 3D FE model of

NSM strengthened RC beams considering the effects of debonding, prestressing, freeze-

thaw exposure and sustained load seems necessary in this field to be used as a predictive

tools in future researches and designs. In this context, a parametric study was conducted

on the flexural behaviour of the prestressed NSM-CFRP strengthened RC beam

considering the effects of the prestressing level, tension steel ratio, and concrete

compressive strength that leads to a better understanding of this strengthening system.

1.4.5 Analytical Model of the Exposed Prestressed NSM-FRP Strengthened RC Beams

The analytical studies on the NSM-CFRP strengthened concrete members need to

be pursued in the evolution of this strengthening system parallel to the experimental

investigations. Therefore, an analytical model is developed to simulate the load-

deflection response of the prestressed or non-prestressed NSM-CFRP strengthened beams

subjected to freeze-thaw cycling exposure. The model needs to be capable of assigning

the exposed freeze-thaw concrete material, the compression and tension steel

reinforcements, the partial prestressing length of the NSM-CFRP reinforcement along the

length of the beam (since the beams might not be strengthened for entire length with

NSM-CFRP), and the type of loading. Also, the developed model was verified with the

7

experimental test results to be confidently used as an analytical predictive tool for the

load-deflection response of the prestressed NSM-FRP strengthened RC beams.

1.4.6 Anchorage for Prestressed NSM-FRP Strengthening Method

One of the challenges for using the prestressed NSM-FRP method is developing a

practical method for prestressing. Most research in this area was performed while the

NSM-FRP was prestressed for the entire length of the beam against both ends of the

beam or against an external independent steel reaction frame from the beam itself

(Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Badawi and Soudki, 2009).

Moreover, in the research performed by Gaafar (2007) the advantage is the NSM-FRP

was prestressed against the bottom/side of the beam itself. Gaafar (2007) applied

prestressing using an innovative mechanical anchorage system that consists of two steel

anchors bonded to the ends of the CFRP rebar or strips and movable brackets temporarily

mounted on the beam. In this research, the performance of this anchorage system is

addressed more in detail and required modifications were performed by conducting

experimental and analytical investigations. Furthermore, a 3D FE model of the end

anchor was developed along with a parametric study considering the effects of bond

strength, length, and section dimensions on the anchorage capacity and interfacial stress

distribution. The findings lead to better understanding of the anchorage performance.

1.4.7 Modification of NSM-FRP Prestressing System

In earlier research (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007;

Badawi and Soudki, 2009), prestressing of the NSM-CFRP reinforcements was

8

performed against both ends of the RC beam or against an independent steel reaction

frame that made the prestressed NSM method unsuitable for field applications. The

practical issue of the prestressed NSM-FRP method was solved with the development of

an innovative prestressing and anchorage system enabling prestressing the NSM-CFRP

strips or rebars against the bottom/side of the concrete beam itself (Gaafar, 2007; El-

Hacha and Gaafar, 2011). An issue related to the developed prestressing system, reported

by Gaafar (2007) and also Oudah (2011), is that cracks occur at the location of the

brackets at high prestress levels (above about 40% of the CFRP ultimate tensile strength).

Therefore, the prestressing system requires modification to avoid these types of cracks

during prestrtessing.

1.4.8 Deformability and Ductility of the Prestressed FRP Strengthened RC Beams

In spite of the conventional ductility factors (displacement or curvature ductility)

which are appropriate for steel reinforced concrete members, a variety of deformability

indices have been proposed for concrete members reinforced with prestressed and non-

prestressed FRP (Naaman and Jeong, 1995; Abdelrahman et al., 1995; Zou, 2003; Rashid

et al., 2005; ACI 440.1R, 2006; CAN/CSA–S6–06, 2011). In this context, there is a gap

for the appropriate deformability or ductility models that need to be developed for the RC

members strengthened with prestressed and non-prestressed FRP; furthermore,

reasonable limits for the developed deformability or ductility models need to be proposed

to be used in design.

9

1.5 Research Objectives

The author mainly focuses on the issues mentioned earlier; therefore, the

following principal and secondary objectives are outlined for this research.

1.5.1 Principal Objectives

To study the long-term performance of RC beams strengthened in flexure using

prestressed NSM-CFRP strips/rebars subjected to freeze-thaw cycling exposure

and tested under quasi-static monotonic loading in terms of damage due to

exposure, load-deflection response, energy absorption and ductility

performance, and CFRP geometry (strip versus rebar)

To investigate the long-term performance of RC beams strengthened in flexure

with prestressed NSM-CFRP strips subjected to combined freeze-thaw cycling

exposure and sustained load and tested under static monotonic loading in terms

of damage due to exposure, load-deflection response, energy absorption and

ductility performance

To propose appropriate deformability or ductility models for RC beams

strengthened with the non-prestressed and prestressed FRP, and to propose the

reasonable limits for the developed deformability or ductility models

To develop nonlinear 3D FE models that can simulate the exact behaviour of

prestressed NSM-CFRP strengthened RC beams without any environmental

exposure and validate the model with experimental data from beams tested by

Gaafar (2007)

10

To develop nonlinear 3D FE models of the tested beams subjected to combined

freeze-thaw exposure and sustained load conditions

To develop an analytical model that can produce the load-deflection responses

of the tested beams exposed to freeze-thaw cycles

1.5.2 Secondary Objectives

To study the instantaneous and long-term prestress losses in the NSM-CFRP

To propose and analyze the practical concepts of optimum prestressing level

and beneficial prestressing level for tested beams

To conduct a paramedic study using the developed 3D FE models and

investigate the effects of the prestressing level, tension steel reinforcement

ratio, and concrete compressive strength on the flexural performance of the

prestressed NSM-CFRP strengthened RC beams

To develop 3D FE models of the end anchors and to conduct a parametric

study considering the effects of adhesive thickness, bond characteristics, and

anchor length on the anchorage capacity and interfacial shear stress distribution

To modify the prestressing system used for NSM-FRP strengthening

1.6 Scope of Work

The thesis consists of three parts: experimental study, finite element (FE)

analysis, and analytical investigation.

The experimental part of the project consists of two phases and an additional

investigation for the modification of the prestressing system. Phase I consists of nine

11

large-scale (5.15 m long with rectangular section 200×400 mm) beams: one un-

strengthened control RC beam, four strengthened RC beams using CFRP strips, and four

strengthened beams using CFRP rebars. The CFRP rebar and strips with similar axial

stiffness are used for strengthening. The strengthened beams are prestressed to 0, 20, 40,

and 60% of the ultimate CFRP tensile strain reported by manufacturer. The beams in

phase I are initially loaded up to 1.2 times the analytical cracking load for each beam

after strengthening, and then, placed inside an environmental testing facility chamber,

subjected to 500 freeze-thaw cycling exposure where each cycle is programmed between

-34oC to +34

oC with period of 8 hr and a relative humidity of 75% for temperatures

above +20oC. Phase II consists of five beams: one un-strengthened control RC beam and

four beams similar to the strengthened RC beams with CFRP strips in phase I. The beams

in phase II are subjected to the exposure conditions similar to that of phase I (except that

the relative humidity of 75% for temperatures above +20oC was replaced with water

spray, 18 L/min for a time period of 10 min, at temperature +20oC, to increase the

severity of the applied exposure) while each beam is being subjected to a sustained load

equal to 62 kN representing 47% of analytical ultimate load of the non-prestressed NSM-

CFRP strengthened RC beam. After being subjected to exposure and loading, all beams

in phases I and II were tested to failure under a four-point bending configuration and

static monotonic loading.

An experimental investigation is performed on the modification of the

prestressing system used for NSM CFRP strengthening in phases I and II. The temporary

steel brackets were modified by welding two steel plates to the sides to be capable of

changing the eccentricity (the location of the jacks). To investigate the performance of

12

the modified prestressing system, three concrete specimens are fabricated with identical

cross-section with the RC beams tested in phases I and II (200×400 mm) and having a

length of 1500 mm. A dywidag bar with two adjustable nuts at the ends is used instead of

the CFRP reinforcements to facilitate the execution of the experiment. The end anchors

are made to have enough bolts to carry the applied load up to ultimate capacity of the

dywidag bar. Then, the prestressing using the modified system is applied to the dywidag

bar up to a load equivalent to 93% of the CFRP ultimate tensile strength reported by the

manufacturer, for three different eccentricities (distance between the locations of the

jacks and centre of bolt groups at temporary fixed bracket).

The FE analysis consists of four sections performed using finite element software,

ANSYS. In section I, a nonlinear 3D FE model is developed to simulate the behaviour of

the RC beams strengthened with prestressed NSM-CFRP strips. The model considers the

debonding at the concrete-epoxy interface by assigning fracture energies including a

bilinear shear stress-slip model and a bilinear normal tension stress-gap model.

Furthermore, the prestressing is applied to the CFRP strip elements using the equivalent

temperature method. The FE model is compared and validated with experimental test

results reported by Gaafar (2007). In section II, a parametric study is conducted on the

RC beams strengthened with prestressed NSM-CFRP strips. A simplified 3D nonlinear

FE model similar to section I is developed but with a simplified material properties to

facilitate the trend of the parametric study. The model is validated with the experimental

data. Then, it is employed to analyze twenty-three beams to assess the effects of the

prestressing level in NSM-CFRP strips, the tensile steel reinforcement ratio, and the

concrete compressive strength. In section III, a 3D FE model is developed to simulate the

13

behaviour of the end-steel anchor used for the prestressed NSM-CFRP strengthening. The

CFRP-epoxy and epoxy-anchor interfaces are modeled by assigning Coulomb friction

model. Since the analysis is a pure FE one, the accuracy of the model is confirmed by

conducting a sensitivity analysis on the results. Then, fourteen models are analyzed to

investigate the effects of bond cohesion, anchor length, anchor width, and anchor height

on the interfacial stress distributions and anchorage capacity. In section IV, the post-

exposure load-deflection responses of the five beams tested in phase II of the

experimental program are predicted by developing a nonlinear 3D FE model similar to

the section I (FE modeling of unexposed beams) except that in the analysis the material

properties are different since the beams are exposed to environmental effects.

The analytical investigation consists of two sections. In section I, a brief review

was performed on the deformability or ductility indices available in the literature. Then,

three deformability indices are modified to be applicable for NSM-CFRP strengthened

RC beams. Afterwards, results of eighteen large-scale RC beams strengthened with

prestressed and non-prestressed NSM-CFRP strips and rebars are employed to evaluate

their ductility and deformability based on the modified models and conventional indices.

Furthermore, the limits of the design Codes for ductility and deformability of the beams

are checked and new limits are proposed and validated for different models to be used in

practice. In section II, the load-deflection responses of the nine tested beams in phase I of

the experimental program are predicted analytically by developing a code in Mathematica

software. The code has the capabilities of assigning the actual concrete stress-strain curve

based on Loov's equation, elasto-plastic behaviour for compression and tension steel,

linear behaviour for FRP, and different prestressed CFRP length along the length of the

14

beam. Perfect bond is assumed in the analytical model. The mid-span deflection at each

applied moment is calculated using integration of curvatures along the length of the beam

(from support to mid-span).

1.7 Thesis Layout

A summary of the research performed on the performance of RC beams

strengthened using FRP, the effects of environmental exposure, and FE modeling of

strengthened RC beams with more focus on the NSM method is provided in Chapter

Two. The experimental program and the developed testing matrix in this research are

presented in Chapter Three. Chapter Four provides the experimental test results of the

fourteen beams, relevant discussion, and comparison with similar beams tested under

static loading without any environmental exposure found elsewhere in literature. The

development of the finite element and also analytical models of the tested beams are

presented in Chapter Five, and finally, the conclusions and the recommendations are

presented in Chapter Six. Appendices A and B include the beam design and fabrication,

respectively, the ancillary test results are included in Appendix C, the ANSYS files

generated for FE model of the beams are presented in Appendix D, and the source code

developed for the analytical model is included in Appendix E.

15

Chapter Two: Literature Review

2.1 Introduction

This chapter is categorized to five sections based on the topics to be covered in

the research. The first two sections include a summary about Fibre Reinforced Polymer

materials and NSM strengthening methods, then, a brief review of the research conducted

on prestressed FRP-strengthened RC beams, long-term behaviour of FRP-strengthened

RC beams and components mainly subjected to freeze-thaw exposure and sustained load,

and FE modeling of FRP strengthened RC beams. At the end of this chapter, the

identified research gaps are outlined which were studied and summarized in the following

chapters (these gaps are considered in the objectives listed in Chapter One).

2.2 History of Engineering Materials

Ashby (1987) presented the evolution of conventional and advanced engineering

materials (comprising four classes: ceramics, composites, polymers, and metals) for

mechanical and civil engineering from 10000 BC to 2020. The relative importance for

each class of material in life as a function of time is presented in Figure ‎2-1. The diagram

is schematic and does not describe any value or tonnage. Before 2000 BC metals played

almost no role and engineering structures (houses, boats, weapons etc) were made of

ceramics (stone, pottery, and glass), composite (straw bricks), and polymers (wood,

straw, and skins). After finding the ways to make metals (around 1500 BC for bronze and

1850 for steel), they dominated the engineering design. After 1960, the rate of metal

development started to decrease and the new materials in the other three classes started to

16

be widely produced. For instance, the production of carbon based composites is rising

about 30% per year. The diagram shows the world is experiencing a revolution and a

transition from the steel age to an age consisting of more advanced materials which

demonstrates the importance of the research in this field.

Figure ‎2-1: The evolution of materials for civil engineering (Ashby, 1987).

2.3 Fibre Reinforced Polymer

FRP is a composite material. In general, a composite material signifies two or

more materials, which are combined on a macroscopic scale to form a useful third

material (Jones, 1999). Some of the properties, which can be enhanced or affected by

forming a composite material, are listed below:

Strength

Stiffness

17

Corrosion resistance

Weight

Fatigue life

Wear resistance

Attractiveness

Temperature-dependent behaviour

Thermal insulation

Thermal conductivity

Acoustical insulation

Not all of these properties are simultaneously improved by forming a composite

material. The composite is produced based on the design task and demand. FRP is made

of two components: fibre and matrix; to make FRP it is known that long fibres of a

material are much stronger than the same material in bulk form (strength of ordinary

glass=20 MPa while strength of glass fibres=2800 MPa to 4800 MPa). The fibres need to

be bonded together to behave as an efficient structural element. The binder material

usually has lower stiffness and strength and is called a matrix. Some applications of the

polymer composites materials are presented in Table ‎2-1.

18

Table ‎2-1: Some application of polymer composites (Sheikh-Ahmad, 2008).

Application area Examples

Aerospace Space structures, satellite antenna, rocket motor cases, high pressure fuel

tanks, nose cones, launch tubes

Aircraft

Fairings, access doors, stiffeners, floor beams, entire wings, wing skins, wing

spars, fuselage, radomes, vertical and horizontal stabilizers, helicopter

blades, landing gear doors, seats, interior panels

Chemical Pipes, tanks, pressure vessels, hoppers, valves, pumps, impellers

Construction Bridges and walkways including decks, handrails, cables, frames, grating

Domestic Interior and exterior panels, chairs, tables, baths, shower units, ladders

Electrical Panels, housing, switchgear, insulators, connectors

Leisure Tennis racquets, ski poles, skis, golf clubs, protective helmets, fishing rods,

playground equipment, bicycle frames

Marine Hulls, decks, masts, engine shrouds, interior panels

Medical Prostheses, wheel chairs, orthofies, medical equipment

Transportation Body panels, dashboards, frames, cabs, spoilers, front end, bumpers, leaf

springs, drive shafts

2.3.1 Fibres

Fibres are the main components of the FRP materials. The diameter of a fibre is

varied from 1-100 µm (Jones, 1999). Three types of fibres are mostly used in civil

engineering domain: Carbon, Glass, and Aramid; the composite is called by its

reinforcing fibre, e.g. Glass Fibre Reinforced Polymer (GFRP). Each type of fibre has

different mechanical properties as plotted in Figure ‎2-2 along with conventional steel bars

and steel tendons. Carbon fibre has been employed extensively in civil engineering

applications in comparison with the other fibre types. For the purpose of comparison,

properties of a few fibre materials and common structural materials are presented in

Table ‎2-2 to Table ‎2-6.

19

Figure ‎2-2: Typical stress-strain curves of the different fibres and common steel

reinforcements (ACI 440R, 2007).

2.3.1.1 Carbon

Carbon fibres possess a high modulus of elasticity, 200-800 GPa, and their

ultimate elongation varies from 0.3-2.5 %. As an advantage when compared to Aramid

and glass, carbon fibres do not absorb water and are resistant to most chemical solutions,

withstand fatigue excellently, do not stress corrode, show insignificant creep or

relaxation, have less relaxation compared to low relaxation high tensile prestressing steel

strands. The main disadvantage of the carbon fibre is being electrically conductive and,

therefore, might initiate galvanic corrosion when in direct contact with steel (Carolin,

2003). The carbon fibres are categorized based on their modulus or strength as presented

in Table ‎2-2.

20

Table ‎2-2: Tensile properties of typical carbon fibres (Akovali, 2001).

Fibre type Young’s modulus

(GPa)

Tensile strength

(GPa)

Strain to failure

(%)

Polyacrylonitrile (PAN)-

based high modulus 350-550 1.9-3.7 0.4-0.7

PAN-based intermediate

modulus 230-300 3.1-4.4 1.3-1.6

PAN-based high strength 240-300 4.3-7.1 1.7-2.4

2.3.1.2 Glass

Glass fibres are significantly cheaper than carbon fibres and aramid fibres.

Therefore, glass fibre composites have become popular in many applications outside the

civil engineering domain, e.g. the boat industry. The modulus of elasticity of the glass

fibres varies from 70-85 GPa with ultimate elongation of 2-5% based on type and quality.

Glass fibres are: sensitive to moisture, stress corrosion at high stress levels, and also may

have problems with relaxation; these drawbacks can be overcome with the correct choice

of matrix which protects the fibres (Carolin, 2003). Typical properties of different glass

fibres are presented in Table ‎2-3.

Table ‎2-3: Typical properties of different glass fibres (Akovali, 2001).

Material Density

(kg/m3)

Tensile

strength (MPa)

Young’s

modulus (GPa)

Coefficient of

thermal expansion

(10-6

/oC)

Strain to

failure (%)

Electrical

(E)-glass 2620 3450 81 5 4.9

High strength

(S)-glass 2500 4590 89 5.6 5.7

High alkali

(A)-glass 2500 3050 69 8.6 5

21

2.3.1.3 Aramid

Aramid is the abbreviation for aromatic polyamide. A well-known trademark of

aramid fibres is Kevlar. The modulus of elasticity of the aramid fibres varies from 70-200

GPa with ultimate elongation of 1.5-5%. Aramid has a high fracture energy and therefore

is used for helmets and bullet-proof garments. Aramid fibres are sensitive to elevated

temperatures, moisture and ultra-violet radiation and have problems with relaxation and

stress; therefore, they are not widely employed in civil engineering applications (Carolin,

2003). Properties of some aramid fibres are listed in Table ‎2-4.

Table ‎2-4: Properties of some aramid fibres (Akovali, 2001).

Fibre type Density

(kg/m3)

Young’s modulus

(GPa)

Tensile strength

(MPa)

Strain to failure

(%)

Kevlar 29

(High toughness) 1440 85 3000-3600 4

Kevlar 49

(High modulus) 1440 131 3600-4100 2.8

Kevlar 149

(Ultra-high modulus) 1470 186 3500 2

2.3.2 Matrices

The matrix performances comprise: durability, inter-laminar toughness,

shear/compressive/transverse strengths by binding the components together, and thermo-

mechanical stability of the composite, protecting the fibres from environmental damages,

transferring the forces to the fibres, maintaining the desired fibre orientations and

spacing. Thermosetting resins (thermosets) are almost exclusively employed in civil

engineering. Epoxy and vinylester are the most common thermoset matrices. Epoxy is

extensively used in comparison with vinylester but is also more costly. Epoxy has a pot

22

life around 30 minutes at 20oC but can be changed with different formulations. The

curing rate increases with increased temperature. Table ‎2-5 and Table ‎2-6 present the

mechanical and thermal properties of matrix materials and some applications of the

conventional matrix materials, epoxy and polyester.

23

Table ‎2-5: Mechanical and thermal properties of matrix materials at room temperature (Sheikh-Ahmad, 2008).

Type of matrix Density

(kg/m3)

Young’s

modulus

(GPa)

Tensile

strength

(MPa)

Strain to

failure

(%)

K

(W/m oC)

Cp

(kJ/kg oC)

α

(10-6

/oC)

Tg

(oC)

Tm

(oC)

Poly

mer

s-T

her

mose

ts

Unsaturated polyester 1.1-1.23 3.1-4.6 50-75 1-6.5 0.17-0.22 1.3-2.3 55-100 70 -

Epoxy 1.1-1.2 2.6-3.8 60-85 1.5-8 0.17-0.2 1.05 45-65 65-175 -

Phenolics (Bakelite) 1-1.25 3-4 60-80 1.8 0.12-0.24 1.4-1.8 25-60 300 -

Bismaleimide 1.2-1.32 3.2-5 48-110 1.5-3.3 - - - 230-345 -

Vinylesters 1.12-1.13 3.1-3.3 70-81 3-8 - - - 70 -

Po

lym

ers-

Ther

mopla

stic

s Polypropylene 0.9 1.1-1.6 31-42 100-600 0.11-0.17 1.8-2.4 80-100 -20-5 165-175

Polyamide (nylons) 1.1 2 70-84 150-300 0.24 1.67 80 55-80 265

Poly (phenylene sulfide) 1.36 3.3 84 4 0.29 1.09 49 85 285

Poly (ether ether ketone) 1.26-1.32 3.2 93 50 0.25 1.34 40-47 145 345

Poly (ether sulfone) 1.37 3.2 84 40-80 0.26 1 55 225 -

Poly (ether imide) 1.27 3 105 60 0.07 47-56 - 215 -

Poly (amide imide) 1.4 3.7-4.8 93-147 12-17 - - 245-275 - -

Cer

amic

s Alumina Al2O3 (99.9% pure) 3.98 380 282-551 - 39 0.775 7.4 - -

Silicon nitride Si3N4 (sintered) 3.3 304 414-650 - 33 1.1 3.1 - -

Silicon carbide SiC (sintered) 3.2 207-483 96-520 - 71 0.59 4.1 - -

Met

als Aluminum alloys (7075 T6) 2.8 71 572 11 1.3 0.96 23.4 - -

Steel alloy (1020 Cold drawn) 7.85 207 420 15 51.9 0.486 11.7 - -

K= thermal conductivity, Cp= specific heat, α= coefficient of thermal expansion, Tg= glass transition temperature, Tm= melting temperature

23

24

Table ‎2-6: Some aspects of epoxy and polyester thermosets (Akovali, 2001).

Thermoset Some characteristics Main uses Limitations

Epoxy

Good electrical properties

Chemical resistance

High strength

Filament winding

Printed circuit-board

tooling

Required heat curing

for maximum

performance

Cost

Polyester

Good all-around properties

Ease of fabrication

Low cost

Versatile

Corrugated

Sheeting

Boats, piping, tanks

Ease of degradation

2.3.3 FRP Composite

In a FRP composite, the fibres may be placed in one direction (unidirectional) or

may be woven or bonded in many directions (bi-or multi-directional). Unidirectional

composites are commonly employed for strengthening purposes. FRP composites can be

produced by different methods: hand lay-up, pultrusion, filament winding, and moulding;

and also, in different shapes such as rebar, strip, plate, and section as shown in Figure

‎2-3. The composites’ mechanical properties are based on the fibres, matrix, fibre content,

and fibre direction. Also, the volume or size of the composite will affect the mechanical

properties. The fibre content by volume, (volume of fibre to volume of the composite)

varies from 30-70%, but in most cases about 30-40% of composite volume is made of

matrix (fibre content of 60-70%). In order to provide the reinforcing function, the fibre-

volume fraction should be more than 55% for FRP bars and rods and 35% for FRP grids

(ISIS Design Manual No.3, 2007). Normally, the volume fraction of fibres in FRP

strips/plates is about 50-70% and that in FRP sheets is about 25-35% (Setunge et al.,

2002). Typical stress-strain relationships for matrix, fibres, and produced FRP composite

are shown Figure ‎2-4. FRP materials react differently in miscellaneous environmental

25

conditions as presented in Table ‎2-7. Mechanical properties of some commercially

available FRP bars are listed in Table ‎2-8.

Figure ‎2-3: Different types of FRP composites (Sireg, 2011).

Table ‎2-7: Environmental considerations for different FRP materials (NCHRP,

2004).

Consideration Carbon Glass Not tolerant

Alkalinity/acidity

exposure Highly resistant Not tolerant Not tolerant

Thermal expansion Near zero, may cause

high bond stress Similar to concrete

Near zero, may cause

high bond stress

Electrical conductivity High Excellent insulator Excellent insulator

Impact tolerance Low High High

Creep rupture and fatigue High resistance Low resistance Low resistance

FRP strips/plates FRP rebars

Fabric/sheets FRP sections

26

Str

es

s (

MP

a)

Strain (%)

Fibres

FRP

Matrix

0.4 - 4.8 > 10

1800 - 4900

34 - 130

600 - 3000

Figure ‎2-4: Typical stress-strain curves for matrix, fibres, and resulted FRP

composite (ISIS Design Manual No.3, 2007).

Table ‎2-8: Typical properties of FRP bars (ISIS Design Manual No.3, 2007).

Trade name Tensile strength

(MPa)

Modulus of elasticity

(GPa) Ultimate tensile strain

Carbon fibre

V-rod 1596 120 0.013

Aslan 2068 124 0.017

Leadline 2250 147 0.015

NEFMAC 1200 100 0.012

Glass fibre

V-rod 710 46.4 0.015

Aslan 690 40.8 0.017

NEFMAC 600 30 0.02

2.4 Strengthening Concrete Structures Using FRP Materials

Generally, concrete members are strengthened with FRP in two methods:

Externally Bonded (EB) and Near-Surface Mounted (NSM) which are briefly explained

within this section.

27

2.4.1 Externally Bonded Strengthening Method

In EB method, the FRP fabrics, sheets or plates are bonded on the tension face of

the concrete members using epoxy adhesive. The concrete surface should be cleaned and

concrete cover should be in reasonable condition to be able to transfer the loads to the

installed FRP sheets/plates. The concrete surface could be ground or sand blasted to the

level of aggregate to ensure the appropriate performance of the bond between concrete-

epoxy interface. EB strengthening can be performed in two methods: hand-applied wet

lay-up system and pre-cured system. To implement hand-applied wet lay-up

strengthening, first, where required, primer and putty should be applied to the surface,

then, dry or pre-impregnated fibre sheets and fabrics are installed on the surface using a

saturating resin. The FRP ply orientation and the ply stacking sequence needs to be

specified and performed in the exact manner. If multiple layers of FRP materials are

used, all layers must be fully impregnated within the appropriate resin to be able to

transfer the shearing load between layers and FRP-concrete. To implement pre-cured

system, the FRP plates are installed using paste epoxy-based adhesive which is uniformly

applied to the prepared surface. In both EB methods, entrapping the air under the

laminates should be avoided. A schematic of the EB strengthening method is shown in

Figure 2-5a.

2.4.2 Near-Surface Mounted Strengthening Method

NSM strengthening is a method classified as pre-cured strengthening system. To

implement this method, the FRP strip/rebar, is bonded into the groove cut in concrete as

shown in Figure 2-5b and c. The cross-section of the bar can be round, oval, square or

28

rectangular with a sand-coated, ribbed or plain surface. The depth of the groove and

dimensions of the reinforcements are limited by the depth of the concrete cover. The

groove filler can be epoxy adhesive or cement mortar. A few field applications of NSM-

FRP based strengthening are presented in Figure 2-6. The NSM strengthening should be

implemented based on the following steps:

Sawing groove in concrete cover

Cleaning the groove carefully with air pressure or water pressure (100-150 bar)

Filling the groove using epoxy or cement grout, the groove should be dry when

the epoxy is employed as a filler and should be wet when cement grout is

employed as a filler

Cleaning the FRP rebar/strip using acetone and mounting the reinforcement in

the groove

Removing the extra epoxy using spatula

(a) (b) (c)

Figure ‎2-5: Schematic of flexural strengthening using FRP: (a) EB FRP, (b) NSM-

FRP strips, and (c) NSM-FRP rebars.

29

(a) Trenchard Street eleven-storey parking strengthened with NSM-CFRP rebar

(DTI MMS 6, 2005)

(b) Strengthening of parking garage decks using NSM-CFRP bars (Tumialan et al.,

2007)

(c) Strengthening of bridge in Switzerland in 1999 using NSM-CFRP laminate

(Carolin, 2003)

Figure ‎2-6: Some field applications of NSM-FRP based strengthening.

30

(d) Strengthening a bridge deck using NSM-CFRP strip (Casadei et al., 2003)

(e) Cement silo repair and upgrade using NSM-CFRP bar (Concrete repair

bulletin, 2001)

Figure 2-6: Some field applications of NSM-FRP based strengthening (Cont’d).

2.5 History of NSM Method

NSM-FRP method is one of the latest techniques for strengthening of concrete

members, however, the NSM is not a new method. The use of NSM reinforcement was

developed in Europe for strengthening of RC structures in the early 1950s. In 1948 an RC

bridge deck in Sweden, which needed to be upgraded in its negative moment region due

to an excessive settlement of the steel cage during construction, was strengthened by

31

inserting steel reinforcement bars in grooves made in the concrete surface and filling it

with cement mortar (Asplund, 1949). At the onset of development, the black steel was

replaced using stainless steel. In 1960s, development of high strength adhesive such as

epoxy encouraged the use of epoxy instead of cement grout. Developing the FRP

materials led to use them instead of steel reinforcements for strengthening. In comparison

to FRP, the steel reinforcements are heavy, rigid, difficult to install, highly susceptible to

corrosion, and cheaper. Also, they need bigger grooves. Three shapes of FRP

reinforcement have been used in NSM method: round bars, rectangular/square bars, and

strips. Recently‚ prestressed FRP has been used for strengthening of RC members due to

better utilization of the strengthening material, smaller and better distributed cracks in

concrete, taking a large portion of the tension force from steel reinforcement and higher

steel yielding loads. The significant drawback of strengthening with prestressed FRP is

the design requirement of an anchorage device for end zones that should be practical in

implementation (Nordin and Täljsten, 2006).

2.6 Material Used for NSM

2.6.1 Reinforcements

Three kinds of FRP reinforcements have been used in NSM strengthening. In

most cases, CFRP reinforcements have been used. After CFRP, GFRPs have been used

for most application in timber and masonry. The application of AFRP is very rare. The

CFRP reinforcements have higher modulus of elasticity and tensile strength than those of

GFRP and AFRP, which leads to use of smaller CFRP section for the same tensile

strength, furthermore, this leads to making smaller grooves in the concrete and easer

32

installation. For these reasons, the CFRP is used in most applications. The NSM-FRP

reinforcements are produced in different shapes: round, square, rectangular, and oval.

The surface of a bar can be in different styles: smooth, sand-blasted, sand-coated, spirally

wound with a fibre tow, ribbed, and roughened with a peel-ply surface treatment.

Different shapes of the FRP reinforcements practiced in NSM strengthening are shown in

Figure ‎2-7.

Figure ‎2-7: Different shapes of FRP reinforcements for NSM strengthening (De

Lorenzis and Teng, 2007).

2.6.2 Groove Filler

The groove filler transfers the stresses between FRP reinforcement and substrate

concrete. The shear and tensile strengths of the groove filler are important in structural

behaviour of the member; the shear strength is important to avoid cohesive shear failure

of the bonded reinforcement, on the other hand, tensile strength is important when

deformed rebar is used to resist against high circumferential tensile stress in groove filler.

Two-component epoxy is the most common groove filler used in NSM method. High-

33

viscosity epoxy is used for strengthening in positive moment regions (upper hand

applications) and low-viscosity epoxy is used for strengthening in the negative moment

regions. In some applications cement mortar has been used as groove filler (Täljsten et

al., 2003). The use of cement mortar decreases the cost, reduces the hazard to workers,

allows effective bonding to wet surfaces, causes better resistance in high temperature, and

leads to better thermal compatibility with surrounding concrete, but the main drawback of

the cement mortar is having inferior mechanical properties when compared to common

epoxies.

2.7 Comparison between NSM-FRP and EB-FRP Technique

In comparison to EB, the NSM method provides better protection against

mechanical damages and accidental impacts, better resistance against debonding, the

concrete surface is not completely covered which can lead to less freeze and thaw

problems in future, no surface preparation after sawing the grooves and cleaning, the

ability to replace the epoxy with cement grout due to the harmful effects of it, and the

increase in force transfer and durability. On the other hand, the NSM method requires

more extensive labour, equipment, time, and sufficient clear concrete cover but both of

the strengthening methods are less costly than replacing a structure or structural member

(Quattlebaum et al., 2005; De Lorenzis and Teng, 2007). Different aspects of EB and

NSM are listed in Table ‎2-9.

34

Table ‎2-9: Aspects of EB and NSM strengthening methods (Täljsten et al., 2003).

Plates Sheets NSM

Shape Rectangular strips Thin unidirectional or

bidirectional fabrics

Rectangular strips or

laminates

Dimension:

Thickness

width

1-2 mm

50-150 mm

0.1-0.5 mm

200-600 mm

1-10 mm

10-30 mm

Use Simply bonding of

factory-made profiles

with adhesives

Bonding and impregnation

of the dry fibre with resin

and curing at site

Simple bonding of factory

made profiles with

adhesive or cement mortar

in pre-sawed slots in the

concrete cover

Application

aspects

For flat surfaces

Thixotropic adhesive

for bonding

Not more than one

layer recommended

Stiffness of laminate

and use of thixotropic

adhesive allow for

certain surface

unevenness

Simple in use

Quality guaranteed

from factory

Suitable for

strengthening in

bending

Needs to be protected

against fire

Easy to apply on curved

surface

Low viscosity resin from

bonding and impregnation

Multiple layers can be

used, more than 10

possible

Unevenness needs to be

levelled out

Needs well documented

quality systems

Can easily be combined

with finishing systems,

such as plaster and paint

Suitable for shear and

bending strengthening

Needs to be protected

against fire

For flat surfaces

Depends on the distance to

steel reinforcement

A slot needs to be sawn up

in the concrete cover

The slots needs careful

cleaning before bonding

Bonded with a thixotropic

adhesive

Possible to use cement

mortar for bonding

Protected against impact

and vandalism

Suitable for strengthening

in bending

Minor protection against

fire

2.8 Background of the Topic

Performance of the NSM strengthening method under environmental exposure

and sustained load is an important issue for future applications of this technique in

practical projects. In this context, the performed experimental, numerical, and analytical

studies mainly on the prestressed NSM-FRP method are briefly reviewed to identify the

possible gaps in this field. In each section the most related researches are cited and the

35

rest are presented in a table format at the end. Finally, the existing research gaps are

summarized.

2.9 Prestressed NSM-FRP Strengthened RC Beam

In this context, Täljsten and Nordin (2005) studied the effect of strengthening

with prestressed external steel and NSM-CFRP reinforcement. Eight beams were tested:

one as un-strengthened control beam, two beams strengthened with non-prestressed

NSM-CFRP square bar, three beams strengthened using prestressed external steel tendon

(with 34% prestressing level of the yielding strength of the tendon), one beam

strengthened using external prestressed CFRP square bars anchored at the ends (with

14% prestressing level of the tensile strength of the CFRP bar), and one beam

strengthened with prestressed NSM-CFRP rods (with 19% prestressing level of the

tensile strength of the CFRP rod). The results showed that beams strengthened with

external prestressed steel tendons failed by steel yielding while the beam strengthened

with prestressed CFRP rods failed due to anchorage fracture. The beams strengthened

with non-prestressed NSM-CFRP failed due to anchorage and debonding failure while

the beam with prestressed NSM-CFRP rod failed due to concrete spalling. An increase of

100% at yielding load and 181% at ultimate load was observed for the beam prestressed

with NSM-CFRP rod.

Wu et al. (2005) studied the effectiveness of RC beams strengthened with

prestressed NSM-CFRP tendons (rods) tested under four-point bending configuration and

static monotonic loading. Seven beams (150 × 200 × 2000 mm; width × height × length)

were tested: one reference beam, one strengthened with non-prestressed NSM-CFRP, and

36

five strengthened with prestressed NSM-CFRP tendons (with 14.5% and 30%

prestressing levels of the ultimate tensile strength of the CFRP tendon). Different groove

filers were used, epoxy putty and cement mortar in addition to adding extra layer of both

after curing the filler. Test results revealed the beams with cement mortar failed due to

concrete crushing. Enhancements of 200%, 50%, and 93% were observed at cracking,

yielding and ultimate loads, respectively.

Nordin and Täljsten (2006) tested fifteen beams (200 × 300 × 4000 mm; width ×

height × length) strengthened with prestressed NSM-CFRP quadratic rods under static

loading. The test results showed a significant enhancement in the cracking and yielding

loads. The developed prestressing method by these researchers is not practical because it

needs access to the entire length of the beam. Furthermore, these researchers found that it

is necessary to use a mechanical anchoring device. Lack of the mechanical anchorage

caused a large difference between prestressing losses in CFRP reinforcements at the end-

point and mid-span.

Casadei et al. (2006) tested three full-scale Prestressed Concrete (PC) I-girders

(11 m long); one un-strengthened beam, one impact damaged PC beam strengthened with

prestressed NSM-CFRP bars and one impact damaged PC beam strengthened with EB-

CFRP laminate along the length accompanied by U-wrap. The impact damage was

enforced by cutting two of seven low-relaxation tendon wires prestressed to 75% of

yielding strength. The prestressing force of CFRP bar was calculated to restore the same

level of prestressing prior to damage (33% of ultimate tensile strength of CFRP bar). The

bars were prestressed against both ends of the beam using hydraulic jack. This method is

not practical in implementation. The results revealed that all beams almost had the same

37

stiffness and cracking load as well as the same ultimate load. The EB strengthened beam

failed in a brittle mode by debonding the laminate followed by rupture of the U-warp

sheet. The beam strengthened with the NSM method failed due to splitting of the

concrete cover which caused debonding failure of one of the CFRP bars at the bottom

and slowly led to progressive failure in the system.

Jung et al. (2007) studied the strengthening performance and flexural behaviour of

RC beams strengthened with prestressed CFRP strips using an EB system and CFRP rods

with mechanical interlocking (MI) and prestressed NSM. Eight beams were tested (200 ×

300 × 3000 mm; width × height × length): one as un-strengthened control beam; another

strengthened with EB-CFRP plates; and other six beams strengthened using different

NSM techniques: NSM, NSM+MI, and prestressed NSM (with 20% prestressing level of

the ultimate tensile strength of the CFRP strip/bar) using strips and bars. The EB-CFRP

strengthened beam failed due to debonding at 30% of the ultimate tensile strain of the

CFRP plate. The beams strengthened with NSM-CFRP rods and strips failed due to

separation of CFRP and epoxy from the concrete substrate at 82-87% of the ultimate

tensile strain of the CFRP strip/rebar. The beams strengthened with MI failed due to

CFRP rupture. However, the beam strengthened with prestressed NSM-CFRP strip failed

due to separation of CFRP and epoxy from concrete substrate while the beam

strengthened with prestressed NSM-CFRP rod failed due to CFRP rupture.

Gaafar (2007) developed an innovative anchorage system for prestressed NSM

technique to overcome the practical issue of the earlier studies on the prestressed NSM-

FRP strengthening. Nine large-scale beams (200 × 400 × 5150 mm; width × height ×

length) were tested: one un-strengthened control beam, four beams strengthened with

38

prestressed NSM-CFRP strips (with 0, 20, 40, and 60% prestressing levels of ultimate

tensile strength of CFRP strips), and another four beams strengthened with prestressed

NSM-CFRP rebars (with 0, 20, 40, and 60% prestressing levels of ultimate tensile

strength of CFRP rebars). All strengthened beams failed due to FRP rupture without any

premature failure while up to 68% enhancement in ultimate capacity was achieved in

comparison with un-strengthened control beam. Furthermore, the prestressing enhanced

the cracking and yielding loads, significantly, and leads to delay in crack formation while

the ultimate load almost stayed constant and ductility decreased.

Badawi and Soudki (2009) investigated the effectiveness of strengthening RC

beams using prestressed NSM CFRP rods. Four beams (152 × 254 × 3500 mm; width ×

height × length) were tested: one un-strengthened control beam and three beams

strengthened with prestressed NSM-CFRP rods (with 0, 40, and 60% prestressing levels

of ultimate tensile strength of CFRP rods). The non-prestressed beams failed due to

concrete crushing while the prestressed beams failed due to CFRP rupture and up to 79%

improvement in ultimate capacity was achieved. Also, the load-deflection responses of

the tested beams were predicted by developing an analytical model. The main issue in

this study was using the external seats for prestressing requiring access to both ends of

the beam which is not practical, and furthermore, a significant amount of the prestress

loss was observed at the beam ends while the prestress loss was insiginifacnt at the mid-

span.

The most related researches in the area are reviewed above and the rest are

presented in Table ‎2-10.

39


NSM-FRP reinforcements.

Reference Crasto et al. (1999) De Lorenzis et al. (2000) Blaschko (2001)

Test method and type of NSM

strengthening

Static

Four-point bending

Non-prestressed

Static

Four-point bending

Non-prestressed

Static

Four-point bending

Non-prestressed

Number of specimens N.A.

Four: one control, two strengthened

with NSM CFRP rods, one strengthened

with NSM GFRP rods

N.A.

Bea

m g

eom

etry

Cross section (mm) 152×457

356×914

T shape, total height = 406, web height

= 305, flange width = 381, web width =

152

200×500

600×500

Net span (mm) 2400

7500 3900

2800

7500

Shear span (mm) 800

2500 1830

1150

3250

f'c (MPa) NA 36 44

Bottom

steel

Amount 1.14%

1.19% 2#7 (0.89%)

0.63%

0.84%

fyt (MPa) N.A. 494 N.A.

Top

steel

Amount N.A. 2#4 N.A.

fyc (MPa) N.A. 494 N.A.

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Epoxy Epoxy Epoxy

Tensile strength

[Modulus of

elasticity] (MPa)

30

[N.A.]

13.8

[N.A.]

33.3

[N.A.]

FRP

Type CFRP bar GFRP bar

CFRP bar CFRP strip

shape/surface Round, smooth Round/ribbed

Round/sand-coated Roughened

Dimension

db or tf×hf (mm)

4.75

6.35

12.7

9.5, 12.7 2×20

Number of FRP

reinforcements 4, 11 2 3, 11

Efrp (GPa) 122 GFRP:41.3

CFRP:164.7 156

Tensile strength

(MPa) 1326

GFRP:800

CFRP:1550 1813

Groove dimensions

(mm) 10.2×varying h

19×19

25×25 3.3×23

Cut-off distance

from the support (mm) N.A. Extended over supports 150, 300

Test variables Beam size, steel ratio,

groove size Type of FRP bar, bar diameter

End anchorage, type

of loading

Observed failure modes

Concrete crushing,

secondary debonding

and partial bar rupture

debonding of NSM SB bar, concrete

cover separation

concrete cover

separation, bar

rupture

Increase in capacity (%) 20-50 26-44 67-82

40


NSM-FRP reinforcements (Cont’d).

Reference De Lorenzis (2002) Taljsten et al. (2003) Hassan and Rizkalla (2003)


strengthening

Static

Four-point bending

Non-prestressed

Static

Four-point bending

Prestressed and non-prestressed

Static

Three-point bending

Non-prestressed

Number of specimens N.A.

Eight: two controls, four

strengthened with non-

prestressed NSM CFRP rods,

two strengthened with

prestressed NSM CFRP rods

Nine: one control, eight

strengthened with NSM CFRP

strips

Bea

m g

eom

etry

Cross section (mm) 200×400 200×300

T shape, total height = 300,

web height = 250,

flange width = 300,

web width = 150

Net span (mm) 4000 3600 2500

Shear span (mm) 1750 1300 1250

f'c (MPa) 15 60.7-68 48

Bottom

steel

Amount 0.38-0.64% 2-Ø16 (0.67%) 2-10M

fyt (MPa) N.A. 490 400

Top

steel

Amount N.A. 2-Ø16 2-10M

WWF 51×51 MW5.6×MW5.6

fyc (MPa) N.A. 490 400

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Epoxy Epoxy and cement grout Epoxy

Tensile strength

[Modulus of

elasticity] (MPa)

27.4

[N.A.]

31 [7000] for epoxy

N.A. [N.A.] for cement grout

N.A.

[N.A.]

FRP

Type CFRP bar CFRP rod CFRP strip

shape/surface Round, spirally wound

and sand-coated Square, smooth N.A.

Dimension

db or tf×hf (mm) 7.5 10×10 1.2×25

Number of FRP

reinforcements 1, 2 1, 2 1

Efrp (GPa) 175 230, 160 150

Tensile strength

(MPa) 2214 4140, 2800 2000

Groove dimensions

(mm) 16×16

15×15 (for epoxy bonded)

20×20 (for cement grout

bonded)

5×25

Cut-off distance

from the support (mm) Extended over supports 300 or extended over supports 1100-50

Test variables Steel ratio, number of

FRP bars NSM bar length, groove filler Bar anchorage length


Concrete crushing,

concrete cover

separation, edge failure

Debonding, bar rupture Debonding, bar rupture

Increase in capacity (%) 21-61 56-92 0–54

41



Reference Hassan and Rizkalla (2004) El-Hacha and Rizkalla (2004) Yost et al. (2004)


strengthening

Static

Three-point bending

Non-prestressed

Static

Three-point bending

Non-prestressed

Static

Four-point bending

Non-prestressed

Number of specimens

Eight: one control, seven


bars

Eight: one control, two strengthened

with NSM CFRP strips, two

strengthened with EB CFRP strips,

one strengthened with NSM CFRP

bar, one strengthened with NSM

GFRP strips, one strengthened with

EB GFRP strips

N.A.

Bea

m g

eom

etry

Cross section (mm)


web height = 250,

flange width = 300,

web width = 150


web height = 250,

flange width=300,

web width=150

152-304×188

Net span (mm) 2500 2500 1750

Shear span (mm) 1250 1250 500

f'c (MPa) 48 48 37

Bottom

steel

Amount 2-10M 2#13 (0.48%) 0.83–1.74%

fyt (MPa) 400 400 N.A.

Top

steel

Amount 2-10M

WWF 51×51 MW5.6×MW5.6

2#13

WWF 51×51 MW5.6×MW5.6 N.A.

fyc (MPa) 400 400 N.A.

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Gel epoxy, Epoxy Epoxy Epoxy

Tensile strength

[Modulus of

elasticity] (MPa)

48 [1200] for gel epoxy

62 [3000] for epoxy

48 [1200] (for bars)

70 [3500] (for strips) N.A.

FRP

Type CFRP rod CFRP and GFRP CFRP strip

shape/surface Round-ribbed

CFRP/round/spirally wound

CFRP/strip/ N.A.

CFRP/strip/ N.A.

GFRP/strip/ N.A.

Roughened

Dimension

db or tf×hf (mm) 9.5 9.5, 2×16, 1.2×25, 2×20 0.25×15.5

Number of FRP

reinforcements 1 1, 2 (CFRP), 5 (GFRP) 1, 2

Efrp (GPa) 111 122.5, 140, 150, 45 136.6

Tensile strength

(MPa) 1918 1408, 1525, 2000, 1000 1656

Groove dimensions

(mm) 18×30 18×30, 6.4×19, 6.4×25, 6.4×25 6.4×19

Cut-off distance

from the support (mm) 1100-50 50

Extended over

supports

Test variables Bar anchorage length,

different epoxy Type of FRP bar

Section width,

steel ratio, number

of FRP bars

Observed failure modes Concrete splitting

concrete cover separation (CFRP

round bars and GFRP strips), bar

rupture (CFRP strips)

Concrete crushing, bar

rupture

Increase in capacity (%) 0–41 69-99 15–55

42



Reference Arduini et al. (2004) Kishi et al (2005) Barros and Fortes (2005)


strengthening

Static

Four-point bending

Non-prestressed

Static

Four-point bending

Non-prestressed

Static

Four-point bending

Non-prestressed

Number of specimens N.A. Three: strengthened with

NSM AFRP rods

Eight: four series of two beams

(one control, one strengthened

with NSM CFRP strips)

Bea

m g

eom

etry

Cross section (mm) 200×120 150×250 100×170-180

Net span (mm) 1100 2600 1500

Shear span (mm) 500 1050 500

f'c (MPa) 20-63 34.3 46.1

Bottom

steel

Amount 0.28, 0.57% 2-D13 0.33–0.84%

fyt (MPa) N.A. 362 730-524.2

Top

steel

Amount N.A. 2-D19 2-Ø8

fyc (MPa) N.A. 362 524.2

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Epoxy Epoxy Epoxy

Tensile strength

[Modulus of

elasticity] (MPa)

N.A.

[N.A.]

N.A.

[N.A.]

16–22

[5000]

FRP

Type CFRP bar AFRP rod CFRP strip

shape/surface Round-N.A. N.A. N.A.

Dimension

db or tf×hf (mm) 7 (net), 8 (external) 5, 7.3, 9 1.45×9.59

Number of FRP

reinforcements 1, 3 2 1-3

Efrp (GPa) 201 62.5 158.8

Tensile strength

(MPa) 1940 1450 2739.5

Groove dimensions

(mm) N.A. N.A. 4×12

Cut-off distance

from the support (mm) 50 100 50

Test variables

Number of FRP

bars, concrete

strength

Axial stiffness Steel ratio,

number of NSM FRP strips

Observed failure modes Concrete crushing,

debonding Debonding Concrete cover separation

Increase in capacity (%) 140–430 1.51-1.86 (Pu/Py) 78–98

43



Reference Quattlebaum et al. (2005) Nordin and Täljsten (2006) Teng et al. (2006)


strengthening

Static

Fatigue

Three-point bending

Non-prestressed

Static

Four-point bending


Static

Four-point bending

Non-prestressed

Number of specimens

Four: one control, one

strengthened under static, one

under low-stress fatigue, one

under high-stress fatigue

Fifteen: one control, four


prestressed NSM CFRP rods,

and ten strengthened with


Five: one control, four

strengthened with NSM

CFRP strips

Bea

m g

eom

etry

Cross section (mm) 152×254 200×300 150×300

Net span (mm) 4572 3600 3000

Shear span (mm) 2286 1300 1200

f'c (MPa) 29.5 61-68 44

Bottom

steel

Amount 3-Ø13 2-Ø16 2-Ø12

fyt (MPa) 446 496 532

Top

steel

Amount N.A. 2-Ø16 2-Ø8

fyc (MPa) N.A. 496 375

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Epoxy Epoxy, BPE Lim 456/564 Epoxy

Tensile strength

[Modulus of

elasticity] (MPa)

72.4

[3200]

31

[7000]

42.6

[2620]

FRP

Type CFRP strip CFRP rods: S, M CFRP strip

shape/surface Rectangular, smooth Quadratic, smooth Roughened with peel-ply

surface treatment

Dimension

db or tf×hf (mm) 1.4×25 10×10 2-2×16

Number of FRP

reinforcements 2 1 1

Efrp (GPa) 154.29 S: 160

M: 250 151

Tensile strength

(MPa) 2785.7

S: 2800

M: 2000 2068

Groove dimensions

(mm) 6.4×32 15×15 8×22

Cut-off distance

from the support (mm) 152.5 200 or extended over supports 1250-50

Test variables

Type of loading (static and

fatigue), different types of

strengthening

Prestressing level (0-0.27fu), the

bond length, and the modulus of

elasticity of CFRP

Bar anchorage length


Concrete crushing followed

concrete cover splitting,

fatigue fracture of tension

reinforcements

FRP rupture, Concrete crushing

+ FRP rupture Concrete cover separation

Increase in capacity (%)

Static:33.2

LS Fatigue: failed after 2×106

cycles,

HS Fatigue: failed around

829423 cycles

S: 56-97.3

M: 62.7-76 0–106

44



Reference Aidoo et al. (2006) Tang et al. (2006) Barros et al. (2007)


strengthening

Static

Fatigue

Three-point bending

Non-prestressed

Static

Four-point bending

Non-prestressed

Static

Four-point bending

Non-prestressed

Number of specimens

Four: two controls, two


laminates

Eight: three controls, four


GFRP#5, one strengthened with

NSM GFRP#3

Twelve: six controls, six


CFRP laminates

Bea

m g

eom

etry

Cross section (mm)


web height = 660,

flange width = 927,

web width = 343

180×250 120×170

Net span (mm) 8025 1200 900

Shear span (mm) 4012.5 500 300

f'c (MPa) 45 58, 37, 21 52.2

Bottom

steel

Amount 3#11+3#10+2#8 2- Ø16 2-Ø5, 2-Ø6.5, 3-Ø6.5

fyt (MPa) 364 398, 512 788, 627, 627

Top

steel

Amount N.A. N.A. 2-Ø6.5

fyc (MPa) N.A. N.A. 627

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Epoxy+Silica fume Epoxy, XH-111, XH-130 Epoxy, CFK 150/2000

Tensile strength

[Modulus of

elasticity] (MPa)

N.A.

[N.A.]

27, 49

[N.A.]

16-22

[5000]

FRP

Type CFRP laminate GFRP bar CFRP laminate

shape/surface Rectangular, smooth Round, sand coated Rectangular, smooth

Dimension

db or tf×hf (mm) 1.4×25 9.5, 16 1.4×9.6

Number of FRP

reinforcements 4 2 1, 2, 3

Efrp (GPa) 154.29 68, 64 158.8

Tensile strength

(MPa) 2785.7 650, 512 2740

Groove dimensions

(mm) N.A.×32

15×15

20×20 (4-5)×(12-15)

Cut-off distance

from the support (mm) Extended over supports Extended over supports N.A.

Test variables

Strengthening of aged

member (42 years old), type

of loading, different types of

retrofitting

Type of concrete, type of epoxy,

area of GFRP bar Axial stiffness

Observed failure modes Concrete crushing+concrete

cover splitting

Shear failure+GFRP rupture,

shear failure+GFRP debonding,

Concrete crushing+epoxy paste

splitting

Delamination of concrete

cover at cut-off location

Increase in capacity (%) 6-10 23.7-51.6 35-118

45



Reference Gaafar (2007) Al-Mahmoud et al. (2009) Badawi and Soudki (2009)


strengthening

Static

Four-point bending

Prestressed and non-

prestressed

Static

Four-point bending

Non-prestressed

Static

Four-point bending


Number of specimens

Nine: one control, two


prestressed NSM CFRP

rebars/strips, six strengthened

with prestressed NSM CFRP rebars/strips

Eight: one control, seven


CFRP bars

Four: one control, one


prestressed NSM CFRP rod,

two strengthened with


Bea

m g

eom

etry

Cross section (mm) 200×400 150×280 152×254

Net span (mm) 5000 2800 3500

Shear span (mm) 2000 800 1100

f'c (MPa) 40 35.1-38.1

66.5-67.2 45

Bottom

steel

Amount 3-15M 2-12mm 2-15M

fyt (MPa) 475 600

E=210GPa 440

Top

steel

Amount 2-10M 2-6mm 2-10M

fyc (MPa) 500 600 440

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Epoxy Epoxy

Mortar Epoxy

Tensile strength

[Modulus of

elasticity] (MPa)

24

[4500]

29.5 [4940] for epoxy

6.2 [31400] for mortar

N.A.

[N.A.]

FRP

Type CFRP strip and rebar CFRP rod CFRP rod

shape/surface

Strip: rectangular, rough

textured

Rebar: round, sand coated

Round, sand coated Round-N.A.

Dimension

db or tf×hf (mm) Strip:2-2×16, rebar: 9 6,12 9.5

Number of FRP

reinforcements 1

1 (for 12mm)

2 (for 6mm) 1

Efrp (GPa) Strip:124, rebar:124 146 136

Tensile strength

(MPa) 2610 1875 1970

Groove dimensions

(mm)

Strips: 16×25

Rebar: 20×25

12×12

24×24 15×25

Cut-off distance

from the support (mm) 310, mechanical anchor used

350, 50, or extended over

supports Extended over supports

Test variables Prestressing level (0-60% fu),

type of CFRP material

Strengthening length,

concrete strength, groove

filler, area of CFRP rod

Prestressing level (0-60% fu)


Concrete crushing, CFRP

rupture, concrete cover

spalling

CFRP rod pull-out,

concrete peeling-off at

cut-off point, concrete

crushing, debonding at

mortar-concrete interface

Concrete crushing, CFRP rod

rupture

Increase in capacity (%) Strip: 60.7-77.3

Rebar: 60.71-66.67

2-Ø6: 48.8-100.7

Ø12: 121.7-148.1 50-79

46



Reference Rasheed et al. (2010) Oudah (2011)


strengthening

Static

Three-point bending

Non-prestressed

Static

Fatigue

Four-point bending


Number of specimens

Four: two controls, one


strips, one strengthened with

NSM stainless steel (both

strengthened in shear too)

Nine: one control, two


prestressed NSM CFRP

rebars/strips, six strengthened

with prestressed NSM CFRP rebars/strips

Bea

m g

eom

etry

Cross section (mm) 254×457 200×400

Net span (mm) 4720 5000

Shear span (mm) 2360 2000

f'c (MPa) 34.5 40

Bottom

steel

Amount 4#6 3-15M

fyt (MPa) 576 (beam with NSM CFRP)

477 (beam with NSM steel) 440

Top

steel

Amount 2#3 2-10M

fyc (MPa) 576 (beam with NSM CFRP)

477 (beam with NSM steel) 440

Str

eng

then

ing

mat

eria

ls

Groove

filler

Type Epoxy Epoxy

Tensile strength

[Modulus of

elasticity] (MPa)

N.A.

[N.A.]

24.8

[4500]

FRP

Type CFRP strip

Stainless steel bar CFRP strip and rebar

shape/surface Rectangular, smooth

Round, deformed bar

Strip: rectangular, rough

textured

Rebar: round, sand coated

Dimension

db or tf×hf (mm)

2-2×16

#4 Strip:2-2×16, rebar: 9.5

Number of FRP

reinforcements

4

3 1

Efrp (GPa) 131

200 Strip:124, rebar:124

Tensile strength

(MPa)

2068

883 (fy=683)

Strip: 2610

Rebar: 1896

Groove dimensions

(mm)

6×19

19.1×19.1

Strips:16×25

Rebar:20×25

Cut-off distance

from the support (mm) Extended over supports 310, mechanical anchor used

Test variables

Type of strengthening

materials, type of

strengthening

Prestressing level (0-60% fu),

type of CFRP material

Observed failure modes Concrete crushing Concrete crushing, CFRP

rupture

Increase in capacity (%) NSM CFRP: 46.4

NSM Steel: 46.1

Strip: 58-63

Rebar: 58-75

47

2.10 Environmental Exposure

To use NSM-FRP system confidently in practice, the performance of this system

under different environmental conditions should be studied. Durability is defined by

Karbhari et al. (2003) as “the ability to resist cracking, oxidation, chemical degradation,

delaminating, wear, and/or the effects of foreign object damage for a specified period of

time, under appropriate load conditions and specified environmental conditions”. Several

environmental factors causes deterioration including (the last four factors are considered

in this research):

Chemical solution (salt, alkaline, and acid)

Oxidation

UV radiation

Fatigue

Fresh water/ sea water

Thermal cycling

Humidity

Freeze-thaw

Creep and relaxation

2.10.1 Effect of Freeze-Thaw Exposure on Concrete

When concrete freezes, the volume of the water in the pores increases due to

freezing (approximately by 9%) and this behaviour produces high energy/pressure in a

small volume that can causes severe damage to the structure of the concrete. If thawing

and freezing take place, additional expansion of concrete will occur; This damage

48

appears as the cracks on the surface of the concrete and can cause a decrease of about

75% in strength of the plain concrete (observed by the author based on testing the

concrete cylinder specimens exposed to 500 freeze-thaw cycles) while increase the

ductility due to presence of the cracks. Entraining air to the concrete mix provides closely

spaced micro voids which decrease the pressure and avoid severe damage and

breakdown. An air entrainment of 5-8% provides sufficient protection for normal and

high-strength concrete exposed to thermal cycling (Neville, 2011). Also, the following

conditions need to be met to avoid possible damage to the concrete due to freeze-thaw

cycling exposure: the specimen should be fully cured, a water-cement ratio less than 0.45,

a minimum cement content of 335 kg/m3, adequate drainage, a minimum of seven days

of moist curing above 10°C, a minimum 30 day drying period after curing, and a

minimum compressive strength of 24 MPa at the time of first frost exposure (Neville,

2011; Kosmatka, 1998). If these conditions are taken into account, no adverse effects to

concrete from freeze-thaw cycling exposure will be observed. Figure ‎2-8 shows the

damage on concrete cylinder specimen after 500 cycles of freeze-thaw from +34oC to -

34oC and relative humidity of 75% for temperatures above +20

oC.

Figure ‎2-8: Damage done to the concrete cylinder after 500 cycles of freeze-thaw

(tested in this research).

49

The typical signs of freeze-thaw exposure are classified as:

Spalling and scaling of the surface

Large pieces (cm size) are spalled

Exposing of aggregate

Usually exposed aggregate are un-cracked

Surface parallel cracking

Gaps around aggregate

Furthermore, the thermal expansion coefficient of concrete is affected due to

temperature changes. Table ‎2-11 represents the thermal expansion coefficient of partially

dried concrete at different temperature; the changes are negligible when temperature

change from +20oC to -70

oC.

Table ‎2-11: Thermal expansion coefficient of concrete in different temperature

(Oldershaw, 2008).

Study Temperature

(oC)

Coefficient of thermal expansion

(10-6

/oC)

Browne and Bamforth (1981) 20 10 to 12

-165 5 to 6

Yamane et al. (1978) 20 12

-70 10

2.10.2 Effect of Freeze-Thaw Exposure on Steel Rebar

In RC members the steel is covered by the concrete and is not exposed to severe

environmental condition directly; this fact decreases the concern about the damage on

steel in RC member subjected to freeze-thaw. However, when the section is cracked there

will be a concern about the corrosion and possible damage to the steel rebar. Browne and

50

Bamforth (1981) performed tests on a wide range of the steel rebar with different strength

when the temperature was changed from 20oC to -140

oC. These researchers concluded

that the regular steel rebar strength enhances in a rate of 1 MPa/oC when temperature

decreases. However, the thermal expansion coefficient of steel remains constant 11.3×10-

6/oC from 20

oC to -165

oC.

2.10.3 Effect of Freeze-Thaw Exposure on CFRP Reinforcement

FRPs subjected to freeze-thaw cycling exposure are affected by thermal

incompatibility and polymer embrittlement (Green, 2007). Thermal incompatibility

which is a result of different thermal expansion coefficients of fibres and matrix produces

residual stresses in the FRP at low and high temperatures. The coefficients of thermal

expansion for most epoxies, glass fibres, and carbon fibres are about 45 to 65×10-6

/oC,

5×10-6

/oC, and -0.2 to 0.6×10

-6/oC, respectively (Mufti et al., 1991). The simple concept

of the residual stress in a composite at low and high temperatures is illustrated in Figure

‎2-9. The high enough residual tensile stress in matrix may lead to formation of micro

cracking, furthermore, thermal cycling can increase the size of these cracks or propagate

them which can result in strength degradation or failure (Dutta, 1989). The polymer

embrittlement is the increase in brittleness of polymer due to low temperature. Green et

al. (2006) concluded that polymer embrittlement may reduce the ability of the matrix in

transferring the stress to the individual fibres, or between the composite and substrate

concrete.

51

Figure ‎2-9: Concept of residual stresses in composite at high and low temperatures

(Dutta, 1989).

Among the studies performed on the freeze-thaw exposure effects on FRP

materials, Bisby and Green (2002) reported that for uniaxial CFRP and GFRP material

subjected to 300 freeze-thaw cycles, there is insignificant effect on the strength and

stiffness. Dutta (1989) concluded that tensile strength and stiffness of glass and carbon

fibres are not affected by thermal cycling. Micelli (2004) studied the effects of

accelerated aging on CFRP and GFRP bars subjected to accumulative 200 freeze-thaw

cycling exposure (-18oC to 4

oC), 480 high humidity cycles (in constant temperature), 600

high temperature cycles (16oC to 49

oC), and ultraviolent radiation (during the high

temperature and high humidity cycles as shown in Figure ‎2-10. Tensile test results

indicated that the longitudinal mechanical properties of the CFRP bars were not affected

by the applied environmental exposure, however, a slight reduction in average strength of

GFRP bars was observed after exposure. Furthermore, the transverse material properties

which are most influenced by resin properties did not significantly alter. On the other

hand, the freeze-thaw effect can also be beneficial. Karbhari et al. (2003) reported that

52

temperature below zero can result in matrix hardening which can lead to enhancements in

modulus, tensile and flexural capacity, creep and fatigue resistance (GangaRao et al.,

2007).

Figure ‎2-10: Applied exposure on the FRP specimens (Micelli, 2004).

2.10.4 Effect of Freeze-Thaw Exposure on Epoxy Adhesive

The effect of freeze-thaw exposure combined with humidity or moisture on epoxy

is important in two aspects: the effect on the matrix properties, and the effect on the bond

behaviour. Moisture affects matrix mechanical properties such as shear strength. There is

always a potential for possible air voids in the epoxy or between FRP and concrete. The

water can penetrate to these voids and by subsequent freezing and thawing gradually the

voids will grow and causes a weakness in the interface. Colombi et al. (2010) concluded

that the bond of CFRP plates to concrete attached with Sikadur 30 is not affected by 200

freeze-thaw cycles.

53

2.10.5 Effect of Sustained Loading on Concrete

Sustained loading on a structural member produces time dependant increases in

strain known as creep and time dependant decreases in stress known as relaxation. The

instant deformation when a load is applied to concrete member enhances under sustained

load due to creep (Neville, 2011). Creep in concrete occurs at a microscopic level due to

the meta-stability of the concrete, which is related to the pore structure and the amount

and type of water in the pores (Bisby, 2006). On the other hand, creep is a function of the

volumetric content of the cement paste in the concrete and only the hydrated cement in

concrete undergoes creep while the aggregate acts as a resistant (Neville, 2011).

Therefore, concrete with higher modulus aggregates undergoes smaller creep deformation

under load. The magnitude of the sustained load plays a significant role in creep so that

the creep strain can be several times larger than the strain generated during the instant

loading. After removing the sustained load, some a large amount of creep strain is not

recoverable, the amount of irrecoverable strain/deformation known as residual

strain/deformation (Neville, 2011). The subsequent gradual decrease in strain is known as

creep recovery. The residual deflection is a result of the re-orientation of particles with

the diffusion of water, as the microstructure attempts to achieve a more stable state

(Bisby, 2006). Overall, the creep amount in concrete is affected by the moisture content,

the degree of hydration, the aggregate properties, the volume to surface ratio, the relative

humidity, the temperature, the concrete strength, and the existence of admixture.

Concepts of elastic strain, creep strain, elastic recovery, creep recovery, and residual

deformation are illustrated by Figure ‎2-11.

54

Figure ‎2-11: Creep strain-time relationship for concrete under uni-axial stress

(Bisby, 2006).

2.10.6 Effect of Sustained Loading on FRP and Adhesive

Creep is not only related to concrete, it also occurs in FRP composite and

adhesives. The creep strain-time relationship for FRPs subjected to uni-axial stress is

similar to concrete creep strain-time relationship (Oldershaw, 2008), as shown in Figure

‎2-11. GangaRao et al. (2007) illustrated the sustained stress damage on the FRP

composites using three stages: (1) random fibres rupture and the matrix around those

ruptured fibres relaxed which results in stiffness reduction; (2) more cracking occurs,

fibre/matrix interface debonds, and more fibre ruptures which leads to rapid drop in

stiffness; (3) total failure due to stress rupture. Karbhari et al. (2003) reported stress

levels of 50% and 75% for glass and carbon fibres, respectively, under ambient

conditions with 10% failure possibility. On the other hand, polymer matrix is visco-

elastic and can undergo higher amount of the creep than fibres (Bisby, 2006). In

comparison with other materials in the case of creep, Hollaway and Leeming (1999)

55

found that CFRPs are better than standard steels and comparable with low relaxation

steels. The creep response of FRPs is related to (Hollaway and Leeming, 1999):

The type of polymer matrix and its stress history

The direction, type, and volume fraction of the fibre reinforcement

The nature of the applied loading

The temperature and moisture conditions

GFRPs are more vulnerable to creep than CFRPs and AFRPs. Canadian Highway

Bridge Design Code (CAN/CSA-S6-06, 2011) limits the allowable stress (creep rupture

stress) in the CFRP, AFRP, and GFRP to 65%, 35%, and 25% of the ultimate tensile

strength of the corresponding reinforcements, respectively. On the other hand, for the

FRP loaded axially in the direction of the fibres, ACI 440.1R (2006) limits the permanent

stresses in the CFRP, AFRP, and GFRP to 50%, 30%, and 20% of the their capacity.

Furthermore, Ceroni et al. (2006) indicated the 50 year period creep rupture failure

strengths of 79-93% for CFRP, 47-66% for AFRP, and 29-55% for GFRP.

2.10.7 Synergistic Effect of Sustained Load and Freeze-Thaw Exposure

A major research gap exists in combination of freeze-thaw cycling exposure and

sustained loading for prestressed NSM-FRP strengthened RC beams. Combining

environmental factors might rapidly increase or decrease the amount of degradation

which occurs on the components of a structural member. For example, low temperature

might decrease the amount of creep due to improvement in modulus of elasticity while

high temperature might accelerate the amount of creep.

56

Vijay and GangaRao (1999) studied the combined and separate effects of salt/

alkaline exposure and sustained stress on GFRP rebars. Results revealed decreases of

24.5% and 30% in ultimate tensile strength at room temperature, after 30 months of

exposure to salt and alkali respectively. On the other hand, a decrease of 25.2% in

ultimate strength was observed after 10 months of exposure to sustained load (32% of

ultimate tensile strength) and salt exposure. Similarly, a decrease of 14.2% in capacity

was reached after 8 months of exposure to sustained load (25% of ultimate tensile

strength) and alkaline exposure. It is estimated by Turner (1979), that at temperatures

between -10oC to -30

oC the value of the concrete creep is about half of that at 20

oC. The

reason is increasing the modulus of elasticity with decreasing the temperature below the

freezing point of capillary water (about -2oC). Oldershaw (2008) reported that beams

subject to a period of sustained load prior to testing displayed greater stiffness than

control beams, likely a result of the stiffening effect on concrete which experiences creep.

2.10.8 Effect of Environmental Exposure on FRP-Strengthened RC Beam

The effects of environmental exposure (including sustained load and freeze-thaw

exposure) on the RC beams strengthened with prestressed NSM-CFRP reinforcements

have not been addressed by the researchers. Therefore, in this section, the researches that

have been performed on the beams strengthened with non-prestressed NSM-CFRP and

also related subjects are briefly reviewed. In this context, Toutanji and Gómez (1997)

investigated the performance of the small-scale EB-FRP strengthened RC beams (300 ×

50 × 50 mm) subjected to wet/dry cycling exposure. 56 RC beams were fabricated: half

were exposed to 300 wet/dry cycles including salt water for the wet cycles (4 hr-35g of

57

salt per 1 litre of water) and hot air at 35oC and 90% humidity for dry cycles (2 hr); the

other half were kept in room temperature (20oC). The beams were strengthened with

different types of Carbon and Glass fibre sheets while 8 beams considered as un-

strengthened control beams. Three different types of the epoxy were implemented in

strengthening. All beams which were tested under the four-point bending configuration

failed due to FRP debonding. The results revealed that epoxy with higher elongation and

higher modulus has a better performance in strength increase for the beams.

Lopez-Anido et al. (2004) evaluated the freeze-thaw resistance of fibre-reinforced

polymer composites (E-glass/vinyl ester) adhesive bonds with underwater curing epoxy

to repair wood piles in the field. These researchers discriminated the effect of freeze-thaw

cycling exposure on the performance of the adhesive bond and compared the lap shear

strength and the mode of failure of the control and exposed samples. Twenty cycles were

adopted for the freeze-thaw exposure: 8 hr in the freezer (-18oC) and 16 hr in the hot-

water immersion bath (+38oC). The authors concluded that the shear strength of the

underwater curing epoxy is sensitive to freezing and thawing cycles where the mean

shear strength decreased to 57% of the control value. Furthermore, the exposure to

freeze-thaw cycles leads to a change in the mode of failure from predominantly adhesive

type to combined adhesive/cohesive type.

El-Hacha et al. (2004) studied the performance of RC beams strengthened with

non-prestressed and prestressed EB-CFRP sheets exposed to room and low temperatures.

The beams were also subjected to both short and long-term loading. Low temperature can

induce micro-cracks in matrix or resin-fibre interface due to large differences in

coefficients of thermal expansions (in order of magnitudes). Eight large scale T-beams

58

were tested: Four beams at room temperature and four at -28°C. At each temperature, one

beam was considered as un-strengthened control, one tested for short-term behaviour, one

tested for long-term behaviour under self-weight and one tested for long-term behaviour

under sustained load (50% of the strengthened beam capacity). At room temperature,

results revealed a significant prestress loss (12% after 7 days) in short-term test with 50%

prestressing level of the CFRP capacity. The loss increased to 18% after 13 months.

However, sustained load did not cause significant additional losses (the prestress loss

measured was 22%). In spite of the losses in both short and long-term beam tests, the

ultimate load almost remained unchanged with 1% difference. At -28°C, 19%

prestressing loss after 7 days of strengthening was reported for the short-term test while

long-term test had a 22% loss. The same results were observed in the specimens

subjected to sustained load. The difference between beams’ capacities in short-term and

long-term tests was insignificant. However, strengthened beam subjected to long-term

sustained load showed slight degradation (8% reduction) in ultimate strength when tested

at -28 °C. The authors concluded that strengthened beams were enhanced considerably in

strength and stiffness compared to the un-strengthened beams. The long-term behaviour

with or without sustained load had no effect on the beam capacity, but the combined

effects of sustained load and low temperature reduced the ultimate strength of beam

slightly (8%).

Frigione et al. (2006) studied the water effects on the bond strength of the

concrete-epoxy joints by performing experimental tests on the immersed samples. The

specimens were made by cutting the concrete cylinder in inclined surface at 30o from

bottom surface. Then, two surfaces were glued together. The authors examined three

59

parameters including properties of adhesive and concrete, thickness of the adhesive layer

(0.5, 2, 5 mm), and presence of the water (0, 2, 7, 14, 28 days). It was concluded that the

performance of the concrete-resin is influenced by the mechanical properties of the

concrete and the epoxy, the joint effectiveness gradually decreases by increasing the

thickness of the adhesive layer, a maximum decrease of 40% in bond strength is possible

after 28 days of immersion.

Derias (2008) studied the long-term flexural performance of concrete beams (150

× 300 × 300 × 50 × 2500; web width × height × flange width × flange thickness × length)

strengthened with NSM-FRP reinforcements subjected to combined accelerated synthetic

weathering conditions including saline solutions with high concentration (15%) and

elevated temperature (+55oC). Eight beams with different type of FRP materials and

shapes were tested. Four beams were subjected to sustained load (40% of ultimate

capacity of the beams) and other beams were unloaded and tested at room temperature

(+22oC). A significant degradation in the epoxy-concrete interface was observed due to

harsh environmental conditions which caused change in failure mode in comparison with

the similar beams at room temperature.

Subramaniam et al. (2008) investigated the effects of freeze-thaw exposure on

interface fracture energy of EB-FRP-concrete using a direct shear test. The shear stress-

slip relations of the interface were developed for damage associated with freezing and

thawing action. The concrete specimens (125 × 125 × 330 mm, width × height × length)

were placed inside an environmental chamber for 100, 200, and 300 cycles. Each cycle

was accomplished in 12 hr where the temperature changed from +5oC to -18

oC (4.2 hr at

+5oC, 2.4 hr from +5

oC to -18

oC, 2.4 hr at -18

oC, and 3 hr from -18

oC to +5

oC). One day

60

before being subjected to exposure, the specimens were placed in the chamber at 99%

RH and 23oC. Then, each two days after starting the cycling exposure, water was sprayed

in the middle of the thawing part. The chamber was kept sealed and a pool of water was

placed below the specimens to maintain the moisture constant. The results revealed that:

there was no decrease in the elastic modulus of the FRP sheet under freeze-thaw cycling

exposure (up to 300 cycles), furthermore, there was a consistent decrease in load-carrying

capacity of the specimens subjected to freeze-thaw exposure, there was a significant

decrease in the length of the cohesive stress transfer zone with increasing the number of

freeze-thaw cycles (78 and 68mm, 82 mm, and 92 mm for 300, 200, and 100 freeze-thaw

cycles, respectively), the maximum interface shear stress at debonding decreases from

5.97 MPa to 4.85 MPa after 300 freeze-thaw cycles, and the fracture energy decreases

from 0.65 N.mm to 0.42 N.mm after 300 freeze-thaw cycles.

Tan et al. (2009) examined the effects of sustained load and tropical weathering

on the EB-GFRP strengthened RC beam experimentally and analytically. In the analytical

part, flexural strength was calculated based on the modulus of elasticity of concrete and

FRP which were modified due to effect of creep and creep plus tropical weathering,

respectively. The experimental was performed on the small-scale (100 × 100 × 700 mm)

and large-scale (100 × 100 × 2100 mm) specimens strengthened with different GFRP

configuration. The large-scale and small-scale specimens were subjected to 59% and 53%

of the calculated capacity of the un-strengthened beams, respectively. The sustained load

was applied up to 1 and 2.75 years. The authors applied tropical weathering as a hot and

humid condition (temperature between 23oC to 33

oC, relative humidity between 80-90%

at night and 50-60% during the day, and monthly rainfall of 100-180 mm). The deflection

61

and crack width were measured at different time intervals (1-30 days) using gauges and a

hand-held microscope, respectively. The results showed 16% increase in deflection and

18% increase in crack width of the specimens under sustained load after 1 year and 2.75

years outdoor weathering, respectively. Also the beams were tested and a reduction of

15-50% was observed in ductility (ratio of deflection at ultimate to deflection at yielding)

and the failure mode changed from concrete crushing or FRP debonding to FRP rupture.

Mitchell (2010) investigated the combined effects of freeze-thaw exposure and

sustained load (125% of un-strengthened control specimen) on flexural performance of

strengthened RC slab strips using non-prestressed NSM-CFRP tape (Aslan 500).

Furthermore, pull-out bond tests were carried out. 21small-scale slabs (254 × 102 × 1524

mm) were tested, as presented in Table 2-12, to study the effects of adhesive type (grout

or epoxy) and exposure condition (room temperature, freeze-thaw, sustained load, or

freeze-thaw under sustained load). The results revealed insignificant effects on the

performance of the grout strengthened members after exposure to freeze-thaw cycles or

sustained load. The slabs strengthened with epoxy adhesive and exposed to freeze-thaw

cycle or sustained load showed negligible changes in ultimate load (less than three

percent). The combined effect of freeze-thaw cycles and sustained load caused an

average reduction of eight percent in ultimate capacity. The epoxy adhesive strengthened

pull-out bond tests experienced a 27% average drop in ultimate load after 150 freeze-

thaw cycles.

The most related researches in the area are reviewed above and the rest are

presented in Table 2-12.

62

Table ‎2-12: Summary of some existing research on freeze-thaw exposure (study of the considered cycles).

Reference Test method Number of specimens

Beam geometry Freeze thaw exposure

Geometry Guideline

Temperature

Period of each cycles No of cycles Min

oC Max oC

Santofimio

(1997)

Confined cylinders

with FRP composite 6 confined cylinders expose to freeze-thaw 36×305 mm

ASTM

C-666-97 -17.8 4.4 4 hr

300- in a salt water

solution

Bisby and

Green (2002)

EB bonded FRP

sheets, freeze-thaw cycles

39 small-scale flexural beams reinforced

in tension with externally bonded FRP sheets

102×152×1220 mm ASTM

C-666-97 -18 18

24 hr ( 16 hr at -18oC,

thawing in a water bath for 8 hrs)

0-300

El-Hacha et

al. (2004)

Prestressed EB-CFRP

sheets, sustained load plus low temperature

8 T-beams: 4 at room temperature, 4 at -28oC (one control, one strengthened, one

strengthened under self-wight., one under

sustained load +low tem.)

T shape, total height

= 375,

web height = 300, flange width = 535,

web width = 60

N.A. -28 N.A. 13 months N.A.

Dent (2005)

Small scale flexural test,

EB strengthened, 0 or

200 freeze-thaw cycles 0-2×106 fatigue cycles

45 RC beams EB strengthened

15 under fatigue loading, 15 under freeze-

thaw and fatigue loading, 15 at room temperature

102×152×1220 mm ASTM

C-666-97 -18 20

24 hr ( 16 hr at -18oC,

thawing in a water bath

for 8 hrs)

200

Wu et al. (2006)

GFRP composite bridge deck

N.A. N.A. ASTM

C-666-97 -17.8 4.4 2hr and 5 hr

625 salt water,

distilled water, and dry air, prestrained

specimens subjected

to 250 cycles (16,40,100,250,625)

Laoubi et al.

(2006)

Concrete beams reinforced with GFRP

bars under freeze-thaw

and sustained load

21 130×180×1800 mm N.A. -20 20

12 hr (6 hr to -20oC and 6 hr to 20oC), Humidity

50% during all freeze-

thaw exposure

100,200,360

62

63

Table 2-12: Summary of some existing research on freeze-thaw exposure (study of the considered cycles) (Cont’d).

Reference Test method Number of specimens

Beam geometry Freeze thaw exposure

Geometry Guideline

Temperature

Period of each cycles No of cycles Min

oC Max oC

Tam (2007)

Bond test, FRP to

concrete prisms,

single-lap bond test,

48 CFRP and GFRP coupons, 48 sngle lap specimens, 48 FRP-to-concrete prisms

N.A. N.A. 20 -20

6 hr (2 hr from 20oC to -

20oC, 1 hr at -20oC, 2 hr from -20oC to 20oC, 1 hr

at 20oC)

300

Oldershaw (2008)

EB strengthened small

scale concrete beam,

freeze-thaw, freeze-

thaw and sustained loading

48:3 control, 45 strengthened, groups of 3 as control, and groups of 4 as exposed

102×152×1220 mm ASTM

C-666-97

-30

(-18 in

core)

20

(5 in

core)

5 hr: 25 min (30 min from 10oC to 1oC, 1 hr

from 1 to -30oC, 2 hr at -

30oC, 45 min from -30oC to 1oC, 40 min from 1oC

to 10oC use a water bath

for thawing, 30 min from10oC to 20oC)

300, (10-20 yrs for

exterior application

in Toronto)

Saiedi (2009)

CFRP-prestressed

comvrete beams,

sustained load and fatigue loading at low

temperature

7 : five CFRP-prestressed and two steel-

prestressed concrete beams

T shape, total height

= 300,

web height = 250, flange width = 500,

web width = 130

N.A. -27

-28 N.A. 163 days N.A.

Mitchell

(2010)

Non-prestressed NSM

FRP strips,

strengthened slab specimens

21:5 bond test (3 with grout, 2 with epoxy), 5 under freeze-thaw(3 with grout,

2 with epoxy), 6 under sustained load(3

with grout, 3 with epoxy), 5 under sustained load and freeze-thaw(3 with

grout, 2 with epoxy)

254×102×1524 mm N.A

-30

(-13 in

core)

20

(8 in

core)

6 hr: 10 min (5 hr from

0oC to -30oC, and 70

min thawing using a water bath)

300, (10-20 yrs for

exterior application

in Toronto)

Abdelrahman

(2011)

EB Strengthened RC

columns, freeze-thaw 38: wrapped with CFRP and SRP sheets

1200×300 mm

900×150 mm 600×150 mm

300×150 mm

CAN/CSA-

S6-06 -34 34

8 hr (20 min at 20oC, 2 hr: 40 min at -34oC, 5

min at 20oC, 2 hr: 20

min at 34oC having 75% humidity, 10 min at

20oC)

500

63

64

2.11 FE Modeling of FRP-Strengthened RC Beams

In this section a brief review of the performed researches on the FE modeling of

FRP strengthened RC beams is presented with more focus on the modeling procedure. In

this context, Vecchio and Bucci (1999) presented a finite element algorithm to analyze

rehabilitated concrete structures using EB-FRP method. To consider the damage effects,

the authors defined appropriate plastic offset strains for concrete and reinforcement.

These offsets were assigned to the model by prestrain nodal forces. The FE model was

formulated to consider both the initial beam and the plate added beam. After enforcing

the damage on the initial beam the bonded plate was engaged and became active. The

authors validated the 2D FE model with glass and carbon FRP-strengthened RC beams

under monotonic loading and shear wall under cyclic loading.

Kachlakev et al. (2001) developed finite element models for reinforced concrete

beams and bridge that had been strengthened with EB-FRP (Unidirectional Carbon and

Glass) composites under static loading. The models were 3D performed in ANSYS

software validated with the results from laboratory tests, (McCurry, 2000), and the actual

bridge measurements. Four strengthened RC beams were modeled similar to (Chansawat,

2003). The authors assumed perfectly plastic behaviour for concrete material after

ultimate compressive strength (f′c) and complete bond between FRP layers and adjacent

concrete elements. Comparison between FE and experimental results showed a relatively

good agreement. In general, load-strain curves for CFRP, steel rebar and concrete were

softer than those from experimental curves. Comparison between Load-deflection curves

showed that FE load-deflection curves were stiffer than those experimental curves by 12-

66% in linear range and by 14-28% after cracking. a 5-24% difference at ultimate loads

65

(FE was smaller) and 6-34% difference at cracking loads (FE was bigger) was observed.

FE crack pattern at failure for the flexural strengthened beam confirmed that the beam

failing in flexure. In addition, the author modeled the Horsetail Creek Bridge before and

after strengthening under static loading, and concluded that the FE results on strain and

trends of strain versus truck location have a reasonable agreement with the field data. In

comparison with parallel research Chansawat (2003), the results of this research showed

slightly more difference with the experiments, due to difference in mesh, material data,

load-step size, and type of analysis.

Buyle-Bodin et al. (2002) proposed a non-linear 2D finite element model to

analyze the flexural behaviour of EB-CFRP strengthened RC beams under four-point

bending configuration. The FE model was intended to investigate effects of initial

damage and the number of CFRP layers. The experimental tested beams (150 × 300 ×

3000 mm) were modeled using French Code Castem 2000 program. The authors

assumed: concrete behaves as an elasto-plastic material, and interface elements for steel-

concrete and CFRP-concrete interfaces. A load-unload cycle was applied to the FE model

to implement the precracking effects. The precracking load was applied to result in a 3%

strain in tension steel reinforcement. Comparison between FE and experimental load-

deflection curves showed that the FE curve is stiffer than experimental curve at high load

level. A maximum difference of 12% was observed between FE and experimental mid-

span deflection.

Jia (2003) simulated RC beams strengthened with EB CFRP sheets using 3D FE

model in ANSYS program. Nine RC beams (110 × 160 × 1800 mm) were modeled under

four-point bending configuration: one un-strengthened control beam, four beams

66

strengthened with organic epoxy, and four beams strengthened with inorganic epoxy. The

number of CFRP layers was varied from 2-4. The author assumed complete bond

between different materials and perfect plastic behaviour for concrete curve after ultimate

compressive strength. The same procedure as Kachlakev et al. (2001) was employed for

FE modeling. Comparison between FE and experimental results was carried out in terms

of load-deflection curve, load-strain plots for CFRP sheets, cracking, yielding, and failure

loads. After cracking, the FE load-deflection curves were stiffer than those of

experimental results. Results of strain plots for CFRP sheets showed the same trend as

the load-deflection curve. The FE model overestimates the cracking load, yielding load,

and failure load by 6.5-15.8%, 1.1-9.5%, and 2.1-8.6%, respectively. In general the

author achieved a good correlation between FE and experimental results.

Chansawat (2003) performed nonlinear finite element analysis of full-scale

strengthened reinforced concrete beams and bridge strengthened with EB FRP sheets and

beams and bridge using 3D models in ANSYS. Four RC beams (305 × 770 × 6095 mm)

tested by (McCurry, 2000) were modeled: one un-strengthened control beams, one

flexural-strengthened beam using unidirectional CFRP sheets, one shear-strengthened

beam using unidirectional GFRP sheets and one flexural/shear-strengthened beam using

combination of unidirectional CFRP and GFRP sheets tested under four-point bending

configuration. In the FE models, the author considered a confined concrete constitutive

model where the GFRP sheets or loading plates were located. The model for the GFRP-

confined concrete was assigned similar to a model for stirrup-confined concrete.

Complete bonding was assumed between different materials at interfaces. Furthermore,

FRP rehabilitated Horsetail Creek Bridge was modeled before and after strengthening

67

under static and dynamic loading. The existing damage of the bridge and soil interaction

effects were considered in the bridge FE models and a realistic concrete strength based on

in-situ test was employed. A sensitivity analysis was performed by comparing the results

with field data at service stage to find the best model. Comparison showed that the FE

models are in a very good agreement with the experiments in terms of load-deflection

curve and load-tension steel strain plot, and are in a reasonable agreement in terms of

load-FRP strain plot, crack pattern, and load-compressive strain at extreme fibre of the

section. The FE load-deflection curves are stiffer than those from experimental curves.

Comparison between FE and experimental ultimate loads showed 6% to 18% difference

(under estimation). The flexural/shear strengthened beam was tested up to the capacity of

the testing machine and did not fail. The FE results showed that strengthening of the

bridge with FRP could increase the capacity of the bridge by 37% based on mass-

proportional loading and by 28% based on scaled truck loading. Dynamic response of the

bridge showed that the bridge may fail due to collapse in columns.

Supaviriyakit et al. (2004) presented 2D finite element analysis of reinforced

concrete beams strengthened with EB FRP plates and compared the results to the

experiment. The concrete model considered the effect of cracks and steel reinforcement

was smeared over the entire concrete elements at specified locations. Perfect bond was

considered between FRP and substrate concrete and nonlinear FE models was employed

to predict the end and shear-flexural peeling failure load base on strain concentration at

the plate end and along the length of the FRP plate . The authors modeled two FRP-

strengthened beams: one under four-point and another under three-point bending

configuration, and also one un-strengthened control beam (120 × 220 × 2200 mm) under

68

three-point bending configuration. The FE results showed a good agreement with

experimental results in terms of load-deflection curve, ultimate load, failure mode, and

crack propagation.

Kang et al. (2005) examined the flexural behaviour of RC beams strengthened

with non-prestressed CFRP strips using NSM method, experimentally and analytically.

Five beams (200 × 300 × 3400 mm), one un-strengthened control beam, two beams with

different groove depths as well as CFRP strip widths (15 mm and 25 mm), and two

beams with two CFRP strips (2 - 1.2 × 25 mm) disposed at different groove spacing (60

mm and 120 mm) were tested experimentally under four-point bending configuration and

static monotonic loading. Also, the authors performed parametric study on the area and

spacing of CFRP strips. In developed 3D FE models in ABAQUS software, perfect

bonded interfaces were considered while CFRP widths/groove depths were variable from

5-35 mm and groove spacing was variable from 20-180 mm. Through experimental

investigations, the authors concluded that: strengthening efficiency is not only related to

the amount of CFRP strips and also depends on the arrangement of them in the beam;

NSM strengthening method can cause an increase in the ultimate load of un-strengthened

control beam from 40-95%; and there exists a critical groove depth beyond which the

increase of the ultimate load of strengthened beam becomes very slight. Through

parametric study the following were concluded: there exists a minimum spacing (40 mm)

between adjacent CFRP strips to avoid mutual interference; there exists a minimum

distance (40 mm) from CFRP strip to the concrete edge to prevent the influence of the

concrete cover in the vicinity of the edge; there exists an optimum groove spacing of

80mm which causes the highest ultimate load; the ultimate load versus the CFRP ratio

69

curve is a downward-facing parabola; and for a specific amount of CFRP reinforcement,

strengthening efficiency could be enhanced using several reinforcements at regular

spacing near the surface instead of a single reinforcement but decision should be made

after consideration of the workability and economical efficiency (cutting of the grooves

or the epoxy filling).

Pham and Al-Mahaidi (2005) studied the nonlinear finite element modeling of

reinforced concrete beams strengthened with EB CFRP fabrics followed by a parametric

study considering the effects of CFRP thickness, steel reinforcement ratio, and CFRP

bond length. These authors noticed that all finite element analysis using smeared crack

cannot capture debonding failure modes. The developed FE model was 2D considering

debonding failure of the strengthened beams. The modeled beams were simply supported

under four-point bending with a cross section of 140×260 mm and span length of 2300

mm. A bond-slip relationship obtained from lap-test was assigned to the CFRP-concrete

interface. Eighteen beams were modeled, and it was confirmed that the proposed FE

model can simulate the crack pattern, load-deflection curve, mode of failure, and strain in

CFRP reinforcement. A difference at ultimate load up to 18% was observed between FE

and test results. The main flexural debonding modes were identified as: end-plate

debonding and intermediate debonding. When the number of FRP layer increased from 1

to 3, the ultimate capacity increased by maximum 16%. As the amount of CFRP

reinforcement increased further, the failure mode changed to end-plate debonding and the

load capacity reduced relatively. By increasing the amount of steel, the failure mode

shifted from intermediate debonding to end-plate debonding. Changing the amount of

Steel reinforcement had the most effect in increasing the ultimate load. Furthermore, the

70

debonding capacity reduced slightly with decreasing the bond length, an increase of 28%

at ultimate load was observed by extending the bond length from half shear-span to

whole shear-span length.

Kishi et al. (2005) performed 3D elasto-plastic FE analysis of RC beams

reinforced with CFRP and AFRP sheets considering FRP sheet peel-off mode using

DIANA program. Geometrical discontinuities were considered in FE model by applying

stress-relative displacement model to the interface element. Three stress-relative

displacement models consist of: discrete cracking, steel rebar bond-slip, and FRP sheet

debonding models were considered in the FE model. Smeared crack approach was

assigned to the concrete elements. The model was validated and comparison between FE

and experimental results was performed in terms of load-deflection curve, strain profile

along the length of CFRP sheet at yield and ultimate loads, and failure mode showing

very good agreement between FE and experiment results.

Coronado and Lopez (2006) performed 2D finite element modeling and

sensitivity analysis of the RC beams strengthened with EB CFRP and GFRP sheets on

tensile strength, fracture energy, tension softening, compression model, and angle of

dilatancy in ABAQUS software. The FE models were validated by comparing the FE

results in terms of load-deflection curve and failure mode with the results of 19 beams,

which failed either due to concrete crushing or FRP debonding. Up to 10% difference in

ultimate load was observed between FE and experimental results. A damage mechanism

based on the crack propagation was used to consider the plate debonding mode. The

sensitivity analysis revealed that change in concrete tensile strength value from 0.5ft to

2ft, where ft is the tensile strength of the control specimen, has a slight effect on

71

increasing the stiffness; change in fracture energy from 0.5Gf to 2Gf, where Gf is the

fracture energy of the control specimen, has a significant effect on delaying the FRP

debonding failure mode but has an insignificant effect on the behaviour of the beam

failed by concrete crushing; type of softening model (linear, bilinear, and exponential)

has a slight effect on the load-deflection curve; type of concrete stress-strain curve in

compression has a very slight effect on the load-deflection curve; and change in angle of

dilatancy from 20o to 40

o has no effect on the beam failed by concrete crushing but

increase the peak load of the beam failed by FRP debonding. Also, the authors concluded

that modeling of epoxy has a minor effect on the flexural behaviour of the strengthened

beams.

Nour et al. (2007) developed 3D FE models of concrete beams externally

strengthened with CFRP laminates, concrete beams internally reinforced with GFRP bars,

one-way concrete slabs reinforced with GFRP bars, damaged concrete beams externally

strengthened with CFRP laminates, and concrete columns confined with FRP sheets

using a user-defined subroutine at Gauss integration point level for concrete material in

ABAQUS software. Perfect bond was assumed between different materials in FE models.

The authors showed that the numerical responses including load-displacement curves and

failure mechanisms agreed very well with experimental results.

Camata et al. (2007) performed nonlinear FE and experimental analysis of RC

beams strengthened with EB-FRP plates. Four beams (200 × 300 × 3250 mm) (one un-

strengthened and the rest strengthened with one 1.2 × 50 mm CFRP strip) and four one-

way slabs (800 × 120 × 3250 mm) (one un-strengthened and the rest strengthened with

two CFRP strips) were tested monotonically up to failure under four-point bending

72

configuration. An increase of 72% and 35% at ultimate load of beam and slab was

observed due to strengthening in comparison with the un-strengthened specimens. The

FE analysis was performed using Merlin program considering smeared crack model for

concrete material and applied discrete cracks for two sets (set A: under the load and at

concrete-epoxy interface, set B: at the level of reinforcing steel and concrete epoxy

interface). Both models were validated well with the experimental results in terms of

load-deflection curve and mode of failure. The authors compared the strengthening using

CFRP versus GFRP and concluded that using bigger contact area of FRP reinforcement

(width) with the same axial stiffness increases the value of ultimate deflection

significantly; the lower ratio of FRP plate width to RC member width decreases the

probability of concrete splitting failure.

Aram et al. (2008) studied debonding failure modes of EB-FRP-strengthened RC

beams analytically and numerically and also compared the results with international

codes and guidelines. Four beams were tested (2400 × 250 × 150 mm): three beams

strengthened with different CFRP plates and one un-strengthened control beam. The

analytical solution was performed based on the section analysis considering complete

bond. To consider the plate end debonding, Kupfer-Gerstle and Mohr-Coulomb failure

criterion were applied. The proposed FE model was 2D developed using ATENA

software. Smeared crack and bilinear bond-slip model of Ulaga et al. (2003) were

implemented. One FE model with nonlinear adhesive behaviour was developed to predict

the debonding failure at the plate end regions. Also debonding criteria of the codes were

classified and compared with the FE and analytical results. Comparison showed that the

FE load-deflection curves are stiffer than experimental ones while the analytical load-

73

deflection curves are softer than the experimental ones. Up to 250% difference was

observed between the predicted debonding failure loads and calculated value from

different codes. It was concluded that assuming the linear properties for adhesive does

not have a significant effect on interfacial stresses. The authors recommended a strain

limitation of 0.008 in CFRP plate to avoid debonding in flexural cracks and a shear stress

limitation equal to concrete tensile strength in high shear stress regions.

Barbato (2009) developed a simple 2D frame FE model to investigate the load-

deflection curve and failure mode of the EB CFRP and GFRP strengthened RC beams

including concrete crushing, CFRP/GFRP rupture, and CFRP/GFRP debonding.

Debonding criteria was employed in the model based on the maximum allowable stress in

EB-FRP sheet and corresponding effective bond length proposed by Monti-Renzelli

(Monti et al., 2003). The FE analysis was implemented using a MATLAB toolbox

considering static, dynamic, linear, and nonlinear features. The model was validated with

many experimental results reported in literature. A maximum difference of 39% between

numerical and experimental ultimate loads was observed. The numerical load-deflection

curve is softer than the experimental one.

2.12 Research Gaps

Based on the performed literature review in this chapter, the following research

gaps related to NSM-FRP strengthening method are identified by the author. In this

context, the existing gaps are classified in different major aspects such as

implementation, performance, type of loading, environmental exposure, FE analysis and

74

analytical investigation. Some of these major gaps are outlined as the research objectives

in Chapter One to be covered in this research.

Implementing a practical prestressed NSM-FRP strengthening system. In this

context, modification of the anchorage system proposed by Gaafar (2007)

needs to be performed. Also, the effect of FRP reinforcement geometry needs

to be addressed.

Studying the long-term performance of the prestressed NSM-FRP strengthened

RC beams under different types of environmental exposure. In this context,

behaviour of the prestressed NSM-FRP strengthened RC beams subjected to

freeze-thaw exposure and sustained load has never been examined. Most

studies applied 300 freeze-thaw cycles and the effects of higher number of

freeze-thaw cycles have not been investigated.

The long-term prestressing loss in NSM-FRP reinforcement needs to be

addressed.

Developing a comprehensive FE model to simulate the behaviour of the NSM-

CFRP strengthened RC beam considering prestressing and debonding aspects.

Furthermore, developing a FE model that predicts the static behaviour of the

prestressed/non-prestressed NSM-FRP strengthened RC beams subjected to

freeze-thaw exposure and also combined freeze-thaw exposure and sustained

load.

Analyzing the effects of concrete, steel and prestressing level in prestressed

NSM-CFRP strengthened RC beams. In this context, a parametric study needs

to be done on strengthened RC beams using FE model.

75

Performing a parametric study on the FRP anchorage system considering the

effects of bond capacity, dimensions etc.

Performing an analytical study to derive the load-deflection response of the

prestressed/non-prestressed NSM-FRP strengthened RC beams subjected to

environmental exposure.

Performing an analytical study on the practical anchorage system for

prestressing the NSM-FRP that needs to address the distribution of interfacial

stresses.

Studying the performance of pre-damaged/deteriorated beams/slabs

strengthened using prestressed NSM-FRP method. In this context, cracking

and damage to the concrete cover of the steel reinforcement may have a

significant effect on the failure process and performance.

Investigating the fatigue, seismic, and dynamic loading on the prestressed

NSM-FRP strengthened beams. Also, the effects of environmental exposure

factors such as Chemical solution (salt, alkaline, and acid), Oxidation, UV

radiation have never been examined on prestressed NSM-FRP strengthened

members.

Studying the deformability and ductility of the prestressed NSM-FRP

strengthened RC beams and proposing appropriate deformability models and

limits.

Studying the application of the prestressed NSM-FRP on the timber structure

and long-term performance of that.

76

2.13 Summary

A comprehensive literature review on the behaviour of RC beams strengthened

using NSM system was presented in this chapter. First, a brief review about the evolution

of the engineering material, different types of the FRP products, and strengthening

methods using FRP materials was provided. Then, the history of the NSM method,

materials used for this type of strengthening, and a comparison between EB-FRP and

NSM-FRP strengthening methods were presented. Afterwards, the recent development

and research progress on the prestressed FRP-strengthened RC beam, long-term

behaviour of FRP-strengthened RC beam and components mainly subjected to freeze-

thaw exposure and sustained load, and FE modeling of FRP strengthened RC beams were

summarized. Finally, the identified research gaps in the area of the NSM-FRP

strengthening method were categorized. In the following chapter, the experimental test

program is presented.

77

Chapter Three: Experimental Program

3.1 Introduction

A survey on the body of literature performed in Chapter Two indicated

insufficient experimental investigation on a practical prestressed NSM-FRP strengthening

system to strengthen RC beams in flexure and also the long-term performance of the

system under the freeze-thaw exposure and sustained loading when combined with

humidity. Furthermore, the effects of prestressing level and shape of FRP reinforcement

(rebar and strip) required investigation. Details of the experimental program conducted in

this research are presented in this chapter. First, the testing matrix of the specimens is

provided followed by a description of the beams’ details, manufacturer material

properties, design, fabrication, and instrumentation. Then, the considered freeze-thaw

cycling exposure and application of the sustained load are illustrated in detail. At the end,

the static testing procedure and configuration are described. It should be noted that the

design and fabrication of the beams, and results of the ancillary tests of the steel,

concrete, and FRP materials are presented in Appendices A, B, and C, respectively.

3.2 Test Matrix

The main experimental part of the project consists of two phases to examine the

long-term performance and effects of different types of loading on the prestressed NSM-

CFRP strengthened RC beams.

During the first phase, the effects of severe environmental conditions on the

flexural behaviour of prestressed NSM-CFRP strengthened beams were studied under

78

static loading. Nine large-scale simply supported RC beams (5.15 m long with

rectangular section 200×400 mm) were tested under four-point bending configuration:

one un-strengthened beam, four strengthened beams using Aslan 500 CFRP strips (2-

2×16 mm, 62.4 mm2), and four strengthened beams using Aslan 200 CFRP rebars (Φ9.5

mm, 71.3 mm2). The CFRP strips/rebar were mounted in one groove made in the

concrete cover on the tension face (named as NSM method). The target prestressing

levels were 0, 20, 40, and 60% based on the ultimate tensile strength of the CFRP

reinforcement reported by the manufacturer. The CFRP strips/rebar were prestressed

using an innovative anchorage system that consisted of two steel anchors bonded to the

ends of the CFRP strips/rebar and using movable and fixed brackets and a hydraulic jack

temporarily mounted on the beam. After strengthening, the beams were precracked

(loaded up to 1.2 times the analytical cracking load for each beam) and placed inside a

testing facility chamber exposed to 500 freeze-thaw cycles (-34oC to +34

oC in 8 hrs) and

average humidity of 75% for temperatures above +20oC.

In the second phase, the focus was on the type of loading where the combined

effects of the sustained load and freeze-thaw exposure were investigated. Five large-scale

RC beams (similar to the beams of phase one strengthened with CFRP strips) were

fabricated and subjected to sustained service load (47% of the analytical ultimate load of

the non-prestressed strengthened beam), 500 freeze-thaw cycles, and fresh water spray

(18 L/min for a time period of 10 min) at a temperature of +20oC. After being exposed to

500 freeze-thaw cycles, the beams were tested under static monotonic loading up to

failure. A summary of the test matrix is presented in Table ‎3-1.

79

Table ‎3-1: Test matrix.

Phase # Beam ID

Description

NSM

strengthening

material

Target prestressing

level %ffrpu

(prestrain)

Freeze-thaw

exposure

Sustained

load

I

B0-F N.A. N.A. 500 cycles N.A.

BS-NP-F Two CFRP strips

(2-2×16 mm)

0

(0) 500 cycles N.A.

BS-P1-F Two CFRP strips

(2-2×16 mm)

20

(0.0034) 500 cycles N.A.


(2-2×16 mm)

40

(0.0068) 500 cycles N.A.


(2-2×16 mm)

60

(0.0102) 500 cycles N.A.

BR-NP-F One CFRP rebar

(9.5 mm)

0

(0) 500 cycles N.A.

BR-P1-F One CFRP rebar

(9.5 mm)

20

(0.0034) 500 cycles N.A.


(9.5 mm)

40

(0.0068) 500 cycles N.A.


(9.5 mm)

60

(0.0102) 500 cycles N.A.

II

B0-FS N.A. N.A. 500 cycles 62 kN

BS-NP-FS Two CFRP strips

(2-2×16 mm)

0

(0) 500 cycles 62 kN

BS-P1-FS Two CFRP strips

(2-2×16 mm)

20

(0.0034) 500 cycles 62 kN


(2-2×16 mm)

40

(0.0068) 500 cycles 62 kN


(2-2×16 mm)

60

(0.0102) 500 cycles 62 kN

It should be mentioned that, in the initial project plan, phase II consisted of nine

beams (one un-strengthened control beam, four strengthened beams using CFRP strips,

and four strengthened beams using CFRP rebars) to be subjected to the same freeze-thaw

exposure as applied in phase I plus sustained load. However, after testing the beams in

phase I and analyzing the results, it was concluded that there is no significant difference

between the overall flexural behaviour of the beams strengthened with CFRP strips and

80

the ones strengthened with CFRP rebars. Furthermore, the applied exposure had

insignificant effects on the flexural performance of the beams. Therefore, in phase II,

only the beams strengthened with CFRP strips were fabricated and tested, and the

considered 75% relative humidity was replaced with fresh water spray to increase the

severity of the applied freeze-thaw exposure.

In addition to the main experimental part of the research, a small experimental

program was defined after completion of the tests in phases I and II on the modification

of the temporary movable and fixed steel brackets used for prestressing the NSM CFRP.

This part was done to avoid the occurrence of cracks during prestressing process (jacking

stage) at the locations of the temporary brackets in the RC beams strengthened using

NSM CFRP strips and rebar with high prestress level of 60% (presented in Table ‎3-1).

Therefore, the temporary steel brackets were modified by adding steel plates to the side

to be capable of changing the location of the jacks, and to test the efficiency of the

modified brackets, three small concrete specimens (1500 mm long with rectangular

section 200×400 mm) were fabricated and very high prestress level (93% based on the

ultimate tensile strength of the CFRP reinforcements reported by the manufacturer) was

applied to them. The concrete specimens had similar cross-sections and target material

properties to the RC beams in phases I and II. To facilitate the execution of the

experiment, the concrete specimens had pre-formed grooves and a dywidag thread steel

bar with two adjustable nuts at the ends was used instead of CFRP reinforcements. A

summary of the specimens are presented in Table ‎3-2.

81

Table ‎3-2: Summary of the specimens used for modification of the brackets.

Specimen ID Length

(mm)

Cross-section

(mm×mm)

Target prestressing level

%ffrpu (prestrain)

Target prestressing force

in the dywidag bar (kN)

SP-1 1500 200×400 93 (0.0158) 122.8

SP-2 1500 200×400 93 (0.0158) 122.8

SP-3 1500 200×400 93 (0.0158) 122.8

3.3 RC Beam Specimens

The geometry of the RC beams were selected based on prior research performed

by Gaafar (2007) who examined the flexural behaviour of the prestressed and non-

prestressed NSM-CFRP strengthened RC beams at room temperature.

3.3.1 Design

The dimensions of the RC beams were selected to be similar to those from prior

research on the flexural behaviour of the prestressed and non-prestressed NSM-CFRP

strengthened RC beams at room temperature performed by Gaafar (2007), in order to

provide the opportunity for future comparison between the results. Since flexural

strengthening in practice is usually done on the beams with insufficient steel ratios, the

RC beams had small reinforcement ratios: 0.87% for tension steel reinforcements and

0.29% for compression steel reinforcements, which are within the maximum and

minimum reinforcement ratios. To avoid shear failure in the strengthened beams, a shear

span to effective depth ratio of 5.8 with sufficient stirrups along the length was

considered. The beams were considered to be strengthened using one CFRP rebar or two

glued CFRP strips mounted in one groove, and therefore, were designed to provide

sufficient concrete cover at the soffit for cutting the groove and implementing the NSM

strengthening. The groove dimensions were selected to be greater than the minimum

82

ratios recommended by ACI 440.2R (2008) to decrease the possibility of premature

failure due to NSM CFRP debonding; These ratios are 3.2 for width of the groove-to-

width of strips, 1.6 for height of the groove-to-height of the strips, 2.1 for width of the

groove-to-width of rebar, and 2.6 for height of the groove-to-height of the rebar versus

the minimum limits of 3, 1.5, 1.5, and 1.5, respectively. The maximum initial prestress

level was selected to be 60% of the tensile strength of the CFRP reinforcements reported

by the manufacturer, which is recommended by CAN/CSA-S806-12 (2012) and

considers creep rupture stress of the CFRP reinforcements and reserve strain capacity

(required deformability limits) for the strengthened beam. The dimensions of the end

anchors and the number of the bolts were designed to avoid any issues such as shear

failure of the bolts, bearing failure of the anchor plate, and failure of the anchor tube/pipe

to anchor plate weld during the prestressing.

Capacity of the designed beam and type of failure based on manufacturer material

properties and target prestressing length of 4320 mm (centre-to-centre of the exterior end

anchor bolts) are presented in Table ‎3-3. The key points of the load-deflection curves are

calculated by developing a code in Mathematica software that can account for negative

camber due to prestressing, concrete cracking, steel yielding, CFRP rupture, and concrete

crushing of the prestressed and non-prestressed NSM-CFRP strengthened RC beams.

More details regarding the design of the un-strengthened and strengthened beams are

provided in Appendix A. Furthermore, more details on geometry, manufacturer material

properties, fabrication, and instrumentation of the test beams are provided in the

following sections.

83

Table ‎3-3: Summary of designed specimens.

Beam ID ɛp Δo

(mm)

Δcr*

(mm)

Pcr*

(kN)

Δy*

(mm)

Py*

(kN)

Δu*

(mm)

Pu*

(kN) ɛc@u ɛfrp@u

Failure

Mode

B0 N.A. 0 1.70 22.70 21.85 82 121.47 85.73 0.0035 N.A. CC

BS-NP 0 0 1.71 22.91 22.16 88.88 96.92 131.78 0.00302 0.017 FR

BS-P1 0.0034 0.45 1.76 29.60 21.58 97.83 75.74 131.65 0.00259 0.017 FR

BS-P2 0.0068 0.90 1.81 36.28 21.03 106.73 56.36 131.26 0.00217 0.017 FR

BS-P3 0.0102 1.35 1.86 42.97 20.53 115.58 38.85 130.31 0.00173 0.017 FR

BR-NP 0 0 1.71 22.94 22.21 89.86 93.06 135.17 0.00295 0.016 FR

BR-P1 0.0034 0.51 1.77 30.58 21.55 100.08 71.47 134.99 0.00251 0.016 FR

BR-P2 0.0068 1.02 1.82 38.22 20.94 110.24 51.87 134.48 0.00208 0.016 FR

BR-P3 0.0102 1.54 1.88 45.85 20.37 120.33 34.34 133.20 0.00162 0.016 FR

ɛp = target prestrain value in CFRP reinforcement ɛc@u = concrete strain at extreme compression fibre at ultimate load

Δo = initial camber due to prestressing ɛfrp@u = maximum CFRP strain at ultimate load

Pcr and Δcr = load and deflection at cracking CC = concrete crushing

Py and Δy = load and deflection at yielding FR = CFRP rupture

Pu and Δu = load and deflection at ultimate

* self-weight is ignored in calculations (to consider the self-weight effects, values of 6 kN and 0.47 mm should be deducted from the loads and deflections,

respectively)

83

84

3.3.2 Details of Beams

The beams were 5150 mm long with 5000 mm span length (centre-to-centre of

the supports) and a rectangular cross-section of 200×400 mm. All beams were simply

supported and tested under four-point bending quasi-static monotonic loading. Geometry

of the beams and the test setup are presented in Figure ‎3-1. The compression steel

reinforcement consisted of 2-10M deformed steel bars (nominal diameter of 11.3 mm)

with a total area of 200 mm2 and the tension steel reinforcement consisted of 3-15M

deformed steel bars (nominal diameter of 16 mm) with a total area of 600 mm2. The shear

reinforcement consisted of double leg closed 10M deformed steel bars. The beams were

strengthened with either one 9.5 mm sand coated CFRP rebar or two 2×16 mm rough

textured CFRP strips, which were glued together, mounted in one groove on the tension

face of the beam as plotted in Figure ‎3-2a. The CFRP strips/rebar was prestressed against

the beam itself using the anchorage system developed by Gaafar (2007). The CFRP

rebars and strips were connected to the proper end anchors, as plotted in Figure ‎3-2b, to

be capable of enforcing the desired prestressing for each beam without any issues.

85

Figure ‎3-1: Geometry of the beams and test setup.

85

86

(a) Cross-section of the beams and details of the grooves

(b) End anchor details

Figure ‎3-2: Details of the beams.

87

3.3.3 Manufacturer Material Properties

3.3.3.1 Steel Reinforcements

The tension, compression, and shear reinforcements possessed a specified yield

strength of 440 MPa and a modulus of elasticity of 200 GPa.

3.3.3.2 Concrete

The designed target 28 days concrete compressive strength was 40 MPa having a

maximum aggregate size of 20 mm, an air content of 1%, and a slump value of 80 mm.

3.3.3.3 CFRP Reinforcements

The CFRP materials used for strengthening consisted of Aslan 500 Tape and

Aslan 200 Rebar produced by Hughes Brothers Inc. with the specified properties


Table ‎3-4: Properties of CFRP strip and rebar recommended by the manufacturer

(Hughes Brothers, 2010a and b).

CFRP product Surface

treatment

Dimensions

(mm)

Afrp

(mm2)

ffrpu

(MPa)

Efrp

(GPa) ɛfrpu

Aslan 500 CFRP Tape Rough textured 2×16 31.2 2068 124 0.017

Aslan 200 CFRP Rebar Sand coated Ф9.5 71.26 1896 124 0.016

3.3.3.4 Epoxy Adhesives

Two types of epoxy adhesives, produced by Sika Inc., were employed for NSM

strengthening. Sikadur® 330 was used to connect the CFRP strips and rebars into the steel

88

anchors, and Sikadur® 30 was used to fill in the groove in concrete. The material

properties of these adhesives are presented in Table ‎3-5.

Table ‎3-5: Properties of epoxy adhesives reported by the manufacturer (Sika, 2010a

and b).

Epoxy product

(Type)

Mix Ratio

(Mix Method)

Tensile

strength

(MPa)

Elongation

at break

Tensile modulus

of elasticity

(GPa)

Sikadur® 30

(Two-component)

3:1

(by weight) 24.8 0.01 4.5

Sikadur® 330

(Two-component)

4:1

(by weight) 30 0.015 N.A. (3.8

*)

* Flexural modulus of elasticity

3.3.3.5 Anchor Bolts

Carbon Steel Kwik Bolt 3 Expansion Anchor produced by Hilti Inc. was used to

connect the steel anchor to the substrate concrete having a nominal bolt diameter of 15.9

mm and a steel material factored strength of 54.4 kN in shear (Hilti, 2008). This bolt had

a nominal ultimate shear capacity of 65 kN by providing an embedment depth of 70 mm

and enough edge distance in normal weight concrete with compressive strength of 40

MPa (Hilti, 2008).

3.3.4 Fabrication

Fabrication of the RC beam specimens including building of formwork and steel

cage, casting, and implementation of prestressed NSM strengthening are presented in

Appendix B in detail.

89

3.3.5 Instrumentation

The beams were instrumented as shown in Figure ‎3-3a and b. Six horizontal

Linear Strain Conversions (LSCs) were installed on the beams at mid-span to measure

the strains at the extreme concrete compression fibre, the compression steel level, and the

tension steel level as shown in Figure ‎3-3. Two laser displacement sensors were used to

measure the vertical deflection at mid-span as shown in Figure ‎3-3b. Aluminium angles

were attached to both sides of the beams as laser reflectors and the laser sensors, having a

working range of 50 to 250 mm, were connected to the steel stands. For prestressing

application, four horizontal LSCs were installed on the beam at mid-span: two on one

side and two on top face of the beam. In addition, four vertical LSCs were used to

monitor the vertical deflection, two at the mid-span and one at each point load location.

Four Strain Gauges (SGs) were installed on the steel reinforcement at mid-span of

each beam: two on the tension steel bars and two on the compression steel bars. To

measure the strain along the length of the CFRP strips/rebar, eight SGs were installed on

each CFRP strips/rebar according to the spacing and configuration shown in Figure ‎3-3a.

To monitor the temperature in the concrete core of the beam during freeze-thaw

exposure, one Thermo-Couple (TC) sensor was placed inside each beam at location

shown in Figure ‎3-3a. These TCs were connected to the environmental chamber data

acquisition system to record the temperature in concrete beams during exposure.

90

(a)

(b)

Figure ‎3-3: Beams instrumentation: (a) elevation and (b) cross-section at mid-span location.

90

91

3.4 Prestressed NSM FRP Strengthening System

One of the challenges for using prestressed NSM-FRP method is developing a

practical method for prestressing and anchoring the CFRP reinforcement. Most research

in this area was performed while the beam was prestressed by jacking against both ends

of the beam requiring access to entire length. This procedure is very difficult to be

implemented in the field. The anchorage system used to prestress the NSM CFRP

reinforcement used in this research was developed by Gaafar (2007), which overcomes

the practicality drawbacks of previous research as mentioned in Sections 1.4.6 and 2.9. A

brief description of the anchorage system and the prestressing procedure is presented in

Appendix B, and more details can be found in (Gaafar, 2007; El-Hacha and Gaafar,

2011).

3.5 Initial Loading after Strengthening

To increase the effect of freeze-thaw exposure on the beams, each beam in phase I

was loaded after strengthening up to 1.2 times its theoretical cracking load and the

occurrence of flexural cracks was confirmed by visual inspections. The test setup for

initial loading was according to Figure ‎3-1 where the loading and unloading rates were

0.1mm/min and 0.5 mm/min, respectively. The corresponding deflections and strains

were monitored and the permanent deflection of each beam was recorded for 30 min after

unloading. A summary of initial loading after strengthening and obtained experimental

and theoretical cracking loads for each beam are presented in Table ‎3-6.

92

Table ‎3-6: Summary of initial loading and obtained experimental and theoretical

cracking loads.

Beam ID Papplied

(kN)

Pcr-exp.

(kN)

Pcr-theo.

(kN)

Pcr-theo. sw.

(kN)

B0-F 18.34 10.40 22.66 16.06

BS-NP-F 19.09 14.02 22.85 16.25

BS-P1-F 27.2 21.63 29.53 22.93

BS-P2-F 35.34 27.30 36.22 29.62

BS-P3-F 43.34 35.51 42.90 36.30

BR-NP-F 17.73 13.12 22.88 16.28

BR-P1-F 25.69 18.00 30.51 23.91

BR-P2-F 33.57 26.00 38.14 31.54

BR-P3-F 44.07 36.28 45.78 39.18 Papplied = applied load to each beam for cracking after strengthening

Pcr-exp. = experimental cracking load

Pcr-theo. = theoretical cracking load

Pcr-theo. sw. = theoretical cracking load by considering the effect of self-weight

3.6 Freeze-Thaw Cycling Exposure

Freeze-thaw exposure was performed using the environmental chamber in the

University of Calgary’s Civil Engineering Lab. All fourteen beams, phase I and phase II,

were subjected to freeze-thaw cycling exposure applied based on CHBDC (CAN/CSA-

S6-06, 2011) requirements as shown in Figure ‎3-4 to Figure ‎3-6. According to Figure ‎3-4

and Figure ‎3-5, the average maximum and minimum mean daily temperatures in Canada

are -34oC and +34

oC, respectively, which are selected to simulate the freeze-thaw

exposure inside the environmental chamber. Also according to Figure ‎3-6, the average

annual mean relative humidity in Canada is 75%, which is selected to simulate the

humidity exposure inside the environmental chamber (Abdelrahman, 2011).

93

Figure ‎3-4: Maximum mean daily temperature (CAN/CSA-S6-06, 2011).

Figure ‎3-5: Minimum mean daily temperature (CAN/CSA-S6-06, 2011).

94

Figure ‎3-6: Annual mean relative humidity (CAN/CSA-S6-06, 2011).

In phase I, nine beams were subjected to 500 freeze-thaw cycles, and in phase II,

five beams were subjected to combined effects of sustained load and 500 freeze-thaw

cycles. Each freeze-thaw cycle in phase I consisted of eight intervals that was

programmed to be accomplished in 8 hrs, including the lower temperature bound of -

34oC and the upper temperature bound of +34

oC with a relative humidity of 75% for

temperatures above +20oC. A similar freeze-thaw cycle to phase I was used in phase II

except that the 75% relative humidity at temperature above +20oC was replaced with

fresh water spray (18 L/min for a time period of 10 min) at a temperature of +20oC to

increase the severity of the applied exposure. Details of the intervals and trend of three

freeze-thaw cycles are presented in Table ‎3-7 and Figure ‎3-7 including programmed and

measured temperature in the environmental chamber, temperature in concrete core of the

95

beam, and programmed humidity. The intervals were selected somehow to have

sufficient freezing temperatures at the concrete core. The recorded temperature in the

concrete core shown in Figure ‎3-7 confirms the occurrence of freezing and thawing

throughout the beam in each cycle. It should be mentioned that due to using the water

spray in phase II, it took longer for the chamber to reach to the programmed temperature

and each cycle was accomplished in an average of 9.5 hr.

Most researchers have considered 300 freeze-thaw cycles as presented in Table 2-

12 while in this research 500 freeze-thaw cycles were applied to investigate the effects of

long-term severe exposure and high number of the cycles. Bisby and Green (2002)

estimated that 300 freeze-thaw cycles, with the details presented in Table 2-12,

correspond to somewhere between 10 to 20 years for an exterior application in Toronto;

Laoubi et al. (2006) estimated that freeze-thaw cycles ranging from 100 to 360, with the

details presented in Table 2-12, conservatively covers the lifetime of a structure in North

America. What is obvious is that the selected number of cycles by the researchers is

arbitrary and depends on the location of the structure and many environmental factors,

which almost make it impossible to have an exact estimation for the corresponding

lifetime. However, the author believes that the nature of the cycles is more severe than

what would be typically encountered in reality and it is possible to have an estimation of

the minimum corresponding lifetime having the annual freeze-thaw frequency of the

relevant geographic location. Therefore, considering an average freeze-thaw frequency of

39 cycles per year for Canada (Fraser, 1959), the accelerated 500 cycles used in this

study (500×8 hr = 4000 hr = 166.7 day), that is equivalent to 0.457 year of exposure

inside the chamber, corresponds to a minimum lifetime of 12.8 years.

96

Table ‎3-7: Environmental chamber schedule for one freeze-thaw cycle.

Intervals Air temperature

oC Time

(hr:min) Humidity (for phase I)

Water spray (for phase II)

Loop

from Set point

0 Room

temperature +20 00:05 Off Off

1 +20 +20 00:05 Off On

2 +20 +20 00:05 Off Off

3 +20 +20 00:05 Off On

4 +20 +20 00:05 Off Off

5 +20 -34 2:40 Off Off

6 -34 +20 00:05 Off Off

7 +20 +34 02:20 On Off

8 +34 +20 00:10 On Off

-100

-80

-60

-40

-20

0

20

40

60

80

100

-50

-40

-30

-20

-10

0

10

20

30

40

50

0:00 4:00 8:00 12:00 16:00 20:00 24:00 28:00

Hu

mid

ity (

%)

Te

mp

era

ture

(oC

)

Time (hr:min)

Programmed temperature Actual measured air temperature

Temperature in concrete core Programmed humidity @ phase I

Fresh water spary @ phase II

Figure ‎3-7: Three typical freeze-thaw cycles.

97

3.7 Sustained Loading

Five RC beams in phase II were loaded inside the environmental chamber using a

Self-Reacting Loading System (SRLS) designed for this part of the project. Details of the

SRLS are shown in Figure ‎3-8 to Figure ‎3-11. Using the SRLS, the load was applied

downwards from the top using two hydraulic jacks connected to the system shown in

Figure ‎3-10. The Hollow Structural Steel (HSS) (203×102×13) sections (HSS beam #1

and 2) acted on the five RC beams at the point load locations and pushed the beams

downwards while the Dywidag steel bars (Dywidag bar #1) attached to the HSS sections

(HSS beam #3) moved upward. To have the system locked, the Dywidag bars (Dywidag

bar #1) were connected to two HSS steel beams (HSS beam #3), which were attached to

the strong floor using four Dywidag bars (Dywidag bar #2) as shown in Figure ‎3-10 and

Figure ‎3-11. The applied load to the RC beams was measured through the two load cells

placed between hydraulic jacks and the nuts on the Dywidag bars (Dywidag bar #1).

Then, the permanent nuts were tightened and the jacks and load cells were removed. The

setup and application of the sustained load inside the environmental chamber are

presented in Figure ‎3-12 and Figure ‎3-13, while Figure ‎3-14 and Figure ‎3-15 show the

RC beams under sustained load after 500 freeze-thaw cycles. In this research, to monitor

the value of sustained load in regular time periods during exposure, two strain gauges

were installed on each Dywidag bar (Dywidag bar #1), as shown in Figure ‎3-13a.

Furthermore, the mid-span deflection was monitored for each beam using LSCs shown in

Figure ‎3-13b. The applied load on each beam was 62 kN, which is 47% of the theoretical

ultimate load of the non-prestresesd strengthened beam, BS-NP. The value of sustained

load was selected satisfying a creep-rupture stress limit of 65% of ultimate tensile

98

strength of CFRP strips and a tension steel stress limit of 240 MPa recommended by

CAN/CSA-S6-06 (2011), and also an allowable concrete compressive stress under

service and prestress of 0.45f′c recommended by CAN/CSA-A23.3-04 (2004). The

system was monitored for three days and the loss in load was measured, then the applied

load was modified, by unloading and applying the load again, and checked at regular

intervals of one week to keep the value of the load as constant as possible.

99

Figure ‎3-8: Plan view of chamber floor equipped for sustained loading.

99

100

Figure ‎3-9: Plan view of sustained loading.

100

101

Figure ‎3-10: Side view of sustained loading.

101

102

Figure ‎3-11: Cross view of sustained loading.

103

Figure ‎3-12: Sustained load setup in the environmental chamber.

103

104

(a) Top view of the beams

(b) Bottom view of the beams

Figure ‎3-13: Applying Sustained load in the chamber.

Nut

Load cell

Hydraulic jack

Steel chair HSS beam #1

Alignment bar

HSS beam #2

Dywidag bar #1

Permanent nut

Loading plate

& rubber pad

Strain gauge

Dywidag bar #2

HSS beam #3

HSS beam #4 Vertical LSC

Dywidag bar #1

Chamber sealed duct

105

Figure ‎3-14: Beams under sustained load and after 500 freeze-thaw cycles.

106

(a) Top view of the beams

(b) Bottom view of the beams

Figure ‎3-15: Beams under sustained load and after 500 freeze-thaw cycles.

107

3.8 Testing Procedure

Following the freeze-thaw exposure for beams from phase I and combined freeze-

thaw and sustained load exposures for beams from phase II, the beams were removed

from the chamber, kept for at least three days at room temperature and then, instrumented

and tested to failure under four-point bending configuration. The test was performed by

monotonically increasing two point loads using displacement control at a rate of

1mm/min using a 500 kN MTS hydraulic actuator mounted to a steel frame at mid-span.

The test setup is shown in Figure ‎3-16. After failure, the unloading was performed using

displacement control at a rate of 20 mm/min and the test was terminated. The values of

load, strains, and deflections were recorded using a data acquisition system at a rate of 1

reading/sec.

Figure ‎3-16: Test setup.

108

3.9 Summary

Details of the experimental program were presented in this chapter. First, the test

matrix was presented followed by explaining the design, geometry, material properties,

fabrication, and instrumentation of the beams. Then, the adopted strengthening system,

initial loading after strengthening, freeze-thaw cycling exposure, and sustained loading

were explained in detail. Finally, the testing procedure including details of the applied

monotonic loadings to failure was explained. The experimental test results of the beams

in phase I and II are presented and discussed in the next chapter followed a study of the

prestress losses, deformability and ductility, optimum and beneficial prestressing levels,

effects of CFRP geometry: strips versus rebar, effects of freeze-thaw exposure, and

effects of sustained loading combined with freeze-thaw exposure.

109

Chapter Four: Experimental Results and Discussion

4.1 Introduction

Results of the fourteen tested beams (classified in two phases) and corresponding

ancillary tests are presented in this chapter. Nine RC beams exposed to 500 freeze-thaw

cycles (three cycles per day with temperature ranging between +34oC to −34

oC with a

relative humidity of 75% for temperatures above +20oC) were tested in phase I: one un-

strengthened control beam, four beams strengthened using NSM CFRP rebar with target

prestressing levels of 0%, 20%, 40%, and 60% of the ultimate tensile strength of the

CFRP rebar reported by the manufacturer and four beams strengthened using NSM CFRP

strips with target prestressing level of 0%, 20%, 40%, and 60% of the ultimate tensile

strength of the CFRP strips reported by manufacturer. Five beams were tested in phase II

(one un-strengthened control beam and four beams strengthened using NSM CFRP strips

with target prestressing levels of 0%, 20%, 40%, and 60% of the ultimate tensile strength

of the CFRP strips reported by manufacturer) subjected to 500 freeze-thaw exposure

cycles similar to that of phase I while being subjected to a sustained load equal to 47% of

the analytical ultimate load of the non-prestressed NSM CFRP strengthened RC beam.

Geometry of the beams and details of the experimental program were presented in

Chapter Three. The beams were simply supported and were tested under quasi-static

monotonic loading in four-point bending configuration. In this chapter, the effects of

sustained load and freeze-thaw exposure are shown on the load-deflection response, type

of failure, ductility, energy absorption, and strain in the CFRP by comparing the test

results with the results of similar beams tested without any sustained loading and

110

environmental exposure. Furthermore, the effects of CFRP geometry: rebar versus strip,

the concepts of beneficial and optimum prestressing levels, and the topics of

deformability of NSM CFRP strengthened RC beams are studied in detail. At the end of

this chapter, an experimental investigation was performed by modification of the

prestressing system to avoid the cracking issues observed at the location of the temporary

brackets during prestressing in phases I and II.

The results presented in this chapter were published in refereed conference papers

(Omran and El-Hacha, 2012a, c, and d, and 2013b).

4.2 Phase I: Prestressed NSM-CFRP Strengthened RC Beams under Freeze-Thaw

Exposure

4.2.1 Test Beams and Material Properties

Nine beams exposed to 500 freeze-thaw cycles (based on the test matrix presented

in Chapter Three and Table ‎3-1) were tested in phase I. Details of the beams including

the geometry, test setup, and used end anchors were presented in Section 3.3.3.2.

Material properties of the beams including steel reinforcements, concrete, and CFRP

rebar and strip obtained from ancillary test results performed according to the specific

ASTM standards are presented in Appendix C in detail. A concise description is provided

in this section.


The tension and compression steel bars (3-15M and 2-10M) possessed yield

strengths of 4929 MPa and 48816 MPa, and yield strains of 0.002460.00017 and

111

0.002440.00027, respectively, obtained from tension tests (see Appendix C) having a

modulus of elasticity of 200 GPa. Also, the stirrups (25-10M) had the same properties as

the compression steel bars.

4.2.1.2 Concrete

Two concrete batches were used to cast the beams. Beams B0-F, BS-NP-F, BS-

P1-F, BS-P2-F, and BS-P3-F were cast from batch #1 with an average concrete

compressive strength of 41.56.2 MPa at the time of testing to failure. Beams BR-NP-F,

BR-P1-F, BR-P2-F, and BR-P3-F were cast from batch #2 with an average concrete

compressive strength of 39.44.2 MPa at the time of testing to failure. The average

concrete compressive strength of the freeze-thaw exposed cylinders from batch #1 and

batch #2 were 32.110.8 MPa and 286.8 MPa, respectively, at the time of testing the

beams to failure; the high standard deviation in the concrete strength is a results of the

severe environmental exposure on the specimens which results in a greater variability. It

should be mentioned that the beams strengthened with NSM CFRP strips and the un-

strengthened control beam were about 21-months old, and the beams strengthened with

NSM CFRP rebars were about 11-months old at the time of testing to failure. Also, the

static testing for each set was performed within two weeks. More details about the

compressive strengths of the concrete cylinders representing each beam at 28 days and at

times of strengthening, preloading (for initial cracking), and testing the beams to failure

are provided in Appendix C, including the date and the number of the tested cylinders.

112


The material properties of the CFRP reinforcements obtained from tension tests

are presented in Table ‎4-1.

Table ‎4-1: CFRP material properties obtained from tension tests.

CFRP product

(Manufacturer)

Dimension

(mm)

Afrp

(mm2)

ffrpu

(MPa)

Efrp

(GPa) ɛfrpu

Aslan 500 CFRP tape

(Hughes Brothers Inc) 2×16 31.2 2624±28 124.4±6.7 0.021±0.0009

Aslan 200 CFRP rebar

(Hughes Brothers Inc) Ф9.5 71.3 2896

* 115.9±1.5 0.025

*

* Only one specimen reached CFRP rupture


Two types of epoxy adhesives were used as groove filler for NSM strengthening:

Sikadur® 330 was used in the end groove regions (around and inside the end anchors) and

Sikadur® 30 was used to fill in the intermediate concrete groove regions between the end

anchors. Properties of these epoxy adhesives are presented in Section 3.3.3.4.


Carbon Steel Kwik Bolt 3 Expansion Anchors were used to connect the end

anchor to the substrate concrete. Properties of these bolts are presented in Section 3.3.3.5.

4.2.2 Load-Deflection Response

The load-deflection curves of the tested beams in phase I are presented in Figure

‎4-1. The permanent deflections due to initial loading after strengthening (presented in

113

Section 3.5) that caused cracking after strengthening, are considered in the plotted curves.

The load-deflection responses of the prestressed NSM CFRP strengthened RC beams can

be considered as a tri-linear slope curve until failure that include the negative camber due

to prestressing, initiation of flexural cracks, yielding of tensile steel rebar, failure due to

CFRP rupture or concrete crushing which causes a drop in total load at ultimate stage,

and post failure behaviour. All of tested beams showed a typical failure mode, i.e.,

tension steel reinforcements yielding followed by CFRP rupture or concrete crushing.

The failure mode of each beam is marked on Figure ‎4-1. A summary of the results are


114

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)

Mid-span deflection (mm)

BS-NP-F BS-P1-F BS-P2-F BS-P3-F B0-F

BR-NP-F BR-P1-F BR-P2-F BR-P3-F

: Concrete crushing : FRP rupture

Figure ‎4-1: Load-deflection curves of the beams subjected to freeze-thaw exposure (phase I).

114

115

Table ‎4-2: Summary of the test results of the beams subjected to freeze-thaw exposure (phase I).

Beam ID ɛp

(µɛ)

Δo

(mm)

ɛpe

(µɛ)

Δoe

(mm)

Pcr

(kN)

Δcr

(mm) Pcr/Pcn

Δop

(mm)

Py

(kN)

Δy

(mm) Py/Py0 Py/Pyn

Pu

(kN)

Δu

(mm) Pu/Pu0 Pu/Pun FM

B0-F N.A. N.A. N.A. N.A. 10.4 2.22 N.A. 0.65 75.5 18.78 1.00 N.A. 97.8 142.88 1.00 N.A. CC

BS-NP-F 0 0 0 0 14.0 1.36 1.00 0.61 92.4 22.53 1.22 1.00 132.2 104.26 1.35 1.00 CC

BS-P1-F 3574 -0.42 3463 -0.49 21.6 1.43 1.54 0.13 104.1 23.99 1.38 1.13 134.7 82.9 1.38 1.02 CC

BS-P2-F 6900 -0.93 6723 -1.09 27.3 1.24 1.95 -0.81 114.8 25.56 1.52 1.24 149.5 87.85 1.53 1.13 FR

BS-P3-F 10112 -1.39 9884 -1.70 35.5 1.45 2.53 -1.43 124.3 25.91 1.64 1.34 141.7 58.55 1.45 1.07 FR

BR-NP-F 0 0 0 0 13.1 1.23 1.00 0.6 91.6 23.78 1.21 1.00 132.3 102.71 1.35 1.00 CC

BR-P1-F 3801 -0.46 3662 -0.48 18.0 1 1.37 -0.07 105.1 24.98 1.39 1.15 147.5 107.62 1.51 1.11 CC

BR-P2-F 6585 -0.67 6548 -0.92 26.0 1.2 1.98 -0.52 113.4 25.86 1.50 1.24 157.5 98.05 1.61 1.19 CC

BR-P3-F 10272 -1.25 9950 -1.71 36.3 1.21 2.77 -1.4 125.2 25.36 1.66 1.37 157.5 71.28 1.61 1.19 FR

ɛp and Δo = initial prestrain and initial camber due to prestressing Pcr and Δcr = load and deflection at cracking

ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing Py and Δy = load and deflection at yielding

Δop = permanent deflection after initial cracking Pu and Δu = load and deflection at ultimate

Pcr/Pcn = ratio of the cracking load of each beam to that of the corresponding non-prestressed strengthened beam FM = failure mode

Py/Py0 and Pu/Pu0 = ratios of the yielding and ultimate loads of each beam to those from B0-F FR and CC= CFRP rupture and concrete crushing

Py/Pyn and Pu/Pun = ratios of the yielding and ultimate load of each beam to those from corresponding non-prestressed strengthened beam

Note: The quantities for the deflections, loads, and strains are the recorded values from the corresponding instruments and can be round to the nearest number.

115

116

4.2.2.1 Pre-Cracking Behaviour

At jacking stage, an upward initial camber (Δo) ranging from 0.42-1.39 mm for

strengthened beams with CFRP strips and 0.46-1.25 mm for strengthened beams with

CFRP rebar was observed; seven days after prestressing, the camber increased and these

ranges reached to 0.49-1.70 mm and 0.48-1.71 mm, respectively, as presented in Table

‎4-2 as the effective negative camber (Δoe). Although, the creep after one week is a reason

for the increase in the upwards deflection, but the main reason for the increase in negative

camber is removing the temporary bracket. The mechanism of this behaviour is

illustrated in Figure ‎4-2. The enforced prestressing force is transferred to the beams

through the bolts which connect the temporary brackets to the side of the beam. At

jacking stage, this eccentricity results in an axial load and an additional positive moment

on the beam length between the movable and fixed brackets while the rest of the beam is

under negative curvature. When the temporary brackets are removed from the side of the

beam these transferred loads are eliminated which results in an increase in negative

camber. If the value of the tensile stress produced by the additional loads (moment and

axial) is greater than the tensile strength of the concrete, then inclined tension cracks

form in concrete between the two brackets during prestressing. Consideration should be

given to avoid cracking during prestressing. In this research, the section between two

brackets was strengthened using externally bonded CFRP sheet for the beams BR-P3-F,

BS-P3-F, and BS-P3-FS with high prestressing levels of 41%, 48%, and 49% of the

CFRP tensile strength, respectively. A modification in the location of the applied

prestressing force on the temporary brackets (hydraulic jacks) in a way that minimizes

the produced additional moment during prestressing can solve the cracking issue. This

117

system is demonstrated in Section 4.10 where the modification on the prestressing system

is performed.

Figure ‎4-2: Interaction between temporary brackets and beam due to prestressing.

The values of the initial and effective prestrain calculated from the three strain

gauges installed at constant moment region of the beams are presented in Table ‎4-2. The

effective prestrains are provided for seven days after prestressing and show an average

loss of 2.5 ±1.1%. The beams were initially loaded and cracked after strengthening; the

118

obtained cracking loads show significant enhancement in cracking strength (up to 153%

for the beams strengthened with prestressed NSM CFRP strips and up to 177% for the

beams strengthened with prestressed NSM CFRP rebars) due to prestressing with respect

to the non-prestressed strengthened beam of each group. The un-strengthened control

beams showed a low cracking load which is due to presence of the micro-cracks in the

large-scale beams before testing, mainly caused from moving the beams during the

testing process. In fact, the cracking load of the un-strengthened control beam should

have been close to that of the non-prestressed strengthened beam. The beams

strengthened with CFRP strips (BS-NP-F, BS-P1-F, and BS-P2-F) showed higher value

of cracking loads (ranging from 5-16%) than the corresponding beams strengthened with

CFRP rebars while beam BS-P3-F showed smaller value of cracking loads than beam

BR-P3-F by 2%. This behaviour is mainly due to difference in concrete compressive

strength of the two sets of the beams (the average of the concrete cylinder compressive

strengths for the beams strengthened with CFRP strip and the beams strengthened with

CFRP rebars at the time of initial cracking are presented in Table C-1).

The permanent deflections in the beams dafter initial loading, as described in

Section 3.5, recorded at 0.5 hr after termination of each test for initial cracking, are

presented in Table ‎4-2, which are the start points of the load-deflection curves plotted in

Figure ‎4-1.

4.2.2.2 Post-Cracking Behaviour

Comparing the un-strengthened control RC beam B0-F with the non-prestressed

strengthened RC beams, BS-NP-F and BR-NP-F, shows that the flexural performance of

119

these beams is similar before yielding of the un-strengthened control RC beam. The

results reveals that although strengthening the RC beams using non-prestressed NSM

CFRP rebars or strips enhances the flexural performance by improving the yield and

ultimate loads, and stiffness of the beam in the plastic domain (after yielding of tension

steel bars), but has insignificant effects on the flexural performance in the elastic domain

(before yielding of the tension steel bars). Besides, comparing the results of beams

strengthened with prestressed NSM CFRP strips and rebars (BS-P1-F, BR-P1-F, BS-P2-

F, BR-P2-F, BS-P3-F, and BR-P3-F) with beams strengthened with non-prestressed NSM

CFRP strips and rebar (BS-NP-F and BR-NP-F) shows that strengthening using

prestressed NSM CFRP rebars or strips enhances the flexural performance at every

domain. In fact, strengthening RC beams using prestressed NSM CFRP reinforcement

enhanced the serviceability performance of the RC beam by postponing the formation of

flexural cracks, decreasing the crack width, delaying yielding, and increasing further the

ultimate strength of the beam through changing the mode of failure from concrete

crushing to CFRP rupture.

Analyzing the results reveals that up to 64% and 66% increase in yielding load of

the strengthened beam with CFRP strips and rebar, respectively, were achieved with

respect to the un-strengthened control RC beam, as presented in Table ‎4-2; in which 22%

out of 64% and 21% out of 66% are related to increase due to strengthening and the rest

(which are 42% and 45%) are due to prestressing effect. Besides, up to 53% and 61%

increase in ultimate load of the strengthened beam with CFRP strips and rebar were

recorded; in which 35% out of 61% and 53% are reached by strengthening with non-

prestressed CFRP reinforcement and the remaining is due to prestressing effect. As

120

expected, this behaviour shows more contribution of the prestressing in enhancing of the

yielding load than the ultimate load.

4.2.2.3 Failure Mode and Cracking Pattern

The failure mode of each beam is marked on the curves in Figure ‎4-1 and shown

in Figure ‎4-3 to Figure ‎4-11. The un-strengthened control RC beam (B0-F) failed due to

concrete crushing that occurred between two point loads after steel yielding, as shown in

Figure ‎4-3. The fluctuations in the load-deflection curve after yielding are due to

occurrence of major flexural cracks in the beam. These cracks got wider as the load

increased further and lead to a large ultimate deflection at mid-span of the beam.

The non-prestressed strengthened RC beams (BS-NP-F and BR-NP-F)

experienced similar behaviour. Debonding at the concrete-epoxy interface initiated from

the point load locations at the deflections and corresponding loads of 71 mm and 121 kN

for beam BS-NP-F and 76 mm and 124 kN for beam BR-NP-F, and propagated towards

the supports as the load applied further before reaching the peak load. These longitudinal

debonding cracks at the concrete-epoxy interface caused a slight decrease in the load-

deflection slopes. The fluctuations in the load-deflection curves are the result of large

flexural cracks’ openings and debonding cracks. For these two beams (BS-NP-F and BR-

NP-F), the failure happened due to concrete crushing between one of the point loads and

mid-span. No further increase in the load was observed while the test continued, and

complete debonding of the NSM-CFRP rebar and strips from concrete substrate occurred.

At this point, the force in the CFRP reinforcement was completely transferred to the end

anchors and complete failure (the last drop in the load-deflection curves) occurred due to

121

end anchor separation from the concrete. Images of the beams BS-NP-F and BR-NP-F at

failure are presented in Figure ‎4-4 and Figure ‎4-5, respectively.

Beams BS-P1-F and BR-P1-F, strengthened using prestressed NSM CFRP strips

and rebar with prestress levels of 17% and 15%, respectively, failed due to concrete

crushing but a difference was observed at the ultimate stage of the two load-deflection

curves, as shown in Figure ‎4-1, mainly caused by the difference in the ultimate tensile

strain of the CFRP rebar and strip presented in Table ‎4-1. Photos of beams BS-P1-F and

BR-P1-F at failure are presented in Figure ‎4-6 and Figure ‎4-7, respectively. For beam

BS-P1-F, concrete crushing started between one of the point load and mid-span at a

deflection and corresponding load of 70.6 mm and 130.6 kN that caused a small drop in

the load-deflection curve. As the load increased further, longitudinal debonding cracks

formed at the concrete-epoxy interface at location of the point load at a deflection and

corresponding load of 79 mm and 133 kN. The test continued and the failure occurred

due to concrete crushing at mid-span region between the two point loads as shown in

Figure ‎4-6. Afterwards, no future increase in the load was recorded, and finally the CFRP

strips ruptured causing a large drop in the load value. For beam BR-P1-F, debonding

cracks started at concrete-epoxy interface at the point load location at deflection and

corresponding load of 78 mm and 138.8 kN. The concrete crushing occurred between the

point load and mid-span at a load and corresponding deflection of 147.4 kN and 95.9 mm

and then the load dropped to 141.4 kN. The test continued and an increase in the load was

observed; thereafter, the beam failed due to concrete crushing between two point loads at

a load of 147.5 kN and a corresponding deflection of 107.6 mm. No more increase in the

load was recorded after this point and by continuing the test, the CFRP rebar ruptured.

122

Beam BS-P2-F, strengthened using prestressed NSM CFRP strips with prestress

level of 33%, failed due to rupture of the CFRP strips as shown in Figure ‎4-8; and beam

BR-P2-F, strengthened using prestressed NSM CFRP rebar with prestress level of 26%),

failed due to concrete crushing followed by rupture of the CFRP rebar as shown in Figure

‎4-9. The failure of beam BR-P2-F was very close to balanced failure condition, since the

CFRP rebar almost ruptured simultaneously with concrete crushing. The differences at

ultimate deflection, ultimate load, and type of failure of beams BR-P2-F and BS-P2-F are

due to the difference between material properties of the CFRP rebar and strip at ultimate

as presented in Table ‎4-1. Longitudinal debonding cracks at the concrete-epoxy interface

were observed during the test at the point load locations initiated from the deflections and

corresponding loads of 70 mm and 141.6 kN and 82 mm and 149.8 kN for beams BS-P2-

F and BR-P2-F, respectively.

Beams BS-P3-F and BR-P3-F, strengthened using prestressed NSM CFRP strips

and rebar with high prestress levels of 48% and 41%, respectively, failed due to CFRP

rupture at mid-span after tension steel yielding as shown in Figure ‎4-10 and Figure ‎4-11,

respectively. The small fluctuations in the load-deflection curves after yielding are due to

formation of flexural cracks at mid-span. No sign of debonding was observed up to CFRP

rupture. After rupture, the load dropped and the behaviour was similar to that of the un-

strengthened control beam.

Comparison between the initiation of debonding cracks at concrete-epoxy

interface for RC beams strengthened with non-prestressed and prestressed NSM-CFRP

strips or rebar, as presented in earlier discussion in this section, demonstrates that these

cracks are almost initiated simultaneously. Therefore, it can be concluded from the results

123

that at a constant beam’s deflection, a combination of interfacial stresses, interfacial slip,

and interfacial gap leads to total dissipation of the fracture energy of the interface, and the

value of this deflection is independent from induced prestressing level in the CFRP rebar

or strips.

(a) Side view of the beam

(b) The other side view of the beam

(c) Bottom view of the beam

Figure ‎4-3: Photos of beam B0-F at failure.

Concrete crushing

Concrete crushing

124




(d) End of the beam close to the support (e) Bottom view at the end of the beam

Figure ‎4-4: Photos of beam BS-NP-F at failure.

End anchor separation: secondary failure

Concrete crushing

Concrete crushing

125




(d) Side view at end anchor (e) Bottom view at end anchor (f) Anchor seperation

Figure ‎4-5: Photos of beam BR-NP-F at failure.

End anchor separation: secondary failure

Concrete crushing

Concrete crushing

126

(a) Bottom view showing debonding cracks at concrete-epoxy interface

(b) Side view of the beam

(c) The other side view of the beam

(d) Bottom view of the beam

Figure ‎4-6: Photos of beam BS-P1-F at failure.

Concrete crushing

Concrete crushing

127




(d) Bottom view of the beam showing debonding cracks at concrete-epoxy interface

Figure ‎4-7: Photos of beam BR-P1-F at failure.

Concrete crushing

Concrete crushing

128




(d) Bottom view showing debonding cracks (e) Bottom view at CFRP rupture


CFRP rupture

129




(d) Top view of the beam showing concrete crushing


Concrete crushing

Concrete crushing

130




(d) Bottom view of the beam showing the CFRP rupture


Location of the CFRP rupture

131





4.2.3 Load-Strain Response

In this section, a comparison is performed between the load-strain relations of the

beams strengthened with CFRP rebar versus similar beams strengthened with CFRP

strips. The relation between the load and strains in the CFRP strips or rebar, tension steel,

compression steel, and the extreme compression fibre of concrete at mid-span location

Location of the CFRP rupture

132

are presented in Figure ‎4-12 to Figure ‎4-15. For all tested beams, the compression steel

strain almost showed linear elastic behaviour up to failure. The load-strain relation for the

concrete at extreme compression fibre, tension steel, and CFRP strips or rebar consists of

three stages: from start of the test to concrete cracking in tension, from concrete cracking

to yielding of tension steel, and from yielding of tension steel to failure by either concrete

or CFRP rupture. From start of the test up to the concrete cracking in tension, the load-

strain relation is linear, the flexural stiffness of the beam decreases after cracking causing

a reduction in the load-strain slope, however, the relation remains linear up to yielding of

the tension steel. Yielding of the tension steel causes a significant reduction in flexural

stiffness of the beam leading to a decrease in the slope of the load-strain curves.

Afterwards, the curve reaches a point in which CFRP rupture or concrete crushing

occurs. It should be mentioned that the load-steel strain curves were calculated based on

the LSCs installed on the side of the concrete beam at the level of the longitudinal tension

steel because the strain gauges on the steel reinforcements were damaged after yielding,

and therefore, no yielding plateau is observed in the plotted curves.

Strain values in the concrete, top steel, bottom steel, and CFRP at different stages

are presented in Table ‎4-3. Due to prestressing, top steel and top concrete goes to tension

while the bottom steel goes to compression means the neutral axis is somewhere between

top and bottom steel; these strain values are very small and cannot be visible in the

curves.

Comparison between the strain values of the strengthened RC beams using NSM

CFRP rebar versus strengthened beams using NSM CFRP strips shows similar behaviour

of these two sets at different stages, it should be mentioned that the difference at ultimate

133

stage in Figure ‎4-13 to Figure ‎4-15 is due to different ultimate tensile strain of the CFRP

rebar and strip, as presented in Table ‎4-1. However, the difference at ultimate stage does

not exist in Figure ‎4-12 because both beams, BS-NP-F and BR-NP-F, failed due to

concrete crushing and are not affected by the difference of the CFRP ultimate tensile

strain. The loads versus strain values in the CFRP rebars and strips are compared in

Figure ‎4-16 for all strengthened beams; the strains are plotted including permanent values

after initial loading described in Section 3.5, showing a minor difference at zero loads

which is caused by: the losses, the initial loading, and the applied strain at prestressing.

The load-strain relation for the CFRP rebar shows stiffer behaviour than that for CFRP

strips. The sudden increase in strain at constant load, which is observed for CFRP strain

of beams BS-P2-F and BS-P3-F is most likely a local effect caused by the major cracks

close to the mid-span or less likely detachment of the two bonded CFRP strips from each

other. This behaviour was not observed in beams BS-P1-F and BS-P2-F (strengthened

using NSM CFRP strips with low prestress level of 17% and 33%, respectively), and also

in the beams strengthened with NSM CFRP rebar. The curves show the same stiffness

after yielding at the plastic range. The concrete strains at top extreme fibre and the strains

in tension steel reinforcements are compared in Figure ‎4-17 and Figure ‎4-21,

respectively, for all beams. The results show that the load-strain behaviour of the beams

strengthened using NSM CFRP strips is similar to the corresponding beams strengthened

using NSM CFRP rebars except at ultimate state. In this regards, the difference at

ultimate is mainly due to different mode of failure. On the other hand, although the

instrumentation was performed at mid-span but the location of the concrete crushing

might not be the same to capture the maximum strain reached at failure; this fact results

134

in underestimation of the actual concrete compressive strain and tension steel strain at

failure. The strains in the compression steel reinforcements are compared in Figure ‎4-19

for all beams. In this figure, the load-strain curve for beam BS-P1-F is calculated based

on the LSCs installed at the compression steel levels since the strain gauges installed on

the compression steel were damaged for this beam, however, the rest of the curves are

plotted based on the reading from strain gauges installed on the compression steel at mid-

span. It can be seen in Figure ‎4-19 that the load-strain is not perfectly linear. For beams

B0-F, BS-NP-F, BR-NP-F, BS-P1-F, and BS-P2-F, the strain in compression steel

decreases prior to failure; this is due to local buckling of the compression steel at mid-

span location after start of the concrete crushing as shown in Figure ‎4-20. The occurrence

of the slip between the epoxy and concrete can be identified by changing the slope of the

load-strain curve for bottom steel and CFRP. Comparison between the slope of the curves

related to bottom steel and CFRP at elastic and plastic ranges shows that slip between

concrete and CFRP rebar or strip is insignificant.

135

0

20

40

60

80

100

120

140

160

-0.005 0 0.005 0.01 0.015 0.02 0.025

Lo

ad

(k

N)

Strain at mid-span

BS-NP-F, Concrete Strain

BS-NP-F, Top Steel Strain

BS-NP-F, Bottom Steel Strain

BS-NP-F, CFRP Strain

BR-NP-F, Concrete Strain

BR-NP-F, Top Steel Strain

BR-NP-F, Bottom Steel Strain

BR-NP-F, CFRP StrainTensionCompression

Ultimate load of BR-NP-F= 132.3 kNUltimate load of BS-NP-F= 132.2 kN

Figure ‎4-12: Load-strain curves: BS-NP-F vs BR-NP-F.

0

20

40

60

80

100

120

140

160

-0.005 0 0.005 0.01 0.015 0.02 0.025

Lo

ad

(k

N)

Strain at mid-span

BS-P1-F, Concrete Strain

BS-P1-F, Top Steel Strain

BS-P1-F, Bottom Steel Strain

BS-P1-F, CFRP Strain

BR-P1-F, Concrete Strain

BR-P1-F, Top Steel Strain

BR-P1-F, Bottom Steel Strain

BR-P1-F, CFRP Strain

TensionCompression

Ultimate load of BS-P1-F= 134.7 kN

Ultimate load of BR-P1-F= 147.5 kN

Figure ‎4-13: Load-strain curves: BS-P1-F vs BR-P1-F.

136

0

20

40

60

80

100

120

140

160

-0.005 0 0.005 0.01 0.015 0.02 0.025

Lo

ad

(k

N)

Strain at mid-span








BR-P2-F, CFRP Strain

TensionCompression




0

20

40

60

80

100

120

140

160

-0.005 0 0.005 0.01 0.015 0.02 0.025

Lo

ad

(k

N)

Strain at mid-span








BR-P3-F, CFRP StrainTensionCompression




137

0

20

40

60

80

100

120

140

160

0 0.005 0.01 0.015 0.02 0.025

Lo

ad

(k

N)

Strain in CFRP strip or rebar at mid-span

BS-NP-F BS-P1-F BS-P2-F BS-P3-F


Figure ‎4-16: Load-CFRP strain curves for all beams.

0

20

40

60

80

100

120

140

160

-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0

Lo

ad

(k

N)

Concrete strain in extreme compression fiber at mid-span



Figure ‎4-17: Load-concrete strain curves for all beams.

138

0

20

40

60

80

100

120

140

160

-0.0005 0.003 0.0065 0.01 0.0135 0.017 0.0205 0.024

Lo

ad

(k

N)

Strain in tension steel at mid-span (mm)



Figure ‎4-18: Load-tension steel strain curves for all beams.

0

20

40

60

80

100

120

140

160

-0.0014 -0.001 -0.0006 -0.0002 0.0002

Lo

ad

(k

N)

Strain in compression steel at mid-span (mm)



Figure ‎4-19: Load-compression steel strain curves for all beams.

139

Figure ‎4-20: Local buckling of compression steel bars at mid-span of beam B0-F.


compression steel, and tension steel at mid-span at different stages.

Beam ID ɛf-i

(µɛ)

ɛf-7days

(µɛ)

ɛf-cr

(µɛ)

ɛc-i

(µɛ)

ɛc-7days

(µɛ)

ɛc-cr

(µɛ)

ɛsc-i

(µɛ)

ɛsc-7days

(µɛ)

ɛsc-cr

(µɛ)

ɛst-i

(µɛ)

ɛst-7days

(µɛ)

ɛst-cr

(µɛ)

B0-F N.A. N.A. N.A. N.A. N.A. -100 N.A. N.A. -54 N.A. N.A. 23

BS-NP-F 0 0 110 N.A. N.A. -50 N.A. N.A. -26 N.A. N.A. 103

BS-P1-F 3574 3463 3522 0 0 -25 15 16 -10 -39 -46 59

BS-P2-F 6900 6723 6749 50 125 100 33 32 16 -79 -97 -64

BS-P3-F 10112 9884 9968 75 100 125 53 62 46 -118 -129 -108

BR-NP-F 0 0 76 N.A. N.A. 0 N.A. N.A. -24 N.A. N.A. 91

BR-P1-F 3801 3662 3234 25 50 0 15 67 50 -39 -87 6

BR-P2-F 6585 6548 6521 50 75 25 30 37 13 -66 -117 -60

BR-P3-F 10272 9950 9971 100 125 75 50 28 6 -124 -183 -162

ɛf-i, ɛc-i, ɛsc-i, and ɛst-i = initial prestrain in CFRP strips or rebar, extreme concrete fibre at top, top steel and

bottom steel due to prestressing

ɛf-7days, ɛc-7days, ɛsc-7days, and ɛst-7days = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel and

bottom steel at 7 days after prestressing

ɛf-cr, ɛc-cr, ɛsc-cr, and ɛst-cr = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel, and bottom

steel after cracking (initial loading presented in Section 3.5)

Strain gauges on compression steel bars at mid-span

Buckled compression steel bars

140

4.2.4 Strain Profile along the CFRP Strips or Rebar

The strain profiles along the length of the NSM CFRP strip versus the NSM

CFRP rebar at cracking, yielding, and ultimate loads are presented in Figure ‎4-21 to

Figure ‎4-23, respectively. The profiles are plotted based on the reading of strains from the

installed strain gauges at specified locations on the CFRP reinforcements. For beam BS-

NP-F and BR-NP-F the strains are close to zero at the ends of the CFRP strip or rebar at

different load levels (as shown in Figure ‎4-21 to Figure ‎4-23). This implies the presence

of the full bonding at the end and also complete contribution of the epoxy adhesive in

transferring the forces between the CFRP rebar or strip and the surrounding concrete. On

the other hand, the presence of the end anchors bolted to the concrete at both ends of the

CFRP strips/rebar helps in transferring the load to the beam after occurrence of

debonding at the concrete-epoxy interfaces, which results in a more effective

strengthening method. Furthermore, these anchors avoid initiation of the debonding

cracks at concrete-epoxy interface at the end portions of the NSM CFRP rebar or strip

where highly affected by interfacial stress concentration. In fact, the end anchors have

partial contribution in transferring the load from the NSM CFRP to the concrete before

occurrence of debonding and complete contribution in transferring the load from the

NSM CFRP to the concrete after occurrence of debonding. Therefore, it is very important

that during the prestressing process, i.e., after removing the temporary brackets, that the

end anchors are in contact with the bolts and there is no gap between them.

In Figure ‎4-21, except for beam BR-P1-F, the drop in strain at length 4350 mm is

a result of small slippage after removing the brackets and transferring the prestressing

force to the steel end anchor; this value of loss at the end location increases when

141

prestressing level increases, but it affects a very short length (100-200 mm) and can be

avoided by making sure that the anchor is in complete contact with bolts before removing

the brackets. In cases where there is a gap, it can be filled with epoxy to minimize the

possible slippage. A very good correlation at cracking is observed between CFRP strip

profiles in comparison with CFRP rebar profiles. The sudden increase in strain level that

can be seen in Figure ‎4-21 at location 2000 mm (point load location of the beams) for

beams BR-P1-F and BR-P2-F is most likely a local effect caused by formation of the

cracks under the point load. As can be seen in Figure ‎4-22 as well as Figure ‎4-23, these

sudden increases get larger as the load applied further up to yielding and the cracks under

the point load get wider.

Comparison between Figure ‎4-21, Figure ‎4-22, and Figure ‎4-23 reveals that as the

load increases further, more fluctuations occur in the strain profile since new cracks form

in the beams. In Figure ‎4-22, ignoring the sudden increase in the profiles, the strain

profile values for CFRP rebar are smaller than the corresponding profile values for CFRP

strips while, as presented in Table ‎4-2, the corresponding beams have similar yielding

load. This is most likely due to the reason that the axial stiffness (EfAf where Ef is the

modulus of elasticity and Af is the total cross-sectional area) of the CFRP rebar, based on

Table 4-1, is 6.5% larger than the axial stiffness of the CFRP strips, which leads to

smaller strain in CFRP rebar versus the CFRP strips for the corresponding beams under

similar load. In Figure ‎4-23, at ultimate load, the strain values of CFRP strips at constant

moment regions are smaller than those from CFRP rebars due to higher strain capacity of

the CFRP rebars versus CFRP strips. For all beams, the highest strain in CFRP strip or

rebar is observed at constant moment region of the beams (location 2000-3000 mm).

142

Comparison between Figure ‎4-21, Figure ‎4-22, and Figure ‎4-23 at locations 650

mm and 4350 mm for each beam reveals that the strain at both ends near the end anchors

remained almost constant during the static test showing no slippage at the ends of the

CFRP rebar/strips and appropriate performance of the epoxy in transferring the forces.

0

0.003

0.006

0.009

0.012

0 1000 2000 3000 4000 5000Str

ain

in

CF

RP

str

ips

or

reb

ar

at

cra

ck

ing

Distance from the support (mm)



Figure ‎4-21: Strain profile along the length of the CFRP strips or rebar at cracking.

143

0

0.003

0.006

0.009

0.012

0.015

0 1000 2000 3000 4000 5000Str

ain

in

CF

RP

str

ips

or

reb

ar

at

yie

ldin

g




Figure ‎4-22: Strain profile along the length of the CFRP strips or rebar at yielding.

0

0.005

0.01

0.015

0.02

0.025

0.03

0 1000 2000 3000 4000 5000Str

ain

in

CF

RP

str

ips

or

reb

ar

at

ult

ima

te




Figure ‎4-23: Strain profile along the length of the CFRP strips or rebar at ultimate.

144

4.2.5 Strain Distribution at Mid-span

The strain distributions at mid-span section along the depth of the beams at

cracking, yielding, and ultimate loads are presented in Figure ‎4-24 to Figure ‎4-26 and

Table ‎4-4. Each strain distribution is plotted using the strain values in concrete,

compression steel, tension steel, and CFRP rebar or strip including the strain due to

prestressing.

The strain distribution from the extreme concrete compression fibre to the

centroid of the bottom steel (along effective depth of the beam) is linear at cracking, as

shown in Figure ‎4-24(a) and (b). The increases in the CFRP strains are due to

prestressing. At cracking stage, the curvature at mid-span (which is defined as the slope

of the strain distribution along the effective depth) is the highest for the un-strengthened

control RC beam and as the prestressing level increases the curvature decreases. Similar

behaviour is observed for the RC beams strengthened with NSM CFRP rebar and NSM

CFRP strip.

At yielding, strain distributions are nonlinear. The nonlinearity is caused by

concrete material behaviour and can be observed in top portion of the plots in Figure

‎4-25(a) and (b). In tension zone, the distribution excluding the prestrain in the CFRP

reinforcements is almost linear as can be seen for beams BS-NP-F and BR-NP-F, which

don’t have the increase in the CFRP strain due to prestressing.

At ultimate, the strain distribution is nonlinear. The un-strengthened control RC

beam, B0-F, showed a very high curvature in comparison with the other beams. By

comparing the slope of the strain distribution between steel level and the CFRP level at

yielding and ultimate loads the occurrence of debonding at mid-span can be identified.

145

During the test, debonding was observed at mid-span regions at concrete-epoxy interface.

The occurrence of the slip between the epoxy and concrete at mid-span can be identified

if there is any difference in the slope of the strain distribution from tension steel level to

CFRP level at yielding stage in comparison with the one at ultimate stage. Therefore,

analyzing the results reveal that beams BS-NP-F, BS-P1-F, BR-NP-F, and BR-P1-F

showed debonding signs at mid-span. These outcomes from the strain distributions are in

accordance with the observations during the test.

146

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.0005 0.002 0.0045 0.007 0.0095 0.012

Se

cti

on

de

pth

(m

m)

Strain at cracking

B0-F BS-NP-F BS-P1-F BS-P2-F BS-P3-F

Bottom steel centroid @ 343 mm

NSM CFRP strips centroid @ 387.5 mm

Top steel centroid @ 35 mm

Top fibres of the beam

(a) Un-strengthened beam and strengthened beams using NSM CFRP strips

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.0005 0.002 0.0045 0.007 0.0095 0.012

Se

cti

on

de

pth

(m

m)

Strain at cracking

B0-F BR-NP-F BR-P1-F BR-P2-F BR-P3-F


NSM CFRP rebar centroid @ 387.5 mm



(b) Un-strengthened beam and strengthened beams using NSM CFRP rebar

Figure ‎4-24: Strain distribution at mid-span at cracking.

36

36

147

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Se

cti

on

de

pth

(m

m)

Strain at yielding







-400

-350

-300

-250

-200

-150

-100

-50

0

-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Se

cti

on

de

pth

(m

m)

Strain at yielding







Figure ‎4-25: Strain distribution at mid-span at yielding.

36

36

148

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.006 0 0.006 0.012 0.018 0.024 0.03

Se

cti

on

de

pth

(m

m)

Strain at ultimate







-400

-350

-300

-250

-200

-150

-100

-50

0

-0.006 0 0.006 0.012 0.018 0.024 0.03

Se

cti

on

de

pth

(m

m)

Strain at ultimate







Figure ‎4-26: Strain distribution at mid-span at ultimate.

36

36

149


tension steel, and CFRP strips or rebar at mid-span.

Beam ID ɛc-cr

(µɛ)

ɛsc-cr

(µɛ)

ɛst-cr

(µɛ)

ɛf-cr

(µɛ)

ɛc-y

(µɛ)

ɛsc-y

(µɛ)

ɛst-y

(µɛ)

ɛf-y

(µɛ)

ɛc-u

(µɛ)

ɛsc-u

(µɛ)

ɛst-u

(µɛ)

ɛf-u

(µɛ)

B0-F -250 -147 261 N.A. -1200 -696 1951 N.A. -5625 -250 22650 N.A.

BS-NP-F -150 -92 106 133 -1150 -563 2428 3131 -3325 -370 14475 14899

BS-P1-F -175 -116 121 3504 -1125 -600 2549 7002 -2475 -675 12161 16592

BS-P2-F -100 -130 34 6889 -1175 -745 2678 10332 -3050 -762 13325 21464

BS-P3-F -100 -161 53 10175 -1425 -808 2620 14246 -2750 -886 10300 21118

BR-NP-F -100 -86 87 48 -1050 -583 2465 2719 -3425 -301 11650 14599

BR-P1-F -75 -27 32 3297 -1275 -700 2500 6014 -4125 -1350 9875 22067

BR-P2-F -125 -117 5 6631 -1150 -787 2496 9212 -3250 -987 10500 23879

BR-P3-F -150 -173 -20 10156 -1350 -535 2231 13010 -3450 -598 12400 24247

ɛc = strain in extreme compression fibre of concrete (compression is negative value) cr = at cracking

ɛst = strain in tension steel y = at yielding

ɛsc = strain in compression steel u = at ultimate

ɛf = strain in CFRP rebar or strips

4.3 Effects of CFRP Geometry: Rebar versus Strips

Comparison between the results of the beams strengthened using NSM method

with sand coated CFRP rebar versus rough textured CFRP strips shows that the flexural

behaviour (load-deflection curve) is similar prior to the ultimate stage. At the ultimate

stage the behaviour depends on three items: concrete material property, CFRP ultimate

strain, and debonding. Two types of failure modes were observed in the experiments:

concrete crushing and CFRP rupture. Beams BS-NP-F and BR-NP-F showed similar

behaviour that confirms there is almost no difference at the load-deflection curves of the

beams strengthened with non-prestressed NSM CFRP rebar versus strips. The other

beams did not show such similar behaviour at ultimate stage due to difference in the

material properties of exposed concrete and CFRP reinforcement in the BS-F set versus

the BR-F set in phase I. The difference between the NSM strengthened beam using CFRP

strip and rebar is more obvious in bond performance and crack pattern than the overall

150

flexural performance. Due to the difference in geometry of the CFRP (rebars versus

strips), groove width (20 mm for the rebar and 16 mm for the strips), and therefore,

distribution of stresses in the groove, the crack pattern in the beams strengthened using

CFRP rebar is different than the beam with CFRP strips as shown in Figure ‎4-27 for all

strengthened beams at failure. The beams strengthened with sand coated CFRP rebar

showed less damage to bond than the beams strengthened with rough textured CFRP

strips at any specified deflection and at failure as well based on observation during the

tests, e.g., see BR-P2-F and BS-P2-F in Figure ‎4-27. Furthermore, the CFRP strip or

rebar rupture is accompanied by a loud sound during the test. In the case of the CFRP

rebar, the location of rupture is not visible and the epoxy should be removed to see the

CFRP rebar rupture; this behaviour does not occur in the case of CFRP strip rupture.

BS-NP-F

BR-NP-F

Figure 4-27: Damage done to the non-prestressed NSM CFRP strengthened beams

at failure (bottom view).

151

BS-P1-F

BR-P1-F

BS-P2-F

BR-P2-F

BS-P3-F

BR-P3-F

Figure ‎4-27: Damage done to the prestressed NSM CFRP strengthened beams at

failure (bottom view) (Cont’d).

152

4.4 Calculation of Optimum and Beneficial Prestressing Levels

In this section, two practical concepts are defined and analyzed, the optimum

prestressing level and the beneficial prestressing level. A procedure is illustrated to

achieve an optimum prestressing level in the NSM CFRP reinforcements (taken as a

percentage of the ultimate tensile strength of the CFRP reinforcements) which enhances

the beam performance under service and ultimate states by maintaining the amount of

energy absorption (area under the load-deflection curve up to the peak load) in the

strengthened beam equal to the un-strengthened control beam. A procedure to determine

the optimum prestressing level (intersection of the energy absorption curve of the

strengthened beams with the un-strengthened beam) is plotted in Figure ‎4-28. The energy

absorption is calculated up to different load levels: (a) up to the peak load, (b) up to 75%

of the post-peak load, and (c) up to the point that load-deflection curve of the

strengthened beam intersects with the un-strengthened one (B0-F). When the beam fails

due to concrete crushing, the amounts of energy absorption calculated by methods (a),

(b), and (c) result in different values. In this case, methods (b) and (c) are more

appropriate, which avoid underestimation of the energy absorption of the beam. Method

(c) is slightly less conservative than (b). When the beam fails due to CFRP rupture, the

energy values achieved by the different methods are almost the same; this behaviour is

observed in Figure ‎4-28 by comparing the last two prestressing levels (33 and 48%)

versus the first two (0 and 17%) for beams strengthened with CFRP strips (in BS set),

and furthermore, by comparing the last prestressing level (41%) with the first three

prestressing levels (0, 15, and 26%) for beams strengthened with CFRP rebars (in BR

set).

153

0

3000

6000

9000

12000

15000

18000

0 10 20 30 40 50Are

a u

nd

er

loa

d-d

efl

ec

tio

n c

urv

e (

kN

.mm

)

Prestressing level (% of CFRP tensile strength)

Energy up to intersection with B0-F, BS-F set Energy up to intersection with B0-F, BR-F set

Energy up to 75% of post-peak load, BS-F set Energy up to 75% of post-peak load, BR-F set

Energy up to peak load, BS-F set Energy up to peak load, BR-F set

B0-F energy up to peak load

Figure ‎4-28: Effects of prestressing on energy absorption and calculation of

optimum prestressing level

Considering the case (b) or (c), and energy absorption of the un-strengthened

beam up to the peak load, the experimental results yield an optimum prestressing level of

27.5% (corresponding to strain value 0.005775 in CFRP strips) for beam strengthened

with CFRP strips versus 31.5% (corresponding to strain value 0.007875 in CFRP rebar)

for beam strengthened with CFRP rebar. These obtained optimum prestressing levels are

less than the maximum prestressing level allowed by the design codes; generally, if the

obtained optimum prestressing level is higher than the maximum prestressing level

allowed by the design codes, then the latter should be used in design. It should be

154

mentioned that the CFRP material creep-rupture stress limit should be considered as the

maximum prestressing level, which can be enforced for design purposes. A creep-rupture

stress limit of 65% of the ultimate tensile strength of the CFRP reinforcement is

recommended by CHBDC (CAN/CSA-S6-06, 2011).

The beneficial prestressing level is defined as a prestressing level which produces

the maximum improvement in energy absorption of the strengthened RC beam with

respect to the un-strengthened control RC beam. The concept of the improvement in

energy absorption with respect to the un-strengthened beam is demonstrated in Figure

‎4-29; which is the difference between the energy absorption of the strengthened and un-

strengthened beam calculated up to ultimate deflection of the strengthened beam. The

values of improvement in energy values for the beams in phase I are presented in Figure

‎4-30; by interpolating a polynomial curve for the three highest points corresponding to

each set of the beams (BS-F or BR-F as presented in Figure ‎4-30) a beneficial CFRP

prestrain values of 0.006603 (corresponding to prestressing level of 31.4% in CFRP

strips) for RC beams strengthened with CFRP strips and 0.006029 (corresponding to

prestressing level of 24.1% in CFRP rebar) for RC beams strengthened with CFRP rebar

are achieved.

155

Figure ‎4-29: Schematic for the concept of improvement in energy absorption.

y = -5.703796E+7(-0.014792+x)(0.002734+x)

y = -1.125482E+8(-0.012329+x)(-0.000878+x)

2000

3000

4000

5000

0 0.002 0.004 0.006 0.008 0.01

Imp

rove

me

nt

in e

ne

ry a

bs

orp

tio

n w

.r.t

B

0-F

(k

N.m

m)

Prestressing level (CFRP strain)

Energy additional to B0-F, BR-F set Energy additional to B0-F, BS-F set

Poly. (Energy additional to B0-F, BR-F set) Poly. (Energy additional to B0-F, BS-F set)

Figure ‎4-30: Calculation of the beneficial prestressing level.

156

4.5 Effects of Freeze-Thaw Cycling Exposure

In this section, the flexural behaviour of RC beams strengthened with non-

prestressed and prestressed NSM CFRP rebar and strips subjected to freeze-thaw cycling

exposure are compared to similar beams without any environmental exposure tested by

Gaafar (2007).

4.5.1 Material Properties of the Unexposed Beams

A summary of material properties of the unexposed beams are presented in this

section. More details can be found in Gaafar (2007) and El-Hacha and Gaafar (2011).


The tension and compression steel bars (3-15M and 2-10M) possessed yield

strengths of 475 MPa and 500 MPa, respectively, obtained from tension test.


The material properties of the CFRP reinforcements are presented in Table ‎4-5.

Table ‎4-5: CFRP material properties for unexposed beams.

CFRP product

(surface treatment)

Dimension

(mm)

Afrp

(mm2)

Manufacturer Tension test

ffrpu

(MPa)

Efrp

(GPa) ɛfrpu

ffrpu

(MPa)

Efrp

(GPa) ɛfrpu

Aslan 500 CFRP tape

(Rough textured) 2×16 31.2 2068 124 0.017 2610

† 130.5

† 0.02

†


(Sand coated) Ф9 65.2 2068 124 0.017 2167

†† 130

†† 0.0167

††

† Gaafar (2007)

†† El-Hacha and Gaafar (2011)

157

4.5.1.3 Concrete

Two concrete batches were used to cast the beams. The average compressive

strength of the concrete cylinders from both batches was 40±4.4 MPa.


Two types of epoxy adhesives were used: Sikadur® 330 was used in the end

groove regions (around and inside the end anchors) which has an ultimate tensile strength

of 30 MPa and Sikadur®

30 was used to fill in the intermediate concrete groove regions

between the end anchors which has an ultimate tensile strength of 24.8 MPa (Sika, 2007a

and b).


The anchor bolts were “carbon steel kwik bolt 3 expansion anchor” made of

carbon steel with nominal bolt diameter of 15.9 mm and steel shear strength of 54.4 kN

(Hilti, 2008). This bolt had a nominal ultimate shear capacity of 65 kN by providing an

embedment depth of 70 mm and enough edge distance in normal weight concrete with

compressive strength of 40 MPa (Hilti, 2008).

4.5.2 Error Analysis

An error analysis is performed based on the material properties of the exposed

and unexposed beams to measure the uncertainty of the comparison. The uncertainty in

this section is defined to find the relative difference produced by the axial stiffness and

strength of the components between two sets of the beams. It simply shows the validity of

158

the comparison and is not an exact amount of the difference between two sets for a

particular response. Finding the exact amount of the difference between two

corresponding beams for a particular type of the response, e.g. load-deflection curve,

requires calculation of the load-deflection curve for each beam analytically, and then,

obtaining the exact known difference between two beams at each level of the curve,

which is not the aim of this section. Therefore, four percentages of uncertainty are

obtained: up to yielding that considers the axial stiffness of the components of the beam,

from yielding up to failure, and at failure for concrete crushing and CFRP rupture, which

consider the strength and axial stiffness of the components. Since the load and deflection

can be derived using multiplication and division operations, therefore, the following

equations are employed to calculate uncertainty in comparison. The uncertainty up

yielding of the beam is calculated using Equation 4-1. Due to minor contribution of the

compression steel up to yielding of the beam, it is ignored in calculation of uncertainty up

to yielding. The uncertainty from yielding up to failure, and for CFRP rupture and

concrete crushing failure modes are calculated using Equation 4-2 to Equation 4-4,

respectively, with respect to the unexposed beams. The components of Equations 4-1 to

4-4 are calculated using Equations 4-5 to 4-11.

222100 cstfrp ssss Equation ‎4-1

2222100 cscstyfrp sssss Equation ‎4-2

2222100 cscstyfrpu sssss Equation ‎4-3

159

2222100 cuscstyfrpu sssss Equation ‎4-4

expunfrpfrp

expunfrpfrpexpfrpfrp

frpEA

EAEAs

Equation ‎4-5

expunstst

expunststexpstst

stEA

EAEAs

Equation ‎4-6

expuncc

expunccexpcc

cEA

EAEAs

Equation ‎4-7

expunytst

expunytstexpytst

styfA

fAfAs

Equation ‎4-8

expunfrpufrp

expunfrpffrpexpfrpufrp

frpufA

fAfAs

Equation ‎4-9

expunscsc

expunscscexpscsc

scEA

EAEAs

Equation ‎4-10

expuncc

expunccexpcc

cufA

fAfAs

Equation ‎4-11

where s is the percentage of uncertainty, sfrp the uncertainty due to axial stiffness of the

CFRP material, sst the uncertainty due to axial stiffness of the tension steel

reinforcements, sc the uncertainty due to axial stiffness of the concrete material, ssty the

uncertainty due to strength of the tension steel reinforcements, sfrpu the uncertainty due to

strength of the CFRP material, ssc the uncertainty due to axial stiffness of the

160

compression steel reinforcements, and scu is the uncertainty due to strength of the

concrete material. Also, AfrpEfrp is the axial stiffness of the CFRP material, AstEst the axial

stiffness of the tension steel reinforcements, AcEc the axial stiffness of the concrete

material, Astfyt the axial tensile strength of the tension steel reinforcements, Afrpffrpu the

axial tensile strength of the CFRP material, AscEsc the axial stiffness of compression steel

reinforcements, and Acf′c is the axial compressive strength of the concrete material. The

subscripts “exp” and “unexp” refer to the properties of the beams from exposed and

unexposed sets, respectively.

The results of the error analysis for different sets of the exposed beams with

respect to the corresponding set of the unexposed beams are presented in Table ‎4-6,

which confirms the validity of the comparisons (to be performed in the next sections)

between the exposed beams tested in this research and the unexposed beams tested by

Gaafar (2007) in most cases. For the beams in set BR-F, the high uncertainty of 46.3% at

failure stage is due to difference at ultimate strain of the CFRP from two sets. In other

cases, a maximum uncertainty of 6.7% is probable due to the difference in material

properties of the exposed and unexposed sets of the beams.

Table ‎4-6: Uncertainty in comparison of the exposed and unexposed beams based on

material properties.

Set

Uncertainty (%)

Up to

yielding (Eq. 4-1)

Yielding up

to failure (Eq. 4-2)

At failure

CFRP rupture (Eq. 4-3)

Concrete crushing (Eq. 4-4)

BS-F w.r.t. BS-R 4.6 5.9 4.1 6.7

BR-F w.r.t. BR-R 2.5 4.4 46.3 4.6

161


4.5.3.1 Beams Strengthened with CFRP Strips

The results of the exposed and unexposed beams strengthened with CFRP strips

are presented in Figure ‎4-31 and Table ‎4-7. The beams (as presented in Table ‎4-7) were

categorized into two sets: set BS-R were unexposed and tested by Gaafar (2007) while set

BS-F were exposed and tested in this research. The curves of the exposed beams are

plotted with considering the permanent deflections due to initial cracking of the beams

after strengthening. The load-deflection curves include the negative camber due to

prestressing, initiation of flexural cracks, yielding of tensile steel rebar, CFRP rupture or

concrete crushing which causes a large drop in the load at ultimate stage, and post failure

behaviour.

One week after prestressing, an upward camber ranging between 0.49-1.7 mm for

beams from set BS-F and between 0.47-1.6 mm for beams from set BS-R were recorded.

The values of the initial and effective pre-strain in the CFRP strip, computed by taking

the average of the strain values at the constant moment region of the beams, are presented

in Table ‎4-7 showing an average prestressing loss of 1.7±1.1% one week after

prestressing that is mainly due to combination of the anchorage seating loss, the elastic

shortening, and less likely the creep of the concrete beam within a week.

162

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)



BS-NP-R BS-P1-R BS-P2-R BS-P3-R B0-R

: Concrete crushing : FRP rupture : Concrete cover spallingR: Room temperature (unexposed beam)F: Freeze-thaw (exposed beam)

Figure ‎4-31: Comparison between exposed and unexposed RC beams strengthened using CFRP strips.

162

163

Table ‎4-7: Summary of the test results for strengthened beam using CFRP strips. S

et

Beam ID ɛp

(µɛ)

ɛpe

(µɛ)

Δoe

(mm)

Pcr

(kN)

Δcr

(mm)

Δop

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) μD

Φ

(kN. mm)

ɛfrp@u

(µɛ) FM

BS

-R,

un

exp

ose

d*

B0-R N.A. N.A. N.A. 12.5 1.25 N.A. 78.9 25.13 83.8 109.89 4.37 8050 N.A. CC

BS-NP-R 0 0 0 16.8 1.55 N.A. 90.8 25.83 135.1 118.79 4.60 12357 14190 CCS

BS-P1-R 3474 3454 -0.47 22.1 1.24 N.A. 103 24.12 148 103.65 4.30 11829 19405 FR

BS-P2-R 5868 5805 -0.93 30.1 1.69 N.A. 105.8 23.62 148.2 77.96 3.30 8711 17978 FR

BS-P3-R 10287 10237 -1.60 42.1 2.64 N.A. 122.8 25.77 149.2 58.13 2.26 6529 20000 FR

BS

-F,

exp

ose

d B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 7.61 7052

† N.A. CC

BS-NP-F 0 0 0 14 1.36 0.61 92.4 22.53 132.2 104.26 4.63 10649 14900 CC

BS-P1-F 3574 3463 -0.49 21.6 1.43 0.13 104.1 23.99 134.7 82.9 3.46 8667 16592 CC

BS-P2-F 6900 6723 -1.09 27.3 1.24 -0.81 114.8 25.56 149.5 87.85 3.44 10214 21464 FR

BS-P3-F 10112 9884 -1.70 35.5 1.45 -1.43 124.3 25.91 141.7 58.55 2.26 6510 21118 FR

F = the beam under freeze-thaw exposure ɛp = initial prestrain due to prestressing

R = the beam under room temperature ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing

Pcr and Δcr = load and deflection at cracking Δop = camber after initial loading (cracking)

Py and Δy = load and deflection at yielding ɛfrp@u = maximum CFRP strain at failure

Pu and Δu = load and deflection at ultimate Φ = area under P-Δ curve

μD = ductility index = Δu /Δy FM = failure mode

CC = concrete crushing CCS = concrete cover spalling FR = CFRP rupture † calculated based on concrete strain 0.004125 to be consistent with the other beams failed by crushing

* (Gaafar, 2007)

163

164

The beams were cracked after strengthening; the obtained cracking loads show

significant increase due to prestressing (up to 153% for set BS-F and up to 151% for set

BS-R) with respect to the non-prestressed strengthened beam of each set. The un-

strengthened control beams, B0-F and B0-R, showed a low cracking load, which is due to

presence of the micro-cracks in the beams before testing, mainly caused from moving the

beams after casting and during the testing process. In fact, the cracking load of the un-

strengthened control beams should have been close to that of the beams strengthened

with non-prestressed NSM CFRP strips.

Up to 56% and 64% increase in the yielding load of the strengthened beams in set

BS-R and set BS-F, respectively, were observed with respect to the corresponding un-

strengthened control beam of each set. Enhancements of 15% out of the 56% and 22%

out of the 64% are related to the increase due to CFRP strengthening and the rests (which

are 41% and 42%, respectively) are due to the prestressing effect. Besides, up to 78% and

53% increase in ultimate load of the strengthened beams in set BS-R and set BS-F,

respectively, were recorded with respect to the corresponding un-strengthened control

beam of each set; 61% out of the 78% and 35% out of the 53% are reached by

strengthening with non-prestressed CFRP strip and the remaining (which are 17% and

18%, respectively) are due to the prestressing effects. In fact, strengthening has more

contribution in enhancement of the ultimate load while prestressing has more

contribution in enhancement of the yield load than the ultimate load.

Five exposed beams in set BS-F showed a typical failure mode, i.e., tension steel

reinforcements yielding followed by CFRP rupture or concrete crushing. The type of

failure modes are marked in Figure ‎4-31. Comparing the load-deflection curves of the

165

exposed and unexposed beams reveals that freeze-thaw exposure has its major effects on

the ultimate stage, particularly on failure mode; by shifting the mode of failure from

CFRP rupture to concrete crushing as presented in Figure ‎4-31 for beams BS-NP-F and

BS-P1-F in comparison with beams BS-NP-R and BS-P1-R, respectively. This shift

resulted in 2.1% and 12.2% decrease in ultimate load and deflection at ultimate load of

beam BS-NP-F in comparison with beam BS-NP-R, respectively; furthermore, it resulted

in 9% and 20% decrease in ultimate load and deflection at ultimate load of beam BS-P1-

F in comparison with beam BS-P1-R, respectively. On the other hand, for the beams with

high prestressing level, BS-P2-F and BS-P3-F, the negative effects of freeze-thaw

exposure is negligible. In fact, when the beam is highly prestressed the failure is

governed by CFRP rupture and occurs while the concrete strain in the extreme

compression fibre is small; hence, the damage done to the concrete due to freeze-thaw

exposure should be extremely high to result in a significant reduction in concrete

crushing strain and leads to changing the mode of failure from CFRP rupture to concrete

crushing at small strain. Such behaviour has not been experienced in the cases of beams

BS-P2-F and BS-P3-F.

4.5.3.2 Beams Strengthened with CFRP Rebar

Results of the beams strengthened with CFRP rebars subjected to freeze-thaw

exposure (set BR-F) are compared with similar unexposed beams (set BR-R) as presented

in Figure ‎4-32 and Table ‎4-8. The beams showed typical failure modes either by CFRP

rupture or concrete crushing. As shown in Figure ‎4-32, it is not appropriate to compare

BR-P3-F with BR-P3-R, since the unexposed beam was prestressed much less than the

166

planned prestrain. an upward camber ranging between 0.48-1.71 mm for beams from set

BR-F and between 0.5-1.3 mm for beams from set BR-R were recorded one week after

prestressing. An average prestressing loss of 5.4±3% occurred one week after

prestressing computed by taking the average of the strain values at the constant moment

region of the six beams. Enhancements of 87% and 177% in cracking load for set BR-F

and BR-R was reached, respectively, with respect to the non-prestressed strengthened

beam of each set.

The exposed and unexposed beams had similar yielding loads (with an average

difference of 1.6% ranging from -1% to 6.3% with respect to corresponding unexposed

beam) as presented in Table ‎4-8. The exposed beams showed smaller deflection at

yielding than the unexposed beams. Up to 66% and 49% increase in the yielding load of

the strengthened beams in set BR-F and set BR-R, respectively, were observed with

respect to the corresponding un-strengthened control beam of each set. Enhancements of

21% out of the 66% and 14% out of the 49% are related to increase due to NSM CFRP

strengthening and the rest (which are 45% and 35%, respectively) are due to prestressing

effect.

Besides, up to 61% and 69% increase in ultimate load of the strengthened beams

in set BR-F and set BR-R, respectively, were recorded with respect to the corresponding

un-strengthened control beam of each set; 35% out of the 61% and 63% out of the 69%

are reached by strengthening with non-prestressed NSM CFRP strip and the remaining

(which are 26% and 6%, respectively) are due to prestressing. In fact, strengthening has

more contribution in enhancement of the ultimate load while prestressing has more

contribution in enhancement of the yield load than the ultimate load. Also, an average

167

difference of -7.4% at ultimate load for the exposed beams with respect to the

corresponding unexposed beams was obtained ranging from -3% to 16.9%.

168

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)


BR-NP-F BR-P1-F BR-P2-F BR-P3-F B0-F

BR-NP-R BR-P1-R BR-P2-R BR-P3-R B0-R


Figure ‎4-32: Comparison between exposed and unexposed beams strengthened with CFRP rebars.

168

169

Table ‎4-8: Summary of the test results for strengthened beam using CFRP rebars. S

et

Beam ID ɛp

(µɛ)

ɛpe

(µɛ)

Δoe

(mm)

Pcr

(kN)

Δcr

(mm)

Δop

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) μD

Φ

(kN. mm)

ɛfrp@u

(µɛ) FM

BR

-R,

un

exp

ose

d*

B0-R N.A. N.A. N.A. 12.5 1.25 N.A. 78.9 25.13 83.8 109.89 4.37 8050 N.A. CC

BR-NP-R 0 0 0 18.4 1.6 N.A. 90.2 25.3 136.4 114.5 4.53 11899 16250 FR

BR-P1-R 3460 3240 -0.5 22.1 1.5 N.A. 105.7 27.7 141.0 92.5 3.34 9917 17710 FR

BR-P2-R 6610 6210 -0.6 27.9 1.7 N.A. 114.5 28.6 141.7 79.3 2.77 8669 18910 FR

BR-P3-R 9910 8960 -1.3 34.4 2.4 N.A. 117.7 28.2 134.7 49.7 1.76 6529 17450 FR

BR

-F,

exp

ose

d B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 7.61 7052

† N.A. CC

BR-NP-F 0 0 0 13.1 1.23 0.595 91.6 23.78 132.3 102.71 4.32 10344 14599 CC

BR-P1-F 3801 3662 -0.48 18 1 -0.065 105.1 24.98 147.5 102.62 4.31 12658 22067 CC

BR-P2-F 6585 6548 -0.92 26 1.2 -0.52 113.4 25.86 157.5 98.05 3.79 11797 23879 CC

BR-P3-F 10272 9950 -1.71 36.3 1.21 -1.395 125.2 25.36 157.5 71.28 2.81 8734 24247 FR

F = the beam under freeze-thaw exposure ɛp = initial prestrain due to prestressing

R = the beam under room temperature ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing

Pcr and Δcr = load and deflection at cracking Δop = camber after initial cracking

Py and Δy = load and deflection at yielding ɛfrp@u = CFRP strain at failure at mid-span

Pu and Δu = load and deflection at ultimate Φ = area under P-Δ curve

μD = ductility index = Δu /Δy FM = failure mode

CC = concrete crushing CCS = concrete cover spalling FR = CFRP rupture † calculated based on concrete strain 0.004125 to be consistent with the other beams failed by crushing

* (El-Hacha and Gaafar, 2011)

169

170

4.5.3.3 Beams Strengthened with CFRP Rebar versus Strips

Effects of freeze-thaw exposure on the load-deflection behaviour of the NSM

strengthened RC beams are presented in Figure ‎4-33. Furthermore, a summary of the test

results is presented in Table ‎4-7 and Table ‎4-8. For the NSM strengthened beams tested

in this research the freeze-thaw exposure has its major effects on the concrete materials.

The damage done to the concrete due to the freeze-thaw exposure reduces the ultimate

capacity and ductility of the beams by shifting the failure mode from CFRP rupture to

concrete crushing, as marked in Figure ‎4-33 for beams BS-NP-F and BR-NP-F in

comparison with beams BS-NP-R and BR-NP-R, respectively. The exposed non-

prestressed strengthened beams (BS-NP-F and BR-NP-F) have an average of 13.4%

smaller energy absorption (Φ) than the unexposed beams (BS-NP-R and BR-NP-R) kept

at room temperature. Furthermore, thermal incompatibility which is a result of different

thermal expansion coefficients of concrete, epoxy, and CFRP likely produces residual

stresses in the CFRP during the freeze-thaw cycles at low and high temperatures which

affects the bond behaviour. High temperature causes tension on the CFRP reinforcement

and increases the strain in the CFRP while the low temperature causes compression in

CFRP reinforcement and decreases the strain in the CFRP. A slight strain fluctuation of

0.0002 in the CFRP rebars and strips strain values were monitored during the freeze-thaw

cycling. For the prestressed NSM CFRP strengthened RC beams (BS-P2-R, BS-P2-F,

BR-P2-R, and BR-P2-F), comparison of the load-deflection curves in Figure ‎4-33 reveals

negligible effects of the freeze-thaw exposure on the flexural behaviour. The difference at

ultimate stage is caused by the differences in the CFRP ultimate tensile strains (that is

171

0.0226 for BS-P2-F versus 0.018 for BS-P2-R and 0.0239 for BR-P2-F versus 0.0189 for

BR-P2-R).

172

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135 155 175 195 215

Lo

ad

(k

N)


B0-R BS-NP-R BR-NP-R BS-P2-R BR-P2-R

B0-F BS-NP-F BR-NP-F BS-P2-F BR-P2-F

: Concrete crushing : FRP rupture: Concrete cover spallingR: Room temperature (unexposed beams)F: Freeze-thaw (exposed beams)

Figure ‎4-33: Comparison between exposed and unexposed beams.

172

173

4.5.4 Effects of Prestressing

The effects of prestressing on cracking, yield, and ultimate loads, and deflection

at ultimate load are plotted in Figure ‎4-34 to Figure ‎4-37 with respect to the non-

prestressed strengthened beam in each set of tested beams. For cracking load, the highest

increase occurred in set BR-F with a value of 177%, as shown in Figure ‎4-34. The sets

BS-R and BS-F showed almost similar behaviour with maximum enhancements of 151%

and 153%, respectively, with respect to the corresponding non-prestressed strengthened

beams. In set BR-R, a low percentage of increase in cracking load was reached, up to

87%, with respect to the non-prestressed strengthened beam in this set; the reason is that

beam BR-NP-R (that comparison is performed based on this beam) showed a high

cracking load in comparison with beams BS-NP-F, BS-NP-R, and BR-NP-F. It should be

mentioned that the cracking loads were obtained when all beams were unexposed.

0

40

80

120

160

200

0 0.002 0.004 0.006 0.008 0.01

Ch

an

ge in

cra

ck

ing

lo

ad

(%

)

Prestrain in CFRP strips or rebar

BS-F w.r.t BS-NP-F

BS-R w.r.t BS-NP-R

BR-F w.r.t BR-NP-F

BR-R w.r.t BR-NP-R

Figure ‎4-34: Effects of prestressing on cracking load w.r.t non-prestressed NSM

CFRP strengthened beam in each set.

174

The percentage of change in yield load versus prestrain in CFRP strip or rebar is

presented in Figure ‎4-35 for the unexposed and exposed beams. The two exposed sets of

the beams (BS-F and BR-F) showed similar results with a maximum increase of 37% in

yield load of the BR-F set. The two unexposed sets (sets BS-R and BR-R tested by

Gaafar (2007)) did not show perfect similar trend, however, the average of the two sets is

in a very good correlation with the exposed beam curve. Based on the results, it can be

concluded that the effect of 500 freeze-thaw cycling exposure on the yield load of the RC

beams strengthened with prestressed NSM CFRP strips or rebar appears to be negligible.

0

5

10

15

20

25

30

35

40

0 0.002 0.004 0.006 0.008 0.01

Ch

an

ge in

yie

ld l

oad

(%

)


BS-F w.r.t BS-NP-F

BS-R w.r.t BS-NP-R

BR-F w.r.t BR-NP-F

BR-R w.r.t BR-NP-R

Figure ‎4-35: Effects of prestressing on yield load w.r.t non-prestressed NSM CFRP

strengthened beam in each set.

The percentage of changes in the ultimate load and deflection for the exposed and

unexposed sets are presented in Figure ‎4-36 and Figure ‎4-37, respectively. Percentage of

175

change in the ultimate load is affected by the type of the failure and does not follow a

specific trend. It can be concluded that by increasing the prestressing level, whenever the

failure is governed by concrete crushing, the ultimate load increases with respect to the

non-prestressed strengthened beam. For any prestressing level greater than the balanced

prestressing level (which causes CFRP rupture and concrete crushing, simultaneously),

the failure is due to CFRP rupture and the ultimate load stays almost constant. Among

compared sets, set BR-F showed highest percentages of increase at ultimate load due to

prestressing (19%) while set BR-R showed the lowest percentage of increase due to

prestressing (4%). Sets BS-F and BS-R showed maximum increases of 13% and 10% at

ultimate load, respectively.

-5

0

5

10

15

20

25

0 0.002 0.004 0.006 0.008 0.01

Ch

an

ge

in

ult

ima

te lo

ad

(%

)


BS-F w.r.t BS-NP-F

BS-R w.r.t BS-NP-R

BR-F w.r.t BR-NP-F

BR-R w.r.t BR-NP-R

Figure ‎4-36: Effects of prestressing on ultimate load w.r.t non-prestressed

strengthened beam in each set.

176

One of the main concerns for prestressed beams is decreasing the deflection at

ultimate load as well as the ductility (conventional definition, i.e. displacement,

curvature, and rotational ductility indices). The percentage of change in deflection at

ultimate load versus prestrain in CFRP rebar or strip is presented in Figure ‎4-37. Sets BR-

F and BR-R showed the lowest (up to 31%) and highest (up to 58%) decreases in

deflection at ultimate load, respectively, with respect to the deflection at ultimate load of

the corresponding non-prestressed NSM CFRP strengthened beam of each set. The

exposed beams showed lower decreases in deflection at ultimate load than the unexposed

beam. This behaviour is a result of the freeze-thaw cycling exposure that caused the

exposed non-prestressed strengthened beams (which are the reference of the comparison

for the sets BR-F and BS-F) to fail due to concrete crushing with deflections at ultimate

loads less than the ones for unexposed non-prestressed strengthened beams in sets BS-R

and BR-R.

The energy absorptions of the beams which are defined as the area under the load-

deflection curve up to the peak load are presented in Figure ‎4-38. For the beams

strengthened with NSM CFRP strips, the decreases of 13.8% and 26.7% in energy

absorption of beams BS-NP-F and BS-P1-F obtained with respect to the corresponding

unexposed beams, BS-NP-R and BS-P1-R, respectively. The reason is that the freeze-

thaw exposed beams showed different failure mode than the unexposed beams resulting

in smaller peak load and deflection at ultimate load. Highly prestressed beams, BS-P3-F

and BS-P3-R, showed similar energy absorption values that reveals the negligible effect

of freeze-thaw on them; on the other hand, the difference in energy absorption of beam

BS-P2-F and beam BS-P2-R is not caused by freeze-thaw exposure since the mode of

177

failure of the exposed and unexposed beam is the same; The difference is due to the

different CFRP rupture strains at ultimate (that is 0.0226 for BS-P2-F versus 0.018 for

BS-P2-R). For the beams strengthened with NSM CFRP rebar, a 13.1% decrease in

energy absorption of beam BR-NP-F was observed in comparison with BR-NP-R. For the

other beams, the difference is due to the different CFRP rupture strain at ultimate causing

the exposed beams to have greater energy absorption values than the unexposed beams

where failure is governed by CFRP rupture. According to results of the tested beams, it

can be concluded that at low prestressing levels (less than 26% of the ultimate tensile

strain of the CFRP strips, and 6% for CFRP rebar) the energy absorption of the exposed

beams are smaller than the unexposed beams mainly caused by shifting the mode of

failure from CFRP rupture to concrete crushing due to freeze-thaw cycling exposure.

-60

-50

-40

-30

-20

-10

0

10

0 0.002 0.004 0.006 0.008 0.01Ch

an

ge in

de

fle

cti

on

at

ult

ima

te lo

ad

(%

)


BS-F w.r.t BS-NP-F

BS-R w.r.t BS-NP-R

BR-F w.r.t BR-NP-F

BR-R w.r.t BR-NP-R

Figure ‎4-37: Effects of prestressing on deflection at ultimate load w.r.t non-

prestressed NSM CFRP strengthened beam in each set.

178

0

2000

4000

6000

8000

10000

12000

14000

0 0.002 0.004 0.006 0.008 0.01

En

erg

y a

bso

rpti

on

(a

rea u

nd

er

load

-d

efl

ecti

on

cu

rve)

kN

.mm


Energy absorption (BS-F set)

Energy absorption (BS-R set)

Energy absorption (BR-F set)

Energy absorption (BR-R set)

Figure ‎4-38: Effects of prestressing on the energy absorption of the exposed and

unexposed NSM CFRP strengthened RC beams.

4.6 Deformability and Ductility of NSM CFRP Strengthened RC Beams

The prestressed or non-prestressed NSM CFRP strengthened RC beams should be

designed for adequate strength and ductility to satisfy the ultimate limit states and avoid

brittle failure. The concept of ductility is related to the safety of the structure to provide

an opportunity for the deflections to be observed if the loads become too large. Therefore

appropriate remedial actions can be performed before failure.

Ductility is the ability of a member to undergo deformation after its initial

yielding without any significant reduction in yield strength while deformability is the

member capability to deform before failure (Bertero, 1988). Conventional ductility

indices, which are developed for conventional steel RC beams, use displacement,

179

curvature, or rotation at yielding and ultimate stages as basis for the computations. In this

case, the load-deflection response is almost an elasto-plastic curve where there is a

negligible difference between the yield and ultimate loads. From a design perspective, the

ductility index of a concrete beam reinforced with steel bars (conventional RC beam)

provides a measure of the energy absorption capability (Naaman and Jeong, 1995; Jaeger

et al., 1997). Since beams reinforced with FRP materials do not have the yield point to be

considered in the calculation of the conventional ductility indices, and also, the RC

beams strengthened with FRP materials acquire a significant portion of their capacity in

plastic range (there is a significant difference between the yield and ultimate loads in the

load-deflection response), hence, for those type of beams, the conventional ductility

indices are not an appropriate measure of the energy absorption capacity. Therefore, the

use of the concept of deformability as a measure of the energy absorption is more

appropriate than the concept of conventional ductility which is a measure of deflection

capability.

In spite of the conventional ductility indices (displacement or curvature ductility)

which are appropriate for steel reinforced concrete members, a variety of deformability

indices are proposed by different researchers for concrete members reinforced with

prestressed/non-prestressed FRP (Naaman and Jeong, 1995; Abdelrahman et al., 1995;

Zou, 2003; Rashid et al., 2005; ACI 440.1R, 2006; CAN/CSA–S6–06, 2011). In this

context, there is a gap for an appropriate deformability index for prestressed/non-

prestressed FRP strengthened RC members, and reasonable deformability limit for each

model to be applicable for design purposes.

180

In this section, a brief review is performed on the available deformability/ductility

indices. Then, three deformability indices are modified to be applicable for NSM CFRP

strengthened RC beams. Afterwards, to validate the models and compare with the

conventional models, results of four series of tests on eighteen large scale (5.15 m long)

RC beams are employed to evaluate their ductility and deformability based on the

modified models and conventional indices. The RC beams were strengthened with

prestressed and non-prestressed NSM CFRP strips and rebars as presented in Table 3-1.

The test variables include prestressing level (0, 20, 40 and 60% of ultimate tensile

strength of the CFRP reinforcement), CFRP reinforcement geometry (strip versus rebar

with the same axial stiffness), and environmental exposure (room temperature versus

freeze-thaw cycling as mentioned earlier in this chapter). Furthermore, the design Codes’

limits for ductility and deformability of the beams are checked and new limits were

proposed and validated for different models to be used in practice.

The conventional definition of structural ductility refers to the behaviour of an

under-reinforced concrete member reinforced with steel bars. In this case, the yielding of

the steel bars provides a base for a rational definition of ductility. When an RC member is

strengthened with material other than steel without a yield plateau (such as FRP) or when

a concrete member is reinforced with FRP, in these cases, the conventional definition of

structural ductility is not valid and needs to be modified. Hence, Naaman and Jeong

(1995) and Mufti et al. (1996) proposed new definitions of structural deformability for

concrete members reinforced with FRP materials. However, there is no appropriate

model for a concrete beam reinforced with conventional steel and strengthened with

prestressed or non-prestressed FRP materials where the load capacity is partly

181

supplemented by FRP materials. These members shows various load-deflection responses

affected by the ratio of existing internal steel area to the balanced steel area, ratio of

equivalent reinforcement area (i.e., transformed FRP plus internal steel) to the balanced

steel area, FRP strength and stiffness, ratio of the external to internal reinforcement areas

(area of transformed external reinforcement to area of internal reinforcement), failure

mode, and debonding issues and the effectiveness of anchorage system. Furthermore, the

prestressing effects on the load-deflection response need to be considered in the proposed

ductility model. A brief review of the existing ductility and deformability models are

presented in the following sections.

4.6.1 Existing Ductility and Deformability Models

4.6.1.1 Displacement Ductility Index

Displacement ductility is defined as the ratio of the displacement at ultimate (Δu)

to the displacement at the commencement of yielding (Δy), as represented in Equation 4-

12 This conventional index of ductility is appropriate for concrete beams reinforced with

steel bars.

y

uD

Equation ‎4-12

where µD is the displacement ductility index, Δu the mid-span deflection at peak load or

75% of post-peak load (for the cases in which the failure occurs gradually i.e. concrete

crushing), and Δy is the mid-span deflection at yielding.

182

4.6.1.2 Curvature Ductility Index

Curvature ductility is defined as the ratio of the angle of curvature in the member

at ultimate to that at the commencement of yielding as presented in Equation 4-13. This

ductility index is appropriate for concrete beams reinforced with steel bars and loaded by

a bending moment.

y

u

Equation ‎4-13

where µ is the curvature ductility index, u the mid-span curvature at peak load or 75%

of post-peak load, and y is the mid-span curvature at yielding.

4.6.1.3 Rotational Ductility Index

Rotation ductility is defined as the ratio of the rotation of the plastic hinge at

ultimate to the value at commencement of yielding, as presented in Equation 4-14. This

ductility index is appropriate for conventional RC members under bending moment and

axial force.

y

u

Equation ‎4-14

where µ is the rotation ductility index, u the plastic hinge rotation at peak load or 75%

of post-peak load, and y is the value of rotation at plastic hinge location at

commencement of yielding.

183

4.6.1.4 Deformability Factor

Deformability factor is defined as the ratio of the energy absorption at ultimate to

the energy absorption at service or a limiting curvature or yielding, as presented in

Equation 4-15 (ACI 440.1R, 2006). The energy absorption is the area under load-

deflection curve. The deformability factor can be applied to any type of structure.

s

uE

E

E

Equation ‎4-15

where µE is the deformability factor, Eu the area under load-deflection curve up to peak

load or 75% of post-peak load, and Es is the area under load-deflection curve at service

(which can be at a limiting curvature or at yielding).

4.6.1.5 Naaman and Jeong (1995) Index

The Naaman and Jeong index is a deformability model proposed by Naaman and

Jeong (1995) given as Equation 4-16. This index is based on the assumption that the

prestressed concrete beam has a fully elasto-plastic behaviour.

150

el

totJN

E

E.

Equation ‎4-16

where Etot is the total energy absorption (area under load-deflection curve up to peak load

or failure load) and Eel is the part of the total energy as demonstrated in Figure ‎4-39. In

the absence of an experimental unloading curve, the slope S for calculation of Eel can be

defined as Equation 4-17.

184

2

21211

P

S)PP(SPS

Equation ‎4-17

The first and second slopes, S1 and S2 in Equation 4-17, corresponding to applied

load P1 and P2, are presented in Figure ‎4-39.

Figure ‎4-39: Total, elastic, and inelastic energies (Retrieved from Naaman and

Jeong, 1995).

4.6.1.6 Abdelrahman Index

Abdelrahman et al. (1995) established a deformability index for concrete beams

prestressed by FRP tendons. This index is defined as the ratio of the maximum deflection

corresponding to the failure or peak load to the equivalent deflection of the uncracked

section for peak load given as:

l

ubA

Equation ‎4-18

185

where Ab is the Abdelrahman deformability index, Δu the mid-span deflection at peak

load, and Δl is the equivalent uncracked deflection at peak load as demonstrated in Figure

‎4-40.

Figure ‎4-40: Equivalent deflection, Δ1, and failure deflection, Δu (Retrieved from

Abdelrahman et al., 1995).

The Abdelrahman index overestimates the ductility as much as three times greater

than the value of deflection ductility given by displacement ductility index for concrete

beams prestressed with steel tendons (Abdelrahman et al., 1995). As can be seen this

index is developed for a beam that its load-deflection response consists of two slopes

(from zero to cracking and from cracking to ultimate).

4.6.1.7 CHBDC Deformability Factor

The CHBDC (CAN/CSA-S6-06, 2011) proposes a deformability factor (called J

factor) for concrete members reinforced with FRP materials, as presented in Equation 4-

186

19. The factor is based on both strength and deformability and can be regarded as the

ratio of two energy values calculated from a linear moment-curvature response, one

associated with the ultimate limit state condition and the other when concrete at the

extreme compression fibre reaches its proportional limit. Jaeger et al. (1995) proposed the

J factor and Mufti et al. (1996) and Jaeger et al. (1997) elaborated on its concept. The J

factor is defined as:

cc

uu

M

MJ

Equation ‎4-19

where Mu and u are the moment and curvature at ultimate state, respectively, and Mc and

c are the moment and curvature corresponding to maximum concrete compressive strain

of 0.001, respectively.

4.6.1.8 Zou Index

Zou (2003) proposed a deformability index for concrete beam prestressed with

FRP based on deflection and moment values given as:

cr

u

cr

u

M

MZ

Equation ‎4-20

where Mu and Δu are the moment and deflection at ultimate state, respectively, while Mcr

and Δcr are the moment and deflection at cracking, respectively.

187

4.6.1.9 Rashid Index

Rashid et al. (2005) developed a deformability index for FRP reinforced high

strength concrete beams with confined concrete in compression zone given as:

crush

uR

Equation ‎4-21

where R is the Rashid index, Δu the mid-span deflection at peak load, and Δcrush is the

mid-span deflection at the initiation of concrete cover crushing. The Rashid index is

applicable when the load-deflection response of FRP reinforced concrete beam shows a

first peak at the initiation of concrete crushing and a second peak, usually higher than the

first one, before the confined concrete in the compression zone finally disintegrated.

A summary of the existing ductility and deformability indices and their

applications are presented in Table ‎4-9.

188

Table ‎4-9: Summary of existing ductility and deformability indices.

Description Equation Parameters Application

Displacement

ductility y

uD

µD = the displacement ductility index

Δu = the mid-span deflection at peak load

or 75% of post-peak load Δy = the mid-span deflection at yielding

conventional ductility index;

appropriate for RC beams;

not suitable for beams reinforced with FRP

Curvature

ductility y

uφ

φ

φμ

µ = the curvature ductility index

u = the mid-span curvature at peak load

or 75% of post-peak load

y = the mid-span curvature at yielding

appropriate for RC beams

loaded by a bending moment

Rotation

ductility y

uθ

θ

θμ

µ = the rotation ductility index

u = the plastic hinge rotation at peak load

or 75% of post-peak load

y = the rotation at plastic hinge location at

commencement of yielding

appropriate for RC members

under bending moment and

axial force

Abdelrahman

index

(Abdelrahman

et al., 1995) l

ub

Δ

ΔA

Ab = the Abdelrahman deformability index

Δu = the mid-span deflection at peak load

Δl =the equivalent un-cracked deflection at peak load

appropriate for concrete

beams prestressed by FRP tendons; overestimates the

ductility as much as three

times greater than the value of deflection ductility; for

prestressed concrete beams

with steel tendons

Naaman and

Jeong index

(Naaman and

Jeong, 1995)

150

el

totJ-N

E

E.μ

µN-J = the Naaman and Jeong index

Etot = the total energy absorption Eel = the elastic energy released at failure

due to unloading

based on the assumption that

the prestressed concrete

beams has a fully elasto-plastic behaviour;

appropriate for prestressed

RC beams

Deformability

factor (ACI

440.1R, 2006) s

uE

E

Eμ

µE = the deformability factor Eu = the area under load-deflection curve

up to peak load or 75% of post-peak load

Es = the area under load-deflection curve at service or a limiting curvature

applicable to any type of structure

Rashid index

(Rashid et al.,

2005) crush

u

Δ

ΔR

R = the Rashid index

Δu = the mid-span deflection at peak load Δcrush = the mid-span deflection at the

initiation of concrete cover crushing.

appropriate for FRP reinforced high strength

concrete beams with

confined concrete in compression zone

CHBDC

deformability

(J) factor

(CAN/CSA-S6-

06, 2011) cc

uu

φM

φMJ

J = the CHBDC deformability factor

Mu and u = the ultimate moment capacity

and curvature of the section

Mc and c = the moment and curvature

corresponding to maximum concrete

compressive strain of 0.001.


members reinforced with

FRP

Zou index

(Zou, 2003)

cr

u

cr

u

M

M

Δ

ΔZ

Z = the Zou index

Mu and Δu = the moment and deflection at

ultimate state Mcr and Δcr = the moment and deflection at

cracking


beam prestressed with FRP

189

4.6.2 Modification of the Deformability Models for FRP Strengthened RC Beams

As mentioned earlier, the deformability and ductility for a member needs to be

computed based on a reference point in the load-deflection or moment-curvature

response. For an RC beam strengthened with FRP material the yielding is a rational

reference point. On the other hand, the FRP strengthened beams gain a significant portion

of their capacity at plastic range after steel yielding. Therefore, assuming elasto-plastic

behaviour in deriving the deformability/ductility index leads to a major difference with

reality and underestimation of the actual ductility or deformability values. On the other

hand, strengthening using prestressed FRP causes a significant increase in cracking stage;

therefore, it is required to consider this stage in the deformability model. In this context,

the appropriate available deformability indices are modified to be applicable for

prestressed and non-prestressed FRP strengthened RC beams.

4.6.2.1 Modified Deformability Factor

For RC beams strengthened with prestressed FRP reinforcements which have the

yielding point in their responses, the deformability factor can be defined as Equation 4-22

and can be modified as Equation 4-23, which is derived by idealizing the actual load-

deflection curve with a tri-linear slope load-deflection response as shown in Figure ‎4-41.

yielding

start

ultimate

startEm

dΔP

dΔPμ

Equation ‎4-22

190

Figure ‎4-41: Idealized tri-linear slope load-deflection response.

cryyyocr

yuuy

EmΔΔPΔΔP

ΔΔPP1μ

Equation ‎4-23

where µEm is the modified deformability factor, Δo the deflection due to prestressing

(absolute value should be used in Equation 4-23), Pcr and Δcr the load and deflection at

cracking, respectively, Py and Δy the load and deflection at yielding, respectively, and Pu

and Δu are the load and deflection at ultimate, respectively.

4.6.2.2 Modified CHBDC Deformability Index

For reinforced concrete beams strengthened with prestressed FRP material which

has the yielding point the J factor can be modified as below by considering the area under

moment-curvature curve:

yielding

start

ultimate

startm

dφM

dφMJ

Equation ‎4-24

191

By idealizing a moment-curvature curve with a tri-linear slope moment-curvature

response as shown in Figure ‎4-42, Jm is simplified as:

Figure ‎4-42: Idealized tri-linear slope moment-curvature response.

cryyyocr

yuuym

φφMφφM

φφMM1J

Equation ‎4-25

where Jm is the modified J factor, o the curvature due to prestressing (absolute value

should be used in Equation 4-25), Mcr and cr the moment and curvature at cracking,

respectively, My and y the moment and curvature at yielding, respectively, and Mu and

u are the moment and curvature at ultimate, respectively.

4.6.2.3 Modified Zou Index

The Zou index is developed for concrete beams prestressed using FRP

reinforcements where the load-deflection curve mainly can be considered as a two–slope

curve (from zero to cracking and from cracking to peak load). For an RC beam

192

strengthened with prestressed FRP reinforcement, which has the yielding point in its

response, the Zou index can be modified as:

y

u

y

um

M

M

Δ

ΔZ

Equation ‎4-26

where Zm is the modified Zou index, Mu and Δu the moment and deflection at ultimate

state, respectively, and My and Δy are the moment and deflection at yielding, respectively.

4.6.3 Deformability of NSM-CFRP Strengthened RC Beam

4.6.3.1 Considered Beams

Results from eighteen beams were considered to assess the deformability and

ductility: (nine beams tested in phase I and nine beams tested by Gaafar (2007)). The

variables in the experimental program comprise CFRP reinforcement geometry (rebar

versus strip with the same axial stiffness), prestressing level in the CFRP reinforcement

(0-60% of ultimate tensile strength of CFRP reinforcements), and environmental

exposure (room temperature versus freeze-thaw cycling). Results of the beams are

presented in Table ‎4-10 and Table ‎4-11.

193

Table ‎4-10: Results of the beams (load-deflection). S

et

Beam ID ɛp (µɛ) ɛpe

(µɛ)

Δoe

(mm)

Pcr

(kN)

Δcr

(mm)

Δop

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm)

ɛfrp@u

(µɛ) FM

Gro

up A

-un

expo

sed

*

B0-R N.A. N.A. N.A. 12.5 1.25 N.A. 78.9 25.13 83.8 109.89 N.A. CC

BS

-R

BS-NP-R 0 0 0 16.8 1.55 N.A. 90.8 25.83 135.1 118.79 14190 CCS

BS-P1-R 3474 3454 -0.47 22.1 1.24 N.A. 103 24.12 148 103.65 19405 FR

BS-P2-R 5868 5805 -0.93 30.1 1.69 N.A. 105.8 23.62 148.2 77.96 17978 FR

BS-P3-R 10287 10237 -1.60 42.1 2.64 N.A. 122.8 25.77 149.2 58.13 20000 FR

BR

-R

BR-NP-R 0 0 0 18.4 1.6 N.A. 90.2 25.3 136.4 114.5 16250 FR

BR-P1-R 3460 3240 -0.5 22.1 1 N.A. 105.7 27.2 141 92 17710 FR

BR-P2-R 6610 6210 -0.6 27.9 1.1 N.A. 114.5 28 141.7 78.7 18910 FR

BR-P3-R 9910 8960 -1.3 34.4 1.1 N.A. 117.7 26.9 134.7 48.4 17450 FR

Gro

up B

-ex

po

sed

B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 N.A. CC

BS

-F

BS-NP-F 0 0 0 14 1.36 0.61 92.4 22.53 132.2 104.26 14900 CC

BS-P1-F 3574 3463 -0.49 21.6 1.43 0.13 104.1 23.99 134.7 82.9 16592 CC

BS-P2-F 6900 6723 -1.09 27.3 1.24 -0.81 114.8 25.56 149.5 87.85 21464 FR

BS-P3-F 10112 9884 -1.70 35.5 1.45 -1.43 124.3 25.91 141.7 58.55 21118 FR

BR

-F

BR-NP-F 0 0 0 13.1 1.23 0.6 91.6 23.78 132.3 102.71 14914 CC

BR-P1-F 3801 3662 -0.48 18 1 -0.07 105.1 24.98 147.5 107.62 22067 CC

BR-P2-F 6585 6548 -0.92 26 1.2 -0.52 113.4 25.86 157.5 98.05 23879 CC

BR-P3-F 10272 9950 -1.71 36.3 1.21 -1.4 125.2 25.36 157.5 71.28 24247 FR

BS = the beam strengthened with CFRP strips BR = the beam strengthened with CFRP rebar

F = the beam under freeze-thaw exposure ɛp = initial prestrain due to prestressing R = the beam under room temperature ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing

Pcr and Δcr = load and deflection at cracking ɛfrp@u = CFRP strain at failure at mid-span

Py and Δy = load and deflection at yielding FM = failure mode Pu and Δu = load and deflection at ultimate CC = concrete crushing CCS = concrete cover spalling

Δop = camber after initial cracking FR = CFRP rupture

*(Gaafar, 2007; El-Hacha and Gaafar, 2011)

194

Table ‎4-11: Results of the beams (moment-curvature).

Set

Beam ID

oe

(µ rad/mm)

Mcr (kN.m)

cr (µ rad/mm)

Mc (kN.m)

c (µ rad/mm)

My (kN.m)

y (µ rad/mm)

Mu (kN.m)

u (µ rad/mm)

Gro

up A

-un

expo

sed

*

B0-R 0 12.5 1.09 71.3 10.22 78.9 11.61 83.8 71.73

BS

-R

BS-NP-R 0 16.8 2.38 62.8 7.95 90.8 11.62 135.1 55.53

BS-P1-R -0.19 22.1 0.74 73.7 7.51 103 11.45 148 53.28

BS-P2-R -0.35 30.1 1.56 80.6 8.19 105.8 11.19 148.2 44.35

BS-P3-R -0.91 42.1 1.71 83.0 7.32 122.8 12.37 149.2 34.37

BR

-R

BR-NP-R 0 18.4 2.16 64.4 9.17 90.2 12.86 136.4 52.45

BR-P1-R -0.24 22.1 1.42 63.1 7.82 105.7 13.77 141 51.23

BR-P2-R -0.41 27.9 1.08 84.3 8.52 114.5 12.29 141.7 37.02

BR-P3-R -0.52 34.4 1.47 72.0 6.66 117.7 13.08 134.7 26.36

Gro

up B

-ex

po

sed

B0-F 0 10.4 1.49 61.6 7.22 75.5 9.19 97.8 82.43

BS

-F

BS-NP-F 0 14 0.7464 82.9 9.06 92.4 10.43 132.2 51.9

BS-P1-F -0.13 21.6 0.86 93.2 9.26 104.1 10.71 134.7 42.67

BS-P2-F -0.65 27.3 0.39 101.9 9.34 114.8 11.23 149.5 47.74

BS-P3-F -0.67 35.5 0.44 94.9 7.87 124.3 11.79 141.7 38.05

BR

-F

BR-NP-F 0 13.1 0.54 86.4 9.41 91.6 10.25 132.3 43.95

BR-P1-F -0.4 18 0.31 84.3 8.17 105.1 11.01 147.5 43.22

BR-P2-F -0.56 26 0.38 99.4 9.03 113.4 10.63 157.5 40.09

BR-P3-F -0.9 36.3 0.38 99.4 7.61 125.2 10.44 157.5 37.03

BS = the beam strengthened with CFRP strips oe = effective curvature 7 days after prestressing

BR = the beam strengthened with CFRP rebar Mcr and cr = moment and curvature at cracking

R = the beam under room temperature My and y = moment and curvature at yielding

F = the beam under freeze-thaw exposure Mu and u = moment and curvature at ultimate

Mc and c = the moment and curvature corresponding to maximum concrete compressive strain of 0.001

4.6.3.2 Deformability Analysis and Discussions

Results of the five models applied to the eighteen beams listed in Table ‎4-10 and

Table ‎4-11 are presented in Figure ‎4-43 and Figure ‎4-44, and also in Table ‎4-12. The

results reveal that the conventional displacement ductility (µD) and curvature ductility

(µ) almost result in the same values while for some sets of the tested beams the value of

195

the curvature ductility is slightly higher, see Figure ‎4-43b and Figure ‎4-44b. This

anomalous behaviour can be easily interpreted. The curvatures for the tested beams was

calculated based on the measured concrete surface strain from LSCs installed at the mid-

span section. The mid-span section is under the maximum cracking density, which affects

the actual magnitudes of the measured surface strain. Also, curvatures based on surface

strains do not accurately reflect the parameters involved in measurements of rotational

capacity (Spadea et al., 2001). Therefore, it can be generally concluded that ductility

based on surface concrete measurements are likely to be less reliable. The modified Zou

index (Zm) results in a value greater than those obtained from displacement and curvature

ductility indices but smaller than those obtained from modified J factor (Jm) and modified

deformability factor (µEm). The modified J factor results in higher values than the other

models. The CHBDC (CAN/CSA-S6-06, 2011) requires that the J factor should be

greater than 4 and 6 for rectangular and T-sections concrete beams reinforced with FRP

reinforcements, respectively. However, there are no deformability limits for the other

models considered in this study. The statistical analysis of the results obtained from

sixteen strengthened beams reveals that the average value obtained by µEm, Zm, µD and µ

are 88%, 69%, 57%, and 52% of the value obtained by Jm, respectively. Therefore,

considering a limit of 4 for Jm and based on statistical analysis of the results, the

corresponding limits for µEm, Zm, µD and µ are 3.5±0.5, 2.8±0.3, 2.3±0.3, and 2.1±0.2,

respectively. This finding covers a major gap in ductility and deformability of the FRP

strengthened RC beam and provides an opportunity for designers to use different

equations in order to check the ductility or deformability of RC beams strengthened with

FRP. Furthermore, comparison between ductility/deformability values of the un-

196

strengthened control beams with those values for strengthened beams, presented in Table

‎4-12, reveals that in most cases the un-strengthened beam shows larger

deformability/ductility; this fact is more obvious for the exposed beam in Group B.

Table ‎4-12: Ductility or deformability indices of beams.

Set

Beam ID ɛpe

(µɛ) µD µ µE µEm J Jm Z Zm

Gro

up A

-un

expo

sed

B0-R N.A. 4.37 6.18 7.38 7.28 8.25 11.03 591.44 4.64

BS

-R

BS-NP-R 0 4.60 4.78 9.42 8.96 15.02 10.59 616.30 6.84

BS-P1-R 3454 4.30 4.65 7.69 7.88 14.25 8.72 559.78 6.17

BS-P2-R 5805 3.30 3.96 5.55 5.51 9.96 7.16 227.13 4.62

BS-P3-R 10237 2.26 2.78 3.19 3.20 8.43 4.20 78.03 2.74

BR

-R

BR-NP-R 0 4.53 4.08 9.27 8.76 12.12 8.47 530.50 6.84

BR-P1-R 3240 3.38 3.72 5.57 5.73 14.64 6.72 586.97 4.51

BR-P2-R 6210 2.87 3.01 4.18 4.47 7.30 4.86 363.37 3.55

BR-P3-R 8960 1.80 2.01 2.32 2.35 7.40 2.83 172.29 2.06

Gro

up B

-ex

po

sed

B0-F N.A. 7.61 8.97 14.12 15.88 18.11 19.75 604.99 9.85

BS

-F

BS-NP-F 0 4.63 4.97 8.70 9.08 9.13 9.94 722.84 6.62

BS-P1-F 3463 3.46 3.98 5.69 5.89 6.66 7.06 362.18 4.47

BS-P2-F 6723 3.44 4.25 5.43 5.68 7.50 7.15 388.00 4.48

BS-P3-F 9884 2.26 3.23 3.02 3.16 7.22 4.77 161.15 2.58

BR

-F

BR-NP-F 0 4.32 4.29 8.09 8.43 7.15 8.37 845.63 6.24

BR-P1-F 3662 4.31 3.93 7.62 8.01 9.25 7.12 882.08 6.05

BR-P2-F 6548 3.79 3.77 6.30 6.60 7.04 6.49 494.96 5.27

BR-P3-F 9950 2.81 3.55 4.07 4.24 7.71 5.50 255.69 3.54

µD = the displacement ductility index µ = the curvature ductility index

µE = the deformability factor µEm = the modified deformability factor

J = the original J factor Jm = the modified J factor

Z = the original Zou index Zm = the modified Zou index

ɛpe = effective prestrain in CFRP at 7 days after prestressing

197

0

2

4

6

8

10

12

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

de

form

ab

ilit

y

Prestrain in CFRP rebar

Em

Jm

Zm

Dd

Cd

µEm

Jm

Zm

µD

µ

(a) Beams strengthened using NSM CFRP rebar.

0

2

4

6

8

10

12

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

de

form

ab

ilit

y

Prestrain in CFRP strip

Em

Jm

Zm

Dd

Cd

µEm

Jm

Zm

µD

µ

(b) Beams strengthened using NSM CFRP strips.

Figure ‎4-43: Deformability and ductility models applied to the unexposed beams.

198

0

2

4

6

8

10

12

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

de

form

ab

ilit

y


Em

Jm

Zm

Dd

Cd

µEm

Jm

Zm

µD

µ


0

2

4

6

8

10

12

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

defo

rmab

ilit

y


Em

Jm

Zm

Dd

Cd

µEm

Jm

Zm

µD

µ


Figure ‎4-44: Deformability and ductility models applied to the exposed beams.

199

A comparison between the original and the modified deformability models is

presented in Figure ‎4-45 and Figure ‎4-46 and also in Table ‎4-12. The results reveal that

there is a large difference between the modified Zou index (Zm) and the original one (Z).

For the beams listed in Table ‎4-12, the average value obtained by Z is 90.4 times the

value obtained by Zm. The reason is that the original Zou index is appropriate for the

concrete beams prestressed with FRPs and defined is based on Mcr and Δcr (the moment

and deflection at cracking, respectively, see Equation 4-20), while the modified Zou

index is defined based on My and Δy (the moment and deflection at yielding, respectively,

see Equation 4-26) to be applicable to the FRP strengthened steel reinforced concrete

beams. The modified deformability factor (µEm) obtained from Equation 4-23 and the

deformability factor (µE) calculated based on actual energy result in similar values (less

than 3% difference); µEm has the advantage of simplicity in application which does not

have the difficulty in calculation of the actual energy absorption in comparison with µE.

Comparison between the modified J factor (Jm) and the original J factor (J) shows that

the original J factor results in higher value than the modified one for the unexposed

beams (Figure ‎4-45), while it gives similar value to the modified one for the exposed

beams (Figure ‎4-46). The average value obtained by J is 1.7 and 1.1 times the value

obtained by Jm for the unexposed and exposed beams, respectively. It should be noted

that the original J factor is defined based on Mc and c, the moment and curvature

corresponding to maximum concrete compressive strain of 0.001, which makes it seems

to be appropriate for concrete beams reinforced with FRPs that have no yield points in

their load-deflection responses. On the other hand, as mentioned earlier, the curvatures

for the tested beams were calculated based on the measured concrete surface strain from

200

LSCs installed at the mid-span section. Since, the mid-span section is under the

maximum cracking density, which affects the actual magnitudes of the measured surface

strain and ductility based on surface concrete measurements are likely to be less reliable.

0

3

6

9

12

15

18

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

de

form

ab

ilit

y


Jm

Dd

Em

Df

Zm

Cd

Jm

J

µEm

µE

Zm

Z/100


0

3

6

9

12

15

18

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

de

form

ab

ilit

y


Jm

Dd

Em

Df

Zm

Cd

Jm

J

µEm

µE

Zm

Z/100


Figure ‎4-45: Comparison between the original and the modified deformability

models applied to the unexposed beams.

201

0

3

6

9

12

15

18

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

defo

rmab

ilit

y


Jm

Dd

Em

Df

Zm

Cd

Jm

J

µEm

µE

Zm

Z/100


0

3

6

9

12

15

18

0 0.002 0.004 0.006 0.008 0.01

Du

cti

lity

or

defo

rmab

ilit

y


Jm

Dd

Em

Df

Zm

Cd

Jm

J

µEm

µE

Zm

Z/100


Figure ‎4-46: Comparison between the original and the modified deformability

models applied to the exposed beams.

202

The results from each deformability and ductility model applied to the

strengthened beams are presented in Figure ‎4-47 to Figure ‎4-51. On the other hand, the

calculated limit for each model is applied and plotted in the figures considering upper

bound values mentioned earlier. The investigation reveals that the limits used for

different models present almost the same prestrain in the CFRP rebar/strip that can be

applied to meet the ductility criteria and have an acceptable design. In this context and

based on the proposed upper bound limit, the modified deformability factor (µEm)

represents the most conservative model which results in a smaller prestrain to be applied

to meet the limit. The results obtained from µEm show that for sets BS-R, BR-R, BS-F,

and BR-F, prestressing by the maximum values presented in Table ‎4-10 leads to

decreases of 64.2%, 73.1%, 65.2%, and 49.7%, respectively, in comparison with the

corresponding non-prestressed strengthened beam of each set; an average decrease of

63.1% is obtained in this case. Correspondingly, the results obtained from Zm (the

modified Zou index) for sets BS-R, BR-R, BS-F, and BR-F reveal that prestressing

causes the decreases of 59.9%, 69.9%, 61.1%, and 43.3%, respectively, in comparison

with the corresponding non-prestressed strengthened beam of each set; an average

decrease of 58.6% occurred in this case.

203

0

2

4

6

8

10

12

0 0.00275 0.0055 0.00825 0.011

Cu

rvatu

re d

ucti

lity

in

dex

(µ)

Prestrain in CFRP strip or rebar

µj (BS-F set)

µj (BS-R set)

µj (BR-F set)

µj (BR-R set)

µ

µ

µ

µ

µ upper bound limit

µ limit

Figure ‎4-47: Verification of proposed limit for curvature ductility index (µ).

0

2

4

6

8

10

12

0 0.00275 0.0055 0.00825 0.011

Dis

pla

ce

me

nt

du

cti

lity

in

de

x (

µD)


µD (BS-F set)

µD (BS-R set)

µD (BR-F set)

µD (BR-R set)

µD

µD

µD

µD

µD upper bound limit

µD limit

Figure ‎4-48: Verification of proposed limit for displacement ductility index (µD).

204

0

2

4

6

8

10

12

0 0.00275 0.0055 0.00825 0.011

De

form

ab

ilit

y i

nd

ex

(J

m)


Jm (BS-F set)

Jm (BS-R set)

Jm (BR-F set)

Jm (BR-R set)

Jm

Jm

Jm

Jm

Jm limit (CAN/CSA–S6–06)

Figure ‎4-49: Verification of proposed limit for modified J factor (Jm).

0

2

4

6

8

10

12

0 0.00275 0.0055 0.00825 0.011

De

form

ab

ilit

y i

nd

ex

(Z

m)


Zm (BS-F set)

Zm (BS-R set)

Zm (BR-F set)

Zm (BR-R set)

Zm

Zm

Zm

Zm

Zm upper bound limit

Zm limit

Figure ‎4-50: Verification of proposed limit for modified Zou index (Zm).

205

0

2

4

6

8

10

12

0 0.00275 0.0055 0.00825 0.011

De

form

ab

ilit

y i

nd

ex (

µE

m)


µEm (BS-F set)

µEm (BS-R set)

µEm (BR-F set)

µEm (BR-R set)

µEm upper bound limit

µEm limit

µEm

µEm

µEm

µEm

Figure ‎4-51: Verification of proposed limit for modified deformability factor (µEm).

Also, the results calculated from Jm model (the modified J factor) show that for

sets BS-R, BR-R, BS-F, and BR-F, prestressing causes the decreases of 60.3%, 66.6%,

52%, and 34.3%, respectively, in comparison with the corresponding non-prestressed

strengthened beam of each set; an average decrease of 53.3% is obtained in this case.

Analyzing the results obtained from µD (the displacement ductility index) for sets BS-R,

BR-R, BS-F, and BR-F reveal that prestressing leads to decreases of 51%, 60.2%, 51.2%,

and 34.9%, respectively, in comparison with the corresponding non-prestressed

strengthened beam from each set; an average decrease of 49.3% is obtained in this case.

Furthermore, the results calculated from µ (the curvature ductility index) for sets BS-R,

BR-R, BS-F, and BR-F show that prestressing causes the decreases of 41.8%, 50.6%,

35.1%, and 17.3%, respectively, in comparison with the corresponding non-prestressed

206

strengthened beam; an average decrease of 36.2% is obtained in this case. In fact,

comparison between the averages of decreases for each index reveals the sensitivity of

each index to prestressing which increases by the following order: µ, µD, Jm, Zm, and

µEm.

4.7 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under Combined

Sustained Load and Freeze-Thaw Exposure

Five beams were tested in phase II including one un-strengthened control beam

and four beams strengthened using NSM CFRP strips with target prestressing level of

0%, 20%, 40%, and 60% of the ultimate tensile strength of the CFRP strips reported by

manufacturer. The test matrix is presented in Table ‎3-1. The beams in phase II were

exposed to 500 freeze-thaw cycles as described in Section 3.6 while each beam was

subjected to a sustained load of 62 kN, equal to 47% of the theoretical ultimate load of

the non-prestressed NSM CFRP strengthened RC beam (BS-NP in Table ‎3-3). Geometry

of the beams and details of the experimental program are presented in Chapter Three.

4.7.1 Test Beams and Material Properties

Five beams subjected to sustained load and 500 cycles of freeze-thaw (based on

the test matrix presented in Table ‎3-1) were tested in phase II. The material properties of

the strengthened beams including steel reinforcements, concrete, and CFRP strip obtained

from ancillary tests are presented in Appendix C in detail. However, a brief description is

presented in this section.

207


The tension and compression steel bars (3-15M and 2-10M) possessed the yield

strengths of 5330.8 MPa and 48816 MPa, and the yield strains of 0.002660.00022

and 0.002440.00027, respectively, obtained from tension tests having a modulus of

elasticity of 200 GPa. Also, the stirrups (25-10M) had the same properties as the

compression steel bars.

4.7.1.2 Concrete

The beams in phase II were cast from the same concrete batch with a 28 days

average concrete compressive strength of 37.81.2 MPa. After subjecting to 500 freeze-

thaw cycles, the concrete cylinders were severely damaged due to exposure so that

nothing was left from the cylinders to be tested. However, a 19.18.5 MPa average

concrete compressive strength was obtained using the Schmidt hammer test on the

exposed beams at the time of testing to failure. It should be mentioned that the top

surfaces of the beams (to a depth of 50 mm) were severely deteriorated in comparison to

the other parts of the beams. More detailed investigations showed average exposed

concrete compressive strengths of 10.16.8 MPa and 28.110.1 MPa for the top layer

and side of the beams. More details about the concrete compressive strengths are

presented in Table C-1. The capacity and also failure mode of the beams were mostly

related to the concrete strength in the compression region.

208

4.7.1.3 CFRP Strips

The material properties of the CFRP strips are presented in Table ‎4-13. Beam BS-

P3-FS was strengthened using different batch of CFRP strips due to shortage of the CFRP

strips, however, the CFRP material property from the two batches are almost similar.

Table ‎4-13: CFRP material properties obtained from tension tests.

CFRP product

(Manufacturer)

Dimension

(mm)

Afrp

(mm2)

ffrpu

(MPa)

Efrp

(GPa) ɛfrpu

Aslan 500 CFRP tape*

(Hughes Brothers Inc) 2×16 31.2 2624±28 124.4±6.7 0.021±0.0009

Aslan 500 CFRP tape**

(Hughes Brothers Inc) 2×16 31.2 2707±5 132±3.1 0.0205±0.0005

* Used for beams BS-NP-FS, BS-P1-FS, and BS-P2-FS ** Only used for beam BS-P3-FS


Two types of epoxy adhesives were used similar to phase I with the properties

presented in Section 3.3.3.4.


The anchors bolts used in phase II are the same as the ones used in phase I. The

material properties of the bolts are presented in Section 3.3.3.4.

4.7.2 Results from Sustained Load and Freeze-Thaw Exposure

After strengthening, the beams in phase II were placed inside the environmental

chamber and the sustained load was applied to the beams using the system and procedure

described in Section 3.3.6. Prior to sustained loading, two trial instant loadings were

209

applied to the system to check the performance of the frame system developed for

loading and the instrumentations. Then, the sustained load was applied and the system

was locked. The system was monitored for three days and the loss in load was measured,

then the applied load was modified and checked in regular time period of one week to

keep the value of the load constant. Therefore, three stages of sustained loading were

applied during the period of the exposure (204 days). The average sustained load value

was to 47% of the analytical ultimate load of beam BS-NP-FS. The load-deflection

history for each beam is presented in Figure ‎4-52 to Figure ‎4-56 showing the two instant

loadings and unloadings, and three sustained loading and unloading stages. The sustained

load history is presented in Figure ‎4-61 to Figure ‎4-61, which shows the beams were

under slightly different sustained loads (ranging from 59.8 kN to 64.6 kN) which is

expected due to the different stiffness of the beams under the loading system. The

deflection history for each beam is presented in Figure ‎4-62 to Figure ‎4-66. In the first

stage, the beams were subjected to sustained load for 4 days at room temperature to

investigate the performance of the developed sustained loading system. In the second

stage, the beams were subjected to sustained load and freeze-thaw cycles for 3 weeks.

Then, the load was adjusted for the third stage, and the beams were subjected to sustained

load and freeze-thaw cycles for 6 months. During the exposure, the system was checked

and adjusted in regular period of one week, also, the strain in tension and compression

steel bars at mid-span, strain in CFRP strip at mid-span, and vertical deflection at mid-

span were all recorded at a rate of one reading every 1 min. It should be noted that the

LSCs placed at mid-span of the beams B0-FS, BS-NP-FS, BS-P1-FS, and BS-P2-FS

were damaged under freeze-thaw cycles and the after exposure permanent deflection in

210

these beams was estimated using the trend-line as shown in Figure ‎4-62 to Figure ‎4-66. It

should be noted that in Figure ‎4-52 to Figure ‎4-61, the sustained load corresponding to

the recorded deflection of each beam was calculated using the load-deflection responses

of the beams from set BS-F (presented in Figure ‎4-1) that were similar to the beams in set

BS-FS (for example the value of measured deflection under sustained load for each beam

was pluged into Figure ‎4-1 and the corresponding load was determined for the same

beam, this value of the load is used in Figure ‎4-52 to Figure ‎4-61). The effects of the

applied exposure (combined sustained load and 500 freeze-thaw cycles) on the beams

were significantly severe in phase II, and therefore, resulted in large permanent

deflections ranging from 8-15.6 mm.

0

10

20

30

40

50

60

70

80

0 3 6 9 12 15 18 21 24 27 30

Lo

ad

(k

N)

Mid-span deflection of beam B0-FS (mm)

Instant loading Sustained loading-stage 1

Sustained loading-stage 2 Sustained loading-stage 3

O : Estimated Permanent deflection

The fluctuation at peak load is due to load adjustment and freeze-thaw cycles

Figure ‎4-52: Load-deflection history for beam B0-FS.

211

0

10

20

30

40

50

60

70

80

0 3 6 9 12 15 18 21 24 27 30

Lo

ad

(k

N)

Mid-span deflection of beam BS-NP-FS (mm)





Figure ‎4-53: Load-deflection history for beam BS-NP-FS.

0

10

20

30

40

50

60

70

80

0 3 6 9 12 15 18 21 24 27 30

Lo

ad

(k

N)

Mid-span deflection of beam BS-P1-FS (mm)





Figure ‎4-54: Load-deflection history for beam BS-P1-FS.

212

0

10

20

30

40

50

60

70

80

0 3 6 9 12 15 18 21 24 27 30

Lo

ad

(k

N)







0

10

20

30

40

50

60

70

80

0 3 6 9 12 15 18 21 24 27 30

Lo

ad

(k

N)




O : Recorded Permanent deflection



213

Sustained load = 63.3-0.0114×(days)

0

15

30

45

60

75

30 60 90 120 150 180 210

Su

sta

ine

d lo

ad

on

b

eam

B0-F

S (

kN

)

Time (day)


Sustained loading-stage 3 Trendline

Figure ‎4-57: Sustained load history for beam B0-F.


0

15

30

45

60

75

30 60 90 120 150 180 210

Su

sta

ine

d lo

ad

on

b

eam

BS

-NP

-FS

(kN

)

Time (day)



Figure ‎4-58: Sustained load history for beam BS-NP-FS.


0

15

30

45

60

75

30 60 90 120 150 180 210

Su

sta

ine

d lo

ad

on

b

eam

BS

-P1-F

S (

kN

)

Time (day)



Figure ‎4-59: Sustained load history for beam BS-P1-FS.

214


0

15

30

45

60

75

30 60 90 120 150 180 210

Su

sta

ined

lo

ad

on

b

eam

BS

-P2-F

S (

kN

)

Time (day)




0

15

30

45

60

75

30 60 90 120 150 180 210

Su

sta

ined

lo

ad

on

b

eam

BS

-P3-F

S (

kN

)

Time (day)


Sustained loading-stage 3


Δ = 25.02-0.0044×(days)

0

5

10

15

20

25

30

0 30 60 90 120 150 180 210

Mid

-sp

an

defl

ecti

on

of

be

am

B0-F

S (

mm

)

Time (day)



Figure ‎4-62: Deflection history for beam B0-FS.

215

Δ = 22.03-0.0059×(days)

0

5

10

15

20

25

30

0 30 60 90 120 150 180 210

Mid

-sp

an

defl

ecti

on

of

be

am

BS

-NP

-FS

(m

m)

Time (day)



Figure ‎4-63: Deflection history for beam BS-NP-FS.

Δ = 19.40-0.0056×(days)

0

5

10

15

20

25

30

0 30 60 90 120 150 180 210

Mid

-sp

an

defl

ecti

on

of

beam

BS

-P1-F

S (

mm

)

Time (day)



Figure ‎4-64: Deflection history for beam BS-P1-FS.

Δ =15.91 -0.0016×(days)

0

5

10

15

20

25

30

0 30 60 90 120 150 180 210

Mid

-sp

an

defl

ecti

on

of

beam

BS

-P2-F

S (

mm

)

Time (day)




216

0

5

10

15

20

25

30

0 30 60 90 120 150 180 210

Mid

-sp

an

de

flec

tio

n o

f b

eam

BS

-P3-F

S (

mm

)

Time (day)


Sustained loading-stage 3


On the other hand, after removing the beams from the environmental chamber it

was observed that debonding occurred at the end regions of the NSM CFRP strips at the

concrete-epoxy interface. The schematic and lengths of the debonded regions are

presented in Figure ‎4-67 and Table ‎4-14. Further, the beams were cracked extensively

due to exposure as can be seen in Figure ‎4-68 to Figure ‎4-72. These observations

revealed that the RC beam strengthened with prestressed NSM CFRP strip is prone to

debonding up to 65% of the total prestressing length; on the other hand, the non-

prestressed NSM CFRP strengthened RC beam is not susceptible to debonding under

freeze-thaw exposure and sustained load since no sign of debonding was observed after

removing the beam from the chamber. The reason is that the concrete surrounding the

prestressed NSM CFRP strips is under shear stress and due to its degradation because of

the freeze-thaw exposure, the bond capacity at the concrete-epoxy interface gradually

decreases and leads to debonding. The debonded length increases when the prestressing

level in the NSM CFRP increases. Also, the debonded length at the jacking end of the

217

NSM CFRP (named as “DL-JE” in Table ‎4-14) is higher than that at the fixed end

(named as “DL-FE” in Table ‎4-14). The reason is that the concrete-epoxy interface is

under more shear stress at the jacking end than the fixed end since the steel anchor at

jacking end was bolted after adhesive cured (24hrs after prestressing) and then the

jacking force was released. This procedure applies more shear stress at the concrete-

epoxy interface at the jacking end. This issue can be solved by modifying the prestressing

procedure, i.e., bolting the steel anchor at the jacking end and releasing the jacking force

prior to hardening the adhesive in the groove. The concern with this solution might be

having more prestressing loss in the NSM CFRP reinforcement due to seating of the steel

anchor on the bolts.

Figure ‎4-67: Debonding occurred at concrete-epoxy interface due to freeze-thaw

exposure and sustained load.

Table ‎4-14: Debonded length of the beams shown in Figure ‎4-67.

Beam ID

DL-FE

(debonded length at fixed

end of NSM CFRP) (mm)

DL-JE

(debonded length at jacking

end of NSM CFRP) (mm)

Total

debonded

length (mm)

Debonded

length to total

length (%)

B0-FS N.A. N.A. N.A. N.A.

BS-NP-FS 0 0 0 0

BS-P1-FS 150 600 750 19.3

BS-P2-FS 905 1435 2340 60.3

BS-P3-FS 665 1865 2530 65.2

218

Figure ‎4-68: Images of beam B0-FS after exposure.

Left end Mid-span Right end

Side view

218

219

Figure ‎4-69: Images of beam BS-NP-FS after exposure.

Side view

Top view at location #1 Top view at location #2

Bottom view at left end anchor Left end Right end

Location #1 Location #2

219

220

Figure ‎4-70: images of beam BS-P1-FS after exposure.

Side view

Bottom view at left end anchor

Left end Right end

Bottom view at location #2 Bottom view at right end

Mid-span

Top view at location #1

Location #1

Location #2

220

221

Figure ‎4-71: Images of beam BS-P2-FS after exposure.

Side view

Mid-span Right end Left end

Bottom view at left end

Bottom view

at left end

Bottom view

at right end


Bottom view at right end

Location #1

221

222

Figure ‎4-72: Images of beam BS-P3-FS after exposure.

Bottom view at left end

Mid-span Left end Right end

Bottom view

at left end

Bottom view

at right end

Side view


Bottom view at right end

Location #1

222

223


The load-deflection responses of the beams tested to failure in phase II are plotted

in Figure ‎4-73 and Figure ‎4-74. The permanent deflections due to sustained loading are

included in the plotted curves in Figure ‎4-73; while these values are not included in

Figure ‎4-74 to have a better comparison on the post-exposure behaviour of the beams

tested in phase II with the beams tested in phase I, hereafter. In addition, a summary of

the results is presented in Table ‎4-15. It should be noted that the cracking loads and the

corresponding deflections for the beams are not presented in the table. Since all the

beams work interdependently under the loading frame used to apply the sustained load

(see Section 3.3.6), finding the exact cracking load for each beam is not possible. Also,

the limited space in the chamber during loading did not allow for the discovery of the

cracking load for each beam by visual inspection.

The load-deflection responses in phase II are significantly different from the ones

in phase I (Figure ‎4-1) where the load-deflection responses of the prestressed NSM CFRP

strengthened RC beams are typically made of three-linear slopes. In phase II, the

responses include the negative camber due to prestressing, yielding of tension steel

rebars, and failure due to concrete crushing or CFRP debonding. Also, the large drop in

load-deflection response at failure (as the ones observed in Figure ‎4-1) does not occur

and the failure is ductile even though the ultimate load is significantly smaller than one

observed in phase I.

After prestressing the beams in phase II, an upward instant deflection (Δo) ranging

from 0.44-1.38 mm was observed; seven days later, these ranges changed to 0.34-1.71

mm as presented in Table ‎4-15 as the effective negative camber (Δoe). As explained

224

earlier in Section 4.2.2.1, removing the temporary bracket and less likely the creep within

one week are the reasons for increasing the upward deflection.

The initial and effective prestrain values obtained from the strain gauges installed

at constant moment region of the beams are provided in Table ‎4-15. The effective

prestrain values were obtained seven days after prestressing which show an average loss

of 2.41±0.34%. Thereafter, the beams were subjected to sustained load and freeze-thaw

cycles and experienced the permanent deflections ranging from 8-15.6 mm, as explained

in Section 4.7.2.

Since, the concrete components of the beams were severely deteriorated due to

combined exposure and sustained load, as shown in Figure ‎4-68 to Figure ‎4-72, all beams

showed the failures related to concrete, i.e., concrete crushing followed by CFRP

debonding at concrete-epoxy interface. In this regards, the failure occurred shortly after

tension steel yielding showing a completely non-typical behaviour. In reinforced concrete

structures, creep results in gradual transfer of load from the concrete to the

reinforcements. Once the steel yields, any increase in load is taken by the concrete so that

the full strength of both the steel and the concrete is developed before failure takes place.

The failure mode of each beam is marked on Figure ‎4-74. Photos of the beams at failure

are presented in Figure ‎4-75 to Figure ‎4-79.

225

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140 160 180

Lo

ad

(k

N)


BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS B0-FS

: Concrete crushingO : Concrete crushing and NSM CFRP debonding, simultaneously

Figure ‎4-73: Load-deflection curves of the beams subjected to combined sustained load and freeze-thaw exposure (phase II, set

BS-FS, including permanent deflection after sustained load and freeze-thaw exposure).

225

226

0

20

40

60

80

100

120

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)



: Concrete crushingO : Concrete crushing and NSM CFRP debonding, simultaneously

Figure ‎4-74: Load-deflection curves of the beams subjected to combined sustained load and freeze-thaw exposure (phase II, set

BS-FS).

226

227

Table ‎4-15: Summary of the test results for phase II (beams subjected to combined sustained load and freeze-thaw exposure).

Beam ID ɛp

(µɛ)

Δo*

(mm)

ɛpe

(µɛ)

Δoe

(mm)

Δop

(mm)

Py

(kN)

Δy*

(mm) Py/Py0 Py/Pyn

Pu

(kN)

Δu*

(mm) Pu/Pu0 Pu/Pun

Φ

(kN. mm)

Failure

mode

B0-FS N.A. N.A. N.A. N.A. 15.6 62.3 13.3 1.00 N.A. 77.9 80.9 1.00 N.A. 5462.9 CC

BS-NP-FS 0 0 0 0.00 13.7 74.4 15.5 1.19 1.00 98.3 57.6 1.26 1.00 4496.6 CC

BS-P1-FS 3644 -0.44 3550 -0.34 11.5 83.8 17.5 1.35 1.13 96.8 35.1 1.24 0.98 2534.5 CC

BS-P2-FS 6907 -0.93 6726 -1.07 10.1 90.5 20.6 1.45 1.22 91.4 21.9 1.17 0.93 1343.8 CC-DB

BS-P3-FS 10290 -1.38 10082 -1.71 8 101.5 19.4 1.63 1.36 106.7 36.7 1.37 1.09 3174.6 DB-CC

ɛp and Δo = initial prestrain and initial camber due to prestressing Δop = permanent deflection after sustained loading and freeze-thaw exposure

Py and Δy = load and deflection at yielding ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing

Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under load-deflection curve) up to peak load

Py/Py0 and Pu/Pu0 = ratios of the yielding and ultimate loads of each beam to those from B0-FS

Py/Pyn and Pu/Pun = ratios of the yielding and ultimate load of each beam to those from corresponding non-prestressed strengthened beam

CC-DB= concrete crushing followed by the NSM CFRP debonding, almost simultaneously CC = concrete crushing

DB-CC= failure initiated by the NSM CFRP debonding and concrete crushing almost simultaneously, and then followed by the concrete crushing

* Δo, Δy, and Δu do not include the values of Δop

227

228




Figure ‎4-75: Photos of beam B0-FS at failure.

Concrete crushing

Concrete crushing

229




Figure ‎4-76: Photos of beam BS-NP-FS at failure.

Concrete crushing

Concrete crushing

230




Figure ‎4-77: Photos of beam BS-P1-FS at failure.

Concrete crushing

Concrete crushing

231





Concrete crushing

Concrete crushing

232





Concrete crushing

Concrete crushing

233

The un-strengthened control RC beam (B0-FS as shown in Figure ‎4-74) showed

a typical behaviour and failed due to concrete crushing occurred between two point loads

after yielding of the tension steel reinforcements‎. The major flexural cracks already

occurred in the beam due to freeze-thaw exposure and sustained load. These cracks got

wider as the applied monotonic load increased further and led to a large ultimate

deflection at mid-span of the beam. Then, the beam failed due to concrete crushing at the

load and deflection values lower than the expected.

For the non-prestressed strengthened RC beam, BS-NP-FS, debonding cracks at

the concrete-epoxy interface initiated from the point load location at a deflection and

corresponding load of 23 mm and 83.3 kN, and propagated towards the supports as the

monotonic loading applied further. Then, the concrete crushing started at a deflection and

corresponding load of 32.9 mm and 90 kN (after yielding of the tension steel bars) and

gradually propagated that caused a slight change in the slope of the load-deflection curve.

Major concrete crushing occurred at mid-span at a deflection and corresponding load of

49 mm and 97.3 kN and increased further to a deflection and corresponding load of 57.6

mm and 98.3 kN, which caused a large drop in the load-deflection curve. While the test

continued, complete debonding of the NSM-CFRP strips from the concrete substrate

occurred (from point load to the support at the right end of the beam that was the jacking

end at the time of prestressing). At this point, the force in the NSM CFRP reinforcement

was completely transferred to the end anchor leading to formation of cracks at the

location of the anchor bolts. Images of the beams BS-NP-FS at failure are presented in

Figure ‎4-75.

234

For beam BS-P1-FS, strengthened using prestressed NSM CFRP strips with

prestress level of 17%, the NSM CFRP debonded from both ends that occurred at the

concrete-epoxy interface due to combined freeze-thaw exposure and sustained load

before starting the static test. The length of the debonded NSM CFRP at each end is

provided in Table ‎4-14. At a load and corresponding deflection of 90 kN and 22 mm, the

debonded length reached to 750 mm from the right end (jacking end at the time of

prestressing) as shown in Figure ‎4-67. The concrete crushing started at mid-span location

at a load and corresponding deflection of 95 kN and 29.2 mm and gradually increased as

the monotonic loading applied further. By continuing the test, debonding from the right

end extended to a wide flexural crack at the point load location and stopped. The beam

failed due to concrete crushing (at a load of 96.8 kN and a corresponding deflection of

35.1 mm) that caused a large drop in the load-deflection response. Afterwards, more

crushing occurred as the secondary failure, and no future increase in the load was

recorded. Finally, the end anchor was separated due to concrete block failure surrounding

the bolts. Photos of beam BS-P1-FS at failure are presented in Figure ‎4-77.

Beam BS-P2-FS, strengthened using prestressed NSM CFRP strips with prestress

level of 33%, had a long debonded length before starting of the static test. The debonded

length included 60.3% of the total NSM CFRP length (front-to-front of the anchor), more

details can be found in Table ‎4-14 and Figure ‎4-71. Due to significant debonding and also

deterioration of concrete materials, the beam failed due to concrete crushing followed by

CFRP debonding almost simultaneously at a load of 91.4 kN and a corresponding

deflection of 21.9 mm shortly after yielding of the tension steel reinforcements (as shown

in Figure ‎4-74). By continuing the test, more concrete crushing occurred at mid-span that

235

caused a drop in the load-deflection response (at a deflection of 35 mm and a

corresponding load of 90.2 kN). The debonding (from the right end of the beam that was

the jacking end at the time of prestressing) reached a wide flexural crack at the location

of the point load and did not extend further. The debonded length from the left end of the

beam (fixed end at the time of prestressing) did not increase significantly during the static

test. No further increase in the load was observed as the test continued and more crushing

occurred at a deflection and corresponding load of 116 mm and 81.3 kN causing a large

drop in the load-deflection response and then the test was terminated.

Beam BS-P3-FS, strengthened using prestressed NSM CFRP strips with high

prestress level of 50%, showed the longest debonded length under combined freeze-thaw

exposure and sustained load (65.2% of total NSM CFRP length) as presented in Table

‎4-14 and Figure ‎4-72. The debonded length from the right end of the beam (jacking end

at the time of prestressing of the NSM CFRP strips) reached the point load location

before starting of the static test. The beam experienced debonding followed by crushing,

almost simultaneously, at a deflection of 22.3 mm and a corresponding load of 103.9 kN

shortly after yielding that caused a small drop in the load deflection response as shown in

Figure ‎4-74. By continuing the test further, an increase in the load was observed and the

beam failed due to crushing between mid-span location and point load at a deflection of

36.7 mm and a corresponding load of 106.7 kN as marked on the curve in Figure ‎4-74.

The debonded length from the right end of the beam extended to a wide flexural crack at

the location of the point load and did not extend further. The third drop in the load

deflection curve is due to more debonding that reached to mid-span from the right side of

the beam (jacking end at the time of prestressing). Debonding from the left end of the

236

beam (fixed end at the time of prestressing) did not increase significantly. Finally, by

continuing the test the end anchor separated due to concrete block failure (at the right

end) and the test was terminated.

Comparison between load deflection response of the tested beams in phase II

reveals that the non-prestressed NSM CFRP strengthening system can increase the

yielding load of the un-strengthened control beam up to 17.7%, furthermore, prestressed

NSM CFRP strengthening system with prestress level ranging from 0-50% can increase

the yielding load of the un-strengthened control beam up to 64.8% where 17.7% of this

value is related to strengthening and the rest, 47.1%, is related to prestressing effects. On

the other hand, the prestressed NSM CFRP strengthening increases the ultimate load of

the un-strengthened control beam up to 36.7% while 26.1% of this value is related to

strengthening and the rest, 10.7%, is related to prestressing effects.

4.7.4 Load-Strain Response

The relation between the load and strains in the extreme concrete compression

fibre, compression steel, tension steel, and CFRP strips at mid-span location of the tested

beams are presented in Figure ‎4-80 to Figure ‎4-87.

For the extreme concrete compression fibre, tension steel, and CFRP strips, the

load-strain relation consists of two parts: from the start of the static test to yielding of

tensile steel, and from yielding of tensile steel to failure. Since, the beams were already

cracked before starting of the static tests due to the applied sustained load; therefore, the

load-strain relation is linear from beginning of the test up to yielding of the tensile steel.

Yielding of the tension steel leads a significant reduction in flexural stiffness of the beam

237

that causes a decrease in the slope of the load-strain curves. By continuing the test

further, the curves reach a point at which the concrete crushing occurs. The load versus

tensile steel strain relations are obtained based on the LSCs installed at the level of the

longitudinal tension steel, since the strain gauges on the tension steel reinforcements were

damaged before yielding; therefore, no yielding plateau is observed in the plotted curves

for tension steel in Figure ‎4-80 to Figure ‎4-87.

Strain in the concrete, top steel, bottom steel, and CFRP strips at different stages

are presented in Table ‎4-16. After prestressing, a negative camber occurs that leads the

top steel and top concrete goes to tension while the bottom steel goes to compression,

these tension and compression strain values are small.

Results of beams BS-NP-FS and BS-P1-FS reveals that these beams experienced

a large concrete compression strain, as presented in Figure ‎4-85. This behaviour is due to

the severe environmental damage that has been done to the concrete materials of the

beams due to the freeze-thaw cycling, which decreases the concrete strength and

increases the ductility of the concrete materials due to presence of the thermal cracks. On

the other hand, although the instrumentation was performed at mid-span but the location

of the concrete crushing might not be at the centre of the beam to capture the maximum

strain reached at failure; this fact results in underestimation of the actual concrete

compressive strain at failure. For beams BS-P2-FS and BS-P3-FS, debonding of the NSM

CFRP at end regions prior to starting of the static test due to combined freeze-thaw

exposure and sustained load affected the ultimate capacity, which resulted in premature

failure in comparison. Therefore, these beams failed shortly after yielding of the tension

steel stage and did not experience high ductility as beams BS-NP-FS and BS-P1-FS. To

238

have a better comparison, the concrete strain at extreme compression fibre, the strain in

CFRP strips, and the strain in tension steel reinforcements versus the load are presented

in Figure ‎4-84 to Figure ‎4-86, respectively.

The strains in the compression steel reinforcements are compared in Figure ‎4-87

for all beams. The curves are plotted based on the reading from strain gauges installed on

the compression steel at mid-span. The compression steel strain almost showed linear

elastic behaviour prior to failure. For beams BS-NP-FS and B0-FS as can be seen in

Figure ‎4-80 and Figure ‎4-87, respectively, the strain in compression steel decreases

shortly before failure; as mentioned earlier in Section 4.2.3, this is due to local buckling

of the compression steel at mid-span location after the start of the concrete crushing. For

beams BS-P1-FS, BS-P2-FS, and BS-P3-F, a sudden increase can be seen in compression

steel strain shortly before failure, this is due to the reason that after the start of the

concrete crushing in these beams more load is transferred to the compression steel.

239

0

20

40

60

80

100

120

-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135

Lo

ad

(k

N)

Strain at mid-span

BS-NP-FS, Concrete Strain

BS-NP-FS, Top Steel Strain

BS-NP-FS, Bottom Steel Strain

BS-NP-FS, CFRP Strain

TensionCompression

Ultimate load = 98.3 kN

Figure ‎4-80: Load-strain curves for BS-NP-FS.

0

20

40

60

80

100

120

-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135

Lo

ad

(k

N)

Strain at mid-span

BS-P1-FS, Concrete Strain

BS-P1-FS, Top Steel Strain

BS-P1-FS, Bottom Steel Strain

BS-P1-FS, CFRP Strain

TensionCompression


Figure ‎4-81: Load-strain curves for BS-P1-FS.

240

0

20

40

60

80

100

120

-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135

Lo

ad

(k

N)

Strain at mid-span





TensionCompression TensionCompression



0

20

40

60

80

100

120

-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135

Lo

ad

(k

N)

Strain at mid-span





TensionCompression TensionCompression TensionCompression TensionCompression



241

0

20

40

60

80

100

120

0 0.003 0.006 0.009 0.012 0.015

Lo

ad

(k

N)

Strain in CFRP strips at mid-span

BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS

Figure ‎4-84: Load-CFRP strain for all beams.

0

20

40

60

80

100

120

-0.021 -0.018 -0.015 -0.012 -0.009 -0.006 -0.003 0

Lo

ad

(k

N)

Concrete strain in extreme compression fiber at mid-span


Figure ‎4-85: Load-concrete strain in extreme compression fibre for all beams.

242

0

20

40

60

80

100

120

-0.0005 0.004 0.0085 0.013 0.0175 0.022 0.0265

Lo

ad

(k

N)

Strain in tension steel at mid-span


Figure ‎4-86: Load-tension steel strain curves for all beams.

0

20

40

60

80

100

120

-0.005 -0.004 -0.003 -0.002 -0.001 0

Lo

ad

(k

N)

Strain in compression steel at mid-span


Figure ‎4-87: Load-compression steel strain curves for all beams.

243


compression steel, and tension steel at mid-span at different stages.

Beam ID ɛf-i

(µɛ)

ɛf-7days

(µɛ)

ɛf-su

(µɛ)

ɛc-i

(µɛ)

ɛc-7days

(µɛ)

ɛc-su

(µɛ)

ɛsc-i

(µɛ)

ɛsc-7days

(µɛ)

ɛsc-su

(µɛ)

ɛst-i

(µɛ)

ɛst-7days

(µɛ)

ɛst-su

(µɛ)

B0-FS N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. -418 N.A. N.A. 1753

BS-NP-FS 0 0 1507 N.A. N.A. N.A. N.A. N.A. -468 N.A. N.A. 1221

BS-P1-FS 3644 3550 4809 75 25 N.A. 16 11 -179 -38 -23 1641

BS-P2-FS 6907 6726 7516 90 220 N.A. 41 30 -414 -76 -100 864

BS-P3-FS 10290 10082 10850 131 109 N.A. 53 46 -285 -121 -149 588

ɛf-i, ɛc-i, ɛsc-i, and ɛst-i = initial prestrain in CFRP strips or rebar, extreme concrete fibre at top, top steel and bottom steel due

to prestressing ɛf-7days, ɛc-7days, ɛsc-7days, and ɛst-7days = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel and bottom steel

at 7 days after prestressing

ɛf-su, ɛc-su, ɛsc-su, and ɛst-su = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel, and bottom steel under

sustained load and freeze-thaw exposure

4.7.5 Strain Profile along the CFRP Strips

The strain profiles along the length of the NSM CFRP strip at yielding, and

ultimate loads are presented in Figure ‎4-89 and Figure ‎4-90, respectively. The profiles are

plotted based on the reading of strain from the installed strain gauges at specified

locations on the CFRP strips. For beam BS-NP-FS the strains are close to zero at the ends

of the CFRP strip at yielding and ultimate load levels (as shown in Figure ‎4-89 and

Figure ‎4-90). This implies the presence of the full bonding at the end and also complete

contribution of the epoxy adhesive in transferring the forces between the CFRP strip and

the surrounding concrete. Furthermore, the concrete-epoxy interface at the end of the

NSM CFRP strip is highly affected by stress concentration which caused debonding at

the end portion of the NSM CFRP strips under sustained load in the prestressed

strengthened beams, BS-P1-FS, BS-P2-FS, and BS-P3-FS. The end anchors have full

contribution in transferring the load after occurrence of debonding. Therefore, it is very

important that during the prestressing process, i.e., after removing the temporary

244

brackets, the end anchors are in contact with the bolts and there is no gap between them

An instance of this gap is shown in Figure ‎4-88. If there is any, these gaps will results in

prestressing loss (seating loss) after debonding. It should be mentioned that this loss (if

there were any) was not captured during the sustained loading under freeze-thaw

exposure. Capturing this strain loss needs waterproof instrumentation along the length of

the NSM-CFRP strips that can provide reading under freeze-thaw exposure and sustained

loading.

Figure ‎4-88: Gap between bolt and jacking end anchor causing future prestress loss.

As observed in Section 4.2.4, when there is no debonding the highest strain in the

CFRP strip occurs at the constant moment region of the beams (location 2000-3000 mm).

This fact is not valid for the prestressed strengthened beams tested in phase II. Since the

Gaps between bolt and anchor plate

245

prestressed strengthened beams debonded under exposure, the strain profile is almost

constant within the NSM CFRP length.

Comparison between strain profiles for beam BS-NP-FS in Figure ‎4-89 and

Figure ‎4-90 shows that the strain at both ends near the end anchors almost remained

constant during the static test showing no slippage at the ends of the NSM CFRP strip

and appropriate performance of the epoxy in transferring the forces.

0

0.003

0.006

0.009

0.012

0.015

0 1000 2000 3000 4000 5000

Str

ain

in

CF

RP

str

ip a

t yie

ldin

g



Figure ‎4-89: Strain profile along the length of the NSM CFRP strip at yielding.

246

0

0.003

0.006

0.009

0.012

0.015

0 1000 2000 3000 4000 5000

Str

ain

in

CF

RP

str

ip a

t u

ltim

ate



Figure ‎4-90: Strain profile along the length of the NSM CFRP strip at ultimate.

4.7.6 Strain Distribution at Mid-span

The strain distributions at mid-span section along the depth of the beams at

yielding and ultimate loads are presented in Figure ‎4-91, Figure ‎4-92 and Table ‎4-17. The

strain distributions are plotted using the strain values in concrete, compression steel,

tension steel, and CFRP strip including the effective strain due to prestressing.

The strain distributions are nonlinear at yielding, in which the nonlinearity is

caused by concrete and can be observed in top portion of the strain distributions in Figure

‎4-91‎.

The un-strengthened control RC beam, B0-FS, showed the highest curvature

among the tested beams at ultimate stage. During the test, debonding was observed at

mid-span regions at concrete-epoxy interface. Using the slope procedure, analyzing the

247

results revealed that the slope of the strain distribution between steel level and the CFRP

level at yielding and ultimate loads changes for the strengthened beams confirming the

occurrence of debonding.

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.005 0 0.005 0.01 0.015

Secti

on

dep

th (

mm

)

Strain at yielding

B0-FS BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS


NSM CFRP strip centroid @ 387.5 mm



Figure ‎4-91: Strain distribution at mid-span at yielding.

36

248

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.02 -0.01 0 0.01 0.02 0.03

Secti

on

dep

th (

mm

)

Strain at ultimate

B0-FS BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS


NSM CFRP strip centroid @ 387.5 mm



Figure ‎4-92: Strain distribution at mid-span at ultimate.


tension steel, and CFRP strip or rebar at mid-span section.

Beam ID ɛc-y

(µɛ)

ɛsc-y

(µɛ)

ɛst-y

(µɛ)

ɛf-y

(µɛ)

ɛc-u

(µɛ)

ɛsc-u

(µɛ)

ɛst-u

(µɛ)

ɛf-u

(µɛ)

B0-FS -1700 -834 1600 N.A. -19450 -1480 25275 N.A.

BS-NP-FS -2975 -925 1575 1710 -16200 -321 9450 7510

BS-P1-FS -3225 -1184 1475 5154 -7725 -2075 4300 6713

BS-P2-FS -1961 -1503 1604 8347 -2136 -1589 1235 8367

BS-P3-FS -1644 -911 1485 12107 -3019 -1352 2915 12073

ɛc = strain in extreme compression fibre of concrete (compression is negative) ɛsc = strain in compression steel

ɛst = strain in tension steel ɛf = strain in CFRP rebar or strip

y = at yielding u = at ultimate

4.8 Combined Effects of Freeze-Thaw Cycling Exposure and Sustained Load

In Section 4.5, the effects of the applied freeze-thaw cycling exposure in phase I

were analyzed by comparing the exposed and unexposed beams strengthened using NSM

CFRP strips and rebars showing the insignificant effects of the applied cycling exposure

36

249

on the overall flexural performance of the beams. In this section, the overall flexural

behaviour of the RC beams strengthened with non-prestressed and prestressed NSM

CFRP strips subjected to freeze-thaw cycling exposure (phase I: BS-F) are compared to

similar beams subjected to combined sustained load and freeze-thaw cycling exposure

(phase II: BS-FS).

4.8.1 Material Properties of the Compared Beams

A summary of the material properties of the beams strengthened with NSM CFRP

strips in phase I and phase II is provided in Sections 4.2.1 and 4.7.1, respectively.

4.8.2 Error Analysis

An error analysis is performed for the considered beams in phase I and phase II

(BS-F set and BS-FS set) to obtain the uncertainty of the comparison based on the

material properties. The analysis is done using the Equation 4-1 to Equation 4-4 and the

results are presented in Table ‎4-18. The results confirm validity of the comparisons

between the beams under freeze-thaw cycling exposure (set BS-F) and the beams

subjected to sustained load and freeze-thaw cycling exposure (set BS-FS) in which a

maximum uncertainty of 12.2% is probable due to difference between material properties

in sets BS-FS and BS-F.

250

Table ‎4-18: Uncertainty in comparison of sets BS-FS and BS-F based on material

properties.

Set

Uncertainty (%)

Up to

yielding (Eq. 4-1)

Yielding up

to failure (Eq. 4-2)

At failure

CFRP rupture (Eq. 4-3)

Concrete crushing (Eq. 4-4)

BS-FS w.r.t. BS-F 4.6 9.5 9.5 12.2


The results of the beams tested in phase I and phase II (RC beams strengthened

with NSM CFRP strips) are presented in Figure ‎4-93 and Table ‎4-19. The beams were

categorized into two sets: set BS-F subjected to freeze-thaw cycling exposure and set BS-

FS subjected to combined sustained load and freeze-thaw cycling exposure. For set BS-F,

the load-deflection curves include the negative camber due to prestressing, initiation of

flexural cracks, yielding of tension steel rebar, CFRP rupture or concrete crushing which

causes a large drop in load at ultimate stage, and post failure behaviour. On the other

hand, for set BS-FS, the load deflection curves comprise the negative camber due to

prestressing, yielding of the tension steel rebar, concrete crushing or NSM CFRP

debonding, and post failure.

An upward camber ranging between 0.49-1.71 mm for beams from set BS-F and

between 0.34-1.71 mm for beams from set BS-FS were recorded one week after

prestressing. The values of the initial and effective pre-strain in the CFRP strip, computed

by taking the average of the strain values at the constant moment region of the beams, are

presented in Table ‎4-19 showing an average prestressing loss of 2.52±0.37% one week

after prestressing. The beams in set BS-F were cracked after strengthening; the obtained

251

cracking loads show significant increase due to prestressing (up to 153% for set BS-F)

with respect to the non-prestressed strengthened beam of each set. The un-strengthened

control beams showed a low cracking load which is due to the presence of the micro-

cracks in the large-scale beams before testing, mainly caused from moving the beams

during the testing process. After this stage, the freeze-thaw exposure started on both sets.

Set BS-F was placed in the environmental chamber under 500 freeze-thaw cycles, and set

BS-FS was placed in the chamber under 500 freeze-thaw cycles while each beam was

subjected to a sustained load of 62 kN, equal to 47% of the theoretical ultimate load of

the non-prestressed NSM CFRP strengthened RC beam (BS-NP-F in Table ‎3-3). Then

both sets were removed and tested under four-point static monotonic loading.

252

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)




: CFRP rupture : Concrete crushingO : Concrete crushing and NSM CFRP debonding, simultaneouslyF : Freeze-thaw exposed beams

FS: Freeze-thaw and sustained load exposed beams

Figure ‎4-93: Comparison between exposed beams tested in phase I and II (freeze-thaw exposure versus combined sustained

load and freeze-thaw exposure).

252

253

Table ‎4-19: Summary of the test results for strengthened beam using CFRP strips (phases I & II). S

et

Beam ID ɛp

(µɛ)

ɛpe

(µɛ)

Δoe

(mm)

Pcr

(kN)

Δcr

(mm)

Δop

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm)

ɛfrp@u

(µɛ) μD

Φ

(kN. mm)

Failure

Mode

BS

-FS

, su

bje

cted

to

co

mb

ined

free

ze-t

haw

and

su

stai

ned

lo

ad

B0-FS N.A. N.A. N.A. N.A. N.A. 15.6 62.3 13.26 77.9 80.86 N.A. 6.10 5462.9 CC

BS-NP-FS 0 0 0.00 N.A. N.A. 13.7 74.4 15.47 98.3 57.59 7510 3.72 4496.6 CC

BS-P1-FS 3644 3550 -0.34 N.A. N.A. 11.5 83.8 17.52 96.8 35.13 6713 2.01 2534.5 CC

BS-P2-FS 6907 6726 -1.07 N.A. N.A. 10.1 90.5 20.60 91.4 21.95 8367 1.07 1343.8 CC-DB

BS-P3-FS 10290 10082 -1.71 N.A. N.A. 8 101.5 19.41 106.7 36.74 12073 1.89 3174.6 DB-CC

BS

-F,

sub

ject

ed t

o

free

ze-t

haw

B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 N.A. 7.61 7052†

CC

BS-NP-F 0 0 0 14 1.36 0.61 92.4 22.53 132.2 104.26 14900 4.63 10649 CC

BS-P1-F 3574 3463 -0.49 21.6 1.43 0.13 104.1 23.99 134.7 82.9 16592 3.46 8667 CC

BS-P2-F 6900 6723 -1.09 27.3 1.24 -0.81 114.8 25.56 149.5 87.85 21464 3.44 10214 FR

BS-P3-F 10112 9884 -1.70 35.5 1.45 -1.43 124.3 25.91 141.7 58.55 21118 2.26 6510 FR

ɛp = initial prestrain due to prestressing, ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing,

Pcr and Δcr = load and deflection at cracking Δop = camber after exposure for set BS-FS and after initial loading (cracking) for set BS-F

Py and Δy = load and deflection at yielding ɛfrp@u = CFRP strain at failure at mid-span

Pu and Δu = load and deflection at ultimate μD = ductility index = Δu /Δy

CC and FR= concrete crushing and CFRP rupture Φ = energy absorption (area under P-Δ curve)

CC-DB= concrete crushing followed by the NSM CFRP debonding, almost simultaneously

DB-CC= failure initiated by the NSM CFRP debonding and concrete crushing almost simultaneously, and then followed by the concrete crushing † calculated based on concrete strain 0.004125 to be consistent with the other beams failed by concrete crushing

253

254

Comparison between yield loads shows the average decreases of 19.2±1.4% and

26.4±4.6% in the load and the deflection at yielding of the beams in set BS-FS with

respect to the corresponding beams in set BS-F, respectively. Besides, an average

decrease of 27.5±7% was observed in ultimate load of the beams in set BS-FS in

comparison to set BS-F. Furthermore, the deflection at ultimate for the beams in set BS-

FS shows an average decrease of 51.6±15% in comparison with beams BS-F.

Five exposed beams in set BS-F showed a typical failure mode, i.e., tension steel

reinforcements yielding followed by CFRP rupture or concrete crushing while the

exposed beams in set BS-FS failed at early stage after yielding due to concrete crushing;

concrete crushing followed by the NSM CFRP debonding, almost simultaneously; or an

initial NSM CFRP debonding and concrete crushing, almost simultaneously, followed by

the concrete crushing. The failure modes of the beams are marked in Figure ‎4-93.

Comparing the load-deflection curves of set BS-FS and BS-F reveals that in set BS-FS

the concrete materials were significantly affected and the beams were damaged more than

that in set BS-F. This damage caused an early concrete crushing failure and in some cases

NSM CFRP debonding shortly after the concrete crushing as the secondary failure.

The energy absorptions (Φ) of the beams defined as the area under the load-

deflection curve up to the peak load are presented in Figure ‎4-94 showing two sets of

beams. It is clear in Figure ‎4-94 that the beams tested in phase II (set BS-FS) showed a

significant reduction in energy absorption in comparison with the other set (phase I: BS-

F). An average of 63.9±14.9% decrease in energy absorption was observed for set BS-FS

in comparison with set BS-F. Besides, the results presented in Table 4-19 shows an

255

average decrease of 33.3±22.4% in ductility indices of the set BS-FS in comparison with

set BS-F.

0

2000

4000

6000

8000

10000

12000

14000

0 0.002 0.004 0.006 0.008 0.01

En

erg

y a

bso

rpti

on

(a

rea u

nd

er

load

-d

efl

ecti

on

cu

rve)

kN

.mm

Prestrain in CFRP strips

Energy absorption (BS-F set) Energy absorption (BS-FS set)

Figure ‎4-94: Effects of exposure on the energy absorption of the prestressed NSM

CFRP strengthened RC beams.

The overall comparison of the beams tested in this research reveals that the beams

strengthened with the prestressed NSM-CFRP strips subjected to combined severe

environmental exposure and sustained loading, tested to failure in flexure under static

monotonic loading, do not perform well especially after yielding of tension steel

reinforcements. In particular, the NSM-CFRP debonding at end regions of the prestressed

strengthened beams and low ductility and energy absorption resulted from the severe

256

damage to the concrete material are the issues that should be considered in long-term

performance of the prestressed NSM CFRP strengthened RC beams under freeze-thaw

exposure and sustained loading.

4.9 Prestress Losses in Phases I & II

Results of twelve RC beams strengthened with prestressed NSM CFRP strips and

rebars were considered to perform a comprehensive study on the prestress losses. The

beams were classified in three groups; Group A: four beams strengthened with CFRP

rebar subjected to freeze-thaw cycling exposure, Group B: four beams strengthened with

CFRP strips similar to Group A (in terms of prestressing level, CFRP axial stiffness, and

geometry) and subjected to freeze-thaw cycling exposure, and Group C: four beams

similar to Group B kept at room temperature. Strain loss is a reduction in the initial

prestrain in the NSM CFRP rebar or strips that can be categorized into two types,

instantaneous losses and long-term losses. Instantaneous losses occur quickly after

jacking (upon release of the jack and transfer of the prestress in the CFRP reinforcements

to the anchors) including seating losses (anchorage slip due to removing the temporary

brackets) and elastic shortening of concrete which are presented in Figure ‎4-95 to Figure

‎4-98 up to 168 hrs (7 days) after prestressing (obtained from beams in Group A and

Group B). In these figures, the losses are plotted for the beams strengthened with CFRP

strip and rebar at mid-span location.

Time-dependent prestressing losses including creep and shrinkage of the concrete

and CFRP relaxation occur gradually over the life-time of the beam strengthened with

prestressed NSM CFRP reinforcements. The long-term losses of the unexposed beams

257

(obtained from beams in Group C) are presented in Figure ‎4-98 up to five months; the

reason that these losses are calculated for five months is that the beams in Group C were

only kept five months after fabrication at room temperature prior to placing in the

chamber, waiting for phase I of the experimental program and also sustained loading

setup of phase II to be accomplished in the chamber. In addition, the long-term losses of

the exposed beams (obtained from beams in Group A and B under freeze-thaw cycling

exposure) are presented in Figure ‎4-99 to Figure ‎4-105 up to 74 days during exposure

(since the instrumentation were damaged under freeze-thaw cycling exposure after this

period). A 2%-6.2% strain loss is observed after 7 days with an average loss of 2.7±0.9%

for beams strengthened with NSM CFRP strips (Group B), 3.9±2.1% for beams

strengthened with NSM CFRP rebars (Group A) and 3.3±1.6% for all beams (Group A

plus Group B). Analyzing Figure ‎4-95 to Figure ‎4-97 reveals that significant amount of

the 7-day losses (60%-85%) occurs during the 24 hrs after prestressing. In this context,

82.2±4.1% of the 7-day losses of the beams strengthened with NSM-CFRP strips,

70.7±9.6% of the 7-day losses of the beams strengthened with NSM-CFRP rebars, and

76.4±9.1% of the 7-day losses of all beams occurs during the 24 hrs after prestressing.

The strain loss values are 133 µɛ, 172 µɛ, 200 µɛ, 208 µɛ, 126 µɛ, and 375 µɛ for beams

BS-P1-F, BS-P2-F, BS-P3-F, BR-P1-F, BR-P2-F, and BR-P3-F, respectively;

corresponding to the percentages of loss of 3.8%, 2.5%, 2%, 6.2%, 1.9%, and 3.6% for

beams BS-P1-F, BS-P2-F, BS-P3-F, BR-P1-F, BR-P2-F, and BR-P3-F, respectively. In

fact, by increasing the prestressing level in the NSM CFRP strip or rebar, the value of

instantaneous strain loss increases while the percentage of instantaneous loss decreases.

258

0

1

2

3

4

5

6

7

0.003

0.0031

0.0032

0.0033

0.0034

0.0035

0.0036

0 24 48 72 96 120 144 168

Pe

rce

nta

ge

of lo

ss

Pre

str

ain

in

CF

RP

Time (hr)

BS-P1-F

BR-P1-F

BS-P1-F (% of loss)

BR-P1-F (% of loss)

Figure ‎4-95: Losses in prestressed NSM CFRP strip or rebar: BS-P1-F and BR-P1-F.

0

0.5

1

1.5

2

2.5

3

0.0064

0.0065

0.0066

0.0067

0.0068

0.0069

0.007

0 24 48 72 96 120 144 168

Perc

en

tag

e o

f lo

ss

Pre

str

ain

in

CF

RP

Time (hr)

BS-P2-F

BR-P2-F

BS-P2-F (% of loss)

BR-P2-F (% of loss)


259

0

0.5

1

1.5

2

2.5

3

3.5

4

0.0099

0.01

0.0101

0.0102

0.0103

0.0104

0.0105

0.0106

0 24 48 72 96 120 144 168

Perc

en

tag

e o

f lo

ss

Pre

str

ain

in

CF

RP

Time (hr)

BS-P3-F

BR-P3-F

BS-P3-F (% of loss)

BR-P3-F (% of loss)


-140

-120

-100

-80

-60

-40

-20

0

0 30 60 90 120 150

Pre

str

ain

lo

ss in

CF

RP

str

ips (

µɛ)

Time (day)

BS-NP

BS-P1

BS-P2

BS-P3

Figure ‎4-98: Losses in NSM CFRP strip (BS sets) at room temperature.

260

The long-term strain losses in the CFRP strips (at room temperature) up to 150

days after 7 days of initial recording are presented in Figure ‎4-98 for four beams (Group

C). The losses are mainly due to creep and shrinkage of the concrete and CFRP

relaxation. The prestressed strengthened beams showed higher strain losses than strain

changes in non-prestressed strengthened beam, BS-NP. The creep and shrinkage effects

exist and are active for all beams; therefore, the difference between strengthened and un-

strengthened strain losses is mainly due to relaxation of CFRP reinforcement, which is a

relatively small component of the total long-term losses. The maximum strain loss is 123

µɛ for the prestressed beams while it is 96µɛ for the non-prestressed beam after 150 days.

The difference which is 27 µɛ is likely related to relaxation of the CFRP strips.

Therefore, considering a maximum long term loss of 123µɛ, the total strain loss values

(instantaneous plus long-term for five months) are 256 µɛ (7.2%), 295 µɛ (4.3%), 323 µɛ

(3.2%), 331 µɛ (8.7%), 249 µɛ (3.8%), and 498 µɛ (4.8%) for beams BS-P1-F, BS-P2-F,

BS-P3-F, BR-P1-F, BR-P2-F, and BR-P3-F, respectively.

The changes in strain for RC beams strengthened with NSM CRRP strips and

rebars under freeze-thaw cycling exposure are presented in Figure ‎4-99 to Figure ‎4-105.

Due to damage that occurred in instrumentation (strain gauge), the strain fluctuation

graph is not provided for beam BR-P3-F, and also, the results of the other beams are

provided for 74 days. A maximum fluctuation of 220 µɛ is reached due to changes in

temperature from +34oC to -34

oC. The linear average of changes versus time as presented

on the graphs in Figure ‎4-99 to Figure ‎4-105 are insignificant for 74 days; maximum

average values of 37 µɛ as gain (the increase in CFRP strain) and 19.6 µɛ as loss for the

beams strengthened with CFRP strips, and 52 µɛ as gain and 39 µɛ as loss for the beams

261

strengthened with CFRP rebars are monitored after 74 days. On the other hand, the

average of changes in the CFRP strain over the time (linear equations in Figure ‎4-99 to

Figure ‎4-105) increases (called as gain) in some cases while this behaviour does not

occur at room temperature, as shown in Figure ‎4-98. Based on the applied freeze-thaw

cycles in this study and estimated corresponding years in real life (at least 12.8 years for

500 cycles), maximum strain changes of -536 µɛ (loss) and 710 µɛ (gain) are predicted

over 50 years. In this context, the value of loss is more important which should be

considered in design of the prestressed NSM CFRP strengthened RC beams. In fact, by

combining the instantaneous and long-term prestressing losses of the member under

freeze-thaw exposure, there is a possibility that an 8.5-22.8% loss depending on the

induced prestressing level occurs in the CFRP reinforcement during 50 years life-time of

the member strengthened with prestressed NSM CFRP reinforcements.

262

y = -0.0878x

-150

-100

-50

0

50

100

150

0 15 30 45 60 75

Str

ain

flu

ctu

ati

on

in

CF

RP

str

ips

(µɛ)

Time (day)

BS-NP-F

Linear (BS-NP-F)

Figure ‎4-99: CFRP Strain fluctuation in beam BS-NP-F under freeze-thaw exposure.

y = 0.5x

-150

-100

-50

0

50

100

150

0 15 30 45 60 75

Str

ain

flu

ctu

ati

on

in

CF

RP

str

ips

(µɛ)

Time (day)

BS-P1-F

Linear (BS-P1-F)

Figure ‎4-100: CFRP Strain fluctuation in beam BS-P1-F under freeze-thaw exposure.

263

y = 0.127x

-150

-100

-50

0

50

100

150

0 15 30 45 60 75

Str

ain

flu

ctu

ati

on

in

CF

RP

str

ips

(µɛ)

Time (day)

BS-P2-F

Linear (BS-P2-F)


y = -0.265x

-150

-100

-50

0

50

100

150

0 15 30 45 60 75

Str

ain

flu

ctu

ati

on

in

CF

RP

str

ips

(µɛ)

Time (day)

BS-P3-F

Linear (BS-P3-F)


264

y = 0.2405x

-150

-100

-50

0

50

100

150

0 15 30 45 60 75

Str

ain

flu

ctu

ati

on

in

CF

RP

re

ba

r (µɛ)

Time (day)

BR-NP-F

Linear (BR-NP-F)

Figure ‎4-103: CFRP Strain fluctuation in beam BR-NP-F under freeze-thaw exposure.

y = -0.5272x

-150

-100

-50

0

50

100

150

0 15 30 45 60 75

Str

ain

flu

ctu

ati

on

in

CF

RP

re

ba

r (µɛ)

Time (day)

BR-P1-F

Linear (BR-P1-F)

Figure ‎4-104: CFRP Strain fluctuation in beam BR-P1-F under freeze-thaw exposure.

265

y = 0.6984x

-150

-100

-50

0

50

100

150

0 15 30 45 60 75

Str

ain

flu

ctu

ati

on

in

CF

RP

re

ba

r (µɛ)

Time (day)

BR-P2-F

Linear (BR-P2-F)

Figure ‎4-105: CFRP Strain fluctuation in beam BR-P2-F under freeze-thaw exposure.

4.10 Modification of Temporary and Fixed Brackets of the Anchorage System for

Prestressing

The prestressing and anchorage system used in this research was first developed

by Gaafar (2007). The system is presented in Figure ‎4-106 showing the fixed and

movable brackets that are temporarily used for prestressing the NSM CFRP strips or

rebar. The brackets are connected by threaded rods used for maintaining the prestressing

force after releasing the hydraulic jacks. For prestressing the NSM CFRP in phases I and

II of this research, the steel brackets developed by Gaafar (2007) were modified, as

shown in Figure ‎4-107, by welding steel plates to the sides of the fixed bracket and to the

top of the movable bracket, and by drilling more holes to improve the system and avoid

rotation of the brackets at jacking stage.

266

Figure ‎4-106: Prestressing system developed by Gaafar (2007).

Figure ‎4-107: Steel brackets used for prestressing NSM CFRP in phases I and II.

In spite of all efforts performed on the modification of the brackets, although the

performance of the system improved, but still the cracks formed at the location of the

fixed bracket at high prestress levels (above about 40% of the CFRP ultimate strength).

These types of cracks are shown in Figure ‎4-108, and similar issues were reported by

Gaafar (2007) and Oudah (2011). The aim of this short section is to modify the

Temporary brackets

267

prestressing system to avoid these types of cracks and investigate the possible cracking

patterns at very high prestress levels (up to 75% of the CFRP ultimate strength).

Figure ‎4-108: Cracks at the locations of steel brackets at high prestress level.

A schematic of the interaction between the temporary steel brackets and beam is

presented in Figure ‎4-109 that shows the applied forces on the bolts. The forces applied

to the fixed bracket transferred to the beam through the bolts. The applied prestressing

force by the jack produce a moment due to eccentricity with respect to the centre of the

Cracks at location

of fixed bracket

Crack at location

of fixed bracket

Cracks at location

of fixed bracket

268

bolt group (cg). Therefore, the bolts at the fixed brackets need to resist the jacking force

(prestressing force) and the moment due to eccentricity. This combination applies a

downward shear force on the corner bolts at the left side of the fixed bracket as shown in

Figure ‎4-109, that is the main reason for the observed cracks as shown in Figure ‎4-108.

Figure ‎4-109: Interaction between temporary steel brackets and beam.

Two types of cracks were observed at the locations of the bolts: cracks due to

crushing of concrete on a small area around the bolts and tension cracks that extended to

the bottom face of the beams. To avoid these types of cracking, one solution is to increase

the number of the bolts so that the applied shear force on each bolt decreases; In this

regard, to avoid possible crushing around the bolts, the compression stress applied to the

concrete through the bolts should be less than the stress at which the concrete material

starts to crack at compression (about 0.7f′c). The second solution (the most economical

one) is to reduce the force applied to the bolts by reducing the eccentricity of the applied

269

prestressing load with cg of the bolts. To search the feasibility of the second solution,

three concrete specimens (1500×200×400 mm) were made and the fixed and movable

brackets were modified to be capable of changing the eccentricity (location of the jacks)

during the prestressing.

4.10.1 Modified Prestressing System and Material Properties

The modified prestressing system applied to the specimens and its components

are presented in Figure ‎4-110. The temporary steel brackets were modified by welding

steel plates to the sides to be capable of changing the location of the jacks. The three

fabricated concrete specimens had identical cross-section (200×400 mm) to the RC

beams tested in phases I and II except that they were shorter in length, having a length of

1500 mm. The concrete specimens had pre-formed grooves. A dywidag steel bar with

two adjustable nuts at the ends was used instead of the CFRP reinforcements to facilitate

the execution of the experiment. The end anchors were made to have enough bolts to

carry the applied load up to ultimate capacity of the dywidag bar. The material properties

of the specimens are presented in the following sections.

270

(a) Modified prestressing system with jacks placed at maximum eccentricity

(b) Modified prestressing system with jacks placed at low eccentricity

Figure ‎4-110: Modified prestressing system applied to the specimens.

Movable bracket Fixed bracket

Fixed end anchor

Dywidag bar Nut Nut Jacking end anchor Hydraulic jacks

(c) Side view

Holes for placing the jacks

at different eccentricities

Load cells

270

271

4.10.1.1 Concrete

The test specimens were cast from one concrete batch with a 28 days concrete

compressive strength of 45.24.4 MPa, and a concrete compressive and tensile strengths

of 43.45 MPa and 3.280.16 MPa at the time of testing (ten months after casting)

obtained from concrete cylinders. Furthermore, results of the Schmidt hammer tests show

the concrete compressive strength of the 41 MPa, 42 MPa, and 37.5 MPa for specimens

SP-1, SP-2, and SP-3, respectively, at the time of testing.


The properties of the tension and compression steel reinforcements (3-15M and 2-

10M), and stirrups (7-10M) were the same as the steel reinforcements presented in

Section 4.7.1.1.

4.10.1.3 Dywidag Thread-Bar and Nuts

The used dywidag thread-bar (Ø19) had a cross-sectional area, a yield load, an

ultimate load, and a modulus of elasticity of 284 mm2, 147 kN, 196 kN, and 205 GPa,

respectively, having corresponding nuts that can carry the ultimate load of the dywidag

bar (DSI, 2013).

4.10.1.4 Steel Bolts

Carbon Steel Kwik Bolt 3 Expansion Anchor was used to connect the end anchor

to the substrate concrete. Properties of these bolts are presented in Section 3.3.3.5.

272

4.10.2 Testing Procedure

The test was performed on each specimen by doing three steps and the occurrence

of the cracks was checked during each step; step I: placing the jacks at low eccentricity (e

= 110 mm) and prestressing to a load equivalent to 75% of the CFRP tensile strength;

step II: placing the jacks at medium eccentricity (e = 180 mm) and prestressing to load

equivalent to 75% of the CFRP tensile strength; and step III: placing the jacks at high

eccentricity (e = 215 mm) and prestressing to a load equivalent to 75% of the CFRP

tensile strength. The applied steps including low, medium, and high eccentricity values

are presented in Figure ‎4-111. The values of the applied load by hydraulic jacks and the

corresponding prestressing load in the dywidag bar at each step were checked by reading

the load values from load cells and strain values obtained from two strain gauges installed

on the dywidag bar, respectively.

273

(a) Low eccentricity

(b) Medium eccentricity

(c) High eccentricity

Figure ‎4-111: Applied test steps: low, medium, and high eccentricities.

4.10.3 Results and Discussion

The results of the test are presented in Table ‎4-20 including the test steps, the

prestress level (load in the dywidag bar), the applied load by the hydraulic jacks, prestress

loss due to friction of the system, and the prestress level corresponding to the initiation of

the cracks at location of the brackets and end anchor. Also, the photos of the specimens

after three steps of each test are shown in Figure ‎4-112.

Eccentricity to cg bolts=110 mm



274

Table ‎4-20: Modification of the prestressing system test results. S

pec

imen

ID Test

step

Eccentricity

[from jack

level to cg of

bolts at fixed

bracket (mm)]

Prestress level (%)

[Load in dywidag

bar (kN)]

Applied

load by

jacks

(kN)

Prestress loss

due to friction

of the system

(%)

Occurrence of cracks at brackets

[prestress level corresponding to

initiation of cracks (%)]

Prestress level (%)

corresponding to initiation

of cracks at end anchor

Other type of

cracks

SP

-1

I Low

[110]

75.4

[123.4] 174.9 29.4 ― 27 (minor cracks)

Very minor

crushing

around the

bolts at fixed

and movable

brackets

II Medium

[180]

75.8

[124] 160.0 22.5 ―

No extension of previous

crack

III High

[215]

75.8

[124] 160.0 22.5 Fixed bracket [74.1]

No extension of previous

crack

SP

-2

I Low

[110]

74.5

[122] 175.4 30.5 ― 28.5 (minor cracks)

Very minor

crushing

around the

bolts at fixed

and movable

brackets

II Medium

[180]

74.7

[122.3] 143.8 14.9 Fixed bracket [74.3]

Minor extension of previous

crack

III High

[215]

75.8

[124.2] 174.7 28.9

Extension at fixed bracket [67.6]

Movable bracket [74.7]

Minor extension of previous

crack

SP

-3

I Low

[110]

70.0

[114.7] 171.2 33.0 ―

21.3 (minor cracks)

74.7 (start of block rupture) Very minor

crushing

around the

bolts at fixed

and movable

brackets

II Medium

[180]

76.7

[125.7] 181.9 30.9 ―

76.4 (extension of the block

rupture cracks)

III High

[215]

82.4

[134.9] 168.2 19.8

Fixed bracket [78.2]

Movable bracket [81.8]

81.8 (extension of the block

rupture cracks)

274

275

(a) SP-1

(b) SP-2

(c) SP-3

Figure ‎4-112: Damage done to the specimens after three steps of test.

276

The results, presented in Table ‎4-20, show that at low eccentricity (110 mm from

the jack level to cg of bolts) no cracks occurred at the location of the brackets while the

cracks were observed for medium and high eccentricity cases. The minor cracks at end

anchor locations were observed at prestress levels ranging from 21.3% to 28.5%. These

minor cracks can be avoided by increasing the bolt spacing at end anchor location and

providing longer edge distance for the bolts. Specimens SP-1 and SP-2 showed no

significant issues at the end anchor location as can be seen in Figure ‎4-112a and Figure ‎4-

93b. Specimen SP-3 experienced cracks due to concrete block rupture around the end

anchor, during step I of the test at prestress level of 74.7%, these cracks propagated

further in steps II and III, as can be seen in Figure ‎4-112c. In addition, a very minor

surface crushing around the bolts at the locations of the brackets was observed. The tests

show an average of 26% difference between the applied load by the jacks and the

prestress load in the dywidag bar determined from the strain gauges; this difference is due

to the friction of the system caused by the movable bracket and corresponding bolts.

As can be seen in the results, the cracks at the location of the fixed bracket

occurred at very high prestress level (a load equivalent to 74% of the CFRP tensile

strength) while they ocurred in lower prestress level (about 40-48% of the CFRP tensile

strength) for the beams in phases I and II of the experimental program. The difference

might be due to the accumulation of the following reasons. The specimens were

prestressed upside down while the beams in phases I and II were prestressed as in field

condition; therefore, the self-weight of the specimen (although it is small) produces a

compression at top (location of the brackets) that delay the occurrence of the cracks while

the self-weight of the beam results a tension stress at the location of the brackets that

277

expedites the occurrence of the cracks. The specimens are in small scale and the

prestressing length is shorter than the one for the long beams (5 m span), therefore, the

disturbed area (stress concentration) from the end anchors in the specimen applies more

compression to the location of the brackets that delays the occurrence of the cracks in

specimens. Also, the specimens and the beams had different concrete compressive

strengths (the specimens had slightly higher concrete compressive strength by 6%). The

concrete compressive strengths of the concrete cylinders, representing the beams, at the

time of strengthening are presented in Table C-1 for more details.

In general, the results confirm that the modified prestressing system performs

properly and the occurrence of the cracks during the prestressing at the location of the

fixed bracket is avoided by selecting a low value of eccentricity.

4.11 Summary

In this chapter, the experimental test results of fourteen RC beams strengthened

using prestressed and non-prestressed NSM CFRP strips and rebars including two control

un-strengthened RC beams were presented. The test variables comprise freeze-thaw

cycling exposure, sustained loading, prestressing level, and CFRP geometry. Nine beams

were tested in phase I and the results were analyzed. The beneficial and optimum

prestressing levels were defined and calculated for the tested beams. Then, the static

performance of the beams was compared with results of similar beams without any

environmental exposure tested by Gaafar (2007). A general comparison was performed

between the beams in order to evaluate the effect of freeze-thaw exposure, prestressing,

and CFRP geometry (strips versus rebar). Afterward, ductility of the tested beams was

278

examined and appropriate deformability models and corresponding limits were proposed

for FRP strengthened RC beams. Then, results of the five beams tested in phase II were

discussed in detail followed by a general comparison with similar beams in phase I to

investigate the effects of applied freeze-thaw cycles and sustained load in phase II. Then,

the instantaneous and long-term prestress losses in the NSM CFRP were evaluated under

exposure and also at room temperature. At the end, the prestressing system used in phases

I and II was modified to avoid cracking in the concrete at the location of the temporary

brackets during prestressing.

In the next chapter, a comprehensive study was conducted on the numerical

(using finite element method) and analytical simulations of the prestressed NSM CFRP

strengthened RC beams.

279

Chapter Five: Numerical and Analytical Simulations

5.1 Introduction

Comprehensive Finite Element (FE) and analytical simulations of the prestressed

Near-Surface Mounted Carbon Fibre Reinforced Polymer (NSM-CFRP) strengthened

Reinforced Concrete (RC) beams were performed and are presented in this chapter.

Firstly, the unexposed RC beams strengthened using prestressed NSM-CFRP strips are

modeled by developing a nonlinear 3D FE model considering debonding and prestressing

aspects. Then, a parametric study considering the effects of concrete, steel reinforcement,

and prestressing level is performed to present a better understanding of the effects of

these parameters and to cover the gaps in this field. Afterward, the behaviour of the steel

anchor employed to prestress the NSM-CFRP reinforcement is investigated by

conducting a parametric study considering the effects of anchor’s dimensions and bond

characteristics on the performance of the anchorage system. Then, the load-deflection

responses of the exposed RC beams strengthened with prestressed NSM-CFRP strips and

rebars subjected to freeze-thaw exposure are predicted by developing an analytical

model. Finally, a 3D FE model is developed to simulate the behaviour of the exposed RC

beams strengthened with prestressed NSM-CFRP strips subjected to combined freeze-

thaw exposure and sustained load, and the predicted results are compared to experimental

ones.

The results presented in this chapter were published in refereed journal paper

(Omran and El-Hacha, 2012b) and refereed conference papers (Omran and El-Hacha,

2010b and c, 2012e, and 2013a).

280

5.2 Finite Element Modeling of RC Beams Strengthened with Prestressed NSM-FRP

Although many researchers simulated the behaviour of Externally Bonded (EB)

strengthened RC flexural members using 2D/3D FE models considering perfect bond

between interfaces (concrete-epoxy and epoxy-FRP) due to the fact that debonding

failure was not observed in relevant tests (Kachlakev et al. 2001; Chansawat, 2003; Jia,

2003; Supaviriyakit, 2004; Chansawat et al., 2006; Rafi et al, 2007; Camata et al. 2007;

Nour et al., 2007), however, FE modeling of NSM FRP strengthened RC beams is rarely

carried out (Kang et al., 2005; Soliman et al., 2010). Based on an extensive literature

review performed in Chapter Two, the FE modeling of prestressed-NSM-FRP

strengthened RC beams has never been investigated by taking into account the debonding

effects. Therefore, a 3D FE model is developed to simulate the behaviour of RC beams

strengthened with prestressed-NSM-CFRP strips. The FE model is compared and

validated with experimental test results reported by Gaafar (2007). The model considers

the debonding at the concrete-epoxy interface by assigning fracture energies including a

bilinear shear stress-slip model and a bilinear normal tension stress-gap model.

Furthermore, the prestressing is applied to the CFRP strip elements using the equivalent

temperature method. The predicted results and experimental ones are compared in terms

of load-deflection curve, strain profile, failure mode, energy absorption, and bond

performance.

5.2.1 Experimental Program Overview and Material Properties

Five unexposed RC beams were tested by Gaafar (2007): one un-strengthened

control beam, and four beams strengthened with prestressed NSM CFRP strips. Details of

281

the strengthened beams are presented in Figure ‎5-1.

(a) Geometry of the beams tested by Gaafar (2007).

(b) Cross-section of the beams and end-anchor.

Figure ‎5-1: Details of the modeled beams.

Each beam was strengthened using two 2×16 mm CFRP strips glued together on

their sides and embedded in one groove pre-cut in the concrete cover on the tensile face

of the beams. The beams were, 5150 mm long, simply supported with rectangular cross

section of 200×400 mm. Various prestressing levels of 0%, 17%, 29.3%, and 51% of the

282

ultimate tensile strain of the CFRP strips were applied (corresponding to prestrain of 0,

0.0034, 0.0058, and 0.0102 in CFRP strips, respectively). The beams were not subjected

to environmental exposure and were tested under monotonic static loading in four-point

bending configuration.


The stress-strain curves of the tension and compression steel bars (3-15M and 2-

10M) determined from the uni-axial tension tests are depicted in Figure ‎5 2 (Gaafar,

2007). The compression and tension steel reinforcements had the yield strengths of 500

MPa and 475 MPa, respectively, having a modulus of elasticity of 200 GPa.

0

100

200

300

400

500

600

700

0 0.02 0.04 0.06 0.08 0.1 0.12

Str

es

s (M

Pa

)

Strain (mm/mm)

10M Steel Bar

15M Steel Bar

Figure ‎5-2: Stress-strain curves of steel bars.

283

5.2.1.2 Concrete

The concrete material possessed a maximum compressive strength of 40 MPa, a

strain at ultimate strength of 0.002233, and a modulus of elasticity of 27.84 GPa, which

are the average values obtained from the compression tests of concrete cylinders (Gaafar,

2007). Modeling of the concrete stress-strain behaviour is described in Section 5.2.3.1.

5.2.1.3 CFRP Strips

The CFRP strip was type Aslan 500 produced by Hughes Brothers with a tensile

strength of 2610 MPa, an ultimate strain of 0.02, and a modulus of elasticity of 130.5

GPa determined from the tension test (Gaafar, 2007) with a linear-elastic behaviour up to

failure.


Two types of epoxy adhesives were used for NSM strengthening: Sikadur®

330

with a modulus of elasticity of 4.5 GPa and an ultimate tensile strength of 30 MPa (Sika,

2010a) used to connect the CFRP strip into the end steel anchors, and Sikadur®

30 with a

modulus of elasticity of 4.5 GPa and ultimate tensile strength of 24.8 MPa (Sika, 2010b)

used to fill in the groove in concrete.


The anchor bolts, used to connect the end anchor to the substrate concrete, were

type Carbon steel Kwik Bolt 3 Expansion Anchor with nominal bolt diameter of 15.9 mm

and shear strength of 54.4 kN (Hilti, 2008).

284

5.2.2 Description of Finite Element Model

The developed FE model is 3D in which all constitutive materials including

concrete, CFRP strips, internal steel reinforcements, epoxy adhesive, bolts, and end

anchor were simulated using appropriate elements available in the ANSYS program

library (SAS, 2009). As shown in Figure ‎5-3, only one quarter of the beam was modeled

due to the symmetry in geometry and loading conditions, to reduce the computer

computational time, modeling time and volume of the output. Out of two existing mesh

generation techniques: solid modeling and direct generation, the FE model was generated

based on the latter due to intricacy of the NSM strengthened RC beams. Although the

direct mesh generation technique is very time consuming for generating large-scale

model and the modeller needs to focus more on every detail of the mesh, but it has the

advantage of complete control over the geometry of every element and every node in the

complicated models.

Figure ‎5-3: Quarter of the beam to be modeled.

285

5.2.3 Modeling of Materials

5.2.3.1 Concrete

The concrete material was modeled using eight-node solid brick element

(Solid65). Geometry of a Solid65 element is depicted in Figure ‎5-4. This element,

considering a 2×2×2 set of Gaussian Integration points, has eight nodes with three

degrees of freedom at each node, translations in the nodal x, y, and z directions with

capability of plastic deformation, cracking in three orthogonal directions and crushing.

The crushing capability of Solid65 element is omitted in the FE analysis. This procedure

was executed by researchers in the FE models of RC beams (Kachlakev et al., 2001;

Chansawat, 2003; Jia, 2003; Wolanski, 2004; Chansawat et al., 2006). The reason is that,

the FE model prematurely fails when the crushing capability of the Solid65 element is

turned on. This behaviour occurs due to high stress concentration under the loading plate

that leads the crushing to start and develop within a small load and the local stiffness

sharply decreases, afterward, the solution diverges displaying a large displacement

warning. However, when the crushing capability of Solid65 is omitted, the secondary

tensile strain produced by the Poisson’s effect leads to cracking and finally failure of the

beam (Kachlakev et al., 2001). To properly model the concrete, the considered model for

concrete comprises linear and multi-linear elastic/isotropic material properties in addition

to the concrete model defined in ANSYS (Wolanski, 2004; Chansawat et al., 2006; Al-

Darzi, 2007; Özcan et al., 2009). The multi-linear isotropic or elastic material uses the

Von Mises failure criterion or actual stress-strain curve, respectively, along with the

Willam and Warnke model (Willam and Warnke, 1975) to define the failure of the

286

concrete. A Poisson’s ratio of 0.18 was assigned to the concrete material (Wight and

MacGregor, 2009).

Figure ‎5-4: Geometry of Solid65 element (SAS, 2009).

After choosing the concrete element for the FE model, the next step is assigning

the appropriate stress-strain curve. The actual concrete stress-strain curve, obtained from

experimental tests, has been rarely used in FE modeling, and most researchers employed

available analytical stress-strain curve models from the literature. The reason is the

difficulty in identifying the appropriate descending branch of the curve. The descending

branch of the concrete stress-strain curve in compression is affected by test conditions

including loading rate, type of testing machine, gauge length of the measured axial

deformation, etc. and existence of stirrups. To estimate the unconfined concrete

behaviour in compression, the available analytical models in the literature such as

Modified Hognestad (Hognestad, 1951), Thorenfeldt et al. (1987), Desayi and Krishnan

(1964), Todeschini (Todeschini et al., 1964), CEB-FIP model code (CEB-FIP, 1993), and

287

Loov (1991) almost result in similar ascending branch, but produce different strain at

ultimate and also different descending branch. Most of the researchers used Desayi and

Krishnan’s stress-strain curve in the FE models (Kachlakev et al., 2001; Jia, 2003;

Wolanski, 2004; Chansawat et al., 2006; Coronado and Lopez, 2006; Özcan et al., 2009).

On the other hand, the equations proposed by Thorenfeldt et al. (1987) and Loov (1991)

can be used to match an experimental concrete compressive stress-strain curve. The latter

is presented in Equation 5-1. Many researchers used the unconfined concrete stress-strain

curve while some did not even considered the descending branch in modeling the stress-

strain curve of concrete and used perfectly plastic behaviour after maximum concrete

compressive strength (Kachlakev et al., 2001; Jia, 2003). On the other hand, few

researchers considered the confined concrete stress-strain curve in FE modeling

(Chansawat, 2003, Chansawat et al., 2006). Concrete behaves confined due to lateral

support of the steel stirrups, and this happens when the stresses are approaching the uni-

axial strength in disturbed area of a beam. Confinement enhances the stress-strain

behaviour of the concrete at high strain locations (under the loading plate). In the

developed FE model, a confined concrete constitutive model was adopted based on the

experimental ancillary test results in order to perform an exact FE modeling. Most of the

available analytical models for concrete confined by rectangular ties are derived for the

members under axial compression loading and consider enhancement in both strength

and ductility (Chan, 1955; Roy and Sozen, 1965; Soliman and Yu, 1967; Sargin, 1971;

Vallenas et al., 1977; Sheikh and Uzameri, 1980; Park et al., 1982; Mander et al., 1988).

Kemp (1998) proposed a confined concrete model applicable for beams by enhancing

both strength and ductility based on parameters affecting ductility. Kent and Park (1971)

288

derived a confined concrete model which considers the enhancement in ductility due to

confinement by stirrups; Equation 5-2 proposed by these authors for ε50h, results in the

additional ductility due to rectangular stirrups at stress value of 0.5f′c. The Loov’s

equation (Equation 5-1) was used to define an unconfined concrete compressive stress-

strain curve based on two points (points 1 and 2 in Figure ‎5-5) which were obtained from

the experimental concrete stress-strain curve reported by Gaafar (2007).

n

o

c

o

c

o

c

cc

nB

nB

ff

1

11

1

11

Equation ‎5-1

where o = strain at maximum concrete compressive strength cf and c = strain at

concrete compressive stress cf . The two constants, n and B, in Equation 5-1 can be

calculated based on two points so that the analytical curve can match any experimental

concrete stress-strain curve. Therefore, the following values of n and B are reached for

the unconfined concrete using points 1 and 2 obtained from the experimental concrete

stress-strain curve.

123

120

MPa26and004202Point

MPa12and00043101Point

MPa40at0022330

.n

.B

f.:

f.:

f.

unconfined

unconfined

cc

cc

co

289

Figure ‎5-5: Concrete constitutive model in compression under flexural loading.

Then, point 3 on the confined curve in Figure ‎5-5 was calculated based on the

strain h50 at cf. 50 that gives additional ductility due to the stirrups given by Equation

5-2. The ratio of volume of one stirrup to volume of concrete core measured to outside of

the stirrup, ρs, is calculated using Equation 5-3. The strain c50 on the descending branch

of the confined concrete curve at cf. 50 is determined using Equation 5-4.

sh

shS

b

4

350 Equation ‎5-2

sh

shs

Sdb

Adb

2 Equation ‎5-3

huc 505050

Equation ‎5-4

290

where b = width of confined core measured to outside of the stirrup, shS = spacing of

stirrups, b= width of the stirrup (between centre lines of the bar) , d = depth of the

stirrup (between centre lines of the bar), shA = area of one leg of the stirrup, d = depth of

confined core measured to outside of the stirrup, and u50 = unconfined concrete strain on

the descending branch at cf. 50 .

For the tested beams, c50 is determined using Equation 5-2 to Equation 5-4 as

below:

0109230

005017050atcurveunconfined

for15EquationApplying

0059050

mm200

mm6154

0089560

50

50

50

.

.f.f

.

S

.b

.

c

ucc

h

sh

s

At the end, the Loov’s equation was applied considering points 3 and 1 to

calculate n and B for confined concrete and to define the descending branch of confined

curve up to stress 0.2f′c.

31

123



MPa400022330

.n

.B

f.:

f.:

fat.

confined

confined

cc

cc

co

291

The final relation for the stress-strain curve of the concrete is presented by

Equation 5-5. Comparison, performed by the author, showed that the stress-strain curve

defined by this method is similar to that defined by Desayi and Krishnan’s stress-strain

curve, and the advantage is that the proposed curve is derived based on the actual

material properties of the concrete reported by Gaafar (2007).

067346020

06734600022330692627613981

67552

00223307811551

4714

31

123

.f.

....

.f

...

.f

f

cc

c.cc

cc

c.cc

cc

c

Equation ‎5-5

The applied stress-strain curve of the concrete in tension is depicted in Figure ‎5-6

(SAS, 2009). The contribution of the concrete in the tension zone to the rigidity of the

beam is known as tension stiffening. Considering Figure ‎5-6, as the tensile stress meet the

concrete tensile strength, ft, and the crack forms, a tensile stress relaxation occurs. The

defined curve allows considering the strain-softening behaviour for cracked concrete.

Furthermore, it considers the effects of the reinforcement interaction with concrete to be

simulated in a simple manner. In a cracked reinforced concrete, the section between two

cracks is susceptible to carry the forces in the steel reinforcement at the crack. Although

after cracking, the stiffening effect of tension carried by concrete between cracks has much

less significance, and the cracked section properties can be used with little error, but

applying non-zero relaxation after cracking helps in convergence of the problem. For the

292

FE model, a bilinear stress-strain relation, predefined in ANSYS program, is employed to

model the tension stiffening as shown in Figure ‎5-6.

Figure ‎5-6: Concrete constitutive model in tension (Retrieved from SAS, 2009).


Steel reinforcements can be simulated in FE modeling of RC structures using

three methods: discrete model, embedded model, and smeared model as depicted in

Figure ‎5-7 (Tavarez, 2001). In the discrete model (Figure ‎5-7a), the steel reinforcement,

simulated using link, truss or beam elements, is connected to the concrete element nodes.

The main drawbacks of discrete model are that the concrete mesh configuration is

restricted by the location of the reinforcement and the volume of the steel reinforcement

is not deducted from the concrete volume.

293

(a) Discrete model

(b) Embedded model

(c) Smeared model

Figure ‎5-7: Different approaches for modeling of reinforcement (Tavarez, 2001).

294

In the embedded model (Figure ‎5-7b), the reinforcement is embedded into the

concrete which overcome mesh dependency restriction in the discrete model, therefore,

the stiffness is evaluated separately for the concrete material and steel reinforcements.

Displacements of the embedded elements are compatible with those of the surrounding

concrete elements; therefore, the concrete elements and their interaction points with

reinforcement are identified and employed to recognize the nodal location of the

reinforcement mesh. The embedded reinforcing method is beneficial when it is used with

higher order elements or where the reinforcement configuration in concrete member is

complex. A drawback of this approach is that the additional nodes, required for the

reinforcements, increase the degrees of freedom in the model and causes a longer

computer computational time in comparison with the discrete approach. In the smeared

model (Figure ‎5-7c), the reinforcement is uniformly distributed over the concrete

elements. In this approach, the properties of the material model in the element are formed

from individual properties of concrete and reinforcement using composite theory. The

smeared reinforcing method is beneficial for large structural models in which the

reinforcement does not affect the overall response of the model.

In the developed FE model, the discrete model (Figure ‎5-7a) of steel

reinforcement is employed. A two-node link element, Link8, was chosen to simulate the

steel reinforcements as shown in Figure ‎5-8. The Link8 is a 3D spar with three

translational degrees of freedom at each node in x, y, and z directions, and is capable of

plastic deformation. A multi-linear material model was assigned to the Link8 elements, as

presented in Figure ‎5-2, in addition to the related real constant (i.e. the area of cross-

section) assigned to each steel rebar.

295

Figure ‎5-8: Geometry of Link8 element (SAS, 2009).

5.2.3.3 CFRP Strips

Eight-node solid brick element, Solid45, was used to model the CFRP strips.

Geometry of a Solid45 element is depicted in Figure ‎5-9. Solid45 element considering a

2×2×2 set of Gaussian integration points, has eight nodes with three translational degrees

of freedom at each node in x, y, and z directions. This element is capable of assigning

multi-linear elastic material model. The multi-linear stress-strain curve of the CFRP strip

is presented in Figure ‎5-10. In the 3D FE model, to minimize mesh intricacy, a CFRP

strip with the dimension of 5×16 mm was modeled instead of 2-2×16 mm plus 1mm

epoxy in-between (as shown in Figure ‎5-1). Therefore, an equivalent modulus of

elasticity of 104.4 GPa (2×2×16×130.5/(5×16)=104.4 GPa), a tensile strength of 2088

MPa (104400×0.02=2088 MPa), and an ultimate strain of 0.02 were assigned to the

CFRP material in the FE model, to have an identical stress-strain curve with the one

shown in Figure ‎5-10. A Poisson’s ratio of 0.35 was assumed for CFRP (Kabir and

Hojatkashani, 2008).

296

Figure ‎5-9: Geometry of Solid45 element (SAS, 2009).

Figure ‎5-10: Strain-strain curve assigned to CFRP strip elements.


Two types of epoxy adhesive were used in the FE model. Sikadur® 330, with a

modulus of elasticity of 4.5 GPa and ultimate tensile strength of 30 MPa (Sika, 2010a),

was used to bond the CFRP strip to the steel anchor while Sikadur® 30, with a modulus

of elasticity of 4.5 GPa and ultimate tensile strength of 24.8 MPa (Sika, 2010b), was used

to fill in the groove and bond the CFRP strip to the concrete. Both types were modeled

297

using Solid45 elements. The multi-linear elastic material stress-stress curves assigned to

the epoxy adhesives are depicted in Figure ‎5-11 and Figure ‎5-12. A Poisson’s ratio of

0.37 is assumed for the epoxy adhesives (Kabir and Hojatkashani, 2008).

Figure ‎5-11: Strain-strain curve assigned to epoxy elements, Sikadur® 330.

Figure ‎5-12: Strain-strain curve assigned to epoxy elements, Sikadur® 30.

298

5.2.3.5 End Anchor and Loading and Supporting Steel Plates

The end anchor, loading and supporting plates were modeled using Solid45

elements. A linear elastic material is assigned to these elements with a modulus of

elasticity of 200 GPa and a Poisson’s ratio of 0.3.

5.2.3.6 Bolts at End Anchors

The two-node beam element, Beam4, was employed to model the steel bolts at the

end steel anchor. The geometry of a Beam4 element is presented in Figure ‎5-13. This

element has two nodes with three translational and three rotational degrees of freedom at

each node with capabilities of tension, compression, torsion and bending. The Beam4

element is capable to take into account the shear effects by assigning the shear deflection

constants (1.11 for circular cross-section). A linear elastic material property and

corresponding real constants for the anchor bolt including a diameter of 16 mm, a cross-

sectional area of 201 mm2, and a moment of inertia of 3217 mm

4 were assigned to this

element.

299

Figure ‎5-13: Geometry of Beam4 element (SAS, 2009).

5.2.4 Debonding Model

Debonding at the concrete-epoxy interface, which is the weakest layer, is

simulated using contact pairs and Cohesive Zone Material (CZM) model. To implement

debonding aspects in the FE analysis, a normal stress-gap model and a shear stress-slip

model are employed enabling mixed-mode debonding. It should be mentioned that,

considering both models provides an opportunity to appropriately analyze the debonding

behaviour; considering only the shear stress-slip model, as used in most studies (Chen

and Teng, 2001; Buyle-Bodin et al., 2002; Pham and Al-Mahaidi, 2005; Coronado and

Lopez, 2006), leads to an interface mode of separation where the slip dominates the

separation normal to the interface (gap); on the other hand, considering just the tension

stress-gap model leads to a mode of failure where the gap dominates the slip at the

300

interface. Hence, defining the debonding according to only one of the two models means

ignoring the effect of the other and making a difference with what actually happens in

reality, where both models contribute to debonding in NSM strengthened RC beam. In

the developed FE model, the bilinear shear stress-slip and normal stress-gap models are

calculated based on the appropriate fracture energies of the concrete-epoxy interface,

which are identified in the next sections.

Fine mesh was mapped inside the strengthening groove to increase the accuracy

of the results, and there was no need to map fine mesh outside the groove to decrease the

modeling time and computer computational time. Surface-to-surface contact pairs were

assigned to the concrete-epoxy interface to separate the fine mesh mapped inside the

groove from surrounding mesh. The interfacial surface on concrete (target surface) was

modeled using TARGE170 and the interfacial surface on epoxy adhesive (contact

surface) was modeled with CONTA173. Geometry of the assigned elements for the

concrete-epoxy interface is plotted in Figure ‎5-14. TARGE170 is capable of simulating

various 3D target surfaces for the associated contact elements. CONTA173 is employed

to simulate contact and sliding between 3D target surfaces and deformable surfaces,

defined by this element. This element is generated using four nodes, considering a 22

set of Gaussian integration points, and is applicable to 3D structural and coupled field

contact analyses. The related shear stress-slip and tensile stress-gap model were assigned

to the contact surface by developing a subroutine in ANSYS command menu. The CZM

is used for bonded contacts with the Augmented Lagrangian method that needs to be

assigned to the contact properties.

301

(a) Geometry of TARGE170 (b) Geometry of CONTA173

Figure ‎5-14: Geometry of elements for concrete-epoxy interface (SAS, 2009).

The interface separation in mixed-mode debonding depends on both normal and

shear stress components. The bilinear shear stress-slip and normal tension stress-gap

models are plotted in Figure ‎5-15 and Figure ‎5-16. The area under each bilinear model is

equal to the fracture energy of the interface in shear or tension which is the energy

dissipated due to debonding. As shown in Figure ‎5-15 and Figure ‎5-16, debonding

initiates when debonding parameter (dm) is equal to zero. As debonding propagates, dm

increases, and finally, reaches unity as debonding terminates. After this point, any further

separation at the interface occurs without any normal or shear contact stress.

302

Figure ‎5-15: Bilinear shear stress-slip model.

Figure ‎5-16: Bilinear normal tension stress-gap model.

The equations for the contact shear and normal stresses based on the bilinear

models are defined as Equation 5-6 and Equation 5-7, respectively.

)d(uK mttt 1 Equation ‎5-6

303

)d(uK mnnn 1 Equation ‎5-7

where τt= contact shear stress, Kt= contact shear stiffness, ut= contact slip, σn= contact

normal stress, Kn= contact normal stiffness, un= contact gap, and dm= debonding

parameter (scalar) which is defined through Equations. 5-8 to 5-10 (SAS, 2009).

xdm

mm

1 Equation ‎5-8

22

t

t

n

nm

u

u

u

u Equation ‎5-9

tct

ct

ncn

cn

uu

u

uu

ux

Equation ‎5-10

where ūn= contact gap at the maximum contact normal stress (tension), ūt= contact slip at

the maximum contact shear stress, unc= contact gap at the completion of debonding, and

utc= contact slip at the completion of debonding. Note that dm, Δm, and x are scalars. In

the above equations, dm= 0 for Δm ≤ 1 and 0 < dm ≤ 1 for Δm > 1. The constraint on x

(Equation 5-10) is enforced automatically by appropriate scaling the contact stiffness

values.

In mixed-mode, debonding usually occurs before dissipation of the critical

fracture energy because both shear and normal contact stresses contribute to the total

fracture energy dissipation. In the model, it is assumed that no slip occurs at the concrete-

304

epoxy interface under pure normal compressive stress for mixed-mode debonding. There

are two main reasons for this assumption: first, in the NSM strengthening, the concrete-

epoxy interface is mostly under shear and normal tension stresses; and second, debonding

is a combination of shear stress and normal tension stress (as a result of the produced slip

and gap) and even under compressive stress this is the secondary effect of the

compression that causes tension or shear stresses at some regions of the interface and

results in slip or gap which are considered in the FE model based on the defined shear

stress-slip and tension stress-gap models. Therefore, the following energy criterion

(Equation 5-11) is used to define the termination of debonding in the mixed-mode (SAS,

2009).

1

cn

nn

ct

tt

G

du

G

du Equation ‎5-11

where Gct and Gcn are the total values of shear and normal fracture energies, respectively.

These values need to be identified for the NSM strengthened RC beams as described in

the next two sections.

5.2.4.1 Identification of Shear Stress-Slip Model

In the NSM FRP strengthened RC beam, the debonding occurs at the concrete-

epoxy interface which is the weakest interface and the main reason for shortage of

research in this field is the identification of appropriate bond behaviour that can be

reasonably applicable to the NSM technique. Many shear stress-slip models were

305

proposed for the EB strengthening technique the most well-known ones are the models

developed by Chen and Teng (2001) and Lu et al. (2005). However, these models are not

appropriate for the NSM technique because they are developed according to the geometry

of the FRP plate which is approximately considered as the geometry of the debonding

plane in the EB technique. In the NSM strengthening method, it is not a valid assumption

to consider the geometry of the plate/strip instead of the geometry of the actual

debonding plane. Also, the strain in the NSM FRP reinforcement at debonding is

significantly greater than that in the EB technique due to confinement of the surrounding

concrete. Seracino et al. (2007) examined debonding resistance of the EB and NSM

plate-to-concrete joints and overcame the drawbacks of the previous bond-slip models by

considering the geometry of the debonding plane; these authors proposed a fracture

energy and an ultimate shear stress equations for bond based on the statistical analysis of

many experimental test results. The considered shear stress-slip model, used in the FE

model, (Figure ‎5-15) is derived from fracture energy of the interface in NSM

strengthened specimens (Equations 5-12 to 5-15).

6007808020 .cmax f)..( Equation ‎5-12

2

9760 605260 .c

.

ct

f.G

Equation ‎5-13

07808020

9760 5260

..

.u

.ct

Equation ‎5-14

mm2widthgroove

mm1depthgroove

Equation ‎5-15

306

where τmax= maximum shear stress of contact (MPa), γ= aspect ratio of the interface

failure plane (mm/mm), f′c= concrete compressive strength (MPa), Gct= shear fracture

energy (N/mm), and utc= contact slip at the completion of debonding (mm). The values of

τmax= 8.37 MPa and utc= 1.295 mm are derived using Equations 5-12 to 5-15 for the shear

stress-slip model.

5.2.4.2 Identification of Normal Tension Stress-Gap Model

The tensile resistance at the concrete-epoxy interface is assumed to be limited to

the tensile capacity of the weakest material which is the concrete tensile strength

(presented in Equation 5-16 (CAN/CSA-A23.3-04, 2004)). Therefore, when the

interfacial tensile stress exceeds the concrete tensile strength, the debonding occurs due

to cracking of the concrete adjacent to the interface. This behaviour was also observed

during the experimental tests performed by Gaafar (2007). Similar procedure was

employed by Kishi et al. (2005) for debonding analysis of the EB strengthened RC

beams. Therefore, the fracture energy of the interface under tensile stress is considered to

be equal to the fracture energy of the concrete presented in Equation 5-17 proposed by

the CEB-FIP Model Code (1993). The contact gap (Equation 5-18) is derived using

Equation 5-16 and Equation 5-17 to satisfy the tensile fracture energy based on the

concrete tensile strength.

cmax f. 60 Equation ‎5-16

307

70

10

.

cfocn

fGG

Equation ‎5-17

20

324

10.

cfo

cn

.

fGu

Equation ‎5-18

where σmax= maximum tensile stress of contact (MPa), f′c= concrete compressive strength

(MPa), Gcn= total value of the normal fracture energy (N/mm), unc= contact gap at the

completion of debonding (mm), and Gfo= the base value of fracture energy (N/mm),

which depends on the maximum aggregate size. For concrete with maximum aggregate

size of 20 mm, Gfo is calculated as 0.03475 N/mm by nonlinear interpolation between

different values of aggregate size reported in the CEB-FIP Model Code (1993). The

values of σmax= 3.79 MPa and unc= 0.048 mm are derived using Equation 5-16 to

Equation 5-18 for the tension stress-gap model.

5.2.5 Modeling of Prestressing

So far, there exist three methods to enforce prestressing in FE modeling: apply

initial stress, apply initial strain, and apply equivalent temperature to meet the prestrain in

relevant materials. For simplicity in the pre-processing and post-processing operations

and for the considered type of elements as well the assigned material properties for the

CFRP strips, the equivalent temperature method was implemented to enforce the

prestressing effect. The thermal expansion of the CFRP strip in longitudinal direction,

αfrp, is set as -9×10-6

/oC based on the FRP material data sheet (Hughes Brothers, 2010a).

308

The equivalent temperature is computed using Equation 5-19 and applied to the CFRP

strip elements to make the exact prestrain for each prestressed beam. After assigning the

computed equivalent temperature (Δt) to the FE model it was found that the produced

prestrain is slightly (1-1.5%) smaller than the applied prestrain value (εP). In fact, the

slight change in prestressing is a result of the straining of the beam as the self-

equilibrating stress state establishes itself during an equilibrating static analysis step.

Applying the prestressing transfers load to the concrete beam, causing compressive

stresses in the concrete. The resulting deformation due to elastic shortening of the

concrete beam reduces the strain in the CFRP strip due to prestressing. Therefore, the

applied equivalent temperature (Δtapplied) is calculated somehow (by trial and error) to

produce the exact value of εP for each beam. It can be seen from the following values that

the difference between Δt and Δtapplied (strain loss due to elastic shortening) is very small

and even can be ignored without significant effect on the results.

tfrpP Equation ‎5-19

C.tC.t.

C.tCt.

C.tC.t.

oapplied

oP

oapplied

oP

oapplied

oP

16114833113301020

556596520058680

053837837700340

5.2.6 Mesh Sensitivity Analysis

Principally, the developed FE analysis should be objective and the results should

not depend on subjective aspects including element type or mesh size. Sensitivity

analysis is not necessary when there are sufficient experimental results to validate the FE

309

model. In this case, the model can be built based on the modeller experience on the type

of the element and mesh size, and validity and accuracy of the predicted results can be

evaluated to be sufficient by comparing them with experimental ones. In the case of pure

FE analysis (with no experimental results available to check the validity and accuracy),

performing a mesh sensitivity analysis is necessary to make sure about the accuracy and

consistency of the results. However, a mesh sensitivity analysis was performed to identify

the optimum mesh density and appropriate element sizes for the FE model of the tested

beams. In this context, a non-prestressed NSM-CFRP strengthened RC beam was

modeled with five different numbers of elements as shown in Figure ‎5-17. A summary of

the models developed for mesh sensitivity analysis are presented in Table ‎5-1. The

number of the elements varies from 2587 to 22417. The size of the output file (.rst) is

presented which is normalized with respect to the BS-NP-S1; this parameter shows the

volume of the output file for BS-NP-S5 with 22417 elements is 11.93 times the one for

BS-NP-S1 with 2587 elements.

To find the optimum number of elements, the mid-span deflection, concrete

compressive stress at mid-span location at extreme top fibre (at the centre of the top face

of the beam), stress in tension steel at mid-span, and stress in CFRP strip at mid-span

versus the number of elements are plotted in Figure ‎5-18 at load 20 kN, which is in the

linear stage of the load-deflection curve (before cracking). It should be mentioned that the

sensitivity analysis is reasonable when it is evaluated in linear stage of the load-deflection

curve. Many parameters interfere in convergence and the sensitivity curve does not

follow a reasonable trend when the structure (especially concrete member) goes to

nonlinear stages. The optimum is practically achieved when an increase in the mesh

310

density has a negligible effect on the results. On the other hand, the computer

computational time (which is different based on the computer capabilities) should be

considered in achievement of the optimum number of elements. According to the author

best experience, it’s more rational to select the optimum model based on the sensitivity

curve of the deflection versus the number of elements. Eventually, the model with 13614

elements is employed for FE analysis that yields a minimum of 99.2% reliability in

predicted results (as presented in Figure ‎5-18).

311

Table ‎5-1: Mesh sensitivity models.

Beam ID

Total

number of

elements

Total

number

of nodes

Number of elements for: Output

volume

(relative) Solid65

(concrete)

Link8

(steel bar)

Solid45

(CFRP, epoxy,

steel plate)

Beam4

(steel bolt)

Contact

(concrete-epoxy

interface)

BS-NP-S1 2587 2858 900 230 860 10 587 1

BS-NP-S2 6762 7394 2572 329 2660 14 1187 2.78

BS-NP-S3 13614 14914 4754 425 5854 14 2567 5.76

BS-NP-S4 20443 22792 9440 626 7076 14 3287 8.76

BS-NP-S5 22417 24924 11386 626 7104 14 3287 11.93

311

312

(a) BS-NP-S1 (b) BS-NP-S2

(c) BS-NP-S3 (d) BS-NP-S4

(e) BS-NP-S5

Figure ‎5-17: Mesh sensitivity models.

313

1.46

1.462

1.464

1.466

1.468

1.47

0 5000 10000 15000 20000 25000

Mid

-sp

an

de

fle

cti

on

(m

m)

Number of elements

Selected model99.95% reliability

6.8

7

7.2

7.4

7.6

7.8

0 5000 10000 15000 20000 25000Ten

sil

e s

tress in

CF

RP

(M

Pa)

Number of elements


16.7

16.72

16.74

16.76

16.78

16.8

0 5000 10000 15000 20000 25000

Te

ns

ile

str

es

s in

ste

el (M

Pa

)

Number of elements


-3.33

-3.31

-3.29

-3.27

-3.25

0 5000 10000 15000 20000 25000

Co

mp

ressiv

e s

tress

in c

on

cre

te (M

Pa)

Number of elements


Figure ‎5-18: Mesh sensitivity at 20 kN.

314

The meshed beam (selected model) is presented in Figure ‎5-19 to Figure ‎5-24. At

the location of the end anchors, the groove width is 25 mm to account for the embedded

anchors and in between along the length of the CFRP strip the groove width is 16 mm

which is the reason for using some larger aspect ratio elements at the side of the groove

with respect to other regions as shown in Figure ‎5-20.

Figure ‎5-19: The meshed beam (quarter of the tested beam).

Figure ‎5-20: Cross-section of the beam.

315

Figure ‎5-21: Steel reinforcements.

Figure ‎5-22: Mesh at the end groove.

Figure ‎5-23: Contact around the groove.

316

Figure ‎5-24: End-steel anchor.

5.2.7 Nonlinear Analysis

The nonlinear solution was executed using displacement control method in which

the non-zero displacement constraints were assigned to the model (at the loading plate

location) and the corresponding reaction forces were calculated. Therefore, the reaction

load-deflection curve obtained from the nonlinear analysis is the same as the applied

load-deflection curve obtained from the test. Another procedure for the FE analysis is

load control method in which the load is assigned to the model and the deflection is

calculated. The displacement control has a few advantages versus load control that can

overcome both the convergence difficulties and the rigid body modes when two bodies

are disconnected in contact pairs, and analyze the model with assigned material stress-

strain curve having descending branch. Each prestressed strengthened beam was solved

by defining seven load-steps as presented in Table ‎5-2. For instance, the ANSYS files

generated for FE model of the prestressed NSM CFRP strengthened beam, BS-P2-R, are

presented in Appendix D.

317

Table ‎5-2: Summary of load-steps assigned for nonlinear analysis.

Load-step

Time at

end of

load-step

Sub-step Max

number of

iterations

Displacement

convergence

criteria tolerance No. Min Max

1. Zero load-camber

induced by prestressing* 0.0001 1 1 1 40 0.01

2. Applied prestressing-

before first cracking 1.2 10 5 40 40 0.01

3. Before first cracking-

after first cracking 4 80 50 100 40 0.05

4. After first cracking-

before steel yielding 20 20 10 10000 40 0.05

5. Before steel yielding-

after steel yielding 26 40 15 10000 40 0.05

6. After steel yielding-

before ultimate 60 20 10 10000 60 0.05

7. Before ultimate-after

ultimate 120 20 10 10000 60 0.05

* used for prestressed NSM-CFRP strengthened beams

Generally, the number of load-steps in a FE analysis is arbitrary chosen by the

modeller based on the type of the problem, convergence behaviour of the FE model or

system, in particular, response of the structure, and the cost in term of computer

computational time. The main reasons for using seven load-steps instead of one were to:

i) assign the effect of prestressing on the model, and ii) apply the load gradually by

assigning different maximum and minimum numbers of the sub-steps defined for each

load-step. The latter leads to the following advantages: to increase the accuracy of the

results and properly calculate the loads and deflections at different steps (i.e., at

prestressing, surrounding cracking, yielding, and ultimate), to control computer

computational time so as to minimize the number of Newton-Raphson equilibrium

iterations required, and to assist in convergence of the nonlinear problem. After several

trials, a maximum displacement convergence tolerance of 0.05 is applied to the model

based on the convergence sensitivity analysis. To take into account the effect of the self-

318

weight of the beam, a preliminary analysis was performed on the model by applying

density and inertia and the deflection, sw, was calculated at the point load. Then, another

analysis was conducted by applying the same deflection sw as a boundary condition to

the model without the effect of self-weight and the reaction forces which are equivalent

to the reactions due to self-weight are calculated, called Psw. Then, Psw and sw were

subtracted from the reaction forces and deflections obtained from the nonlinear solution

of each beam. By this way, the predicted load-deflection response is in the same manner

as the experimental load-deflection response that already included the self-weight effects.

5.2.8 FE Results, Validation, and Discussion

5.2.8.1 Load-Deflection Curve

Comparison between experimental and numerical load-deflection responses is

depicted in Figure ‎5-25 to Figure ‎5-28 including the un-strengthened control beam, B0-R,

the strengthened beam with non-prestressed NSM CFRP strip, BS-NP-R, and the

strengthened beams with prestressed NSM CFRP strip, BS-P1-R, BS-P2-R, and BS-P3-

R. The FE solutions of the beams were terminated after CFRP rupture or concrete

crushing whichever occurred first accompanied by a non-convergence message from the

program. The predicted load-deflection responses include the negative camber due to

prestressing, initiation of flexural cracks, yielding of tensile steel rebar, local debonding

(which causes small fluctuations at large deflection), and CFRP rupture which causes a

large drop of total load at ultimate stage.

A summary of the results obtained from the tests versus the FE analysis is

presented in Table ‎5-3, including type of failure, ductility index (the ratio of the ultimate

319

deflection to the deflection at yielding), energy absorption (the area under load-deflection

curve up to the peak load), and percentage of difference between corresponding

experimental and numerical values.

At cracking, a relatively large percentage of difference is observed (an average

error of 0.8%±16.1% for cracking load with a maximum of 28% for B0-R, and an

average error of -22%±18.8% for cracking deflection with a maximum of -49.6% for BS-

P3-R) which might be due to presence of the micro cracks in the beams before testing.

Also, the cracking load and corresponding deflection in the tested beams were obtained

based on the visual inspections during the test and in some cases might be overestimated,

as can be seen for beam BS-P3-R. The other reason for underestimation or overestimation

of the cracking load using the FE analysis might be due to difference between concrete

compressive strength in the model and in tested beams; an average concrete compressive

strength was assigned to the FE models (40 MPa for all beams), that might be slightly

different for each beam in reality. Therefore, the obtained difference between FE and test

at cracking is most possibly the accumulation of the mentioned errors.

At yielding stage, the differences between FE and experimental results are

negligible (an average error of 2.3%±2.5% for yield load with a maximum of 5.2% for

BS-P2-R, and an average error of 1.7%±5% for yield deflection with a maximum of -

9.3% for BS-P2-R).

At ultimate stage, the predicted loads are almost the same as those obtained from

the test; however, the predicted ultimate deflections are smaller than those from the

experimental values. This behaviour might be due to the fact that the rupture of the CFRP

strip in FEM occurs when the first fibre in the CFRP strip reaches its ultimate tensile

320

strain, while during the test there is a possibility that the CFRP strip ruptured gradually.

On the other hand, the material properties (i.e., CFRP ultimate strain) are not absolutely

constant values and could be slightly smaller or greater than the specified values that

would lead to a difference at ultimate deflection when the failure governs by CFRP

rupture. An average error of 0.6%±6.1% for ultimate load with a maximum of 10.7% for

B0-R, and an average error of -5.1%±5.9% for ultimate deflection with a maximum of -

14.8% for BS-P1-R were obtained at the ultimate stage. The modeled beams showed

similar type of failure to the tested beams which is concrete crushing for the un-

strengthened control beam, B0-R, and CFRP rupture for the prestressed strengthened

beams except beam BS-NP-R strengthened with non-prestressed NSM CFRP strips

which failed due to concrete cover spalling. The fluctuation of the FE curve for BS-NP-R

observed in Figure ‎5-25 is due to major flexural cracks and also local debonding initiated

from top face of the groove, which could be a warning for this type of failure. Therefore,

the performed comparison indicates that the load-deflection curves obtained from the FE

models are matched with those from the experimental ones.

321

0

20

40

60

80

100

120

140

160

0 15 30 45 60 75 90 105 120 135

Lo

ad

(k

N)


BS-NP-R (Experimental)

BS-NP-R (FE Analysis)

B0-R (Experimental)

B0-R (FE Analysis)

Figure ‎5-25: Comparison between FE and experimental results for B0-R and BS-

NP-R.

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135

Lo

ad

(k

N)


BS-P1-R (Experimental)

BS-P1-R (FE Analysis)

Figure ‎5-26: Comparison between FE and experimental results for BS-P1-R.

322

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135

Lo

ad

(k

N)





0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135

Lo

ad

(k

N)





323

Table ‎5-3: Summary of the results.

Beam

ID#

Prestrain

in CFRP Results

Δo

(mm)

Pcr

(kN)

Δcr

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) μD

Φ

(kN. mm)

Failure

Mode

B0-R N.A.

FE 0 16 1.18 81.9 24.29 92.8 107.49 4.43 8446.6 CC

Test‡ 0 12.5 1.25 78.9 25.13 83.8 109.89 4.37 8050.2 CC

Error % 0 28 -5.6 3.8 -3.3 10.7 -2.2 1.4 4.9 ―

BS-NP-R 0

FE 0 15.4 1.14 93.6 25.42 136.8 111.9 4.4 11816.2 FR

Test‡ 0 16.8 1.55 90.8 25.83 135.1 118.79 4.6 12357.4 CCS

Error % 0 -8.3 -26.5 3.1 -1.6 1.3 -5.8 -4.3 -4.4 ―

BS-P1-R 0.0034

FE -0.48 22.7 1.2 102.1 25.04 140.4 88.26 3.52 9501.8 FR

Test‡ -0.47 22.1 1.24 103 24.12 148 103.65 4.3 11828.7 FR

Error % -2.1 2.7 -3.2 -0.9 3.8 -5.1 -14.8 -18.1 -19.7 ―

BS-P2-R 0.00587

FE -0.82 28.1 1.27 111.3 25.81 144.3 78.27 3.03 8582 FR

Test‡ -0.93 30.1 1.69 105.8 23.62 148.2 77.96 3.3 8813.1 FR

Error % 11.8 -6.6 -24.9 5.2 9.3 -2.6 0.4 -8.2 -2.6 ―

BS-P3-R 0.0102

FE -1.42 37.1 1.33 123.3 25.84 147.3 56.41 2.18 6223.4 FR

Test‡ -1.6 42.1 2.64 122.8 25.77 149.2 58.13 2.26 6529 FR

Error % 11.3 -11.9 -49.6 0.4 0.3 -1.3 -3.0 -3.5 -4.7 ―

Pcr and Δcr = load and deflection at cracking Δo = camber due to prestressing CC = Concrete crushing

Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy CCS = Concrete cover spalling

Pu and Δu = load and deflection at ultimate Φ = area under P-Δ curve up to Pu FR = CFRP rupture ‡

Gaafar (2007).

323

324

5.2.8.2 Strain Profiles and Distributions

Strain profiles along the length of the NSM CFRP strip and strain distribution

across the depth at mid-span of the beams are presented in Figure ‎5-29 to Figure ‎5-36.

The curves are plotted at three different load levels for each beam: cracking, yielding, and

ultimate. The experimental values are based on the reading of the strains in the CFRP

strip, steel rebars, and in the concrete at extreme compression fibre. For all beams, the

predicted strain profiles along the length of the CFRP strip are very well matched with

the experimental values at cracking and yielding. At ultimate stage, a very good

correlation is observed between the experimental and predicted strain profile except for

the non-prestressed strengthened beam, BS-NP-R. The reason is that this beam failed due

to concrete cover spalling at the tension face before CFRP strips reaches its ultimate

strain while in the FE model, the beam failed due to CFRP rupture. It can be seen from

the strain profile at ultimate that the maximum strain in the CFRP strips occurs

somewhere between the applied point load location and mid-span of the beam (from 2000

mm to 2500 mm on the x axis of the graph) which could not be captured experimentally

due to the location of the installed strain gauges. The FE strain distributions at mid-span

in Figure ‎5-33 to Figure ‎5-36 are calculated at the location of the experimental measured

strains and linearly connected together. The distribution shows very good correlation at

cracking and yielding and with negligible difference at ultimate. It should be noticed that

the strain distribution at mid-span section is not linear due to the effect of pre-strain

applied to the CFRP strip. However, the distribution along the effective depth is almost

linear at yielding and nonlinear at ultimate mostly due to concrete behaviour at

compression zone.

325

0

0.005

0.01

0.015

0.02

0 1000 2000 3000 4000 5000

Str

ain


@ Cracking Load, 15.4 kN, FEM-ANSYS @ Cracking Load, 16.8 kN, Experimental

@ Yielding Load, 93.6 kN, FEM-ANSYS @ Yielding Loading, 90.8 kN, Experimental

@ Ultimate Load, 136.8 kN, FEM-ANSYS @ Ultimate Load, 135.1 kN, Experimental

Figure ‎5-29: Comparison between experimental and numerical strain profile along

the CFRP strip for beam BS-NP-R.

0

0.005

0.01

0.015

0.02

0 1000 2000 3000 4000 5000

Str

ain



@ Yielding Load,102.1 kN, FEM-ANSYS @ Yielding Load, 103 kN, Experimental

@ Ultimate Load, 140.4 kN, FEM-ANSYS @ Ultimate Load, 148 kN, Experimental


the CFRP strip for beam BS-P1-R.

326

0

0.005

0.01

0.015

0.02

0 1000 2000 3000 4000 5000

Str

ain



@ Yielding Load, 102.8 kN, FEM-ANSYS @ Yielding Load, 105.8 kN, Experimental




0

0.005

0.01

0.015

0.02

0 1000 2000 3000 4000 5000

Str

ain







327

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.01 -0.005 0 0.005 0.01 0.015 0.02

Se

cti

on

De

pth

(m

m)

Strain




Bottom Steel Level

CFRP Strips Level

Top Steel Level

Top Fibre of the Beam


across the depth at mid-span for beam BS-NP-R.

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.01 -0.005 0 0.005 0.01 0.015 0.02

Se

cti

on

De

pth

(m

m)

Strain


@ Yielding Load, 102.1 kN, FEM-ANSYS @ Yielding Load, 103 kN, Experimental

@ Ultimate Load, 140.4 kN, FEM-ANSYS @ Ultimate Load, 148 kN, Experimental

Bottom Steel Level

CFRP Strips Level

Top Steel Level



across the depth at mid-span for beam BS-P1-R.

328

-400

-350

-300

-250

-200

-150

-100

-50

0

-0.01 -0.005 0 0.005 0.01 0.015 0.02

Se

cti

on

De

pth

(m

m)

Strain




Bottom Steel Level

CFRP Strips Level

Top Steel Level




-400

-350

-300

-250

-200

-150

-100

-50

0

-0.01 -0.005 0 0.005 0.01 0.015 0.02

Se

cti

on

De

pth

(m

m)

Strain




Bottom Steel Level

CFRP Strips Level

Top Steel Level




329

5.2.8.3 Debonding aspects

The initiation of debonding and its propagation at ultimate load for two FE

models (BS-NP-R and BS-P2-R) are shown in Figure ‎5-37 and Figure ‎5-38 to examine

the effect of debonding phenomenon. The debonding parameter value (dm) ranging from

0 to 1 is presented in these figures. Debonding is initiated when dm = 0 and by further

propagation dm approaches to unity. The termination of debonding is defined by Equation

5-11 when the total fracture energy is dissipated. Analysis of the FE results reveals that

debonding occurs at the horizontal concrete-epoxy interface on the top surface of the

NSM groove. Furthermore, the area of the debonded surface at ultimate load is less for

the prestressed NSM CFRP strengthened beam in comparison with the non-prestressed

NSM CFRP strengthened beam. In fact, debonding is a result of high interfacial shear and

tensile stresses caused by high deflection and large crack openings while prestressing

reduces the ductility of the beam, and therefore, avoids the debonding to occur. Results

revealed no debonding occured for beam BS-P3-R up to failure, while for beam BS-P1-

R, debonding occurred before failure and it was much less than beam BS-NP-R.

Therefore, less debonding occurs with increasing the prestressing level in the NSM

CFRP, i.e. the area of the debonded interface at failure decreases.

330

BS-NP-R Debonding Parameter (dm) Contour.983916

HI: Horizontal concrete-epoxy interface

VI: Vertical concrete-epoxy interface

HI

VI

Concrete

Epoxy

CFRP

strips

(a)

BS-NP-R Debonding Parameter (dm) Contour

HI

VI



Concrete

Epoxy

CFRP

strips

(b)

Figure ‎5-37: Debonding Parameter (dm) contour at the concrete-epoxy interface in

the model: (a) BS-NP-R at initiation of debonding (load = 130.4 kN, deflection =

80.14 mm) and (b) BS-NP-R at ultimate.

331

BS-P2-R Debonding Parameter (dm) Contour

HI

VI



Concrete

Epoxy

CFRP

strips

(a)

BS-P2-R Debonding Parameter (dm) Contour

HI

VI



Concrete

Epoxy

CFRP

strips

(b)

Figure ‎5-38: Debonding Parameter (dm) contour at the concrete-epoxy interface in

the model: (a) BS-P2-R at initiation of debonding (load = 140.4 kN, deflection =

68.32 mm) and (b) BS-P2-R at ultimate.

332

5.3 Parametric Study on RC Beams Strengthened with Prestressed NSM-FRP

Conducting experimental investigations is indispensable to assess the actual

performance of structural elements, on the other hand, testing is usually a time

consuming and costly procedure for solving a problem. Therefore, researchers are

encouraged toward numerical or analytical solutions of a problem, even if it is

complicated to figure them out. In this section a parametric study is conducted on RC

beams strengthened with prestressed NSM CFRP. A Finite Element (FE) modeling

procedure similar to what has been presented in Section 5.2 is employed but with

simplified material properties to decrease the solution time for doing the parametric

study. First, the simplified developed 3D nonlinear FE model was validated with the

experimental data to simulate the behaviour of RC beam strengthened with prestressed

NSM-CFRP strips. Afterwards, the model was used and 23 beams were analyzed to

assess the prestressing level in the NSM CFRP strips, the tensile steel reinforcement

ratio, and the concrete compressive strength. The effects of these parameters on the

negative camber caused by prestressing; cracking, yielding, and ultimate loads and

corresponding deflections; mode of failure; and energy absorption were investigated. In

addition, the optimum prestressing level, which preserves the amount of energy

absorption of the NSM CFRP strengthened beam equal to the un-strengthened control

beam was estimated for the beams with different tension steel reinforcement ratios.

5.3.1 Modeled Beams

Geometry of the modeled beams is presented in Figure ‎5-1. More description

about the geometry is provided in Section 5.2.1. To perform a comprehensive parametric

333

study 23 beams were modeled as presented in Table ‎5-4.

Table ‎5-4: Properties of the modeled beams.

Beam ID ɛp

[ɛp/ɛfrpu %]

Afrp (mm2)

[Afrp/(bh) %]

Concrete Properties Area of Steel

f′c (MPa)

fr

(MPa)

Ec

(MPa)

Asc (mm2)

[Asc/(bh) %]

Ast (mm2)

[Ast/(bh) %]

B0-0.75-40 0 0

40 3.79 28460.5 200

[0.25]

600

[0.75]

BS-0-0.75-40 0

64

[0.08]

BS-19-0.75-40 0.0034

[19]

BS-36-0.75-40 0.0065

[36]

BS-58-0.75-40 0.0104

[58]

B0-1.25-40 0 0

40 3.79 28460.5 200

[0.25]

1000

[1.25]

BS-0-1.25-40 0

64

[0.08]

BS-19-1.25-40 0.0034

[19]

BS-36-1.25-40 0.0065

[36]

BS-58-1.25-40 0.0104

[58]

B0-1.75-40 0 0

40 3.79 28460.5 200

[0.25]

1400

[1.75]

BS-0-1.75-40 0

64

[0.08]

BS-19-1.75-40 0.0034

[19]

BS-36-1.75-40 0.0065

[36]

BS-58-1.75-40 0.0104

[58]

B0-2.25-40 0 0

40 3.79 28460.5 200

[0.25]

1800

[2.25]

BS-0-2.25-40 0

64

[0.08]

BS-19-2.25-40 0.0034

[19]

BS-36-2.25-40 0.0065

[36]

BS-58-2.25-40 0.0104

[58]

BS-36-1.25-30 0.0065

[36]

64

[0.08]

30 3.29 24647.5 200

[0.25]

1000

[1.25] BS-36-1.25-50 50 4.24 31819.8

BS-36-1.25-60 60 4.65 34856.9 ɛp= prestrain in CFRP strips ɛfrpu= ultimate tensile strain of CFRP strips

Afrp= area of CFRP strips b and h= width and height of RC beam

f′c, fr, and Ec= compressive strength, tensile strength and modulus of elasticity of the concrete material

Asc and Ast= area of compression and tension steel reinforcements

334

Properties of the modeled beams are presented in Table ‎5-4 including the concrete

properties of each beam, area and reinforcement ratio of CFRP strips, area and

reinforcement ratio of reinforcing steel, and prestressing level as prestrain in CFRP strips

and percentage of the ultimate tensile strain of the CFRP strips. The strengthened beam

ID in Table ‎5-4 refer to: the first part as the type of the beam (BS: beams strengthened

with NSM CFRP strip), the second part as the prestressing level (percentage of the

ultimate tensile strain of the CFRP strips), the third part as the tension steel ratio, and the

fourth part as the concrete compressive strength. It should be mentioned that the un-

strengthened beam ID is similar to the one used for the strengthened beam excepts that it

starts with B0 instead of BS at the first part and the second part used for strengthened

beam is excluded.

5.3.2 Description of FE Model

The developed FE models are 3D and all materials including concrete, CFRP

strips, longitudinal steel reinforcements, steel stirrups, epoxy adhesive, steel bolts, and

steel end anchor were simulated using appropriate elements in the ANSYS program

(SAS, 2004). In this section, it is tried to generate a simplified model for performing the

parametric study, therefore, to reduce the computer computational time, modelling time

and volume of the results, only one quarter of the beam was modeled due to the

symmetry in cross-section and loading span. Furthermore, complete bond was assumed

between different interfaces in the model since the overall flexural behaviour of the NSM

CFRP strengthened beams is not affected by any debonding as reported by Gaafar (2007)

and also to facilitate the trend of the parametric study. The aim of this section is to

335

conduct a parametric study, which is independent from the material properties and the

applied prestressing values in the beams tested by Gaafar (2007), on the other hand, the

simplified developed 3D FE models needs to be validated to be used for parametric study

that is accomplished later on in this section.


5.3.3.1 Concrete

The Solid65 element was considered to model the concrete. Characteristics of this

element are presented in Section 5.2.3.1. The modulus of elasticity and tensile strength of

the concrete are calculated from equations 5-20 and 5-21 (CAN/CSA-A23.3-04, 2004). A

Poisson’s ratio of 0.18 is assigned to the concrete (Wight and MacGregor, 2009). To

properly model the concrete, the considered model for concrete includes linear and multi-

linear material properties in addition to the concrete model defined in ANSYS

(Kachlakev et al., 2001; Wolanski, 2004) as describes in the rest of this section. The

simplified compressive stress-strain curve for the concrete model was obtained by

applying equations 5-22 to 5-25 to form the multi-linear stress-strain curve as plotted in

Figure ‎5-39 (Wolanski, 2004; Wight and MacGregor, 2009).

cc fE 4500 Equation ‎5-20

cr f.f 60 Equation ‎5-21

10if cc Ef Equation ‎5-22

336

o

o

cc

Ef

12if

1

Equation ‎5-23

cuocc ff if Equation ‎5-24

c

c

E

f

20 Equation ‎5-25

where Ec, fr, f′c, 1, fc, , and 0 are the concrete modulus of elasticity (MPa), the concrete

tensile strength (MPa), the concrete compressive strength (MPa), the strain at the end of

the linear part up to fc= 0.3f′c (Wight and MacGregor, 2009), the concrete compressive

stress at strain , the strain at stress fc, and the strain at maximum concrete strength,

respectively.

Figure ‎5-39: Simplified concrete compressive stress-strain curves.

337


The Link8 element was selected to model steel reinforcements. Characteristics of

this element are mentioned in Section 5.2.3.2. The stress-strain curve of the internal steel

reinforcements was determined from the uniaxial tension tests as shown in Figure ‎5-2.

Multi-linear elastic material was considered to model the steel rebars with a Poisson’s

ratio of 0.3 (Wight and MacGregor, 2009).

5.3.3.3 CFRP Strips

The Solid45 element was employed to model the CFRP strips with characteristics

listed in Section 5.2.3.3. A linear-elastic material behaviour up to failure was assigned to

the CFRP elements with a modulus of elasticity of 145 GPa and a tensile strength of 2610

MPa, an ultimate strain of 0.018 (Gaafar, 2007). A Poisson’s ratio of 0.35 was considered

for this material (Kabir and Hojatkashani, 2008). In the model, to minimize mesh

intricacy, a 5×16 mm CFRP strip was modeled instead of 2-2×16 mm CFRP strips plus

1mm epoxy in-between (Figure ‎5-1). Therefore, an equivalent modulus of elasticity of

116 GPa (2×2×16×145/(5×16)=116 GPa), a tensile strength of 2088 MPa

(116000×0.018=2088 MPa), and an ultimate strain of 0.018 were allocated to the CFRP

material in the model, which yielded an identical axial stiffness with the CFRP in the test.

5.3.3.4 Epoxy Adhesive

The epoxy adhesive was modeled using Solid45 elements. It is assumed that the

epoxy adhesive behaves as linear-elastic up to failure, and possessed a Young's modulus

338

of 2.4 GPa and an ultimate tensile strength of 24 MPa (Sika, 2007b). A Poisson’s ratio of

0.37 was assigned to this material (Kabir and Hojatkashani, 2008).

5.3.3.5 Bolts at Steel End Anchor

The Beam4 element was considered to model the steel bolts at the end anchor.

Characteristics of this element are presented in Section 5.2.3.6. A linear elastic material

was assigned to these elements with a modulus of elasticity of 200 GPa and a Poisson’s

ratio of 0.3 (Wight and MacGregor, 2009).

5.3.3.6 Steel End Anchor and Loading and Supporting Steel Plates

The steel end anchors and loading and supporting steel plates were modeled using

Solid45 elements with a linear elastic material assigned to these elements having a

modulus of elasticity of 200 GPa and a Poisson’s ratio of 0.3 (Wight and MacGregor,

2009).

5.3.3.7 Bond at Concrete-Epoxy Interface

Although the complete bond was considered between different materials at the

interfaces, but the surface-to-surface contact elements with multi point constraint (MPC)

algorithm were assigned to interface between concrete and adhesive to separate the fine

mesh mapped inside the groove from surrounding mesh. The target surface (on concrete)

was modeled with TARGE170 and the contact surface (on adhesive) was modeled with

CONTA173. Properties and capabilities of these elements are mentioned in Section 5.2.4.

339

5.3.3.8 Modeling of Prestressing

Prestressing in the NSM CFRP was applied by assigning the initial stress to

Solid45 elements.

5.3.4 Nonlinear Solution

The meshed beam is depicted in Figure ‎5-40. The nonlinear solution was executed

using load control where the load is assigned to the model and the corresponding

deflection is computed. The nonlinearity problem was solved by defining five load-steps

for each model to accurately calculate the cracking, yielding, and ultimate loads and

deflections, to assign the effect of prestressing on the model, to control computer

computational time, and to assist in convergence of the problem. A summary of the

applied load-steps are presented in Table ‎5-5. Based on the developed FE models, the

ultimate load was attained either due to concrete crushing or CFRP rupture whichever

occurred first.


Load-step Time at end of

load-step**

Sub-step** Max

number of

iterations

Displacement

convergence

criteria

tolerance No. Min Max

1. Zero load- induced

prestressing level* 1 1 N.A. N.A. 80 0.01


before first cracking 5000-8000 10 5 50 80 0.01


after first cracking 8000-14000 15-75 15-40 100 100 0.03


before steel yielding 20000-60000 20 10 100 100 0.03


failure 28000-90000 50-10000 40-70 1000-40000 100 0.03


** varies

340

Figure ‎5-40: Meshed beam.

5.3.5 Validation of the Model

Results of one beam, BS-58-0.75-40, are compared to the experimental results

reported by Gaafar (2007) to validate the simplified developed 3D FE model. The load-

deflection response of the modeled beam is stiffer than the experimental one, as shown in

Figure ‎5-41. The difference starts before cracking, extended up to yielding, and slightly

increases in the plastic region. The difference might be due to ignoring the self-weight of

the beam in the FE models (which is ignored to facilitate the parametric study) and also

the slight difference between the reported CFRP material properties obtained from

tension tests and what was observed during the test under flexural performance.

Comparison between the FE and the experimental results for the strain profile along the

length of the CFRP strip in beam BS-58-0.75-40, at cracking, yielding, and ultimate loads

is presented in Figure ‎5-42. At cracking and yielding loads, the predicted strain profile

along the CFRP strip is matched with the experimental values. The modeled and

experimental beams showed similar mode of failure governed by CFRP rupture.

However, the recorded ultimate strain in the NSM CFRP strips for the tested beam is

341

greater than the ultimate tensile strain of 0.018 obtained from the tension test by Gaafar

(2007). Due to this difference, the FEM strain profile at ultimate and also the ultimate

deflection of the beam BS-58-0.75-40 are smaller than those from the experiment.

0

20

40

60

80

100

120

140

160

-5 0 5 10 15 20 25 30 35 40 45 50 55 60

Lo

ad

(k

N)


BS-58-0.75 (Experimental)

BS-58-0.75 (FE Analysis)

: CFRP rupture

Figure ‎5-41: Comparison between experimental and numerical load-deflection

curves of beam BS-58-0.75-40.

342

0

0.004

0.008

0.012

0.016

0.02

0 1000 2000 3000 4000 5000

Str

ain

in

CF

RP

str

ips


@ Cracking Load, 46 kN, FEM-ANSYS @ Cracking Load, 42.1 kN, Experimental




the length of CFRP strips of beam BS-58-0.75-40.

A summary of the comparison between predicted and experimental results are

presented in Table ‎5-6 including a comparison between load-deflection values at

cracking, yielding and ultimate, ductility index (defined as the ratio of deflection at

ultimate to deflection at yielding), amount of energy absorption (determined as the area

under load-deflection curve), failure mode, and the percentage of difference between FE

and test results.

343

Table ‎5-6: Comparison between numerical and experimental results of beam BS-58-

0.75-40.

Beam ID Results Δo

(mm)

Pcr

(kN)

Δcr

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) µD

Φ

(kN·mm) FM

BS-58-0.75-40

Test 1.6 42.1 2.64 122.8 25.77 149.2 58.13 2.26 6529 FR

FEM 1.58 46.0 1.8 131.2 24.84 151.9 45.40 1.83 5067.2 FR

Error % 1.3 9.3 31.8 6.8 3.6 1.8 21.9 19.0 22.4

Pcr and Δcr = load and deflection at cracking Δo = negative camber due to prestressing

Py and Δy = load and deflection at yielding µD = ductility index (Δu /Δy)

Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under P-Δ curve up to Pu)

FM = failure mode FR = CFRP rupture

5.3.6 Parametric Study

Results of a comprehensive parametric study performed on the prestressing level,

the tensile steel reinforcement ratio, and the concrete compressive strength of the RC

beams strengthened with prestressed NSM CFRP strips are presented and discussed in

this section.

5.3.6.1 Effects of Prestressing Level in the NSM CFRP

To assess the effects of prestressing results from four sets of beams analyzed

using FE method were employed. Each set consisted of five beams with equal tension

steel ratio: one un-strengthened control beam and four RC beams strengthened with NSM

CFRP strips. The prestressing levels in the strengthened beams included 0%, 19%, 36%,

and 58% of the ultimate tensile strain of the CFRP strips. The tension steel ratio in each

set was different from the other sets including 0.75%, 1.25%, 1.75%, and 2.25% of the

total cross-sectional area of the RC beam while all the strengthened beams had the same

CFRP reinforcement ratio of 0.08%.

344

0

25

50

75

100

125

150

175

-10 0 10 20 30 40 50 60 70 80 90 100 110 120

Lo

ad

(k

N)


BS-58-0.75-40 (FE Analysis)




B0-0.75-40 (FE Analysis)

: CFRP rupture : Concrete crushing


level on set BS-0.75-40.

0

25

50

75

100

125

150

175

200

225

-10 0 10 20 30 40 50 60 70 80 90 100 110 120

Lo

ad

(k

N)










345

0

25

50

75

100

125

150

175

200

225

250

275

-10 0 10 20 30 40 50 60 70 80 90 100 110 120

Lo

ad

(k

N)










0

25

50

75

100

125

150

175

200

225

250

275

300

-10 0 10 20 30 40 50 60 70 80 90 100 110 120

Lo

ad

(k

N)







: Concrete crushing



346

Table ‎5-7: Summary of the results for the effects of prestressing.

Beam ID Δo

(mm)

Δcr

(mm)

Pcr

(kN)

Δy

(mm)

Py

(kN)

Δu

(mm)

Pu

(kN) µD

Φ

(kN·mm) FM

B0-0.75-40 0 1.68 23 22.3 84.8 118.47 103.8 5.31 10411 CC

BS-0-0.75-40 0 1.58 21.6 25.52 101.9 111.02 160.6 4.35 12922.5 FR

BS-19-0.75-40 0.52 1.68 30 25.29 111.0 87.68 157.2 3.47 10196.8 FR

BS-36-0.75-40 0.99 1.74 37.2 25.12 120.6 67.92 155.5 2.70 7877 FR

BS-58-0.75-40 1.58 1.80 46.0 24.84 131.2 45.4 151.9 1.83 5067.2 FR

B0-1.25-40 0 1.73 24.6 26.75 141.5 80.52 155.8 3.01 10207.8 CC

BS-0-1.25-40 0 1.61 22.9 28.06 154.0 78.69 195.9 2.80 11326.6 CC

BS-19-1.25-40 0.49 1.69 31 28.37 164.2 78.16 205.3 2.76 11975.1 CC

BS-36-1.25-40 0.93 1.76 38.3 28.83 173.7 70.22 209.4 2.44 10979.3 FR

BS-58-1.25-40 1.48 1.88 47.7 29.30 186.1 51.16 208.3 1.75 7685.6 FR

B0-1.75-40 0 1.77 26.2 30.4 195.1 66.78 208.7 2.20 10637 CC

BS-0-1.75-40 0 1.65 24.5 31.71 206.2 62.43 235.6 1.97 10384.9 CC

BS-19-1.75-40 0.46 1.75 32.6 32.09 215.9 60.91 244.4 1.90 10577.6 CC

BS-36-1.75-40 0.87 1.81 39.6 32.51 225.1 60.01 252.1 1.85 10850.4 CC

BS-58-1.75-40 1.39 1.94 49.1 32.88 236.3 53.13 257.8 1.62 9675.2 FR

B0-2.25-40 0 1.81 27.8 33.67 244.3 54.59 255.7 1.62 9712.3 CC

BS-0-2.25-40 0 1.71 26.2 34.74 255.0 52.46 275 1.51 9521.8 CC

BS-19-2.25-40 0.43 1.80 34.2 35.16 263.7 51.54 282.7 1.47 9691.7 CC

BS-36-2.25-40 0.82 1.89 41.4 35.68 272.6 50.32 289.3 1.41 9709.7 CC

BS-58-2.25-40 1.31 2.00 50.6 36.26 283.3 48.89 297.9 1.35 9738.5 CC

Comparison between load-deflection curves of the beams in each set is presented

in Figure ‎5-43 to Figure ‎5-46. A summary of the results of the modeled beams is

presented in Table ‎5-7. Analyzing the results reveals that increasing the prestressing level

in the NSM CFRP strips from 0-58% enlarges the negative camber up to 100% of the

cracking deflection of the non-prestressed strengthened beam in set with 0.75% of

tension steel ratio and up to 76.6% of the cracking deflection of the non-prestressed

strengthened beam in set with 2.25% of tension steel ratio, more details are provided in

Figure ‎5-47.

347

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Neg

ati

ve

cam

be

r to

cra

kin

g d

efl

ec

tio

n

of

BS

-0 i

n e

ac

h s

et

(%

)

Prestressing level (% of CFRP ultimate strength)

Set BS-0.75-40

Set BS-1.25-40

Set BS-1.75-40

Set BS-2.25-40

Figure ‎5-47: Effects of prestressing on negative camber.

At cracking stage; enhancements of 93.1% in cracking load of the non-prestressed

strengthened beam for set with 2.25% of tension steel ratio, and 113.2% in cracking load

of the non-prestressed strengthened beam for set with 0.75% of tension steel ratio were

achieved due to increasing the prestressing level in the NSM CFRP from 0-58%, see

Figure ‎5-48 for more details. Also a maximum increase of 17.6% in cracking deflection

of the non-prestressed strengthened beam was reached by changing the prestressing level

in CFRP from 0-58% for set with 1.75% of tension steel ratio.

348

0

30

60

90

120

0 10 20 30 40 50 60

% o

f ch

an

ge

in

cra

ck

ing

lo

ad

w

.r.t

BS

-0 in

ea

ch

se

t


Set BS-0.75-40

Set BS-1.25-40

Set BS-1.75-40

Set BS-2.25-40

Figure ‎5-48: Effects of prestressing on cracking load.

At yielding stage, enhancements of 28.8% and 11.1% in yielding load of the

beams with 0.75% and 2.25% tension steel ratios were obtained, respectively, with

respect to non-prestressed strengthened beam of each set by changing the prestressing

level in the NSM CFRP from 0-58%, as shown in Figure ‎5-49. In this context, minor

change (less than 4%) on the yielding deflection was observed. The efficiency of the

prestressing can be examined in as much as the non-prestressed strengthening increases

the yielding load of the un-strengthened control beam from 4.4% (in the beam with

2.25% of tension steel ratio) to 20.2% (in the beam with 0.75% of tension steel ratio)

whereas in strengthening with 58% of prestressing these values reach to 16% and 54.7%.

It can be concluded that a linear relationship exists between the prestressing level in

CFRP strip from 0-58% and the percentage of change in cracking and yielding loads.

349

0

10

20

30

0 10 20 30 40 50 60

% o

f ch

an

ge in

yie

ld l

oad

w

.r.t

BS

-0 in

each

set


Set BS-0.75-40

Set BS-1.25-40

Set BS-1.75-40

Set BS-2.25-40

Figure ‎5-49: Effects of prestressing on yield load.

The effect of the prestressing on the ultimate load depends on the type of failure

as presented in Figure ‎5-50. For sets with 1.25% and 1.75% of tension steel ratios, the

ultimate load versus the prestressing level relations are almost downward parabolas,

which is due to change of the type of failure from concrete crushing to CFRP rupture as

the prestressing level increases for these sets, as presented in Table ‎5-7 and Figure ‎5-50.

If failure by CFRP rupture governs, the prestressing results in a small decrease (up to

5.4%) in the ultimate load of the non-prestressed strengthened beam (in the set with

0.75% of tension steel ratio). If failure by concrete crushing governs, the prestressing

causes a small increase (up to 8.3%) in the ultimate load of the non-prestressed

strengthened beam (in set with 2.25% of tension steel ratio). However, non-prestressed

350

strengthening enhances the ultimate load of the un-strengthened beam by 54.7% in set

with 0.75% of tension steel ratio and 7.5% in set with 2.25% of tension steel ratio, as can

be seen by comparing the results (Pu) in Table ‎5-7. It can be concluded that prestressing

of NSM CFRP for strengthening has no significant effect on the ultimate load of the non-

prestressed strengthened beam, as shown in Figure ‎5-50 for analyzed beams. At ultimate

stage, decreases of 59.1% and 6.8% in deflections at ultimate loads of the sets with

0.75% and 2.25% of tension steel ratios were reached, respectively, with respect to the

non-prestressed strengthened beam in each set by changing the prestressing level in NSM

CFRP from 0-58%, more details are provided in Figure ‎5-51.

-10

-5

0

5

10

0 10 20 30 40 50 60

% o

f ch

an

ge in

ult

imate

lo

ad

w

.r.t

BS

-0 in

each

set


Set BS-0.75-40

Set BS-1.25-40

Set BS-1.75-40

Set BS-2.25-40

Figure ‎5-50: Effects of prestressing on ultimate load.

351

-60

-50

-40

-30

-20

-10

0

0 10 20 30 40 50 60

% o

f ch

an

ge in

ult

imate

defl

ecti

on

w

.r.t

BS

-0 in

each

set


Set BS-0.75-40

Set BS-1.25-40

Set BS-1.75-40

Set BS-2.25-40

Figure ‎5-51: Effects of prestressing on ultimate deflection.

Due to decreasing the ultimate deflection, prestressing reduces the ductility index

(deflection at ultimate to deflection at yielding). In this context, decreases of 58% and

10.7% in ductility indices of the sets with 0.75% and 2.25% of tension steel ratios were

achieved, respectively, with respect to the non-prestressed strengthened beam in each set

by changing the prestressing level in NSM CFRP from 0-58%, see Figure ‎5-52 for more

details.

The amount of energy absorption (area under load-deflection response up to peak

load) depends on the type of failure. As shown in Figure ‎5-53 by changing the

prestressing level from 0-58%, a decrease of 60.8% in energy absorption of the set with

0.75% of tension steel ratio occurred with respect to the non-prestressed strengthened

beam in this set. In this context, the amount of decrease is smaller for sets with higher

352

tension steel ratios. The highest amount of energy absorption is reached when balanced

failure occurs (CFRP rupture and concrete crushing simultaneously). This type of failure

utilizes the full capacity of materials. As presented in Table ‎5-7 and Figure ‎5-54 to Figure

‎5-57, the maximum energy absorption is reached when the type of failure changes from

concrete crushing to CFRP rupture. When failure by CFRP rupture governs for a non-

prestressed NSM CFRP strengthened beam, applying and increasing the prestressing

level decreases the energy absorption. When failure by concrete crushing governs for a

non-prestressed NSM CFRP strengthened beam, applying and increasing the prestressing

level enhances the energy absorption. Further, when the tension steel ratio is low

strengthening can cause a wide changes in the energy absorption (e.g., in set with 0.75%

of tension steel ratio, it changes from 24.1% to -51.3% with respect to the un-

strengthened beam, see Figure ‎5-54) but, the changes in the energy absorption are very

small when the tension steel ratio is high (e.g., in set with 2.25% of tension steel ratio, it

changes from -2% to 0.3% with respect to the un-strengthened beam, see Figure ‎5-57).

The type of failure of the strengthened beams changes from concrete crushing to CFRP

rupture with increasing the prestressing level in the NSM CFRP strips.

353

-60

-50

-40

-30

-20

-10

0

0 10 20 30 40 50 60

% o

f ch

an

ge

in

du

cti

lity

in

de

x

w.r

.t B

S-0

in

eac

h s

et


Set BS-0.75-40

Set BS-1.25-40

Set BS-1.75-40

Set BS-2.25-40

Figure ‎5-52: Effects of prestressing on ductility index.

-70

-60

-50

-40

-30

-20

-10

0

10

0 10 20 30 40 50 60

% o

f ch

an

ge in

en

erg

y a

bso

rpti

on

w.r

.t B

S-0

in

each

set


Set BS-0.75-40

Set BS-1.25-40

Set BS-1.75-40

Set BS-2.25-40

Figure ‎5-53: Effects of prestressing on energy absorption.

354

The optimum prestressing level is defined in the previous chapter as the

prestressing level in the NSM CFRP strips (taken as a percentage of the ultimate tensile

strength of the CFRP strips) which maintains the amount of energy absorption in the

strengthened beam equal to the un-strengthened control beam. Calculation of the

optimum prestressing level is illustrated in Figure ‎5-54 to Figure ‎5-57 for each set of

beams. Based on the defined procedure, an optimum prestressing level of 17.5%, 41.1%,

22.8% or 40%, and 38% is obtained for beams with 0.75%, 1.25%, 1.75%, and 2.25% of

tension steel ratio, respectively. It can be seen that as the tension steel ratio increases the

optimum prestressing level increases, however, at a steel ratio of 1.75% two optimum

prestressing levels were obtained (22.8% and 40%) because of the shape of the energy

absorption curve in each steel ratio, which depends on the mode of failure that happens in

the range of applied prestressing levels from 0-58%. If failure by concrete crushing

governs throughout the prestressing range, the curve is ascending. If failure by FRP

rupture governs throughout the prestressing range, the curve is descending. When

balanced failure happens in the prestressing range (i.e., there is a transition in mode of

failure within the prestressing range from concrete crushing to CFRP rupture) the curve is

downward facing parabola, and in this case, there is possibility to have two optimum

prestressing levels that each one is related to separate type of failure.

355

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60

Are

a u

nd

er

loa

d-d

efl

ec

tio

n c

urv

e

(kN

.mm

)

Prestress level (% of CFRP ultimate strength)

Energy absorption (BS-0.75 set)

Energy absorption of unstrengthened beam


Figure ‎5-54: Determination of optimum prestressing level for set BS-0.75.

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60

Are

a u

nd

er

loa

d-d

efl

ec

tio

n c

urv

e

(kN

.mm

)






356

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60

Are

a u

nd

er

load

-de

flec

tio

n c

urv

e

(kN

.mm

)






0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60

Are

a u

nd

er

loa

d-d

efl

ec

tio

n c

urv

e

(kN

.mm

)






357

5.3.6.2 Effects of Tension Steel Reinforcement

To assess the effect of tension steel ratio, the modeled beams were categorized as

presented in Table ‎5-8 in which each set consists of beams with the same prestressing

level and various tension steel ratios.

Table ‎5-8: Summary of the results for the effects of tension steel ratio.

Beam ID Δo

(mm)

Δcr

(mm)

Pcr

(kN)

Δy

(mm)

Py

(kN)

Δu

(mm)

Pu

(kN) µD

Φ

(kN·mm) FM

B0-0.75-40 0 1.68 23.0 22.30 84.8 118.47 103.8 5.31 10411 CC

B0-1.25-40 0 1.73 24.6 26.75 141.5 80.52 155.8 3.01 10207.8 CC

B0-1.75-40 0 1.77 26.2 30.40 195.1 66.78 208.7 2.20 10637 CC

B0-2.25-40 0 1.81 27.8 33.67 244.3 54.59 255.7 1.62 9712.3 CC

BS-0-0.75-40 0 1.58 21.6 25.52 101.9 111.02 160.6 4.35 12922.5 FR

BS-0-1.25-40 0 1.61 22.9 28.06 154.0 78.69 195.9 2.80 11326.6 CC

BS-0-1.75-40 0 1.65 24.5 31.71 206.2 62.43 235.6 1.97 10384.9 CC

BS-0-2.25-40 0 1.71 26.2 34.74 255.0 52.46 275 1.51 9521.8 CC

BS-19-0.75-40 0.52 1.68 30.0 25.29 111.0 87.68 157.2 3.47 10196.8 FR

BS-19-1.25-40 0.49 1.69 31.0 28.37 164.2 78.16 205.3 2.76 11975.1 CC

BS-19-1.75-40 0.46 1.75 32.6 32.09 215.9 60.91 244.4 1.90 10577.6 CC

BS-19-2.25-40 0.43 1.80 34.2 35.16 263.7 51.54 282.7 1.47 9691.7 CC

BS-36-0.75-40 0.99 1.74 37.2 25.12 120.6 67.92 155.5 2.70 7877 FR

BS-36-1.25-40 0.93 1.76 38.3 28.83 173.7 70.22 209.4 2.44 10979.3 FR

BS-36-1.75-40 0.87 1.81 39.6 32.51 225.1 60.01 252.1 1.85 10850.4 CC

BS-36-2.25-40 0.82 1.89 41.4 35.68 272.6 50.32 289.3 1.41 9709.7 CC

BS-58-0.75-40 1.58 1.80 46.0 24.84 131.2 45.4 151.9 1.83 5067.2 FR

BS-58-1.25-40 1.48 1.88 47.7 29.30 186.1 51.16 208.3 1.75 7685.6 FR

BS-58-1.75-40 1.39 1.94 49.1 32.88 236.3 53.13 257.8 1.62 9675.2 FR

BS-58-2.25-40 1.31 2.00 50.6 36.26 283.3 48.89 297.9 1.35 9738.5 CC

Analyzing the predicted results shows that increasing the tension steel ratio from

0.75% to 2.25%:

Reduces the negative camber up to 17% for all sets, as shown in Figure ‎5-58

Increases negligibly the cracking deflection up to 8.2% for the non-prestressed

strengthened set and up to 10.8% for the set with 58% of prestressing

358

Enhances the cracking load up to 9.9% for set with 58% of prestressing and up

to 21.3% for the non-prestressed strengthened set, as shown in Figure ‎5-59

Enlarges the deflection at yielding up to 36.1% for the non-prestressed

strengthened set and up to 45.9% for the strengthened set with 58% of

prestressing

Enlarges the deflection at yielding in the un-strengthened set up to 51%

Increases the yielding load up to 150.2% for the non-prestressed strengthened

set and up to 115.9% for the strengthened set with 58% of prestressing, as

shown in Figure ‎5-60

Enhances the yielding load in un-strengthened set up to 188.1%;

Decreases the ultimate deflection when failure by concrete crushing governs

(as represented in Figure ‎5-62 and Table ‎5-8 for non-prestressed strengthened

set)

Enhances the ultimate deflection when the failure by CFRP rupture governs

(as represented in Figure ‎5-62 and for the strengthened set with 58% of

prestressing)

Results from Table ‎5-8 reveal that the maximum deflection occurs when the type

of failure changes from CFRP rupture to concrete crushing.

Furthermore, changing the steel ratio from 0.75% to 2.25%:

Increases the ultimate load up to 71.2% for the non-prestressed strengthened


shown in Figure ‎5-61

359

Decreases the ductility index up to 65.2% for the non-prestressed strengthened


shown in Figure ‎5-63;

Changes the failure mode from CFRP rupture to concrete crushing

The changes in the amount of energy absorption versus tension steel ratio is

plotted in Figure ‎5-64. The curve reaches to its highest value when there is a transition in

mode of failure (From CFRP rupture to concrete crushing). As long as failure by CFRP

rupture governs, increasing the steel ratio enhances the energy absorption and as long as

failure by concrete crushing governs, increasing the steel ratio decreases the energy

absorption, as can be seen in Figure ‎5-64.

-20

-15

-10

-5

0

0.75 1 1.25 1.5 1.75 2 2.25

% o

f ch

an

ge in

neg

ati

ve c

am

ber

w.r

.t o

f B

S-0

.75 in

each

set

Tension steel ratio (%)

Set BS-19-40

Set BS-36-40

Set BS-58-40

Figure ‎5-58: Effects of tension steel ratio on negative camber.

360

0

5

10

15

20

25

0.75 1 1.25 1.5 1.75 2 2.25

% o

f c

ha

ng

e in

cra

ck

ing

lo

ad

w

.r.t

BS

-0.7

5 in

ea

ch

se

t


Set BS-0-40

Set BS-19-40

Set BS-36-40

Set BS-58-40

B0-40

Figure ‎5-59: Effects of tension steel ratio on cracking load.

0

50

100

150

200

0.75 1 1.25 1.5 1.75 2 2.25

% o

f ch

an

ge in

yie

ld l

oad

w

.r.t

BS

-0.7

5 in

eac

h s

et


Set BS-0-40

Set BS-19-40

Set BS-36-40

Set BS-58-40

B0-40

Figure ‎5-60: Effects of tension steel ratio on yield load.

361

0

40

80

120

160

0.75 1 1.25 1.5 1.75 2 2.25

% o

f ch

an

ge in

ult

imate

lo

ad

w

.r.t

BS

-0.7

5 in

eac

h s

et


Set BS-0-40

Set BS-19-40

Set BS-36-40

Set BS-58-40

B0-40

Figure ‎5-61: Effects of tension steel ratio on ultimate load.

-60

-40

-20

0

20

0.75 1 1.25 1.5 1.75 2 2.25

% o

f c

ha

ng

e in

ult

ima

te d

efl

ec

tio

n

w.r

.t B

S-0

.75

in

ea

ch

se

t


Set BS-0-40

Set BS-19-40

Set BS-36-40

Set BS-58-40

B0-40

Figure ‎5-62: Effects of tension steel ratio on ultimate deflection.

362

-80

-60

-40

-20

0

0.75 1.25 1.75 2.25

% o

f ch

an

ge in

du

cti

lity

in

dex

w.r

.t B

S-0

.75 in

eac

h s

et


Set BS-0-40

Set BS-19-40

Set BS-36-40

Set BS-58-40

B0-40

Figure ‎5-63: Effects of tension steel ratio on ductility index.

-40

-20

0

20

40

60

80

100

0.75 1 1.25 1.5 1.75 2 2.25

% o

f c

ha

ng

e in

en

erg

y a

bs

orp

tio

nw

.r.t

BS

-0.7

5 in

ea

ch

se

t


Set BS-0-40

Set BS-19-40

Set BS-36-40

Set BS-58-40

B0-40

Figure ‎5-64: Effects of tension steel ratio on energy absorption.

363

5.3.6.3 Effects of Concrete Compressive Strength

To examine the effect of concrete compressive strength on the behaviour of the

RC beams strengthened with prestressed NSM CFRP strips, four beams with tension steel

ratio of 1.25% and strengthened with the same prestressing level (36% of CFRP ultimate

tensile strength) but using different concrete compressive strengths of 30 MPa, 40 MPa,

50 MPa, and 60 MPa were analyzed. The load-deflection curves of the strengthened

beams with different concrete compressive strengths are presented in Figure ‎5-65. A

summary of the results for the effects of concrete compressive strength is presented in

Table ‎5-9.

0

25

50

75

100

125

150

175

200

225

-10 0 10 20 30 40 50 60 70 80

Lo

ad

(k

N)


BS-36-1.25-60 (f'c = 60MPa, FE Analysis)





Figure ‎5-65: Effects of concrete compressive strength on the load-deflection curve.

364

When the concrete compressive strength increases: the type of failure changes

from concrete crushing to CFRP rupture; the ductility index slightly increases; the energy

absorption decreases slightly when CFRP rupture governs and reaches to its maximum

value when balanced failure occurs; the camber due to prestressing decreases (up to

22.8%); the cracking and yielding deflections decrease negligibly (up to 4.4% and 13.8%,

respectively); the ultimate deflection slightly decreases when the failure by CFRP rupture

governs; and the cracking, yielding, and ultimate loads increase (up to 17.4%, 2.8%, and

9.8%, respectively). It can be concluded that changing the concrete compressive strength

has a very slight effect on the overall flexural behaviour of the RC beams strengthened

with prestressed NSM CFRP strips.

Table ‎5-9: Summary of the results for the effects of concrete compressive strength.

Beam ID Δo

(mm)

Pcr

(kN)

Δcr

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) µD

Φ

(kN·mm) FM

BS-36-1.25-30 1.04 36.4 1.85 171.2 30.71 197.2 61.93 2.02 8911.2 CC

BS-36-1.25-40 0.93 38.3 1.76 172.4 28.26 209.4 70.22 2.49 10979.3 FR

BS-36-1.25-50 0.85 40.3 1.73 173.9 27.03 213.7 68.05 2.52 10846.7 FR

BS-36-1.25-60 0.80 42.7 1.77 175.9 26.47 216.3 66.86 2.53 10774.2 FR

5.4 FE Modeling of Steel End Anchor and Parametric Study

In this section, a 3D FE model is developed using ANSYS program to simulate

the behaviour of the end-steel end anchor used for the prestressed NSM CFRP

strengthening system. This type of anchor , as shown in Figure ‎5-66, was first developed

and used by Gaafar (2007) to implement a practical prestressing system for the NSM

strengthening and to overcome the drawbacks of the previous systems available in the

literature (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Badawi and Soudki,

2009) explained in more details in Chapter Two. After developing the FE model and

365

making sure about the accuracy of the results, a parametric study was performed, as

presented in this section, to analyze the effects of the adhesive thickness, the bond

characteristics, and the anchor length on the performance of the anchor and interfacial

shear stress distribution.

Figure ‎5-66: Anchorage system for prestressed NSM-CFRP strengthening.

5.4.1 Description of the FE Model

The modeled end anchor is 3D consisting of CFRP strips, epoxy adhesive, steel

anchor and steel bolts which are simulated by using the appropriate solid elements

available in the ANSYS program. Due to symmetry, only half of the anchor was modeled

to facilitate the preprocessing and post processing steps. The CFRP-epoxy and epoxy-

anchor interfaces were modeled by applying contact elements and assigning well-known

Steel end anchor

Kwik anchor bolt

Temporary fixed bracket

CFRP strips

Temporary movable bracket

366

Coulomb friction model (based on cohesion and internal friction) to consider the

interaction between normal and shear stresses. Since this part of the research is a pure FE

one, the accuracy of the model was confirmed by conducting a sensitivity analysis on the

results, then, a parametric study (including 14 models as presented in Table ‎5-10) was

performed to investigate the effects of bond cohesion, anchor length, anchor width, and

anchor height on the interfacial stress distributions and bond performance. The model ID

specifies Lt (the length of anchor tube, mm)-C (cohesion, MPa)-Ha (height of the

adhesive between CFRP and steel tube in the vertical direction, mm)-Wa (width of the

adhesive between CFRP and steel tube in the horizontal direction, mm). More details

about the geometry of the modeled end anchors are presented in Figure ‎5-67.

Table ‎5-10: Summary of the modeled steel end anchors.

Model ID

Anchor tube Interface Adhesive CFRP Bolt Anchor plate

Lt×Wt×Ht×Tt

(mm)

C

(MPa) µ

Ha

(mm)

Wa

(mm)

Lf×Wf×Tf

(mm)

db-dh

(mm)

Lp×Wp×Tp

(mm)

Lt250-C5-Ha1.5-Wa7

250×25×25×3

5

0.65

1.5

7

400×16×5

16-19 150×140×9.5

Lt250-C10-Ha1.5-Wa7 10

Lt250-C15-Ha1.5-Wa7 15

Lt250-C20-Ha1.5-Wa7 20

Lt150-C10-Ha1.5-Wa7 150×25×25×3

10

300×16×5

Lt200-C10-Ha1.5-Wa7 200×25×25×3 350×16×5

Lt300-C10-Ha1.5-Wa7 300×25×25×3 450×16×5

Lt350-C10-Ha1.5-Wa7 350×25×25×3 500×16×5

Lt400-C10-Ha1.5-Wa7 400×25×25×3 550×16×5

Lt450-C10-Ha1.5-Wa7 450×25×25×3 600×16×5

Lt250-C10-Ha1.5-Wa3.5 250×18×25×3 3.5

400×16×5

Lt250-C10-Ha1.5-

Wa10.5 250×32×25×3 10.5

Lt250-C10-Ha4.5-Wa7 250×25×31×3 4.5 7

Lt250-C10-Ha7.5-Wa7 250×25×37×3 7.5

Lt= length of anchor tube Wt= width of anchor tube Ht= height of anchor tube Tt= thickness of anchor tube

Lf= length of CFRP strips Wf= width of CFRP strips Ha= height of adhesive Tf= thickness of CFRP strips

Lp= length of anchor plate Wp= width of anchor plate C= cohesion µ= friction coefficient

db=bolt diameter Wa=adhesive width dh=hole diameter

367

Figure ‎5-67: Details of the modeled end anchors and abbreviation of dimensions.


5.4.2.1 Steel End Anchor

Eight-node solid brick element (Solid45) was employed to model the steel

material of the anchor. Characteristics of this element are provided in Section 5.2.3.3. A

multi-linear stress-strain curve assigned to the steel material is presented in Figure ‎5-68.

Also, a Poissons’s ratio of 0.3 was considered for the steel material (Emam, 2007).

368

Figure ‎5-68: Stress-strain curve of anchor steel (Emam, 2007).

5.4.2.2 CFRP Strip

The CFRP strip was modeled using the Soild45 element. Based on the stress-

strain curve of the CFRP material, a multi-linear elastic material model was assigned to

them as shown in Figure ‎5-10 obtained from experimental results, with a Poisson’s ratio

of 0.22 for CFRP material (Kachlakev et al., 2001).

5.4.2.3 Epoxy Adhesive

In the NSM strengthening system the epoxy adhesive had been used to fill in the

groove and bond the CFRP strip to the inside of the steel anchor. The epoxy was

simulated using the Solid45 element. The employed epoxy adhesive was Sikadur® 330

with a multi-linear elastic material stress-strain curve presented in Figure ‎5-11. A

Poisson’s ratio of 0.3 was assigned to Sikadur® 330 (Haghani, 2010).

369

5.4.2.4 Anchor Bolt

In the developed anchorage system for the prestressed NSM-CFRP strengthening

system (Gaafar, 2007), the end steel anchors are mounted on the substrate concrete using

anchor bolts (Kwik bolt 3 expansion anchor) made of carbon steel (Hilti Inc.). These

bolts were simulated using Solid45 elements in the FE analysis. A multi-linear material

model, obtained from data sheet of these bolts, was assigned to bolt elements as shown in

Figure ‎5-69. A Poisson’s ratio of 0.29 for carbon steel was assigned to the bolts

(Engineers edge, 2012).

Figure ‎5-69: Stress-strain curve for anchor bolts (Hilti Inc).

5.4.2.5 Bond

The CFRP-epoxy, steel-epoxy, and bolt-hole interfaces were modeled using

contact elements. The Coulomb friction model was applied to the interfaces to take into

account the interaction between interface materials in terms of interfacial shear and

pressure. A surface-to-surface contact pairs were applied to the interfaces, the target

surface on stiffer material of the corresponding interface was modeled using TARGE170

370

and the contact surface on softer material of the interface was modeled using CONTA

173. Characteristics of these elements are provided in Section 5.2.4.

The failure at steel-epoxy and CFRP-epoxy interfaces was defined using Coulomb

friction model criteria. In the Coulomb friction model, two contacting materials can carry

shear stresses up to a certain magnitude across their interface before they start sliding

relative to each other; this state is known as sticking. The Coulomb friction model defines

an equivalent shear stress at which sliding on the surface begins as a fraction of the

contact pressure as presented in Equation 5-26 (SAS, 2009):

Cp Equation ‎5-26

where τ is the shear strength (MPa), µ the friction coefficient, p the contact pressure

(MPa), and C is the cohesion sliding resistance (MPa). Once the shear stress exceeds the

shear strength calculated from Equation 5-26, the two surfaces slides relative to each

other; this state is known as sliding. The surface friction coefficient depends on

temperature, time, normal pressure, sliding distance, or sliding relative velocity. In the FE

analysis, a friction coefficient of 0.65 was assigned to the interfaces (Varastehpour &

Hamelin, 1997).

5.4.3 Mesh Sensitivity Analysis

As mentioned earlier in Section 5.2.6, the FE results should not depend on the

element type or size; and since this part is an FE analysis where there is no experimental

results available to validate the FE model, therefore, performing a sensitivity analysis is

371

required. To identify the optimum number of elements four primary FE models,

considering complete bond between interfaces, with 1509, 2813, 5077, and 8309 number

of elements were developed for a 250 mm tube length steel anchor (model Lt250-C5-

Ha1.5-Wa7). These FE models are presented in Figure ‎5-70 to Figure ‎5-73. The optimum

model was selected based on the sensitivity curve obtained for displacement at loaded

end of the CFRP strips at 100 kN applied load, as shown in Figure ‎5-74. As can be seen

in Figure ‎5-74, the major change of the curve occurs at about 2800 number of elements,

therefore, any model with number of elements greater than 2800 leads to high accuracy

whereas the model with 5077 elements was selected (with about 99.3% result reliability

calculated with respect to the model with high number of the elements, 8309 elements).

The selected model based on sensitivity analysis was a primary model considering

complete bond, the final model was developed by assigning the contact elements to the

steel-epoxy and CFRP-epoxy interfaces of the selected primary model and the number of

elements was reached to 7371. It should be mentioned that the optimum model should

result in both the accurate responses and a reasonable computer computational time.

Although picking a model with a very high number of elements (from the last flat part of

the sensitivity curve) leads to the accurate responses, but it does not necessarily mean the

picked model is optimum since it results in an excessive long computer computational

time.

372

Figure ‎5-70: Anchorage model with 1509 elements developed for sensitivity analysis.


373



374

2.5

2.54

2.58

2.62

2.66

2.7

0 1500 3000 4500 6000 7500 9000Dis

pla

cem

en

t at

lo

ad

ed

en

d

of

CF

RP

str

ips (

mm

)

Number of elements


Figure ‎5-74: Mesh sensitivity (at 100 kN).


The nonlinear solution was executed using a displacement control method in

which non-zero displacement constraints were assigned to the nodes at the CFRP free

end. The main reasons for applying displacement control were to obtain any descending

branch in the load-displacement response and a better recognition of failure. After several

trials on convergence of the model, a maximum displacement convergence tolerance of

0.01 was applied to the model. Based on the load response of the anchor, convergence

behaviour, and computer computational time only one load-step was defined with number

of sub-steps varies from a minimum (20) to a maximum (20000) value. The typical

meshed anchor is presented in Figure ‎5-75. Due to symmetry, only half of the steel

anchor was modeled and appropriate constraint was assigned to the plan of symmetry.

The assigned constraints are presented in Figure ‎5-76. It is assumed that the Kwik bolts

are fixed in the concrete; therefore, the fixed constraints were assigned to the model at the

375

top parts of the bolts. The nuts on the bolts which are in contact with the plate were

simulated by assigning the vertical constraints to the steel plate in the bolt vicinity.

376

(a) Isometric view (b) Cross-section

(c) Plan view

Figure ‎5-75: Meshed anchor (steel tube length = 250 mm).

Bolt

Steel plate

Steel tube

CFRP strip

Epoxy adhesive

Wa Ha

376

377

(a) Isometric view (b) Elevation

(c) Plan view (d) Cross-section

Figure ‎5-76: Assigned constraints to the anchor model.

377

378

5.4.5 Numerical Results and Discussion

5.4.5.1 Effects of Bond Cohesion

Four FE models (presented in Table ‎5-11) with different cohesion values for

CFRP-epoxy and steel-epoxy interfaces varies from 5-20 MPa were considered to

investigate the effects of bond cohesion on the performance of the steel end anchor. The

results are plotted in Figure ‎5-77 to Figure ‎5-79 showing the load-displacement at the

CFRP free end response and the interfacial shear stress (friction) distribution at the

CFRP-epoxy and the steel-epoxy interfaces.

0

30

60

90

120

150

180

0 1 2 3 4 5 6 7

Lo

ad

(k

N)

Displacement at CFRP loaded-end (mm)

Lt250-C5-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7

Lt250-C15-Ha1.5-Wa7 Lt250-C20-Ha1.5-Wa7

Figure ‎5-77: Effects of cohesion value (5-20 MPa) on load-displacement curves.

379

0

5

10

15

20

0 50 100 150 200 250

Fri

cti

on

at

vert

ical in

terf

ace b

etw

een

C

FR

P a

nd

ep

oxy (

MP

a)

Distance from anchor end (mm)

Lt250-C5-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7

Lt250-C15-Ha1.5-Wa7 Lt250-C20-Ha1.5-Wa7

Figure ‎5-78: Effects of cohesion value (5-20 MPa) on shear stress at CFRP-epoxy

vertical interface at 50 kN.

0

5

10

15

20

0 50 100 150 200 250

Fri

cti

on

at

vert

ical in

terf

ace b

etw

een

s

tee

l a

nd

ep

ox

y (

MP

a)


Lt250-C5-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7

Lt250-C15-Ha1.5-Wa7 Lt250-C20-Ha1.5-Wa7

Figure ‎5-79: Effects of cohesion value (5-20 MPa) on shear stress at steel-epoxy


CFRP-epoxy

vertical interface

Steel-epoxy

vertical interface

380

Table ‎5-11: Summary of FE results, cohesion effects.

Model ID Pu (kN) Δu (mm) FM

Lt250-C5-Ha1.5-Wa7 53.5 2.54 DB

Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB

Lt250-C15-Ha1.5-Wa7 153.5 5.87 DB

Lt250-C20-Ha1.5-Wa7 161.4 5.89 FR Pu and Δu= load and displacement at ultimate FM= failure mode

DB= debonding at CFRP-epoxy interface FR= CFRP rupture

The results reveal that the ultimate load significantly increases by improving the

bond cohesion property. A 201.5% increase in ultimate capacity was obtained by

changing the cohesion value from 5-20 MPa; on the other hand, the mode of failure

changes from debonding at the CFRP-epoxy interface to CFRP rupture. Furthermore,

analyzing Figure ‎5-77 reveals that the debonding failure in the models with low value of

bond cohesion occurs gradually causing a plastic deformation for anchors Lt250-C5-

Ha1.5-Wa7 and Lt250-C10-Ha1.5-Wa7 at ultimate stage.

The shear stress (friction) distributions at the CFRP-epoxy and the steel-epoxy

vertical interfaces at load 50kN is plotted in Figure ‎5-78 and Figure ‎5-79. These results

reveal that the shape of the distribution is a left-skewed curve where the peak is located

within the last 20 mm of the steel tube at the loaded end. In this context, the superior part

of the skewed curve is limited by the interface strength as can be seen in Figure ‎5-78.

When the cohesion value of the interface decreases more length of the anchor is utilized

to dissipate the energy and transfer the applied load, therefore, the maximum value of the

stress decreases. The smaller area of the CFRP-epoxy interface than the steel-epoxy

interface causes the higher interfacial shear stress at this interface in comparison with

steel-epoxy interface, as it can be seen in comparison between corresponding curves in

Figure ‎5-78 and Figure ‎5-79.

381

5.4.5.2 Effects of Anchorage Length

The effect of the NSM CFRP anchorage bond length was examined by

considering seven different FE models where anchor tube length varies from 150-450

mm as presented in Figure ‎5-80 and Table ‎5-12. The predicted load-displacement curves

and interfacial shear stress distributions are plotted in Figure ‎5-81 to Figure ‎5-83. The

results show that increasing the NSM CFRP anchorage bond length from 150-400 mm

enhances the ultimate capacity up to 145.9% while the mode of failure changes from

debonding at the CFRP-epoxy interface to CFRP rupture occurred at the tip of the steel

tube at the loaded-end. Furthermore, increasing the anchorage bond length from 400-450

mm has no effect on the capacity of the anchorage system. Based on the results, a

minimum bond length of 378 mm avoids debonding failure and allows the CFRP to

achieve its full tensile capacity.

382

(a) Lt150-C10-Ha1.5-Wa7

(b) Lt200-C10-Ha1.5-Wa7

(c) Lt250-C10-Ha1.5-Wa7

(d) Lt300-C10-Ha1.5-Wa7

(e) Lt350-C10-Ha1.5-Wa7

(f) Lt400-C10-Ha1.5-Wa7

(g) Lt450-C10-Ha1.5-Wa7

Figure ‎5-80: Developed FE models for the effects of anchorage length.

383

0

30

60

90

120

150

180

0 1 2 3 4 5 6 7 8

Lo

ad

(kN

)


Lt150-C10-Ha1.5-Wa7 Lt200-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7


Lt450-C10-Ha1.5-Wa7

Figure ‎5-81: Effects of bond length (150-450 mm) on load-displacement curves.

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450

Fri

cti

on

at

ve

rtic

al in

terf

ac

e b

etw

ee

n

CF

RP

an

d e

po

xy (

MP

a)




Lt450-C10-Ha1.5-Wa7

Figure ‎5-82: Effects of bond length (150-450 mm) on shear stress at CFRP-epoxy


CFRP-epoxy

vertical interface

384

0

1

2

3

4

5

6

7

8

9

10

0 50 100 150 200 250 300 350 400 450

Fri

cti

on

at

vert

ical in

terf

ace b

etw

een

ste

el an

d e

po

xy (

MP

a)




Lt450-C10-Ha1.5-Wa7

Figure ‎5-83: Effects of bond length (150-450 mm) on shear stress at steel-epoxy


Table ‎5-12: Summary of FE results, anchor length effects.


Lt150-C10-Ha1.5-Wa7 65.4 2.07 DB

Lt200-C10-Ha1.5-Wa7 85.6 3.46 DB

Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB

Lt300-C10-Ha1.5-Wa7 128.1 5.89 DB

Lt350-C10-Ha1.5-Wa7 149 7.26 DB

Lt400-C10-Ha1.5-Wa7 160.9 7.72 FR

Lt450-C10-Ha1.5-Wa7 160.7 7.71 FR

Pu and Δu= load and displacement at ultimate FM= failure mode

DB= debonding at CFRP-epoxy interface FR= CFRP rupture

Analyzing the shear stress distributions at 50 kN for different bond anchorage

lengths in Figure ‎5-82 and Figure ‎5-83 reveals that in spite of the change in length of the

anchor the distributions and maximum shear stress are similar. In this context, when the

anchorage bond length is short, in case of Lt150-C10-Ha1.5-Wa7 as shown in Figure

Steel-epoxy vertical interface

385

‎5-82, an increase in the shear stress distribution occurs to transfer the loads, which

gradually causes debonding as the applied load increases.

5.4.5.3 Effects of Adhesive Width

The effects of the adhesive width (Wa in Figure ‎5-57) on the load-displacement

curves and interfacial stress distributions were analyzed by developing three FE models

(as presented in Figure ‎5-84) where the adhesive width varies from 3.5-10.5 mm

corresponding to 0.7-2.1 times the CFRP thickness. The results are presented in Figure

‎5-85 to Figure ‎5-89 and Table ‎5-13. All the FE models failed due to debonding at the

CFRP-epoxy interface. Analyzing the results reveals that changing the width of the

adhesive has insignificant effects on the load-displacement response, as presented in

Figure ‎5-85 and Table ‎5-13. On the other hand, comparing the interfacial shear stress

distributions reveals that increasing the adhesive width from 3.5-10.5 mm decreases the

maximum interfacial shear stress at the steel-epoxy vertical interface up to 54.3% as

plotted in Figure ‎5-87, while has insignificant effects on the shear stress distributions at

other interfaces as presented in Figure ‎5-86, Figure ‎5-88, and Figure ‎5-89. It should be

mentioned that if the failure occurs due to debonding at the steel-epoxy interface, any

increase in adhesive width, which leads to a major decrease in steel-epoxy interfacial

stress, results in a significant enhancement on the capacity of anchorage.

386

(a) Lt250-C10-Ha1.5-Wa3.5 (b) Lt250-C10-Ha1.5-Wa7 (c) Lt250-C10-Ha1.5-Wa10.5

Figure ‎5-84: Developed FE models for the effects of adhesive width.

386

387

0

20

40

60

80

100

120

0 1 2 3 4 5 6

Lo

ad

(kN

)


Lt250-C10-Ha1.5-Wa3.5

Lt250-C10-Ha1.5-Wa7

Lt250-C10-Ha1.5-Wa10.5

Figure ‎5-85: Effects of adhesive width (Wa=3.5-10.5 mm) on load-displacement

curves.

Table ‎5-13: Summary of FE results, adhesive width effects.


Lt250-C10-Ha1.5-Wa3.5 106.2 4.43 DB

Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB

Lt250-C10-Ha1.5-Wa10.5 107 4.56 DB


DB= debonding at CFRP-epoxy interface

388

0

2

4

6

8

10

12

0 50 100 150 200 250

Fri

cti

on

at

ho

rizo

nta

l in

terf

ace b

etw

een

ste

el an

d e

po

xy (

MP

a)


Lt250-C10-Ha1.5-Wa3.5 Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa10.5


epoxy horizontal interface at 50 kN.

0

2

4

6

8

10

12

0 50 100 150 200 250

Fri

cti

on

at

vert

ical in

terf

ace b

etw

een

ste

el an

d e

po

xy (

MP

a)




epoxy vertical interface at 50 kN.

Steel-epoxy

horizontal interface

Steel-epoxy

vertical interface

389

0

2

4

6

8

10

12

0 50 100 150 200 250Fri

cti

on

at

ho

rizo

nta

l in

terf

ace b

etw

een

C

FR

P a

nd

ep

oxy (

MP

a)





0

2

4

6

8

10

12

0 50 100 150 200 250

Fri

cti

on

at

vert

ical in

terf

ace b

etw

een

C

FR

P a

nd

ep

oxy (

MP

a)





CFRP-epoxy


CFRP-epoxy vertical interface

390

5.4.5.4 Effects of Adhesive Height

The effects of adhesive height (Ha in Figure ‎5-57) on the performance of the

NSM CFRP anchorage were analyzed by developing three models as presented in Figure

‎5-90 where the adhesive height varies from 1.5-7.5 mm corresponding to 0.094-0.47

times the CFRP width. The results are plotted in Figure ‎5-91 to Figure ‎5-95. Analyzing

Figure ‎5-92 to Figure ‎5-95 shows that increasing the adhesive height has a significant

effect on the shear stress distribution at the horizontal steel-epoxy interface. In this

context, a 62.9% decrease in the maximum interfacial shear stress is reached by

increasing the adhesive height from 1.5-7.5 mm as presented in Figure ‎5-92. On the other

hand, the effects of adhesive height on the shear stress distribution at the CFRP-epoxy

interfaces and the vertical steel-epoxy interface are insignificant as presented in Figure

‎5-93 to Figure ‎5-95. The FE models failed due to debonding at the CFRP-epoxy interface

and increasing the adhesive height almost has no effect on the load-displacement

response of the anchor since it has minor effects on the stress distribution at CFRP-epoxy

interfaces.

391

(a) Lt250-C10-Ha1.5-Wa7 (b) Lt250-C10-Ha4.5-Wa7 (c) Lt250-C10-Ha10.5-Wa7

Figure ‎5-90: Developed FE models for the effects of adhesive height.

391

392

0

20

40

60

80

100

120

0 1 2 3 4 5 6

Lo

ad

(k

N)


Lt250-C10-Ha1.5-Wa7

Lt250-C10-Ha4.5-Wa7

Lt250-C10-Ha7.5-Wa7

Figure ‎5-91: Effects of adhesive height (Ha=1.5-7.5 mm) on load-displacement

curves.

Table ‎5-14: Summary of FE results, adhesive height effects.


Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB

Lt250-C10-Ha4.5-Wa7 106.9 4.42 DB

Lt250-C10-Ha7.5-Wa7 106.9 4.46 DB


DB= debonding at CFRP-epoxy interface

393

0

2

4

6

8

10

12

0 50 100 150 200 250

Fri

cti

on

at

ho

rizo

nta

l in

terf

ac

e b

etw

een

s

tee

l a

nd

ep

ox

y (

MP

a)





0

2

4

6

8

10

12

0 50 100 150 200 250

Fri

cti

on

at

ve

rtic

al in

terf

ac

e b

etw

ee

n

ste

el a

nd

ep

ox

y (

MP

a)





Steel-epoxy


Steel-epoxy vertical interface

394

0

2

4

6

8

10

12

0 50 100 150 200 250Fri

cti

on

at

ho

rizo

nta

l in

terf

ac

e b

etw

een

C

FR

P a

nd

ep

ox

y (

MP

a)





0

2

4

6

8

10

12

0 50 100 150 200 250

Fri

cti

on

at

ve

rtic

al in

terf

ac

e b

etw

ee

n

CF

RP

an

d e

po

xy (

MP

a)





CFRP-epoxy


CFRP-epoxy

vertical interface

395

5.5 Analytical Modeling of RC Beams Strengthened With Prestressed NSM-CFRP

Reinforcements Subjected to Freeze-Thaw Exposure

The Load-deflection responses of the nine tested beams in phase I are predicted

analytically by developing a code in Wolfarm Mathematica software (Wolfarm Research,

2008). It should be mentioned that, since the freeze-thaw cycling exposure had minor

effects on the concrete material and bond at the concrete-epoxy interface, the developed

FE model described in Section 5.2 could have been employed to model the exposed

beams in phase I by assigning the appropriate material properties. But, the FE modeling

of the tested beams in phase II, which is presented in Section 5.6, has all the aspects

required for FE modeling of the beams in phase I and to avoid repetition, the beams in

phase I have been modeled analytically. The developed analytical code aims to generate

the load-deflection response for strengthened/un-strengthened rectangular RC beams with

prestressed/non-prestressed FRP material under four-point bending configuration. It has

the capabilities of assigning the actual concrete stress-strain curve based on Loov's

equation (Loov, 1991), elasto-plastic behaviour for the compression and tension

reinforcing steel bars, linear behaviour for the FRP reinforcements (strip or rebar), and

different prestressed CFRP length along the length of the beam. Since the overall flexural

behaviour of the tested beams in phase I is not affected by debonding as was observed

during the tests, the perfect bond is assumed in the analytical model, therefore, two

failure modes, CFRP rupture or concrete crushing, are considered. The analytical code

can be modified for different type of the loading by making a few changes on the applied

moment along the length of the beam. Conceptually, the mid-span deflection at each

applied moment is calculated using integration of curvatures along the length of the beam

396

(from support to mid-span). To achieve accurate results, the half-length of the beam was

divided to 51 elements in the shear span and one element in the constant moment region.

The main advantage of the developed analytical code versus FE analysis is that the

developed code has a much shorter computer computational time (6 min for analytical

model versus 8 hrs for FE model). Furthermore, the predicted results are in a very good

correlation with the experimental ones.

5.5.1 Experimental Program Overview

Nine RC beams tested in phase I of the experimental program were analyzed by

considering the effects of freeze-thaw exposure. One beam was considered as the un-

strengthened control RC beam, four beams were strengthened using NSM CFRP strips

(2×16 mm strips glued together from the side and mounted in one groove on the tension

side of the beam), and the other four beams were strengthened using NSM CFRP rebars

(9.5 mm diameter rebar). A summary of the test results including the prestrain in the

CFRP rebar or strip was presented in Table ‎4-2. Details of the beams were plotted in

Figure ‎3-1. The beams were exposed to 500 freeze-thaw cycles. Each cycle, consisting of

eight intervals programmed to be accomplished in 8hrs, include the lower temperature

bound of -34oC and the upper temperature bound of +34

oC with a relative humidity of

75% for temperature above +20oC. Details of the intervals and trend of three freeze-thaw

cycles were presented in Section 3.6.

397

5.5.2 Description of Algorithm

The developed analytical model generates the load-deflection response of the

tested RC beams using numerical integration of the curvatures along the length of the

beam. The algorithm includes seven steps to produce the load-deflection response and the

source code is written in Wolfarm Mathematica (Wolfarm Research, 2008), a powerful

automated technical computing software. The inputs include twenty-five constants, which

represent material properties and geometry of the beam. The code is written based on

different variables, arrays for loads, deflections, moments, and curvatures, different loops

and functions available in the software. The output is set to present the type of failure; a

plot of the load-deflection response; and load, deflection, moment, and mid-span

curvature for twenty-four points on the load-deflection curve including prestressing,

cracking, yielding, and ultimate stages.

5.5.2.1 Concepts for Calculation of Deflection at an Arbitrary Load Level

The deflection of a beam at mid-span at an arbitrary load level is calculated by

integration of curvatures along the length as presented in Equation 5-27, where the

curvature at every point is calculated using Equation 5-28. To calculate the mid-span

deflection of a prestressed beam under four-point-bending configuration as shown in

Figure ‎5-96, Equation 5-27 can be expanded as Equation 5-29.

2

0

/L

dxx)xφ(Δ (Park & Paulay, 1975) Equation ‎5-27

398

)xEI(

)xM()xφ( (Park & Paulay, 1975) Equation ‎5-28

IV

2

IIIII

0

I

2

/L

Lp

pL

x

x

gtc

/L

Logtc

p

p

p

cr

cr

xdx)LEI(

)LM(xdx

)xEI(

M(x)xdx

IE

M(x)xdx

IE

)x(MΔ Equation ‎5-29

where Δ is the deflection, x the distance from the support, (x) the curvature at distance x,

M(x) the applied moment at distance x, EI(x) the flexural stiffness at distance x, Mp(x) the applied

moment on the beam at distance x due to prestressing, Lo the un-strengthened length, Ec the

modulus of elasticity of concrete, Igt the moment of inertia of the gross transformed

section, xcr the distance from the support to a point where the applied moment is equal to

the cracking moment of the section, Lp the distance from the support to the point load, M(Lp)

the moment value at point load location (x= Lp), and EI(Lp) is the flexural stiffness at point

load location. More details about the calculations and values of the parameters can be

found in the source code in Appendix E.

The upward deflection at mid-span due to prestressing is calculated using part I of

the integral in Equation 5-29 assuming that the beam remains un-cracked in this part.

Integration of curvatures along the un-cracked length of the beam is calculated using part

II of Equation 5-29. Contribution of the cracked length of the beam in resulted deflection

is computed using parts III and IV of Equation 5-29, in which part IV is related to the

constant moment regions. In the developed analytical model, first, the cracking, yielding,

and ultimate capacities of the beam are calculated. Then, the mid-span deflections are

calculated at 10th

point between cracking to yielding loads on the load-deflection curve,

399

and also, at 10th

point between yielding to ultimate loads. To calculate the corresponding

deflection for an arbitrary applied load (e.g., at a load value between yielding and

ultimate), the integration limit xcr in Equation 5-29 needs to be specified for the applied

load. This integration limit is calculated based on the moment diagram and knowing the

cracking moment capacity of the section (e.g., under four-point bending xcr=Mcr/Papplied)

as shown in Figure ‎5-96. After specifying the integration limits, Equation 5-29 can be

solved by knowing the EI (flexural stiffness) for parts III and IV related to the cracked

regions of the beam. The value of EI in the cracked region depends on the applied

moment and curvature at each section which changes from a point to another point along

the cracked length (EI=M/φ). Therefore, to solve parts III and IV of Equation 5-29, the

cracked length of the beam is divided into equal segments (small lengths) and assumed

that the curvature is constant along each small length. Afterwards, the applied moment at

the centre of each small length is easily calculated by having the moment diagram of the

applied load. Then, the curvature (and also EI) at the centre of each small length was

calculated by applying the force and moment equilibriums of the section and finding the

unknowns (c and c) at each small length (φsegment= c/c, EIsegment= Msegment/φsegment). In the

developed code, for each applied load, part III of Equation 5-29 is calculated by fifty

integrals from xcr to Lp and part IV is calculated by one integral (since the curvature is

constant along the integration limits in part IV). The number of the segments (fifty for

part III) is selected based on a sensitivity analysis on the output. It should be noted that

the load-deflection response is generated based on twenty-four different applied loads

and corresponding deflections. More details can be found in the source code in Appendix

E.

400

Figure ‎5-96: Finding the integration limits for Equation 5-29 using moment

diagram.

It should be clarified that Equation 5-29 is the simplified form of a more detailed

equation for calculation of the mid-span deflection. In fact, in a beam that is not

strengthened for entire length with prestressed NSM-CFRP, the length of the beam

consists of two portions, strengthened and un-strengthened, that both should be

considered in calculation of the deflection. If the cracks form within the un-strengthened

length of the beam (the applied moment along the un-strengthened length is larger than

the cracking moment capacity of the un-strengthened section), therefore, parts II and III

of Equation 5-29 should be replaced with Equation 5-30. On the other hand, if no cracks

401

form within the un-strengthened length of the beam, parts II and III of Equation 5-29

should be replaced with Equation 5-31. For the beams that properly strengthened (same

as the ones employed in this paper), Equation 5-31 can be simplified to Equation 5-32

and be used in Equation 5-29 with insignificant effect on the resulted deflection. The

latter is employed in this research.

xdx)xEI(

M(x)xdx

IE

M(x)

xdx)xEI(

M(x)xdx

IE

M(x)

p

stcr

stcr

uncr

uncr

L

x

x

Lostgtc

Lo

x

x

ungtc

0

IIIII

Equation ‎5-30

xdx)xEI(

M(x)xdx

IE

M(x)xdx

IE

M(x) p

stcr

stcr L

x

x

Lostgtc

Lo

ungtc

0IIIII Equation‎5-31

xdx)xEI(

M(x)xdx

IE

M(x) p

stcr

stcr L

x

x

stgtc

0IIIII Equation ‎5-32

where xcr-un and xcr-st are the distance from the support to a point where the applied

moment is equal to the cracking moment capacity of the un-strengthened and

strengthened sections, respectively, Igt-un and Igt-st the moment of inertia of the gross

transformed un-strengthened and strengthened sections, respectively, and the other

parameters are described earlier.

402


5.5.3.1 Concrete of Exposed Beam

The exposed concrete stress-strain curve was defined based on Loov’s equation

(Loov, 1991). The concrete compressive strength of the exposed beams in phase I was

obtained using Schmidt hammer test performed on the specimens. The other properties of

the exposed concrete including modulus of elasticity and strain at peak stress were

calculated based on the study performed by Duan et al. (2011) on the effects of freeze-

thaw cycles on the stress-strain curves of unconfined and confined concrete. Since the

freeze-thaw cycle used by Duan et al. (2011) was different than the one conducted in this

study, therefore, the equivalent number of the cycles (N) is obtained using Equation 5-33

(Duan et al., 2011) by having the concrete compressive strength at different stages:

0355328200

1

.c

unexposedc

exposedc

f

f

f

N

Equation ‎5-33

where fc exposed is the concrete compressive strength after exposure (MPa), fc unexposed the

concrete compressive strength before exposure (MPa), fc28 the concrete compressive

strength at 28 days (MPa), and N is the number of freeze-thaw cycles.

The strain at peak stress and modulus of elasticity after exposure were calculated

using Equations 5-34 and 5-35 proposed by Duan et al. (2011).

403

)Nf(

exposedun

exposed .ce

1406528661742

0

0

Equation ‎5-34

)Nf.(

unexposedc

exposedc .ce

E

E 7089528

71013451

Equation ‎5-35

where 0 exposed is the concrete strain at peak stress after exposure, 0 unexposed the concrete

strain at peak stress before exposure, Ec exposed the modulus of elasticity of concrete after

exposure (MPa), and Ec unexposed is the modulus of elasticity of concrete before exposure

(MPa).

Finally by finding the properties of the exposed concrete and apply two points of

the stress-strain curve to the Loov’s equation (as presented in Equation 5-1), Equation 5-

36 is derived for the exposed concrete. More details about the calculation of the concrete

stress-strain curve can be found in the source code in Appendix E.

4.9112102.08 173.22 1

709.86 04

cc

ccf

Equation ‎5-36

where fc and ɛc are the compressive stress of concrete (MPa) and the concrete strain,

respectively.

5.5.3.2 Steel Reinforcement

An elasto-plastic behaviour was considered for the steel reinforcements in the

analytical model. The assigned material properties are listed in the input file of the source

code (Appendix E) for the top and bottom steel reinforcements.

404

5.5.3.3 CFRP Strip or Rebar

A linear elastic behaviour was considered for the CFRP strips and rebars with the

material properties presented in the input file of the source code in Appendix E.


The nonlinear analysis in the model is performed by satisfying the moment and

the force equilibriums for cross-section of the beam shown in Figure ‎5-97 and finding the

unknowns (concrete strain at extreme compression fibre and depth of the neutral axis).

These equilibrium equations are presented in Equations 5-37 and 5-38.

00 cssf CCTTF

Equation ‎5-37

appliedstsffscsCcc M)cd(T)cd(T)dc(CyCM 0 Equation ‎5-38

where Tf is the force in CFRP strip or rebar, Ts the force in bottom steel rebars, Cs the

force in compression steel rebars, Cc the compressive force carried by concrete, ӯCc the

distance between neutral axis and point of action of the resultant compressive force on

concrete, c the depth of neutral axis, dsc the depth to the centroid of the top steel rebars, df

the depth to the centroid of the CFRP strips or rebars, dst the depth to the centroid of the

bottom steel rebars, and Mapplied is the applied moment. The components of Equations 5-

37 and 5-38 are calculated using the following equations.

)(EAT peffrpfrpf

Equation ‎5-39

405

ytstytst

ytstststst

s iffA

ifEAT

Equation ‎5-40

ycscycsc

ycscscscsc

s iffA

ifEAC

Equation ‎5-41

c

cc dy)y(fbC0

Equation ‎5-42

c

c

c

c

cC

dy)y(fb

dy)y(fbyy

0

0

Equation ‎5-43

4.91

12102.08 173.22 1

709.86

04

c

y

c

y

c

y

)y(f

cccc

cc

c

Equation ‎5-44

where Afrp is the area of CFRP rebars or strips (mm2), Efrp the modulus of elasticity of

CFRP rebars or strips (MPa), f the strain in CFRP rebar or strip, pe the prestrain in

CFRP rebar or strips, Ast the area of bottom steel rebras (mm2), Est the modulus of

elasticity of bottom steel rebars (MPa), st the strain in bottom steel rebars, fyt the yield

stress of the bottom steel rebars (MPa), yt the yield strain of bottom steel rebars, Asc the

area of top steel rebras (mm2), Esc the modulus of elasticity of top steel rebars (MPa), sc

the strain in top steel rebars, fyc the yield stress of top steel rebars (MPa), yc the yield

strain of bottom steel rebars, b the width of the beam (mm), fc(y) the compressive stress

on concrete at height y defined based on Equation 5-41 (MPa), cc the concrete strain at

406

extreme compression fibre, y the vertical distance from the neutral axis (mm), and c is the

depth of the neutral axis (mm).

Figure ‎5-97: Strain and stress distribution on a prestressed NSM-CFRP

strengthened section.

5.5.5 Analytical Results and Discussion

5.5.5.1 Load-Deflection Curve

Comparison between experimental and analytical load-deflection responses is

presented in Figure ‎5-98 and Figure ‎5-99. The analytical solutions of the beams were

terminated after concrete crushing or CFRP rupture whichever occurred first. The

estimated load-deflection responses include the negative camber due to prestressing,

initiation of flexural cracks, yielding of tensile steel rebar, and failure at ultimate stage. A

summary of the results obtained from the tests versus the analytical solutions are

presented in Table ‎5-15 and Table ‎5-16 for sets BS-F and BR-F, respectively, including

type of failure, ductility index (the ratio of the deflection at ultimate load to the deflection

at yielding), energy absorption (the area under load-deflection curve up to the peak load),

and percentage of difference between corresponding experimental and analytical values.

407

At cracking, a relatively large percentage of difference is observed between

experimental and analytical values. Considering the strengthened beams, an average error

of 11.7±7.8% for cracking load of set BS-F with a maximum of 22% for BS-NP-F, and

an average error of 38.8±10.9% for cracking deflection with a maximum of 54.9% for

BS-P2-F are observed. Furthermore, considering the strengthened beams, an average

error of 22.5±15.2% for cracking load of set BR-F with a maximum of 37.8% for BR-P1-

F, and an average error of 23.9%±12.7% for cracking deflection with a maximum of

40.5% for BR-P1-F are reached. Also, the differences of 62.4% and -18.5% are observed

for cracking load and deflection of B0-F, respectively. The high percentage of the

difference at cracking stage might be due to the presence of the micro cracks in the beams

before testing. The other reason for underestimation or overestimation of the cracking

load using the analytical solution might be due to a difference between concrete

compressive strength in the model and in tested beams. The beams were cracked after

strengthening before being subjected to freeze-thaw exposure, while in the analytical

solution an average exposed concrete compressive strength was assigned to the beams

(40 MPa for all beams), that might be slightly different for each beam that was cracked in

reality. The resulted difference between the analytical solution and the test values at

cracking is most possibly the accumulation of the mentioned errors.

At yielding stage, the differences between analytical solutions and experimental

results are negligible. Considering the strengthened beams, An average error of -3±2.2%

for yield load of set BS-F with a maximum of -5% for BS-P3-F and an average error of

0±9.2% for yield deflection with a maximum of 11.8% for BS-NP-F are reached.

Similarly, considering the strengthened beams, an average error of -1.8±2.4% for yield

408

load of set BR-F with a maximum of -4.5% for BR-P3-F and an average error of -

4.2±6.1% for yield deflection with a maximum of -8.8% for BR-P3-F are obtained.

At ultimate stage, the predicted loads are almost the same as those from the test;

however, the predicted ultimate deflections are different than those from the test values.

On the other hand, the material properties (i.e., CFRP ultimate strain or concrete stress-

strain curve) could be slightly smaller or greater than the specified values that would lead

to a difference at ultimate deflection when the failure governs by CFRP rupture or

concrete crushing. In set BS-F, considering the strengthened beams, an average error of

2.5±4% for ultimate load with a maximum of 6.7% for BS-P1-F, and an average error of

3.3±10.9% for ultimate deflection with a maximum of 16.7% for BS-P1-F are observed at

the ultimate stage. In set BR-F, considering the strengthened beams, an average error of

0.6±3.5% for ultimate load with a maximum of 5.2% for BR-NP-F, and an average error

of -0.6±13.5% for ultimate deflection with a maximum of 18.2% for BR-P3-F are

reached at the ultimate stage. The modeled beams showed similar types of failure to the

tested beams. The fluctuation of the experimental curve at ultimate stage is not observed

in analytical solution which is mainly due to the elimination of local debonding in the

analytical model. Therefore, the performed comparison indicates that the load-deflection

curves obtained from the analytical solutions can accurately predict those values from the

experimental ones.

409

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)


BS-P3-F (Experimental) BS-P3-F (Analytical)

BS-P2-F (Experimental) BS-P2-F (Analytical)

BS-P1-F (Experimental) BS-P1-F (Analytical)BS-NP-F (Experimental) BS-NP-F (Analytical)B0-F (Experimental) B0-F (Analytical)


Figure ‎5-98: Comparison between experimental and analytical load-deflection responses for BS-F set.

409

410

Table ‎5-15: Summary of the results for BS-F set.

Beam

ID#

Prestrain

in CFRP Results

Δo

(mm)

Pcr

(kN)

Δcr

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) μD

Φ

(kN. mm)

Failure

Mode

B0-F N.A.

Analytical 0 16.9 1.81 75.5 18.78 97.8 142.88 7.61 11646.7 CC

Test‡ 0 10.4 2.22 84.8 24.81 87.0 155.31 6.26 12368.6 CC

Error % 0 62.4 -18.5 -10.9 -24.3 12.4 -8.0 21.6 -5.8

BS-NP-F 0

Analytical 0 17.1 1.81 92.4 25.19 137.1 103.59 4.11 10398.9 CC

Test‡ 0 14.0 1.36 92.4 22.53 132.2 104.26 4.63 10649.0 CC

Error % 0 22.0 33.4 0.0 11.8 3.7 -0.6 -11.1 -2.3

BS-P1-F 0.003463

Analytical -0.48 23.9 1.87 101.5 24.61 143.7 96.77 3.93 10419.3 CC

Test‡ -0.49 21.6 1.43 104.1 23.99 134.7 82.90 3.46 8667.1 CC

Error % -1.7 10.6 31.2 -2.5 2.6 6.7 16.7 13.8 20.2

BS-P2-F 0.006723

Analytical -0.94 30.4 1.92 109.9 24.09 145.2 79.81 3.31 8774.7 FR

Test‡ -1.09 27.3 1.24 114.8 25.56 149.5 87.85 3.44 10214.1 FR

Error % -14.2 11.2 54.9 -4.3 -5.7 -2.9 -9.2 -3.6 -14.1

BS-P3-F 0.009884

Analytical -1.38 36.6 1.97 118.1 23.62 145.1 62.11 2.63 6832.1 FR

Test‡ -1.70 35.5 1.45 124.3 25.91 141.7 58.55 2.26 6509.8 FR

Error % -19.1 3.1 35.9 -5.0 -8.8 2.4 6.1 16.4 5.0

Pcr and Δcr = load and deflection at cracking Δo = camber due to prestressing CC = concrete crushing

Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy FR = CFRP rupture


Note: the results include the self-weight effects.

410

411

0

20

40

60

80

100

120

140

160

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)


BR-P3-F (Experimental) BR-P3-F (Analytical)



BR-NP-F (Experimental) BR-NP-F (Analytical)


Figure ‎5-99: Comparison between experimental and analytical load-deflection responses for BR-F set.

411

412

Table ‎5-16: Summary of the results for BR-F set.

Beam

ID#

Prestrain

in CFRP Results

Δo

(mm)

Pcr

(kN)

Δcr

(mm)

Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) μD

Φ

(kN. mm)

Failure

Mode

B0-F N.A.

Analytical 0 16.9 1.81 75.5 18.78 97.8 142.88 7.61 11646.7 CC

Test‡ 0 10.4 2.22 84.8 24.81 87.0 155.31 6.26 12368.6 CC

Error % 0.0 62.4 -18.5 -10.9 -24.3 12.4 -8.0 21.6 -5.8

BR-NP-F 0

Analytical 0 17.1 1.34 92.9 24.74 139.2 102.40 4.14 10423.6 CC

Test‡ 0 13.1 1.23 91.6 23.78 132.3 102.71 4.32 10344.4 CC

Error % 0 30.4 9.7 1.4 4.1 5.2 -0.3 -4.2 0.8

BR-P1-F 0.003662

Analytical -0.5 24.8 1.41 103.1 24.09 146.6 94.92 3.94 10442.3 CC

Test‡ -0.5 18.0 1.00 105.1 24.98 147.5 107.62 4.31 12357.7 CC

Error % 12.9 37.8 40.5 -1.9 -3.5 -0.6 -11.8 -8.6 -15.5

BR-P2-F 0.006548

Analytical -1.0 30.9 1.45 111.1 23.61 152.5 89.54 3.79 10432.9 CC

Test‡ -0.9 26.0 1.20 113.4 25.86 157.5 98.05 3.79 11796.5 CC

Error % 5.9 18.7 21.1 -2.1 -8.7 -3.2 -8.7 0.0 -11.6

BR-P3-F 0.009950

Analytical -1.5 38.0 1.51 120.4 23.08 157.5 79.13 3.43 9671.7 FR

Test‡ -1.7 36.3 1.21 125.2 25.36 157.5 71.28 2.81 8733.6 FR

Error % -13.9 4.7 24.9 -3.8 -9.0 0.0 11.0 22.0 10.7

Pcr and Δcr = load and deflection at cracking Δo = camber due to prestressing CC = concrete crushing

Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy FR = CFRP rupture


Note: the results include the self-weight effects.

412

413

5.6 FE Modeling of RC Beams Strengthened with Prestressed NSM-CFRP

Reinforcement Subjected to Freeze-Thaw Exposure and Sustained Load

The beams tested in phase II of the experimental program, subjected to freeze-

thaw exposure and sustained load, are simulated using FEM as presented in this section

and the predicted load-deflection responses are compared with the experimental ones.

The concepts and aspects of the developed model are similar to Section 5.2 (FE modeling

of unexposed beams) except that in the current analysis the material properties are

different since the beams were exposed to the environmental and loading conditions.

5.6.1 Experimental Program Overview

Five RC beams tested in phase II of the experimental program including one un-

strengthened control beam and four beams strengthened using NSM CFRP strips were

modeled. The beams were subjected to 500 freeze-thaw cycles while each beam was

under a sustained load of 62 kN (47% of analytical ultimate load of the non-prestressed

NSM CFRP strengthened RC beam, BS-NP-F in Table ‎3-3), and tested under four-point

bending static monotonic loading to failure. A summary of the test results including

prestrain in CFRP strips was presented in Table ‎4-15. Details of the beams and test setup

were plotted in Figure ‎3-1. Furthermore, details of three freeze-thaw cycling exposure

and sustained loading were presented in Sections 3.6 and 3.7, respectively.

5.6.2 Description of finite element model

The aim of the FE analysis developed in this section is to predict the flexural

behaviour of the beams after exposure not the behaviour during exposure. Therefore,

414

details of the developed 3D FE model is the same as the unexposed strengthened RC

beams described in Section 5.2.2. The major difference between the model presented in

this section and the model developed for the unexposed beams (Section 5.2.2) is in the

material properties of the exposed beams including concrete, bond at concrete-epoxy

interface, and steel reinforcement. Also, the observed total debonded length after

exposure, as presented in Table ‎4-14, was assigned to the FE model of each beam (by

assigning a zero value for shear and normal fracture energies of the interface) to simulate

the conditions of the beams prior to static testing to failure.

5.6.3 Debonding Model of Exposed Beams

The debonding for the exposed beams were simulated using contact pairs and

Cohesive Zone Material (CZM) model considering a bond-slip model and a normal stress

gap model as described in the following sections. More details on the considered

debonding model can be found in Section 5.2.4.

5.6.3.1 Bond-Slip Model for Exposed Beams

The bilinear shear stress-slip model is obtained based on the procedure described

in Section 5.2.4.1 using the exposed concrete compressive strength of 28.1 MPa

surrounding the groove. The values of maximum shear stress of contact, τmax= 6.62 MPa,

and contact slip at the completion of debonding, utc= 1.19 mm, are derived using

Equations 5-12 to 5-15 for the shear stress-slip model. Comparing the exposed and

unexposed bilinear models shows a decrease of 27.3% in shear fracture energy due to the

exposure applied in phase II.

415

5.6.3.2 Normal Tension Stress-Gap Model for Exposed Beams

The bilinear normal tension stress-gap model is calculated based on the procedure

described in Section 5.2.4.2. The values of maximum tensile stress of contact, σmax= 3.18

MPa, and contact gap at the completion of debonding, unc= 0.045 mm, are derived using

Equations 5-16 to 5-18 and the exposed concrete compressive strength of 28.1 MPa

surrounding the groove. Comparing the exposed and unexposed bilinear models shows a

decrease of 21.3% in normal fracture energy due to exposure applied in phase II.

5.6.4 Modeling of Prestressing

The prestressing was applied by assigning the temperature to the CFRP elements

(equivalent temperature method) as explained in Section 5.2.5. Considering the

longitudinal thermal expansion of the CFRP strip, αfrp, as -9×10-6

/oC (based on the FRP

material data sheet, Hughes Brothers Inc) and using Equation 5-19, the following

temperatures were assigned to the CFRP elements in the FE model to meet the prestrain

in CFRP strip. On the other hand, since the NSM CFRP strip experienced debonding at

the end regions due to exposure (see Section 4.7.2 and Table ‎4-14), the value of prestrain

in the CFRP strip prior to testing is less than that prior to being subjected to

environmental exposure. This loss happens due to seating loss (anchorage slip at the

bolts) after debonding, and therefore, reduces the prestrain in the CFRP strip. Regarding

the debonded lengths presented in Table ‎4-14 and based on the occurred debonding and

end anchor inspections after exposure the values of anchor movement, presented at the

end of this section, are considered for the beams strengthened using prestressed NSM

416

CFRP strips. Furthermore, as explained earlier in Section 5.2.5, the resulting deformation

due to elastic shortening of the concrete beam reduces the strain in the CFRP strip due to

prestressing. Therefore, the applied equivalent temperature (Δtapplied) was calculated by

trial and error to produce the exact value of prestrain, εP, for each beam.

Ct&.

Ct&.

Ct&.

oappliedP

oappliedP

oappliedP

1070debondingtoduemovementanchor1mmgconsiderin010080




5.6.5.1 Concrete of Exposed Beams

The concrete material is modeled with Solid65 elements using the procedure

described in Section 5.2.3.1. Observations and inspections on the exposed beams

confirmed that the severity of the exposure at the top part of the cross-section was

different from the sides and bottom, and core of the beam’s cross-section. The top surface

of the beam had a concrete compressive strength of 10.1 MPa while the sides and bottom

surfaces had a concrete compressive strength of 28.1 MPa obtained from Schmidt

hammer tests presented in Appendix C. The exposure damage done to the core of the

beams was insignificant, and therefore, a concrete compressive strength of 34.5 MPa was

assigned to that part, which is the average strength obtained from compression test of the

unexposed concrete cylinders at the time of the testing to failure. Therefore, the beams

were modeled using three different concrete material properties (stress-strain curves)

assigned to the cross-sections as shown in Figure ‎5-100.

417

Figure ‎5-100: Simulation of the beams with exposed concrete materials.

Results of the static test show that the exposed beams have stiffer load-deflection

response than the unexposed beam before yielding. This behaviour also was observed by

Oldershaw (2008), described in Section 2.10.7 and Table 2-12. The increase in stiffness

is a result of creep on the beams. In fact, the concrete material showed higher modulus

and lower strength than the unexposed specimens. The increase in the modulus of

elasticity is a result of creep and wet condition. The concrete material gets stiffer when it

undergoes creep (Oldershaw, 2008; Neville, 2011). On the other hand, in a saturated

cement paste, the absorbed water in the calcium silicate hydrate (C-S-H) phase is load-

bearing, the disjoining pressure in C-S-H tends to reduce the van-der-Waals force of

attraction, thus lowering the strength of the concrete (Mehta and Monteiro, 2006).

It should be mentioned that finding the exact concrete properties of the heavily

deteriorated beams in phase II was not possible due to variation in concrete properties.

418

Equations 5-45, 5-46 and 5-47 represent the concrete stress-strain curves, assigned to the

beams, obtained using Loov’s equation (Equation 5-1). More details about the calculation

of the concrete stress-strain curves can be found in Appendix E.

95728682804711

81121110

.cc

cc

.

..f

Equation ‎5-45

996391073889457571

69520128

.cc

cc

..

..f

Equation ‎5-46

91941210599454754331

751055534

.cc

cc

..

..f

Equation ‎5-47

where fc and ɛc are the concrete compressive stress (MPa) and the corresponding concrete

strain, respectively.

5.6.5.2 Steel Reinforcement

The steel reinforcement bars were simulated using the procedure described in

Section 5.2.3.2, employing two-node link element, Link8, as shown in Figure ‎5-8. A

multi-linear material model was assigned to the Link8 elements in addition to the related

real constants assigned to cross-section of each steel rebar. Comparison between the un-

strengthened control beam and non-prestressed strengthened beam (in which the yield

load is directly related to the yield stress of tension steel) from phase II and similar beams

from phase I revealed an average decrease of 18.6% at yield load due to the combined

sustained load and freeze-thaw cycles. In fact, subjecting the beams to the sustained load

and freeze-thaw cycles decreased the yield stress of the tension steel reinforcements

419

while had negligible effects on the modulus of elasticity. On the other hand, the tension

steel reinforcements used in phase II had a different yield stress from those used in phase

I, considering this difference, the yield stress of the tension steel reinforcements

decreased by 26% in phase II. Therefore, the following multi-linear stress-strain curves

assigned to the steel reinforcement elements are presented in Figure ‎5-101 in which the

decrease in yield stress is considered.

0

100

200

300

400

500

600

0 0.02 0.04 0.06 0.08 0.1 0.12

Str

ess (

MP

a)

Strain

10M Steel Bar

15M Steel Bar

Figure ‎5-101: Stress-strain curves of the steel bars for exposed beams in phase II.

5.6.5.3 CFRP Strip

The CFRP strips were modeled using Solid45 elements as explained in Section

5.2.3.3. An equivalent multi-linear stress-strain curve was assigned to the CFRP element

for each stress-strain curve presented in Figure ‎5-102a and b obtained from experimental

420

results (Section 4.7.1.3). A Poisson’s ratio of 0.22 was assigned to the CFRP elements

(Kachlakev et al., 2001).

(a) For BS-NP-FS,BS-P1-FS, and BS-P2-FS (b) For BS-P3-FS

Figure ‎5-102: Stress-strain curves assigned to the CFRP strip elements.

5.6.5.4 Epoxy Adhesive, Loading Plate, Steel Anchors, and Steel Bolts

The Epoxy adhesive, loading plate, steel anchors, and steel bolts were modeled

using the elements, materials, and procedures mentioned in Sections 5.2.3.5 and 5.2.3.6.


The nonlinear solution was performed using displacement control method as

explained in Section 5.2.7. Details of the load-steps defined for solving the FE models are


421


Load-step

Time at

end of

load-step

Sub-step Max

number of

iterations

Displacement

convergence

criteria tolerance No. Min Max

1. Zero load-camber

induced by prestressing* 0.0001 1 1 1000 40 0.01


before first cracking 1.2 10 5 40 40 0.01


after first cracking 4 80 50 100 40 0.05


before steel yielding 18 20 10 10000 40 0.05


after steel yielding 26 40 15 10000 40 0.05

6. After steel yielding-

ultimate 60 20 10 10000 60 0.05

7. Before ultimate-after

ultimate** 200 80 40 20000 60 0.05


** used for un-strengthened control beam

5.6.7 Numerical Results and Discussion

Comparison between experimental and numerical load-deflection curves is

presented in Figure ‎5-103 which includes the five beams tested in phase II (un-

strengthened control beam, B0-FS, strengthened beam with non-prestressed NSM CFRP

strip, BS-NP-FS, and strengthened beams with prestressed NSM CFRP strips, BS-P1-FS,

BS-P2-FS, and BS-P3-FS). The FE models were terminated due to concrete crushing

accompanied by a non-convergence message from the program which causes a large drop

of the total load at ultimate stage. A comparison between the results obtained from the

tests versus the FE analysis are provided in Table 5-18, including the type of failure,

ductility index (the ratio of the ultimate deflection to the deflection at yielding), energy

absorption (the area under load-deflection curve up to the peak load), and percentage of

difference between corresponding experimental and numerical values.

422

0

20

40

60

80

100

120

-5 15 35 55 75 95 115 135 155 175

Lo

ad

(k

N)


BS-P3-FS (Experimental) BS-P3-FS (FE)



BS-NP-FS (Experimental) BS-NP-FS (FE)

B0-FS (Experimental) B0-FS (FE)

Figure ‎5-103: Comparison between experimental and numerical load-deflection curves.

422

423

Table ‎5-18: Summary of the results.

Beam

ID#

Assigned

prestrain

to CFRP

Total debonded

length after

exposure (mm)

Results Py

(kN)

Δy

(mm)

Pu

(kN)

Δu

(mm) μD

Φ

(kN. mm)

Failure

Mode

B0-FS N.A. N.A.

FE 65.9 20.7 72.9 68.4 3.3 4088.4 CC

Test‡ 62.3 13.3 77.9 80.9 6.1 5462.9 CC

Error % 5.7 56.5 -6.5 -15.4 -46.0 -25.2 ―

BS-NP-FS 0 0

FE 73.3 20.6 97.3 53.4 2.6 3641.2 CC

Test‡ 74.4 15.5 98.3 57.6 3.7 4496.6 CC

Error % -1.4 32.9 -1.0 -7.2 -30.2 -19.0 ―

BS-P1-FS 0.003034 750

FE 82.5 21.2 106.3 54.9 2.6 4238.6 CC

Test‡ 83.8 17.5 96.8 35.1 2.0 2534.5 CC

Error % -1.6 20.9 9.9 56.3 29.3 67.2 ―

BS-P2-FS 0.004664 2340

FE 85.3 20.8 110.4 55.6 2.7 4515.5 CC

Test‡ 90.5 20.6 91.4 21.9 1.1 1343.8 CC-DB

Error % -5.7 0.8 20.7 153.4 151.4 236.0 ―

BS-P3-FS 0.009567 2530

FE 98.0 20.8 118.5 46.8 2.2 4149.2 CC

Test‡ 101.5 19.4 106.7 36.7 1.9 3174.6 DB-CC

Error % -3.4 7.2 11.1 27.3 18.7 30.7 ―

Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy

Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under P-Δ curve up to Pu) CC = concrete crushing

CC-DB= concrete crushing followed by the NSM CFRP debonding, almost simultaneously

DB-CC= failure initiated by the NSM CFRP debonding and concrete crushing almost simultaneously, and then followed by the concrete crushing

423

424

From starting the test up to the yielding stage, the FE and experimental curves

match satisfactorily with insignificant differences at the yield load and significant

differences at the yield deflection. An average error of -1.3±4.3% for yield load with a

maximum of 5.7% for B0-FS, and an average error of -23.6±22.2% for yield deflection

with a maximum of 56.5% for B0-FS are reached. The experimental load-deflection

responses are stiffer than the predicted ones before yielding. The increase in stiffness

might be a result of creep of the beams which makes the concrete material stiffer at

regions that are not affected by the freeze-thaw cycles such as the core of the beams. It

should be mentioned that finding the amount of this possible increase in concrete

stiffness (modulus of elasticity) was not possible in the test, and therefore, was not

considered in the FE model.

At ultimate stage, the predicted loads are higher than those from the tests; this

difference might be due to combination of a few reasons. The fact is that due to high

exposure the variability in material property is high, and even for one specimen the

concrete behaviour is different from one point to the other point. Therefore, the exact

stress-strain curve of the concrete material might be slightly different than what was

assigned to the FE model. Also, the debonding occurred at the end regions of the NSM

CFRP strip under exposure caused a prestressing loss in CFRP strip due to seating of the

steel anchor on the steel bolts. Finding the exact value of this loss needs extensive

waterproof instrumentations along the length of the NSM CFRP strip while the beams are

under exposure (in the experiment, the strain in the CFRP strip at mid-span was

monitored during the exposure). Therefore, the prestrain in the CFRP strip after exposure

might be different from what was assigned to the models. In addition to the above

425

mentioned reasons, in reinforced concrete members creep results in a gradual transfer of

load from the concrete to the reinforcement, and once the steel reinforcement yields, any

increase in the applied load is carried by the concrete so that full strength of both the steel

and the concrete is developed prematurely before expected failure takes place.

Due to the above mentioned reasons, there is no rational trend in the results

obtained from the tests at failure, and large error are observed between the predicted and

the experimental results. An average error of 6.8±10.7% for ultimate load with a

maximum of 20.7% for BS-P2-FS, and an average error of 42.9±68.1% for deflection at

ultimate load with a maximum of 153% for BS-P2-FS are reached at the ultimate stage.

Also, an average error of 24.7±77.6% for ductility index with a maximum of 151% for

BS-P2-FS, and an average error of 58±106.5% for energy absorption with a maximum of

236% for BS-P2-FS are reached. The modeled beams showed similar type of failure to

the tested beams which is concrete crushing in all cases.

Therefore, the performed comparison indicates that the load-deflection curves

obtained from the FE models shows an acceptable match with those from the

experimental ones up to yielding, but after yielding the trend of the predicted curves are

not in a very good correlation with the experimental ones.

5.7 Summary

In this chapter, the FE and analytical simulations related to RC beams

strengthened using prestressed NSM CFRP strips and rebars were presented. First, five

unexposed RC beams including one un-strengthened control beam, one beam

strengthened using non-prestressed NSM CFRP strips, and three beams strengthened

426

using prestressed NSM CFRP strips were modeled by developing a nonlinear 3D FE

model. Then, a parametric study was performed in which 23 beams were analyzed to

assess the effects of the prestressing level in the NSM CFRP strips, the tensile steel

reinforcement ratio, and the concrete compressive strength on the flexural behaviour of

the NSM CFRP strengthened RC beams. Afterward, the anchorage system used for

prestressing the NSM CFRP strips was modeled followed by a parametric study in which

fourteen anchorage were modeled to investigate the effects of bond cohesion, anchorage

length, adhesive width, and adhesive height on the pullout capacity and interfacial shear

stress distributions at steel-epoxy and CFRP-epoxy interfaces. Then, the load-deflection

responses of nine beams exposed to freeze-thaw cycles, tested in phase I, were simulated

by developing an analytical solution. Finally, the load-deflection responses of five beams

exposed to combined freeze-thaw cycles and sustained loading, tested in phase II, were

simulated by developing a FE model.

In the next chapter, the conclusions and recommendations resulted from this

research are presented.

427

Chapter Six: Conclusions and Recommendations

6.1 Introduction

The research presented herein aims at studying the gaps in the field of prestressed

and non-prestressed NSM CFRP strengthening of RC beams. In this chapter, the

conclusions of this work and the recommendations for future research are presented.

In the experimental part of the research, the conclusions were drawn based on the

studies of the flexural performance of the beams exposed to freeze-thaw cycles, the

deformability of the NSM CFRP strengthened RC beams, the effects of CFRP geometry

strips versus rebar, the flexural performance of the beams exposed to combined freeze-

thaw cycles and sustained loading, the prestress losses in the NSM CFRP strengthened

beams, and the modification of the NSM CFRP prestressing system.

In the numerical and analytical parts of the research, the conclusions were drawn

based on the finite element modeling of the beams strengthened using prestressed NSM

CFRP strips, the parametric study on RC beams strengthened with prestressed NSM

CFRP, the finite element modeling and parametric study on the steel end anchor,

analytical modeling of RC beams strengthened with prestressed NSM CFRP strips and

rebars subjected to freeze-thaw exposure, and the finite element modeling of the beams

strengthened using prestressed NSM CFRP strips subjected to combined freeze-thaw

exposure and sustained load.

On the other hand, the results might not be statistically significant due to the

limited number of the tested beams reported in this research, however, they would

428

provide a better understanding on the performance of the prstressed NSM CFRP

strengthened RC beams subjected to freeze-thaw cycles and sustained load.

6.2 Conclusions

6.2.1 Experimental Test Results

6.2.1.1 Phase I: Experimental Study on RC Beams Strengthened with Prestressed NSM-

CFRP Strips and Rebar Subjected to Freeze-Thaw Exposure

The flexural performance of the RC beams strengthened with prestressed and

non-prestressed NSM-CFRP strips and rebars exposed to 500 freeze-thaw cycles were

examined in phase I. Each freeze-thaw cycle in phase I consisted of eight intervals that

was programmed to be accomplished in 8hrs, including the lower temperature bound of -

34oC and the upper temperature bound of +34

oC with a relative humidity of 75% for

temperatures above +20oC. Based on this part of the research, the following conclusions

can be drawn:

1. The freeze-thaw cycling exposure mainly affects the concrete, concrete-epoxy

interface, and causes residual stress in the NSM-CFRP reinforcement due to

thermal incompatibility of the components.

2. The effects of freeze-thaw cycling exposure on the flexural performance of the

beams strengthened using prestressed NSM CFRP strips and rebars with high

prestress levels of 48% and 41%, respectively, where the failure is governed by

CFRP rupture while the concrete strain in extreme compression fibre is small, are

negligible.

429

3. The damage done to the concrete, due the freeze-thaw cycling exposure, affects

the ultimate state, and particularly the failure mode of the beams, by shifting the

mode of failure from CFRP rupture to concrete crushing and results in smaller

ultimate load, deflection at ultimate load, and energy absorption. A 12.2-20%

decrease in ultimate deflection and a negligible (2.1-9%) decrease in ultimate load

of the exposed beams were observed in comparison with the similar unexposed

beams. The exposed beams experienced a decrease of 13.1-26.7% in energy

absorption in comparison with unexposed beams.

4. The initiation of the longitudinal debonding cracks at the concrete-epoxy interface

appears to be related to the fracture energy of the interface; these cracks almost

initiate at a constant beam’s deflection independent from prestressing level for the

particular beams in this study. Since, prestressing decreases the ductility index

(deflection at ultimate to deflection at yielding), therefore, the longitudinal

debonding cracks at the concrete epoxy interface is less likely to occur in beams

strengthened using prestressed NSM CFRP reinforcements.

5. The beams strengthened using prestressed NSM CFRP strips and rebar with high

prestress levels of 48% and 41%, respectively, showed no sign of debonding

while the beams strengthened using prestressed NSM CFRP strips and rebar with

prestress levels of 33% and 26%, respectively, and lower, showed longitudinal

debonding cracks at the concrete-epoxy interface localized at the constant moment

region with insignificant effects on the overall flexural performance of the beams.

6. The overall flexural performance of the beams strengthened with NSM-CFRP

rebars and strips (which have the similar axial stiffness) is almost the same, but

430

the beams strengthened with sand coated CFRP rebar showed less damage to

bond than the beams strengthened with rough textured CFRP strips.

7. Strengthening with non-prestressed NSM CFRP strips has significant effects in

the plastic range on the load-deflection behaviour while strengthening using

prestressed NSM CFRP strips has significant effects in both the elastic and plastic

ranges.

8. The prestressing of the NSM CFRP reinforcement leads to more contribution in

enhancing the yielding load than the ultimate load. Up to 64% and 66% increase

in the yielding load of the strengthened beam with CFRP strips and rebar,

respectively, were obtained with respect to the un-strengthened control RC beam

in which 22% out of 64% and 21% out of 66% are related to the increase due to

strengthening and the rests, 42% and 45%, are due to the prestressing effects.

Also, up to 53% and 61% increase in the ultimate load of the strengthened beam

with CFRP strips and rebar were recorded in which 35% out of 61% and 53% are

reached by strengthening with non-prestressed CFRP reinforcements and the

remaining is due to the prestressing effects.

9. The anchorage slippage at the jacking end of the NSM CFRP reinforcement (after

removing the brackets and transferring the prestressing force to the steel end

anchor) causes a prestressing loss along a short length (100-200 mm) of the NSM

CFRP, but it has insignificant effects on the overall flexural performance of the

beam.

10. The anchorage system performed well during the exposure and up to the failure.

431

11. An optimum prestressing level can be achieved in order to preserve the beam's

original energy before strengthening. The experimental results yield an optimum

prestressing level of 27.5% for beam strengthened with CFRP strips versus 31.5%

for beam strengthened with CFRP rebar.

12. A beneficial prestressing level is defined as a prestressing level, which produces

the maximum improvement in energy absorption of the strengthened RC beam

with respect to the un-strengthened control RC beam. The improvement is the

difference between the energy absorption of the strengthened and un-strengthened

beam calculated up to the ultimate deflection of the strengthened beam The

experimental results yield a beneficial prestressing level of 31.4% for beam

strengthened with CFRP strips versus 24.1% for beam strengthened with CFRP

rebar.

6.2.1.2 Deformability and Ductility of NSM CFRP Strengthened RC Beams

Ductility and deformability of prestressed and non-prestressed NSM-CFRP

strengthened RC beams have been studied in this research by considering the results of

four series of tests on eighteen beams. Based on this part of the research, the following

conclusions can be drawn:

1. The existing deformability models available in the literature need to be modified

to be applicable for FRP strengthened RC beams; therefore, three deformability

indices (the deformability factor, the Zou index, and the J factor) were modified

to be applicable for these types of beams.

432

2. The value calculated from the modified deformability (µEm), the modified Zou

(Zm), the displacement ductility (µD), and the curvature ductility (µ) indices is

88%, 69%, 57%, and 52% of the value obtained from the modified J factor (Jm).

3. It is recommended that deformability and ductility limits of 4, 3.1, 2.6, and 2.3

be used for checking the design of the FRP strengthened RC beams based on the

µEm, Zm, µD, and µ models, respectively. Among examined models, the modified

deformability factor (µEm) represents the most conservative model and leads to the

lowest permitted prestressing level based on its limit.

4. Due to prestressing, reductions of 63.1%, 58.6%, 53.3%, 49.3%, and 36.2%

occurred for µEm, Zm, Jm, µD, and µ, respectively, in comparison with the non-

prestressed strengthened RC beam.

6.2.1.3 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under Combined

Sustained Load and Freeze-Thaw Exposure

The flexural performance of the RC beams strengthened with prestressed and

non-prestressed NSM-CFRP strips exposed to 500 freeze-thaw cycles while each beam

was subjected to a sustained load of 62 kN, equal to 47% of the theoretical ultimate load

of the non-prestressed NSM CFRP strengthened RC beam. Similar freeze-thaw cycle to

phase I was used in phase II except that the 75% relative humidity at temperatures above

+20oC was replaced with fresh water spray (18 L/min for a time period of 10 min) at

temperature +20oC to increase the severity of the applied exposure. Based on this part of

the research, the following conclusions can be drawn:

433

1. The effects of the applied exposure on the beams were significantly severe in

phase II, the concrete was severely deteriorated, the beams were cracked

extensively, and permanent deflections (after unloading the sustained load)

ranging from 8-15.6 mm occurred at mid-span of the beams.

2. Due to freeze-thaw exposure and sustained loading, debonding (up to 65% of the

total prestressing length) occurred in the prestressed NSM CFRP strengthened RC

beams at the end regions of the NSM CFRP strips at the concrete-epoxy interface;

On the other hand, no sign of debonding was observed in the non-prestressed

NSM CFRP strengthened RC beam.

3. After freeze-thaw exposure and sustained loading, the debonded length at the

jacking end of the NSM CFRP is higher than that at the fixed end.

4. Strengthening the beam using prestressed NSM CFRP strengthening system with

prestress level up to 49% increased the yielding load of the un-strengthened

control beam up to 64.8%; in which 17.7% of this value is related to strengthening

with non-prestressed NSM CFRP and the rest, 47.1%, is related to prestressing

effects.

5. The prestressed NSM CFRP strengthening increases the ultimate load of the un-

strengthened control beam up to 36.7% in which 26.1% of this value is related to

strengthening and the rest, 10.7%, appears to be related to prestressing effects.

6. Since the prestressed strengthened beams debonded under exposure, the strain

profile is almost constant within the NSM CFRP length.

7. The overall flexural behaviour of the beams in phase II is completely affected by

the combined freeze-thaw exposure and sustained load. Five exposed beams in set

434

BS-F showed a typical failure mode, i.e., tension steel reinforcements yielding

followed by CFRP rupture or concrete crushing while the exposed beams in set

BS-FS failed at early stage after yielding due to concrete crushing; concrete

crushing followed by the NSM CFRP debonding, almost simultaneously; or an

initial NSM CFRP debonding and concrete crushing, almost simultaneously,

followed by the concrete crushing.

8. Comparison between yield loads shows the average decreases of 19.2% and

26.4% in the load and the deflection at yielding of the beams in set BS-FS with

respect to the corresponding beams in set BS-F, respectively. Besides, an average

decrease of 27.5% was observed in ultimate load of the beams in set BS-FS in

comparison to set BS-F. Furthermore, the deflection at ultimate for the beams in

set BS-FS shows an average decrease of 51.6% in comparison with beams BS-F.

9. An average of 63.9% decrease in energy absorption (area under the load-

deflection curve up to the peak load) was observed for set BS-FS in comparison

with set BS-F. Besides, an average decrease of 33.3% in ductility indices

(deflection at ultimate to deflection at yielding) occurred in set BS-FS in

comparison with set BS-F.

10. The NSM-CFRP debonding at end regions of the prestressed strengthened

beams and low ductility and energy absorption resulted from the severe damage to

the concrete material are the issues that should be considered in long-term

performance of the prestressed NSM CFRP strengthened RC beams under freeze-

thaw exposure and sustained loading.

435

6.2.1.4 Prestress Losses in Prestressed NSM CFRP Strips and Rebar

The instantaneous and long-term prestress losses in NSM CFRP reinforcements

were studied using the beams strengthened with prestressed NSM CFRP strips and rebars

from phases I and II. Based on this part of the research, the following conclusions can be

drawn:

1. At room temperature and 7 days after prestressing, an average loss of 3.3% in

CFRP strain occurred in the prestressed NSM-CFRP strengthened RC beams

under self-weight in which 76.4% of this loss happened within 24 hrs after

prestressing.

2. At room temperature and 6 months after prestressing, an average loss of 5.3% in

CFRP strain occurred in the prestressed NSM-CFRP strengthened RC beams

under self-weight.

3. Under freeze-thaw exposure and 50 years after presterssing, an estimated value of

8.5-22.8% loss in CFRP strain is possible to occur in prestressed NSM-CFRP

strengthened RC beam. On the other hand, the freeze-thaw cycling exposure can

leads to a gain in CFRP strain in some cases.

6.2.1.5 Modification of the NSM CFRP Prestressing System

The fixed and movable brackets were modified to avoid the occurrence of the

cracks at the location of the fixed bracket and to investigate the possible cracking patterns

at very high prestress levels (up to 75% of the CFRP ultimate strength). Based on this

part of the research, the following conclusions can be drawn:

436

1. The modification done to the prestressing system eliminates the occurrence of the

cracks during the prestressing at the location of the fixed bracket by selecting a

low value of eccentricity.

2. The tests show that up to 26% difference between the applied load by the jacks

and the prestress load in the NSM reinforcement is possible due to friction

between the prestressing system and beam.

6.2.2 Numerical and Analytical Simulations

6.2.2.1 Finite Element Modeling of RC Beams Strengthened with Prestressed NSM-FRP

A comprehensive nonlinear 3D finite element model was developed to investigate

the behaviour of the RC beams strengthened in flexure with prestressed NSM CFRP

strips, and by considering the effect of debonding. The model was validated with the

experimental results. Based on this part of the research, the following conclusions can be

drawn:

1. The proposed 3D FE model was validated with the experimental results and a

very good correlation was observed. The validated FE model properly estimated

the behaviour of the NSM-CFRP-strengthened RC beams. The FEM procedure

and selected elements along with the assigned material constitutive models and

considered mixed-mode-debonding model (normal tension stress-gap and shear

stress-slip models) can be used to generate a FE model for future studies.

2. When a strengthened beam is tested under four-point bending configuration, the

maximum strain in the CFRP strip does not happen at mid-span section, but

occurs at a location somewhere from the point load to mid-span of the beam

437

which could not be possibly captured due to the infinite location of the installed

strain gauges along the length of the CFRP strips. Also, the strain distribution at

mid-span section is not linear due to the effect of pre-strain applied to the CFRP

strip.

3. The results show that debonding propagation at ultimate load which is mainly

caused by high deflection and crack opening is less for the prestressed beam.

6.2.2.2 Parametric Study on RC Beams Strengthened with Prestressed NSM-FRP

An extensive parametric study was performed to analyse the effects of

prestressing level in the NSM CFRP, tensile steel reinforcement, and concrete

compressive strength on the flexural behaviour of RC beams strengthened with

prestressed NSM CFRP strips. According to this study the following conclusions can be

drawn:

1. Increasing the prestressing level in the NSM CFRP reinforcement: significantly

enhances the negative camber; the cracking and yielding loads; and the cracking

deflection of the strengthened beam; on the other hand, reduces the ultimate

deflection and the ductility index of the strengthened beam.

2. Prestressing the NSM CFRP has a minor effect on the yielding deflection and

ultimate load of the strengthened beam and also on the energy absorption of RC

beams with high tension steel ratio. The type of failure of the strengthened beams

changes from concrete crushing to CFRP rupture with an increase to the

prestressing level in the NSM CFRP reinforcement.

438

3. Increasing the tensile steel reinforcement enhances: the cracking and yielding

deflections; the cracking, yielding, and ultimate loads; and the deflection at

ultimate load when CFRP rupture governs; on the other hand, reduces: the

negative camber; the ductility index; and the ultimate deflection when concrete

crushing governs. The type of failure changes from CFRP rupture to concrete

crushing with increasing the tension steel reinforcement ratio.

4. Increasing the concrete compressive strength: slightly enhances the camber due to

prestressing; the cracking and yielding deflections; and the deflection at ultimate

load when CFRP rupture governs; on the other hand, slightly reduces: the ductility

index and the cracking, yielding, and ultimate loads. The type of failure changes

from concrete crushing to CFRP rupture with increasing the concrete compressive

strength. In general, changing the concrete compressive strength has a very slight

effect on the overall flexural behaviour of the RC beams strengthened with

prestressed NSM CFRP strips.

5. The maximum amount of energy absorption happens when balanced failure

occurs. When CFRP rupture governs, the energy absorption decreases as the

prestressing level, tensile steel ratio, or concrete compressive strength increase.

When concrete crushing governs, the energy absorption increases as the

prestressing level, tensile steel ratio, or concrete compressive strength increase.

6.2.2.3 FE Modeling of Steel End Anchor and Parametric Study

A nonlinear 3D finite element model of the steel end anchor used to prestress

NSM CFRP strips for flexural strengthening of RC beams is developed to investigate the

439

effects of various parameters on the overall behaviour and interfacial shear stress

distributions. According to this part of the research, the following conclusions can be

drawn:

1. The cohesion between interfaces (CFRP-epoxy and steel-epoxy) has a significant

effect on the ultimate capacity of the anchorage. A 202% enhancement in ultimate

load is reached by changing the cohesion of the interfaces from 5 to 20 MPa.

2. Increase in the bond length from 150-450 mm leads to a 146% increase in

ultimate capacity and changing the mode of failure from debonding to CFRP

rupture.

3. Increase in the adhesive width and height leads to a significant decrease in the

interfacial shear stress distribution at vertical and horizontal steel-epoxy

interfaces, respectively. Decreases of 54.3% and 63% in the maximum shear

stresses at the steel-epoxy interfaces were reached by increasing the adhesive

width from 3.5-10.5 mm and adhesive height from 1.5-7.5 mm, respectively.

4. The shear stress distribution at interfaces is a skewed curve which is limited to

bond capacity from the top.

6.2.2.4 Analytical Modeling of RC Beams Strengthened With Prestressed NSM-CFRP

Reinforcements Subjected to Freeze-Thaw Exposure

A nonlinear analytical model was developed to generate the load-deflection

responses of the RC beams strengthened in flexure with prestressed or non-prestressed

NSM-CFRP strips and rebars subjected to freeze-thaw exposure (phase I). Based on this

part of the research, the following items can be drawn:

440

1. The reliability of the model was confirmed by comparing the predicted results

with nine experimental load-deflection responses revealing very good accuracy of

the predicted results. The proposed analytical model can be employed with

enough confidence as a predictive method in future studies.

3. The model has the capabilities of assigning the freeze-thaw exposed concrete

stress-strain curve based on Loov's equation, elasto-plastic behaviour for

compression and tension steel, linear behaviour for FRP, and partial prestressed

CFRP length along the length of the beam.

4. The developed model has the main advantage of having much shorter computer

computational time in comparison with finite element analysis of similar beams.

6.2.2.5 FE Modeling of RC Beams Strengthened with Prestressed NSM-CFRP

Reinforcement Subjected to Freeze-Thaw Exposure and Sustained Load

Five RC beams tested in phase II of the experimental program, which were

subjected to freeze-thaw exposure and sustained load, were simulated and the predicted

load-deflection responses are compared with the experimental ones. Based on this part of

the research, the following conclusion can be drawn:

1. The performed comparison indicates that the load-deflection curves obtained from

the FE models acceptably matched those from the experimental ones up to

yielding, but after yielding the trend of the predicted curves are not in a very good

correlation with the experimental ones.

441

6.3 Recommendations

1. The fatigue performance of the RC beams strengthened with prestressed NSM

CFRP reinforcements subjected to freeze-thaw cycles is an interesting issue that

needs to be investigated experimentally and numerically in the evolution of this

strengthening system.

2. Seismic and dynamic behaviour of the RC beams strengthening using prestressed

NSM CFRP reinforcements needs to be studied experimentally and numerically.

3. The performance of the RC beams strengthened using prestressed NSM CFRP

reinforcements subjected to different types of exposure such as chemical solution

(salt, alkaline, and acid), oxidation, UV radiation, etc needs to be studied.

4. There is no valid method to relate the accelerated freeze-thaw cycles to the real-

world considering the parameters involved based on the geographic location and

the weather conditions.

5. Retrofitting the large-scale bridge I girders using prestressed NSM CFRP

reinforcements should be considered by addressing different issues such as type of

prestressing systems (temporary brackets) and end anchors.

6. The behaviour of the retrofitted existing structural member using prestressed

NSM CFRP reinforcements needs to be investigated. In this case, the existing

cracks might affect the efficiency of the NSM CFRP retrofitting. Also, due to

degradation of concrete properties, the occurrence of cracks at the location of the

cracks at the time of presterssing is probable and should be considered.

7. Strengthening the beams under applied particular service loads using the

prestressed NSM CFRP technique needs to be studied in detail.

442

8. Strengthening RC slabs using prestressed NSM CFRP technique needs to be

studied.

9. The behaviour of the prestressed NSM CFRP strengthening technique under fire

needs to be studied and compared to the prestressed EB strengthening system.

10. After completion of the gaps in this field (mostly the items mentioned above),

proposing a design guideline seems necessary for the rational implementation of

the prestressed NSM CFRP retrofitting and strengthening technique.

443

References

Abdelrahman, A. A., Tadro, G., and Rizkalla, S.H. (1995). Test model for the first

Canadian smart highway bridge. ACI Structural Journal, 92(4): 451-458.

Abdelrahman, K. (2011). Effectiveness of steel fibre reinforced polymer sheets for

confining circular concrete columns. MSc Thesis, University of Calgary, Calgary,

Canada.

Aidoo, J., Harries, K. A., and Petrou, M. F. (2006). Full-scale experimental investigation

of repair of reinforced concrete interstate bridge using CFRP materials. Journal of

Bridge Engineering, 11(3): 350-358.

Akovali, G. (2001). Handbook of composite fabrication. Shawbury, UK: Rapra

Technology.

Al-Darzi, S. Y. K. (2007). Effects of concrete nonlinear modeling on the analysis of

push-out test by finite element method. Journal of Applied Sciences, 7(5): 743-

747.

ACI 440.1R (2006). Guide for the design and construction of structural concrete

reinforced with FRP bars. ACI Committee 440, American Concrete Institute,

Farmington Hills, Michigan, USA.

ACI 440.2R (2008). Guide for the design and construction of externally bonded FRP

systems for strengthening concrete structures. ACI Committee 440, American

Concrete Institute, Farmington Hills, Michigan, USA.

444

ACI 440R (2007). Report on Fiber-Reinforced Polymer (FRP) reinforcement for

concrete structures. ACI Committee 440, American Concrete Institute,

Farmington Hills, Michigan, USA.

Al-Mahmoud, F., Castel, A., François, R., and Tourneur, C. (2009). Strengthening of RC

members with near-surface mounted CFRP rods. Composite Structures, 91(2):

138-147.

Aram, M. R., Czaderski, C., and Motavalli, M. (2008). Debonding failure modes of

flexural FRP-strengthened RC beams. Composites Part B: Engineering, 39(5):

826-841.

Arduini, M., Romagnolo, M., Camomilla, G., and Nanni, A. (2004). Influence of concrete

tensile softening on the performance of FRP strengthened RC beams:

experiments. Proceeding of ACMBS-IV, Calgary (Canada), July 20-23, CD-ROM.

Ashby, M. F. (1987). Technology on the 1990s: Advanced material and predictive

design. Philosophical Transactions of the Royal Society of London. Series A,

Mathematical and Physical Sciences, 322(1567): 393-407.

Asplund, S. O. (1949). Strengthening bridge slabs with grouted reinforcements. ACI

Journal, 45(1): 397-406.

ASTM A370. (2010). Standard test methods and definitions for mechanical testing of

steel produces. American Society for Testing and Materials, Pennsylvania, USA.

445

ASTM Standard C39/C39M. (2010). Standard test method for compressive strength of

cylindrical concrete specimens. American Society for Testing and Materials,

Pennsylvania, USA.

ASTM Standard C666. (1997). Standard test method for resistance of concrete to rapid

freezing and thawing. American Society for Testing and Materials, Philadephia,

Pennsylvania, USA.

ASTM Standard D3039/D3039M. (2008). Standard test method for tensile properties of

polymer matrix composite materials. American Society for Testing and Materials,

Pennsylvania, USA.

Badawi, M., and Soudki, K. (2009). Flexural strengthening of RC beams with prestressed

NSM CFRP rods – experimental and analytical investigation. Construction and

Building Materials, 23(10): 3292-3300.

Barbato, M. (2009). Efficient finite element modelling of reinforced concrete beams

retrofitted with fiber reinforced polymers. Computers and Structures, 87(3): 167-

176.

Barros, J. A. O., Dias, S. J. E., and Lima, J. L. T. (2007). Efficacy of CFRP-based

techniques for the flexural and shear strengthening of concrete beams. Cement

and Concrete Composites, 29(3), 203-217.

Barros, J. A. O., and Fortes, A. S. (2005). Flexural strengthening of concrete beams with

CFRP laminates bonded into slits. Cement and Concrete Composites, 27(4): 471-

480.

446

Bertero, V. V. (1988). State-of-the art report: ductility based structural design.

Proceedings of the 9th

Word Conference on Earthquake Engineering, Tokyo-

Kyoto, Japan, August 2-9, Volume VIII: 673-686.

Bisby, L. A., (2006). Advanced infrastructure materials. Graduate course notes, Queen’s

University, Kingston, Ontario, Canada.

Bisby, L. A., and Green, M. F. (2002). Resistance to freezing and thawing of fiber-

reinforced polymer-concrete bond. ACI Structural Journal, 99(2): 215-233.

Blaschko M. (2001) Zum tragverhalten von betonbauteilen mit in schlitze eingeklebten

CFK-lamellen. Bericht 8/2001 aus dem Konstruktiven Ingenieurbau, TU

Mu¨nchen. 147 pp [in German].

Browne, R. D., and Bamforth, P. B. (1981). The use of concrete for cryogenic storage: A

summary of research, past and present. Proceedings of the 1st International

Conference on Cryogenic Concrete, March, London, The Concrete Society, pp.

135-166.

Buyle-Bodin, F., David, E., and Ragneau, E. (2002). Finite element modelling of flexural

behaviour of externally bonded CFRP reinforced concrete structures. Engineering

Structures, 24(11): 1423-1429.

Camata, G., Spacone, E., and Zarnic, R. (2007). Experimental and nonlinear finite

element studies of RC beams strengthened with FRP plates. Composites Part B:

Engineering, 38(2): 277-288.

447

Canadian Standard Association (2006). Canadian highway bridge design code.

CAN/CSA S6-06, Ontario, Canada.

Carolin, A. (2003). Carbon fibre reinforced polymers for strengthening of structural

elements. PhD Thesis, Lulea University of Technology, Sweden.

Casadei, P., Galati, N., Boschetto, G., Tan, K. Y., Nanni, A., and Galecki, G. (2006).

Strengthening of impacted prestressed concrete bridge I-girder using prestressed

near-surface mounted CFRP bar. Proceeding of the 2nd

International Congress,

Fédération Internationale du Béton, Naples, Italy, June 5-8, CD-Rom, 10p.

Casadei, P., Galati, N., Parretti, R., and Nanni, A. (2003). Strengthening of a bridge using

two FRP technologies. ACI, Special Pubblication 215-12, 215:1-20.

Crasto A., Kim R., Ragland W. (1999). Private Communication between De Lozenzis

and Crasto et al. as reported in De Lozenzis and Teng (2007).

CEB-FIP (1993). CEB-FIP Model Code 1990. Thomas Telford Ltd., London.

Ceroni, F., Cosenza, E., Gaetano, M., and Pecce, M. (2006). Durability issues of FRP

rebars in reinforced concrete members. Cement & Concrete Composites,

28(10):857-868.

Chansawat, K. (2003). Nonlinear finite element analysis of reinforced concrete structures

strengthened with FRP laminates. PhD Thesis, Oregon State University, Oregon,

USA.

448

Chansawat, K., Yim, S. C. S., and Miller, T. H. (2006). Nonlinear finite element analysis

of a FRP-strengthened reinforced concrete bridge. Journal of Bridge Engineering,

11(1): 21-32.

Chan, W. W. L. (1955). The ultimate strength and deformation of plastic hinges in

reinforced concrete frameworks. Magazine of Concrete Research (London),

7(21):121-132.

Chen, J. F., and Teng J. G. (2001). Anchorage strength models for FRP and steel plates

bonded to concrete. Journal of Structural Engineering, ASCE, 127(7): 784-791.

Colombi, P., Fava, G., and Poggi, C. (2010). Bond strength of CFRP-concrete elements

under freeze-thaw cycles. Composite Structures, 92(4):973-983.

Concrete repair bulletin (2001). Cement silo repair and upgrade: 2000 award of

excellence winner, industrial category. CRB, September/October: 16-19.

Coronado, C. A., and Lopez, M. M. (2006). Sensitivity analysis of reinforced concrete

beams strengthened with FRP laminates. Cement and Concrete Composites,

28(1): 102-114.

CAN/CSA-S806 (2012). Design and construction of building components with fiber-

reinforced polymers. CAN/CSA-S806-12, Canadian Standards Association,

Rexdale, Canada.

CAN/CSA-A23.3 (2004). Design of concrete structures. CAN/CSA A23.3-04, Canadian

Standards Association, Toronto, Canada.

449

CAN/CSA-S6 (2011). Canadian highway bridge design code (CHBDC). CAN/CSA-S6-

06, Canadian Standards Association, Toronto, Canada.

De Lorenzis, L. (2002). Strengthening of RC structures with near surface mounted FRP

rods. PhD Thesis, Department of Innovation Engineering, University of Lecce,

Italy.

De Lorenzis, L., Nanni, A., and La Tegola, A. (2000). Flexural and shear strengthening

of reinforced concrete structures with near surface mounted FRP rods. Proceeding

of the 3rd

International Conference on Advanced Composite Materials in Bridges

and Structures, Ottawa, Canada, August 15-18: 521-528.

De Lorenzis, L., and Teng, J. G. (2007). Near-surface mounted FRP reinforcement: An

emerging technique for strengthening structures. Composites Part B: Engineering,

38(2): 119-143.

Dent, A. J. S. (2005). Effects of freeze-thaw cycling combined with fatigue loading on

anchorage of fibre-reinforced polymer sheets bonded to reinforced concrete

beams. MSc Thesis, Queen's University, Kingston, Canada.

Derias, M. (2008). Durability of concrete beams strengthened in flexure using near-

surface-mounted fibre-reinforced-polymers. MSc Thesis, University of Calgary,

Calgary, Canada.

Desayi, P., and Krishnan, S. (1964). Equation for stress-strain curve of the concrete. ACI

Journal, 61(3): 345-350.

450

DTI MMS 6 (2005). Classification and assessment of composite materials systems for

use in the civil infrastructure. Technical report No8, Case studies, June:79p.

DSI (2013). DYWIDAG THREADBAR® - TECHNICAL DATA. Dywidag System

International [Internet] 02.2013. www. Dsicanada.ca.

Duan, A, Jin, W, and Qian, J. (2011). Effects of freeze-thaw cycles on the stress-strain

curves of the unconfined and confined concrete. Materials and Structures,

44:1309-1324.

Dutta, P. K. (1989). Fiber composite materials in Arctic environments. Proceedings of

the sessions related to structural materials at Structures Congress, (ASCE), San

Francisco, California, USA, pp. 216-225.

El-Hacha, R., Green, M. F., and Wight, G. R. (2010). Effect of severe environmental

exposures on CFRP wrapped concrete columns. Journal of Composites for

Construction, 14(1): 83-93.

El-Hacha, R., Green, M. F., Wight, R. G. (2004). Flexural Behaviour of concrete beams

strengthened with prestressed CFRP sheets subjected to sustained loading and low

temperature. Canadian Journal of Civil Engineering, 31(2): 239-252.

El-Hacha, R., and Gaafar, M. (2011). Flexural strengthening of reinforced concrete

beams using prestressed near-surface mounted CFRP bars. PCI Journal, Fall

2011: 134-51.

451

El-Hacha, R., Rizkalla, S. (2004). Near-surface-mounted fiber-reinforced polymer

reinforcements for flexural strengthening of concrete structures. ACI Structural

Journal, 101(5):717-726.

Emam, M. (2007). Strengthening of steel-concrete composite girders using prestressed

fibre reinforced polymer. MSc Thesis, University of Calgary, Calgary, Canada.

Engineers edge (2012). Carbon steel specification [Internet], 01.2012.

http://www.engineersedge.com/manufacturing_spec/average_properties_structural

_materials.htm

Fraser, J. K. (1959). Freeze-thaw frequencies and mechanical weathering in Canada.

Arctic, 12(1): 40-53.

Frigione, M., Aiello, M. A., and Naddeo, C. (2006). Water effects on the bond strength of

concrete/concrete adhesive joints. Construction and Building Materials, 20(10):

957-970.

Gaafar, M. (2007). Strengthening reinforced concrete beams with prestressed near

surface mounted fibre reinforced polymers. MSc Thesis, University of Calgary,

Canada.

GangaRao, H. V. S., Taly, N., and Vijay, P. V. (2007). Reinforced concrete design with

FRP composites. CRC Press, Taylor & Francis Group, Boca Raton, FL, USA.

Green, M. F. (2007). FRP repair of concrete structures: performance in cold regions.

International Journal of Materials and Product Technology, 28(1):160-177.

http://www.engineersedge.com/manufacturing_spec/average_properties_structural_materials.htm

http://www.engineersedge.com/manufacturing_spec/average_properties_structural_materials.htm

452

Green, M. F., Bisby, L.A., Fam, A. Z., and Kodur, V. K. R. (2006). FRP confined

concrete columns: behaviour under extreme conditions. Cement concrete

composites, 28(10):928-937.

Haghani, R. (2010). Analysis of adhesive joints used to bond FRP laminates to steel

members-A numerical and experimental study. Construction and building

materials, 24(11): 2243-2251.

Hassan, T., and Rizkalla, S. (2003). Investigation of bond in concrete structures

strengthened with near surface mounted carbon fiber reinforced polymer strips.

Journal of Composites for Construction, 7(3):248-257.

Hassan T., and Rizkalla, S. (2004). Bond mechanism of near-surface-mounted fiber-

reinforced polymer bars for flexural strengthening of concrete structures. ACI

Structural Journal, 101(6):830–839.

Hilti Inc. (2008). Technical information, Tech Guide-Kwik Bolt 3 Exp Anchor [Internet].

06.2008.< http://www.hilti.ca/fstore

/holca/techlib/docs/4.3.5_Kwik_Bolt_3_Expansion_Anchor_(328-352).pdf >

Hognestad, E. (1951). A study of combined bending and axial load in reinforced concrete

members. Bulletin 399, University of Illinois Engineering Experiment Station,

Urbana, Ill., USA, 128 pp.

Hollaway, L., and Leeming, M. (1999). Strengthening of reinforced concrete structures:

using externally-bonded FRP composites in Structural and Civil Engineering.

Woodhead Publishing Ltd., Cambridge, England, 337 pp.

453

Hughes Brothers Inc. (2010a). Technical Information: “Aslan 200 CFRP rebar”. Product

Guide Specification. Web site: http://www.hughesbros.com.

Hughes Brothers Inc (2010b). Technical Information: “Aslan 500 CFRP tape”. Product

Guide Specification. Web site: http://www.hughesbros.com.

ISIS Canada Design Manual. (2007). Reinforcing concrete structures with fibre-

reinforced polymers. The Canadian Networks of Centers of Excellence on

Intelligent Sensing for Innovative Structures, ISIS M03-07, Design Manual No.3,

University of Manitoba, Winnipeg, Manitoba, Canada.

Jaeger, L. G., Mufti, A. A., and Tadros, G. (1997). The concept of the overall

performance factor in rectangular section reinforced concrete members.

Proceedings of the 3rd

International Symposium on Fiber Reinforced Polymer

Reinforcement for Reinforced Concrete Structures (FRPRCS-3), Sapporo, Japan,

October 14-16. Volume II: 551-559.

Jia, M. (2003). Finite element modeling of reinforced concrete beams strengthened with

FRP composite sheets. MSc Thesis, The University of Alabama in Huntsville,

Alabama, USA.

Jones, R. M. (1999). Mechanics of composite materials (second edition). Taylor and

Francis, Philadelphia, PA, USA.

Jung, W., Park, J., and Park, Y. (2007). A study on the flexural behaviour of reinforced

concrete beams strengthened with NSM prestressed CFRP reinforcement.

Proceeding of the 8th

International Symposium on Fiber Reinforced Polymer

454

Reinforcement for Reinforced Concrete Structures (FRPRCS-8), University of

Patras, Patras, Greece, July 16-18, CD-Rom, 8p.

Kabir, M. Z., and Hojatkashani A. A. (2008). Comparison between finite element and

analytical solutions of interfacial stress distribution in a RC beam retrofitted with

FRP composites. International Journal of Science and Technology, 19(68): 55-65.

Kachlakev, D., Miller, T., Yim, S., Chansawat, K., & Potisuk, T. (2001). Finite element

modeling of reinforced concrete structures strengthened with FRP laminates-

final report SPR 316. Oregon Department of Transportation Research Group,

Oregon, USA.

Kang, J. Y., Park, Y. H., Park, J. S., You, Y. J., and Jung, W. T. (2005). Analytical

evaluation of RC beams strengthened with near surface mounted CFRP laminates.


International Symposium on FRP Reinforcement for

Concrete Structures (FRPRCS-7), Kansas City, MO, USA, November 6–9, 779-

794.

Karbhari, V. M., Chin, J. W., Hunston, D., Benmokrane, B., Juska, T., Morgan, R.,

Lesko, J. J., Sorathia, U., and Reynaud, D. (2003). Durability gap analysis for

fiber-reinforced polymer composites in civil infrastructure. Journal of Composites

for Construction, 7(3):238- 247.

Kemp, A. R. (1998). The achievement of ductility in reinforced concrete beams.

Magazine of Concrete Research, 50(2): 123-132.

455

Kent, D. C., and Park, R. (1971). Flexural members with confined concrete. Journal of

Structural Division, ASCE, 97(7):1969-1990.

Kishi, N., Zhang, G., and Mikami, H. (2005). Numerical cracking and debonding analysis

of RC beams reinforced with FRP sheet. Journal of Composites for Construction,

9(6): 507-514.

Kosmatka, S. H. (1998). Concrete construction engineering handbook. CRC Press, Boca

Raton, Florida, USA.

Laoubi, K., El-Salakawy, E., Benmokrane, B. (2006). Creep and durability of sand-

coated glass FRP bars in concrete elements under freeze/thaw cycling and

sustained loads. Cement & Concrete Composites, 28(10): 869-878.

Loov, R. E. (1991). A general stress–strain curve for concrete implications for high

strength concrete columns. Proceeding of the annual conference of the Canadian

society for civil engineering, Vancouver, Canada, May 29–31, 302–311.

Lopez-Anido, R., Michael, A. P., and Sandford, T. C. (2004). Freeze-thaw resistance of

fiber-reinforced polymer composites adhesive bonds with underwater curing

epoxy. Journal of Materials in Civil Engineering, 16(3): 283-286.

Lu, X. Z., Teng, J. G., Ye, L. P., and Jiang, J. J. (2005). Bond–slip models for FRP

sheets/plates bonded to concrete. Engineering Structures, 27(6): 920-937.

Mander, J. B., Priestley, M. J. N., and Park, R. (1988). Theoretical stress-strain model for

confined concrete. Journal of Structural Engineering, 114(8):1804-1826.

456

McCurry, D. (2000). Strengthening of reinforced concrete beams using FRP composite

fabrics: Full-scale experimental studies and design concept verification. MSc

Thesis, Oregan State University, Corvallis, OR, USA.

Mehta, P. K., and Monteiro, P. J. M. (2006). Concrete: microstructure, properties, and

materials, 3rd

ed. McGraw-Hill Inc., New York, USA.

Micelli F. (2004). Durability of FRP Rods for Concrete Structures. Construction and

Building Materials,18(7):491-503.

Mirza, M. S., and Haider, M. (2003). The state of infrastructure in Canada: Implications

for infrastructure planning and policy. Infrastructure Canada, March, Ottawa.

Mitchell, P. (2010). Freeze-thaw and sustained load durability of near surface mounted

FRP strengthened concrete. MSc Thesis, Queen's University, Kingston, Canada.

Monti, G., Renzelli, M., and Luciani, P. (2003). FRP adhesion to uncracked and cracked

concrete zones. Proceedings of the 6th

international symposium on FRP

reinforcement for concrete structures (FRPRCS-6), Singapore, July 8-10.

Mufti, A., Erki, M., and Jaeger, L. (1991). Advanced composite materials with

application to bridges. Canadian Society of Civil Engineering, Montreal, Quebec,

Canada, pp. 21-70.

Naaman, A. E., and Jeong, S. M. (1995). Structural ductility of concrete beams

prestressed with FRP tendons. Proceedings of the 2th

International Symposium on

Non-Metallic Fiber Reinforced Polymer Reinforcement for Reinforced Concrete

Structures (FRPRCS-2), Ghent, Belgium, August 23-25, 379-386.

457

NCHRP (2004). Bonded repair and retrofit of concrete structures using FRP composites.

National Cooperative Highway Research Program, Report 514, Transportation

Research Board, Washington, DC.

Neale, K. W. (1997). Advanced composites and integrated sensing for rehabilitation,

ISIS Canada annual report, 6p.

Neville, A. M. (2011). Properties of concrete, 5th

ed. Pearson, New York, USA.

Nordin, H., and Täljsten, B. (2006). Concrete beams strengthened with prestressed near

surface mounted CFRP. Journal of Composites for Construction, 10(1): 60-68.

Nour, A., Massicotte, B., Yildiz, E., and Koval, V. (2007). Finite element modeling of

concrete structures reinforced with internal and external fibre-reinforced polymers

(1). Canadian Journal of Civil Engineering, 34(3): 340-54.

Oldershaw, B. (2008). Combined effects of freeze-thaw and sustained loads on reinforced

concrete beams strengthened with FRPs. MSc Thesis, Queen's University,

Kingston, Canada.

Omran, H. Y., and El-Hacha, R. (2010a). Finite element modelling of RC beams

strengthened in flexure with prestressed near surface mounted CFRP rebars.


International Conference on Short and Medium Span Bridge

(SMSB 2010), Niagara Falls, Ontario, Canada, August 3-6, CD-ROM, 10p.

Oudah, FS. (2011). Fatigue performance of RC beams strengthened using prestressed

NSM CFRP. MSc Thesis, University of Calgary, Calgary, Canada.

458

Özcan, D. M., Bayraktar, A., Şahin, A., Haktanir, T., and Türker, T. (2009).

Experimental and finite element analysis on the steel fiber-reinforced concrete

(SFRC) beams ultimate behaviour. Construction and Building Materials, 23(2):

1064-1077.

Park, R., and Paulay, T. (1975). Reinforced concrete structures. John Wiley and Sons

Inc., New York, USA.

Park, R., Priestley, M. J. N., and Gill, W. D. (1982). Ductility of square confined concrete

columns. Journal of Structural Division, ASCE, 108(4): 929-950.

Pham, H. B., and Al-Mahaidi, R. (2005). Finite element modelling of RC beams

retrofitted with CFRP fabrics. Proceeding of the 7th

international symposium on

FRP reinforcement for concrete structures (FRPRCS-7), Kansas City, MO, USA

November 6–9, p. 499-514.

Quattlebaum, J. B., Harries, K. A., and Petrou, M. F. (2005). Comparison of three

flexural retrofit systems under monotonic and fatigue loads. Journal of Bridge

Engineering, 10(6): 731-740.

Rafi, M. M., Nadjai, A., and Ali, F. (2007). Analytical modeling of concrete beams

reinforced with carbon FRP bars. Journal of Composite Materials, 41(22): 2675-

2690.

Ramcharitar, M. (2004). Current bridge deck rehabilitation practices: use and

effectiveness. Master of Applied Science thesis, Ryerson Univ., Toronto.

459

Rasheed, H. A., Harrison, R. R., Peterman, R. J., and Alkhrdaji, T. (2010). Ductile

strengthening using externally bonded and near surface mounted composite

systems. Composite Structures, 92(10), 2379-2390.

Rashid, M. A., Mansur, M. A., and Paramasivam, P. (2005). Behaviour of Aramid fiber-

reinforced polymer reinforced high strength concrete beams under bending.

Journal of Composite for Construction, ASCE, 9(2): 117-127.

Rosenboom, O. A., and Rizkalla, S. H. (2005). Fatigue behaviour of prestressed concrete

bridge girders strengthened with various CFRP systems. Proceedings of the 7th

International Symposium on Fiber Reinforced Polymer (FRP) Reinforcement for

Concrete Structures (FRPRCS-7), Kansas City, Missouri, November 7-10, CD-

ROM, 597-612.

Roy, H. E. H., and Sozen M. A. (1965). Ductility of concrete. Proceedings of the

International Symposium on the Flexural Mechanics of Reinforced Concrete, SP-

12, American Concrete Inistitute/American Society of Civil Engineers, Miami,

Florida, USA.

SAS (2004). ANSYS 9 finite element analysis system, SAS IP, Inc.

SAS (2009). ANSYS 12 finite element analysis system, SAS IP Inc.

Saiedi, M. R. (2009). Behaviour of CFRP-prestressed concrete beams under sustained

loading and high-cycle fatigue at low temperature. MSc Thesis, Queen's

University, Kingston, Canada.

460

Santofimio, F. J. (1997). Durability and long-term performance of concrete structural

elements strengthened with FRP sheets. MSc Thesis, University of Puerto Rico at

Mayagüez, Mayagüez, Puerto Rico.

Sargin, M. (1971). Stress-strain relationships for concrete and the analysis of structural

concrete sections. Report No. Study No. 4., Solid Mechanics Division, University

of Waterloo, Ontario, Canada.

Sayed-Ahmed, E. L., Riad, A. H., and Shrive, N. G. (2004). Flexural strengthening of

precast reinforced concrete bridge girders using bonded carbon fibre reinforced

polymer strips or external post-tensioning. Canadian Journal of Civil

Engineering, 31(3): 499-512.

Seracino, R., Saifulnaz, M. R. R., and Oehlers, D. J. (2007). Generic debonding

resistance of EB and NSM plate-to-concrete joints. Journal of Composite for

Construction, 11(1): 62-70.

Setunge, S., Kumar, A., Nezamian, A., De Silva, S., Carse, A., Spathonis, J., Chandler,

L., Gilbert, D., Johnson, B., Jeary, A., and Pham, L. (2002). Review of

strengthening techniques using externally bonded fiber reinforced polymer

composites. Report 2002-005-C-01. CRC for Construction Innovation, Brisbane,

Australia.

Sheikh-Ahmad, J. Y. (2008). Machining of polymer composites. Springer, New York,

NY, USA.

461

Sheikh, S. A., and Uzameri, S. M. (1980). Mechanism of confinement in tied columns.


world conference on earthquake engineering, Istanbul,

Turkey, September, p. 71-78.

Sika Inc. (2007a). “Sikadur® 330”, product data sheet, impregnation resin for fabric

reinforcement [Internet]. 01.2007/v1. Available from:

http://can.sika.com/content/canada/main/en/solutions_products/document_downlo

ad/Structural_Strengthening.html.

Sika Inc. (2007b). “Sikadur® 30”, product data sheet, high modulus, high strength,

structural epoxy paste adhesive for use with sika® CarboDur® reinforcement

[Internet]. 01.2007/v1. Available from:



Sika Inc. (2010a). “Sikadur® 330”, product data sheet, impregnation resin for fabric

reinforcement [Internet]. 06.2010/v1. Available from:



Sika Inc. (2010b). “Sikadur® 30”, product data sheet, high modulus, high strength,

structural epoxy paste adhesive for use with sika® CarboDur® reinforcement

[Internet]. 06.2010/v1. Available from:



http://can.sika.com/content/canada/main/en/solutions_products/document_download/Structural_Strengthening.html








462

Sireg (2011). FRP and civil engineering [Internet]. Available from:

http://www.sireg.it/en/civil-engineering/products-civil-eng/.

Soliman, S. M., El-Salakawy, E., and Benmokrane, B. (2010). Flexural behaviour of

concrete beams strengthened with near surface mounted fibre reinforced polymer

bars. Canadian Journal of Civil Engineering, 37(10): 1371-1382.

Soliman, M. T. M., and Yu C. W. (1967). The flexural stress-strain relationship of

concrete confined by rectangular transverse reinforcement. Magazine of Concrete

Research, 19(61): 223-238.

Spadea, G., Swamy, R. N., Bencardino, F. (2001). Strength and ductility of RC beams

repaired with bonded CFRP laminates. Journal of Bridge Engineering, 6(5): 349-

355.

Subramaniam, K. V., Ali-Ahmad, M., and Ghosn, M. (2008). Freeze–thaw degradation of

FRP-concrete interface: Impact on cohesive fracture response. Engineering

Fracture Mechanics, 75(13): 3924-3940.

Supaviriyakit, T., Pornpongsaroj, P., and Pimanmas, A. (2004). Finite element analysis of

FRP-strengthened RC beams. Songklanakarin Journal of Science and

Technology, 26(4): 497-507.

Täljsten, B., Carolin, A., and Nordin, H. (2003). Concrete structures strengthened with

near surface mounted reinforcement of CFRP. Advances in Structural

Engineering, 6(3): 201–213.

463

Täljsten, B., and Nordin, H. (2005). Concrete beams strengthened with external

prestressing using external tendons and near-surface-mounted reinforcement

(NSMR). Proceeding of the 7th

International Symposium on Fiber Reinforced

Polymer Reinforcement for Reinforced Concrete Structures (FRP RCS-7), Kansas

City, USA, November 7-10, pp. 143-164.

Tam, S. S. F. (2007). Durability of fibre reinforced polymer (FRP) and FRP bond

subjected to freeze-thaw cycles and sustained load. MSc Thesis, University of

Toronto, Toronto, Canada.

Tan, K. H., Saha, M. K., and Liew, Y. S. (2009). FRP-strengthened RC beams under

sustained loads and weathering. Cement and Concrete Composites, 31(5), 290-

300.

Tang, W. C., Balendran,�R. V., Nadeem, A., and Leung, H. Y. (2006). Flexural

strengthening of reinforced lightweight polystyrene aggregate concrete beams

with near-surface mounted GFRP bars. Building and Environment, 41 (10): 1381-

1393.

Tavarez, F. A. (2001). Simulation of behavior of composite grid reinforced concrete

beams using explicit finite element methods. MSc Thesis, University of

Wisconsin, Madison, Wisconsin, USA.

Teng, J. G., De Lorenzis, L., Wang, B., Rong, L., Wong, T. N., and Lam, L. (2006)

Debonding failures of RC beams strengthened with near-surface mounted CFRP

strips. Journal of Composits for Construction, 10(2): 92-105.

464

Thorenfeldt, E., Tomaszewicz, A., and Jensen, J. J. (1987). Mechanical properties of high

strength concrete and application to design. Proceedings of the Symposium on the

Utilization of high strength concrete, Stavanger, Norway, June 15-18, pp. 149-

159.

Todeschini, E. C., Bianchini, A. C., and Kesler, C. E. (1964). Behaviour of concrete

column reinforced with high strength steels. ACI Journal, 61(6): 701-716.

Toutanji, H. A., and Gómez, W. (1997). Durability characteristics of concrete beams

externally bonded with FRP composite sheets. Cement and Concrete Composites,

19(4): 351-358.

Tumialan, J., Vatovec, M., and Kelley, P. (2007). Case study: strengthening of parking

garage decks with near-surface-mounted CFRP bars. Journal of Composites for

Construction, 11(5): 523–530.

Turner, F.H. (1979). Concrete and cryogenics. Cement and Concrete Association.

Ulaga, T., Vogel, T., and Meier, U. (2003). The bilinear stress-slip bond model:

theoretical background and significance. Proceeding of the FRPRCS-6

Conference, July 8-10, Singapore, 10p.

Vallenas, J., Bertero, V. V., and Popov, E. P. (1977). Concrete confined by rectangular

hoops and subjected to axial loads. Report No. UCB/EERC-77/13, Earthquake

Engineering Research Center, College of Engineering, University of California,

Berkeley, California, USA, 114 p.

465

Varastehpour, H., and Hamelin, P. (1997). Strengthening of concrete beams using fiber-

reinforced plastics. Materials and Structures, 30(3): 160-166.

Vecchio, F. J., and Bucci, F. (1999). Analysis of repaired reinforced concrete structures.

Journal of Structural Engineering-ASCE, 125(6): 644-652.

Vijay, P. V., and GangaRao, H. V. S. (1999). Development of fiber reinforced plastics for

highway application: aging behaviour of concrete beams reinforced with GFRP

bars. CFC-WVU Report No. 99 - 265 (WVDOH RP #699-FRPl).

Wight, J. K., and MacGregor, J. G. (2009). Reinforced concrete mechanics and design.

Fifth ed. Pearson Prentice Hall, New Jersey, USA.

Willam, K. J., and Warnke, E. D. (1975). Constitutive model for the triaxial behaviour of

concrete. Proceeding of the international association for bridge and structural

engineering, Bergamo, Italy, ISMES, Volume 19: pp. 174-190.

Wolanski, A. J. (2004). Flexural behaviour of reinforced and prestressed concrete beams

using finite element analysis. MSc Thesis, Marquette University, Milwaukee,

Wisconsin, USA.

Wolfram Research Inc. (2008). Mathematica, Version 7.0, Champaign, IL, USA.

Wu, H., Fu, G., Gibson, R. F., Yan, A., Warnemuende, K., and Anumandla, V. (2006).

Durability of FRP composite bridge deck materials under freeze-thaw and low

temperature conditions. Journal of Bridge Engineering, 11(4): 443-451.

Wu, Z., Iwashita, K., and Sun, X. (2005). Structural performance of RC beams

strengthened with prestressed near-surface-mounted CFRP tendons. Proceeding

466

of the 7th

International Symposium on Fiber Reinforced Polymer Reinforcement

for Reinforced Concrete Structures (FRP RCS-7), Kansas City, USA, November

7-10, pp. 165-178.

Yamane, S., Kasami, H., and Okuno, T. (1978). Properties of concrete at very low

temperatures. International Symposium on Concrete and Concrete Structures,

ACI SP- 55: 207-221.

Yanev, B. S. (2005). Bridges: Structural condition assessment, Wiley, New York, 329–

405.

Yost, J. R., Gross, S. P., Dinehart, D. W., and Mildenberg, J. (2004). Near surface

mounted CFRP reinforcement for the structural retrofit of concrete flexural

members. Proceedings of ACMBS-IV, Calgary (Canada), July 20-23, CD-ROM.

Zou, P. X. W. (2003). Flexural behaviour and deformability of fiber reinforced polymer

prestressed concrete beams. Journal Composite for Construction, ASCE, 7(4):

275-284.

467

List of to Date Publications from the Research Presented in This PhD Thesis

Omran, H.Y., and El‐Hacha, R. (2010b). Finite element modelling of RC beams

strengthened in flexure with prestressed NSM CFRP strips. Proceeding of The 5th

International Conference on FRP Composites in Civil Engineering (CICE2010).

Beijing, China, September 27‐29, pp.718‐721.

Omran, H.Y., and El‐Hacha, R. (2010c). Parametric study of RC girders strengthened in

flexure using prestressed NSM CFRP strips. Proceeding of The 3rd

International

Conference on Seismic Retrofitting (ISCR2010). Tabriz, Iran, October 20‐22,

CD‐ROM, 12p.

Omran, H.Y., and El-Hacha, R. (2012a). Reinforced concrete beams strengthened using

prestressed NSM CFRP reinforcement – effects of CFRP geometry and freeze-

thaw exposure. Proceedings of the 6th

International Conference on Advanced

Composite Materials in Bridges and Structures (ACMBS-VI), Kingston, Ontario,

Canada, May 22 – 25, 8p.

Omran, H. Y., and El-Hacha, R. (2012b). Nonlinear 3D finite element modeling of RC

beams strengthened with prestressed NSM-CFRP strips. Construction and

Building Materials, 31 (June 2012): 74-85.

Omran, H.Y., and El‐Hacha, R. (2012c). Deformability and ductility of reinforced

concrete beams strengthened with NSM‐CFRP reinforcements. Proceeding of The

3rd

International Structural Specialty Conference. Edmonton, Alberta, Canada,

June 6‐9, 10p.

468

Omran, H. Y., and El-Hacha, R. (2012d). Effects of severe environmental exposure on

RC beams strengthened with prestressed NSM-CFRP strips. Proceeding of The 6th

International Conference on FRP Composites in Civil Engineering - CICE2012,

Rome, Italy, June 13-15, 8p.

Omran, H.Y., and El‐Hacha, R. (2012e). Anchorage system to prestress NSM‐CFRP

strip: effects of bond and anchor dimensions on the interfacial stress distributions

and bond performance. Proceeding of The 4th

International Symposium on Bond

in Concrete (BIC2012). Brescia, Italy, June 17‐20, 9p.

Omran, H.Y., and El‐Hacha, R. (2013a). Analytical modeling of RC beams strengthened

with prestressed NSM‐CFRP strips subjected to freeze‐thaw exposure.

Proceeding of The 2nd

Conference on Smart Monitoring, Assessment and

Rehabilitation of Civil Structures (SMAR13). Istanbul, Turkey, September 9-11,

9p.

Omran, H.Y., and El‐Hacha, R. (2013b). Effects of sustained load and freeze-thaw

exposure on RC beams strengthened with prestressed NSM-CFRP strips. The 4th

Asia-Pacific Conference on FRP in Structures (APFIS2013). Melbourne,

Australia, December 11-13, 6p (accepted).

El-Hacha, R. and Omran, H. Y. RC beams strengthened using prestressed NSM-CFRP

reinforcements: effects of freeze-thaw exposure, CFRP geometry, and prestressing

Loss. Composite Structures. (under submission)

469

Omran, H. Y. and El-Hacha, R. Experimental study on RC beams strengthened with

prestressed NSM-CFRP strips subjected to freeze-thaw exposure. Composite

Structures. (under submission)

470

Appendix A: Beam Design

A.1 Introduction

The key points of the load-deflection curves are calculated by developing a code

in Mathematica software that can account for negative camber due to prestressing,

concrete cracking, steel yielding, CFRP rupture, and concrete crushing of the prestressed

and non-prestressed NSM-CFRP strengthened RC beams. The design is performed based

on the material properties reported by the manufacturer that assigned as inputs to the

code.

A.2 Design Concepts, Source Code, and Results

The concept of the code is similar to Section 5.5 by assuming strain compatibility,

and force and moment equilibriums. The deflection at mid-span at each load increment is

calculated using integration from the curvatures along the length of the beams. The

source code includes eight steps to produce the overal load-deflection response and is

written in Wolfarm Mathematica (Wolfarm Research, 2008). The code is written based

on different variables, arrays for loads, deflections, moments, and curvatures, different

loops and functions available in the software.

For instance, the source code is provided in the following pages having the inputs

for solving the load-deflection response of beam BS-P3 followed by the obtained results,

the results for the other beams are summarized in Table A-1. The eight steps are briefly

mentioned in the source code, where Step 1 is the input, Step 2 calculates the load-

deflection response from start to cracking, Step 3 calculates the yield load, Step 4

471

calculates the ultimate load due to concrete crushing, Step 5 calculates the ultimate load

due to CFRP rupture, Step 6 calculates the loads and corresponding deflections from

cracking to yielding of tension steel, Step 7 calculates the loads and corresponding

deflections from yielding of tension steel to ultimate, and the calculated load and

corresponding deflection are plotted in Step 8. More details about the steps can be found

in the source code.

The input of the source code includes twenty-five constants in N and mm units,

which represent material properties and geometry of the beam, where L is the span

length; Lp the shear span length; Lo the un-strengthened length on each side; b and h the

width and the height of the beam, respectively; dst the depth to the tension steel

reinforcements, dsc the depth to the compression steel reinforcements; df the depth to the

CFRP reinforcements; Efrp, ϵfrpu, ffrpu, Afrp, and ϵpe the modulus of elasticity, the

ultimate tensile strain, the tensile strength, the area, and the prestrain in the CFRP

reinforcements, respectively; Bcsc, ncsc, and ϵocsc the constants B, n, and ϵo in the

loov’s equation (Equation 5-1), respectively; fc, Ec, fr, and ϵcCC the compressive

strength, the modulus of elasticity, the tensile strength, and the crushing strain of the

concrete material, respectively; Ast, fyt, and Est the area, the yield stress, and the

modulus of elasticity of the tension steel reinforcements, respectively; and Asc, fyc, and

Esc are the area, the yield stress, and the modulus of elasticity of the compression steel

reinforcements, respectively.

The output is set to present the type of failure; a plot of the load-deflection

response; and load, deflection, moment, and mid-span curvature for twenty-four points on

the load-deflection curve including prestressing, cracking, yielding, and ultimate stages.

472

472

473

473

474

474

476

Table A-1: Summary of designed specimens.

Beam ID ɛp Δo

(mm)

Δcr*

(mm)

Pcr*

(kN)

Δy*

(mm)

Py*

(kN)

Δu*

(mm)

Pu*

(kN) ɛc@u ɛfrp@u

Failure

Mode

B0 N.A. 0 1.70 22.70 21.85 82 121.47 85.73 0.0035 N.A. CC

BS-NP 0 0 1.71 22.91 22.16 88.88 96.92 131.78 0.00302 0.017 FR

BS-P1 0.0034 0.45 1.76 29.60 21.58 97.83 75.74 131.65 0.00259 0.017 FR

BS-P2 0.0068 0.90 1.81 36.28 21.03 106.73 56.36 131.26 0.00217 0.017 FR

BS-P3 0.0102 1.35 1.86 42.97 20.53 115.58 38.85 130.31 0.00173 0.017 FR

BR-NP 0 0 1.71 22.94 22.21 89.86 93.06 135.17 0.00295 0.016 FR

BR-P1 0.0034 0.51 1.77 30.58 21.55 100.08 71.47 134.99 0.00251 0.016 FR

BR-P2 0.0068 1.02 1.82 38.22 20.94 110.24 51.87 134.48 0.00208 0.016 FR

BR-P3 0.0102 1.54 1.88 45.85 20.37 120.33 34.34 133.20 0.00162 0.016 FR

ɛp = target prestrain value in CFRP reinforcement ɛc@u= concrete strain at extreme compression fibre at ultimate

Δo = initial camber due to prestressing ɛfrp@u= maximum CFRP strain at ultimate

Pcr and Δcr = load and deflection at cracking CC = concrete crushing

Py and Δy = load and deflection at yielding FR = CFRP rupture

Pu and Δu = load and deflection at ultimate

* self-weight is ignored in calculations (to consider the self-weight effects, values of 6 kN and 0.47 mm should be deducted from the loads and deflections,

respectively)

476

477

Appendix B: Fabrication of Beams

B.1 Introduction

Fabrication of the RC beam specimens includes building the formwork, steel

cage, instrumentation, concrete casting, and strengthening are presented in this Appendix.

B.2 Fabrication of Formwork

Three formworks (two pairs and one single) were fabricated to cast a maximum of

five RC beams at once. Each pair form were fabricated by connecting two single forms

laterally using wooden bracer sitting on one base as shown in Figure B-1a. The plywood

used for formwork had 19 mm thickness. The sides of the forms were connected to each

other and to the base using angle as shown in Figure B-1b. Pictures of the formwork

fabrication are presented in Figure B-1. Prior to casting, the inner surfaces of the

formworks were sprayed with oil to facilitate the removal of the beams after curing.

(a) Fabrication of the pair forms (b) Fabricated formworks

Figure B-1: Fabrication of formwork.

Bracer

478

B.3 Steel Cage

Fourteen steel cages were built for the experimental program. Each steel cage was

made of 2-5250 mm long 10M deformed steel bars used for top reinforcements, 3-5250

mm long 15M deformed steel bars used for bottom reinforcements, and 25-1200 mm long

10M deformed steel bars used for stirrups (with a 135 degree hook). Top and bottom

reinforcements had a 90 degree bent at each end with a development length of 100 mm.

All reinforcement were tied together using 100 mm long steel ties. Fabrication of steel

cage and also steel cages placed into the formwork are shown in Figure B-2a and b,

respectively. To place the cages into the formwork, plastic chairs were used between the

formwork and the cages (six 38 mm plastic chairs at bottom attach to the stirrups and

twelve 22.5 mm plastic chairs at each sides attach to the stirrups) to provide the necessary

concrete cover for the longitudinal reinforcements. The threaded rods with washers and

nuts were used to keep the width inside the formwork constant and avoid buckling of the

side of formwork during casting. Two 1000 mm long steel wires were tied to each cage at

1200 from each end to work as handle for moving the beams as shown in Figure B-2b.

Furthermore, the wires for strain gauges and thermocouple were passed through a small

hose and hanged from the edge of the formwork to avoid possible future damage to the

wires.

479

(a) Fabrication of the cage (b) Cages placed into the formwork

Figure B-2: Fabrication of the steel cage and placement in the formwork.

B.4 Casting Concrete

Three batches of concrete were used to cast fourteen beams for the test matrix:

batch #1 poured on August 13, 2009 (five beams were cast, BS-F set and B0-F in Table

3-1); batch #2 on July 9, 2010 (four beams were cast, BR-F set in Table 3-1); and batch

#3 on October 12, 2010 (five beams were cast, BS-FS set and B0-FS in Table 3-1). The

concrete was poured in the formwork carefully to avoid the possible damage to the strain

gauges installed on the steel bars. Also during the casting, a vibrator was used to compact

the concrete and to avoid honeycombing. The top surfaces of the beams were levelled

using hand trowels (Figure B-3a). Cylinder specimens (100×200 mm, diameter × height)

were cast to obtain the concrete properties at different stages. At the end, the beams were

covered with plastic sheets to avoid formation of surface cracks during curing, as shown

in Figure B-3b. The beams were stripped from the formworks three days after casting.

Steel rod

Handle

Plastic

chair

Thermocouple

wire

Strain gauge

wire

480

(a) Concrete cast in formworks (b) Covering the concrete with plastic sheets

Figure B-3: Fabrication of RC beams.

B.5 Strengthening Procedure

One of the challenges for using prestressed NSM FRP method is developing a

practical method for prestressing. Most researches in this area were performed while the

beam was prestressed against entire length needing both ends of the beam as mentioned

in Chapters One and Two. The prestressing and anchorage systems used in this research

for prestressing the NSM CFRP strips and rebar was developed by Gaafar (2007), which

overcomes the drawbacks of the previous research and is practical. The steps performed

for strengthening the beams in this research are presented in this section followed by

more detailed description of the major steps.

B.5.1 General Steps

The following steps were performed for strengthening using prestressed NSM

CFRP:

481

1. Preparation of the CFRP reinforcements (the CFRP strips and rebars were cut to

provide the same prestressing length for each beam after elongation, two CFRP

strips were bonded together to from the side to have similar axial stiffness with

rebar)

2. Making end anchors and cleaning the insides of the end anchors by sand blasting

3. Bonding CFRP rebar/strips into the end anchors using epoxy Sikadur® 330 and

leaving for a week to cure (the CFRP strips and rebars were cleaned with Acetone

solvent)

4. Marking the location of the groove on the beam (the elongation of CFRP

reinforcement due to prestressing was considered in marking the groove)

5. Cutting the grooves (the beams were upside down to facilitate the trend, the

grooves at the ends were made wider and deeper to allow for placing the end

anchors)

6. Cleaning the groove with water and air pressure

7. Drilling the location of the bolts for fixed end anchor, fixed bracket, and movable

bracket (the location of the internal steel reinforcements were identified to avoid

hitting the internal steel, enough space was considered between the brackets for

placing the jacks and load cells, the bolts at movable bracket were located such

that allow moving the bracket more than CFRP elongation due to prestressing)

8. Placing the beam on the pedestal to simulate the field condition for overhead

strengthening

9. Filling the groove with epoxy, Sikadur® 30, using epoxy gun and leveling using

spatula (used for overhead applications)

482

10. Attaching the fixed end anchor to the concrete using anchor bolts (that

hammered in holes), holding the anchor at the other end and pushing the CFRP

into the centre of the groove, levelling the epoxy in the groove (the CFRP

reinforcements were cleaned with Acetone before placing in the groove)

11. Installing the fixed and movable brackets, hydraulic jacks, load cells, and

threaded steel bar with adjustable nuts (placed between movable and fixed

brackets)

12. Applying the load by jacking to the about 2% higher than target perstressing

level (to consider possible loss) for each beam

13. Tightening the adjustable nut, removing the ramps of the hydraulic jack, then,

leaveing the system for 24 hrs

14. Drilling and bolting the jacking end anchor

15. Removing the temporary and movable brackets after four days and monitoring

the system up to a week. It should be noted that the end anchors at the ends of

the CFRP reinforcements remained in place.

In the case of the non-prestressed NSM CFRP strengthening the following steps

were performed:

1. Preparation of the CFRP reinforcements

2. Making end anchors and cleaning the insides of the end anchors by sand blasting

3. Bonding CFRP rebar/strips into the end anchors using epoxy Sikadur® 330 and

leaving for a week to cure (the CFRP strips and rebars were cleaned with Acetone

solvent)

483

4. Marking the location of the groove on the beam

5. Cutting the grooves (the beams were upside down)

6. Cleaning the groove with water and air pressure

7. Drilling the location of the bolts for end anchors

8. Filling the groove using epoxy Sikadur® 30

9. Attaching one end anchor to the concrete using anchor bolts, holding the anchor at

the other end and pushing the CFRP into the groove (the CFRP reinforcements

were cleaned with Acetone before placing in the groove)

10. Attaching the other end anchor

11. Levelling the epoxy

B.5.2 Preparation of CFRP Strips or Rebar

The CFRP strips or rebar were cut to provide an equal strengthening length of

3880 mm for all beams. Therefore, the end anchor length and elongation of the CFRP

strips/rebar due to prestressing was considered for each beam. The length of the CFRP

(cut length) and the length of the groove (elongated CFRP length) for each beam are

presented in Table B-1.

484

Table B-1: Groove and CFRP strips/rebar lengths.

Beam ID

Target

prestrain

in CFRP

Elongation due

to prestressing

(mm)

Length of

end anchor

(mm)

Groove length

(elongated CFRP length)

(mm)

CFRP length at rest

(cut length)

(mm)

BS-NP-F

BR-NP-F

BS-NP-FS

0 0 250 4380 4380

BS-P1-F

BR-P1-F

BS-P1-FS

0.0034 13 250 4380 4367

BS-P2-F 0.0068 26 250 4380 4354

BR-P2-F

BS-P2-FS 0.0068 26 400 4680 4654

BS-P3-F

BS-P3-FS 0.0102 40 400 4680 4640

BR-P3-F 0.0102 40 450 4780 4740

After cutting the CFRP strips to the calculated lengths in Table B-1 in order to have

similar axial stiffness for the strengthened beams using CFRP strip and rebar, two strips,

after cleaning the surfaces using Acetone, were attached together from the side using a

thin layer (about 1mm) of Sikadur®

330. Then the two strips were kept in boned position

using multiple steel clamps along the length for 24 hrs. it should be mentioned that the

CFRP strips and rebars were shipped at length of 4573 mm. Therefore, to meet the

lengths calculated in Table B-1, the original length was equally extended from each end.

The CFRP strips were extended by attaching four CFRP sheets to each end, one at the

bottom face, two in between, and one at the top face of the strips. The CFRP rebars were

extended by adding multiple rolls of CFRP sheets.

B.5.3 Steel Bolts for End Anchors and Temporary Brackets

The end anchors were attached to the concrete using expansion bolts named

Carbon Steel Kwik Bolt 3 Expansion Anchor having a diameter of 15.9 mm. The steel

485

brackets were mounted on the sides of the beam using HCA Coil bolts also having a

diameter of 15.9 mm.

B.5.4 Mechanical Anchors

The CFRP mechanical anchor was made of steel plate and tube (for CFRP strips)

or pipe (for CFRP rebar), which were welded together. Different lengths of the tube/pipe

were used for different prestressing level (as presented in Figure 3-2b in detail).

The end anchors (inside the pipes or tubes) were cleaned by sand blasting and the

CFRP reinforcement was connected to the anchors using epoxy adhesive (Sikadur® 330)

and cured for one week. In the case of CFRP strips, two strips were attached together

from one side to make the target area of CFRP needed for strengthening and then, after

one day, were attached to the anchors. The small screws were placed in the anchor to

adjust the CFRP reinforcement, as shown in Figure B-4.

(a) Using CFRP strips (b) Using CFRP rebar

Figure B-4: Attaching the CFRP reinforcements to the end anchors.

486

B.5.5 Temporary Brackets

The prestressing and anchorage system used in this research was first developed

by Gaafar (2007). The system includes the fixed and movable brackets that temporarily

use for prestressing the NSM CFRP strips or rebar as presented in Figure B-5. The

brackets are connected by threaded rods used for maintaining the prestressing force after

releasing the hydraulic jacks. Then, the steel anchor at jacking end is bolted to the

concrete, the jacks are released and temporary brackets are detached.

Figure B-5: Prestressing system developed by Gaafar (2007).

For prestressing the NSM CFRP in phases I and II of this research, the steel

brackets developed by Gaafar (2007) were modified by welding the steel plates to the

sides of the fixed bracket and to the tops of the movable bracket, and drilling few more

holes to improve the system and avoid rotation of the brackets at jacking stage, as shown

in Figure B-6.

487

Figure B-6: Steel brackets used for prestressing NSM CFRP in phases I and II.

B.5.6 Cutting Grooves

The grooves were made in the beams when the beams were upside down using a 6

mm thick diamond blade concrete saw. To avoid making dust and to decrease the

temperature generated in the diamond blade throughout cutting the grooves, a water flow

was connected to the saw as shown in Figure B-7a. The groove depth was 25±2 mm for

all beams however the groove width depends on the type of the NSM strengthening

material, 16±2 mm for CFRP strips and 20±2 mm for CFRP rebar. End groove regions

were cut wider and deeper for the placement of end anchors; 28±2 mm deep and 28±2

mm wide. The finished groove is show in Figure B-7b. The grooves were cleaned with

water pressure and dried with air pressure after cutting as shown in Figure B-8. Each

groove was made in 5 hrs including marking, sawing, and cleaning the groove.

Temporary brackets

488

(a) Saw cutting the groove (b) Finished groove

Figure B-7: Cutting the groove.

(a) Cleaning the groove using water (b) Drying the groove using air pressure

Figure B-8: Groove preparation.

B.5.7 Drilling Holes for Bolts

After cutting the grooves, the beams were drilled in order to make holes for bolts

at the end anchor, temporary fixed and movable brackets. The locations of the hole for

temporary brackets and the end anchors were marked on the beam by: knowing the

Guiding angle

Water hose

Diamond

blade saw

489

locations of the stirrups and longitudinal reinforcements, considering enough space

between the brackets for placing the jacks and load cells, and allowing the CFRP

elongation due to prestressing at the movable bracket. A different number of holes,

depending on the prestress level, were made in temporary fixed bracket: four holes for

BS-P1, six holes for BS-P2, and eight holes for BS-P3. The drilling was performed to 70

mm depth in concrete using drill bit having a diameter of 15.9 mm.

B.5.8 Prestressing System for NSM CFRP

After grooving, the beams were placed on two pedestals to be prestressed in the

same situation as the field. The instrumentations were performed on the beam to measure

the upward deflection due to prestressing at the centre, locations of the point loads, strain

in top and bottom steel reinforcements at mid-span, and strain in CFRP reinforcements.

Prestressing was performed by using hydraulic jack and temporary brackets installed on

the beam. At high prestress levels, for beam BS-P3, the cracks formed at the location of

the fixed bracket during prestressing. These types of cracks are shown in Figure ‎4-108,

and similar issue was reported by Gaafar (2007) and Oudah (2011). Therefore, the

locations of the fixed brackets were strengthened with externally bonded CFRP sheet to

minimize the cracks. The prestressed NSM strengthening are presented in Figure B-9.

More details about prestressing procedure are described by Gaafar (2007).

490

(a) Filling the groove using epoxy (b) Prestressing system

(c) Drilling at jacking end anchor (d) Placing bolt at jacking end anchor

(e) Removing the jacks (f) Removing the brackets

(g) Strengthening using CFRP sheet at fixed bracket location

for beams with high prestress level of NSM CFRP (BR-P3)

Figure B-9: Prestessed NSM strengthening.

491

Appendix C: Ancillary Test Results

C.1 Introduction

The ancillary test results of the materials used in the research are presented in this

appendix including concrete, CFRP rebar and strips, and steel reinforcements.

C.2 Concrete

Three ready mix concrete batches were used to cast fourtheen beams. Batch #1

poured on August 13, 2009 (five beams were cast, BS-F set and B0-F in Table C-1);

batch #2 on July 9, 2010 (four beams were cast, BR-F set in Table C-1); and batch #3 on

October 12, 2010 (five beams were cast, BS-FS set and B0-FS in Table C-1). The

concrete from the batches had similar specified properties as described in Section 3.3.3.2.

The uniaxial concrete compressive strengths of the beam were measured by testing

standard cylinders specimens (100 × 200 mm, diameter × height) as shown in Figure C-1,

according to ASTM C39/C39M (2010). The rate of loading during the application of the

first half of the anticipated loading phase was 10kN/sec then it was decreased to 2-1

kN/sec for the second phase. Two Linear Strain Conversion (LSC) devices were installed

on the cylinders, at a gauge length of 150 mm, to measure the strain in compression as

shown in Figure C-1a.

The concrete compressive strengths of the beams at 28 days, at the time of

strengthening, precracking, and testing to failure are presented in Table C-1 including the

date of the cylinder test and the number of the cylinders tested. It should be mentioned

that the exposed concrete strengths at the time of testing for the beams in phase II were

492

obtained using Schmidt hammer test on the beams, since the cylinders were severely

deteriorated due to freeze-thaw exposure and nothing was left from them to be tested. A

typical concrete stress-strain curve is presented in Figure C-2.

Cylinders from batches #1 and 2 had an unexposed concrete compressive strength

of 41.56.2 MPa and 39.44.2 MPa, respectively, at the time of testing to failure. The

strength of the freeze-thaw exposed concrete cylinders from batches #1 and 2 were

32.110.8 MPa and 286.8 MPa, respectively, at the time of testing the beams to failure.

The results of the hammer test, performed on the beams from batch #1 at the time of

testing to failure, shows an average exposed concrete compressive strength of 39.94.5

MPa and 48.32.6 MPa for the top surface and sides of the beams, respectively, while

these values are 40.37.3 MPa and 44.34.7 MPa for barch #2. Cylinders from batch #3

had an unexposed concrete compressive strength of 34.53.7 MPa. The hammer test

results performed on the beams from batch #3 reveal an average exposed concrete

compressive strength of 10.16.8 MPa and 28.110.1 MPa for the top surface and sides

of the beams, respectively.

493

(a) Compression test (b) Type of failure

Figure C-1: Concrete compression test and type of failure

0

10

20

30

40

50

0 0.001 0.002 0.003 0.004

Stre

ss (

MP

a)

Strain

Specimen #1

Specimen #2

Specimen #3

Figure C-2: Typical stress-strain curves of concrete (from batch#1 at 28 days)

494

Table C-1: Concrete compression test results. P

has

e

Bat

ch

Beam ID

Concrete compressive strength at

28 days (MPa)

(date, No of tests)*

Strengthening (MPa)

(date, No of tests)

Initial cracking (MPa)

(date, No of tests)

Time of testing

Unexposed (MPa)

(date, No of tests)

Exposed (MPa)

(date, No of tests)

Exposed** (MPa)

(location, No of readings)

I

1

B0-F

45.47±2.90

(9-11-2009, 3)

N.A. 42.04±2.57

(6-25-2010, 3)

34.38±2.25

(4-29-2011, 2)

32.03±5.21

(4-29-2011, 3)

40.2±5.6 (Top, 15)

45.5±2.5 (Side, 15)

BS-NP-F 37.96±4.96

(6-15-2010, 2)

35.85±3.34

(6-17-2010, 3)

50.43±0.54

(5-05-2011, 3)

42.88±5.61

(5-05-2011, 3)

39±4.5 (Top, 15)

48±2.3 (Side, 17)

BS-P1-F 41.03±2.54

(6-07-2010, 2)

35.85±3.34

(6-17-2010, 3)

44.08±1.32

(5-07-2011, 2)

39.51±3.79

(5-07-2011, 3)

40.8±4 (Top, 15)

48.4±3.6 (Side, 16)

BS-P2-F 37.96±4.96

(6-15-2010, 2)

42.04±2.57

(6-25-2010, 3)

38.03±5.46

(5-12-2011, 3)

25.81±13.80

(5-12-2011, 3)

40.5±3.25 (Top, 15)

49.5±2.5 (Side, 20)

BS-P3-F 39.32±0.49

(7-05-2010, 3)

37.84±2.89

(7-15-2010, 3)

42.14±0.88

(5-14-2011, 2)

20.12±5.20

(5-14-2011, 3)

39±5 (Top, 15)

50±2 (Side, 18)

2

BR-NP-F

43.48±2.18

(8-07-2010, 3)

44.59±3.16

(8-11-2010, 4)

41.56±4.51

(9-02-2010, 5)

39.27±3.10

(6-09-2011, 3)

23.34±8.65

(6-09-2011, 3)

38.7±9.3 (Top, 25)

44±6 (Side, 17)

BR-P1-F 44.59±3.16

(8-11-2010, 4)

41.56±4.51

(9-02-2010, 5)

39.90±5.71

(6-15-2011, 3)

30.61±3.44

(6-15-2011, 3)

39±7.5 (Top, 17)

42.5±3.5 (Side, 18)

BR-P2-F 44.60±1.02

(8-18-2010, 3)

41.56±4.51

(9-02-2010, 5)

34.96±0.83

(6-17-2011, 3)

27.95±2.18

(6-17-2011, 3)

42±6 (Top, 18)

44±5 (Side, 15)

BR-P3-F 41.29±1.01

(8-26-2010, 3)

38.05±1.02

(9-04-2010, 3)

43.39±1.30

(6-22-2011, 3)

30.01±10.64

(6-22-2011, 3)

41.5±6.5 (Top, 15)

46.5±4.2 (Side, 18)

II

3

B0-FS

37.76±1.19

(11-08-2010, 3)

N.A. N.A. 37.12±1.83

(8-14-2012, 3) ―

9.2±4.8 (Top, 24)

31±7 (Side, 36)

BS-NP-FS 38.03±2.23

(12-04-2010, 3) N.A.

31.77±1.55

(8-17-2012, 3) ―

9±5 (Top, 16)

28±9 (Side, 27)

BS-P1-FS 38.03±2.23

(12-04-2010, 3) N.A.

36.34±5.89

(8-21-2012, 3) ―

10±7 (Top, 15)

27±12 (Side, 44)

BS-P2-FS 36.51±1.83

(12-15-2010, 3) N.A.

33.9±0.28

(8-23-2012, 3) ―

10.2±7.8 (Top, 15)

23.4±13 (Side, 39)

BS-P3-FS 35.01±1.11

(12-23-2010, 3) N.A.

32.33±4.57

(8-24-2012, 3) ―

12±9.6 (Top, 15)

31±9.7 (Side, 33)

* (date, No of tests)=( Month-Day-Year, number of the tested cylinders) **the values are based on Schmidt hammer tests performed on top surface and sides of beams

494

495

C.3 CFRP Strip and Rebar

Three batches of CFRP reinforcements were used in this project, batch #1 CFRP

strips, batch #2 CFRP rebars, and batch #3 CFRP strips. Two specimens were tested from

each batch according to ASTM D 3039/D3039M (2008) for tensile properties. The

anchors were made to avoid premature debonding before CFRP rupture. One strain gauge

(SG) was installed on the CFRP rebar/strip at the centre of each specimen to measure the

strain corresponding to the applied load. The CFRP tension test is shown in Figure C-2,

and the stress-strain relation are plotted in Figures C-3 to C-5. The material properties of

CFRP reinforcements in each batch are represented in Table C-2.

(a) CFRP tension test specimens (b) Tension test

(c) Specimens after test

Figure C-2: Tension tests on CFRP strips and rebars.

496

0

500

1000

1500

2000

2500

3000

0 0.005 0.01 0.015 0.02 0.025

Str

es

s (

MP

a)

Strain

Aslan 500, CFRP strip, Specimen 1


● : CFRP rupture

Figure C-3: Stress-strain relation of CFRP strip from batch #1.

0

500

1000

1500

2000

2500

3000

0 0.005 0.01 0.015 0.02 0.025 0.03

Str

es

s (

MP

a)

Strain

Aslan 200, CFRP rebar, Specimen 1

Aslan 200, CFRP rebar, Specimen 2

● : CFRP ruptureO : DebondingΔ : Strain gauge damaged

Figure C-4: Stress-strain relation of CFRP rebar from batch #2.

497

0

500

1000

1500

2000

2500

3000

0 0.005 0.01 0.015 0.02 0.025

Str

es

s (

MP

a)

Strain



● : CFRP rupture

Figure C-5: Stress-strain relation of CFRP strip from batch #3.

Table C-2: Properties of the CFRP materials obtained from tension tests.

CFRP products

(Manufacturer)

Dimensions

(mm)

Afrp

(mm2)

ffrpu

(MPa)

Efrp

(GPa) ɛfrpu

Used for

beam

Batch #1

Aslan 500 CFRP tape

(Hughes Brothers Inc)

2×16 31.2 2624±28 124.4±6.7 0.0211±0.0009

BS-NP-F

BS-P1-F

BS-P2-F

BS-P3-F

BS-NP-FS

BS-P1-FS

BS-P2-FS

Batch #2



Ф9.5 71.3 2896* 115.9±1.5 0.025

*

BR-NP-F

BR-P1-F

BR-P2-F

BR-P3-F

Batch #3

Aslan 500 CFRP tape


2×16 31.2 2707±5 132±3.1 0.0205±0.0005 BS-P3-FS

* Only one specimen reached CFRP rupture.

498

C.4 Steel Reinforcements

One batch of top reinforcements and two batches of bottom steel reinforcements

were used to make the steel cages: batch #1 includes 15M bars, batch #2 includes 10M

bars, and batch #3 includes 15M bars. Batches #1 and 2 were used to build the steel cages

for the beams in phase I while batches #2 and 3 were used to build the steel cages in

phase II. The specimens were taken from top and bottom steel rebars to obtain the

material properties and corresponding stress-strain curves in tension according to ASTM

A370 (2010). One strain gauge (SG) was installed on each steel bar specimen at the

centre to measure the strain corresponding to the applied load. The 15M bar from batch

#1 had a yield strength of 4929 MPa, a yield strain of 0.002460.00017, and an ultimate

strength of 6546, while the 15M bar from batch #3 had a yield strength of 5330.8 MPa,

a yield strain of 0.002660.00022, and an ultimate strength of 7225 MPa. The 10M bar

from batch #2 had a yield strength of 48816 MPa, a yield strain of 0.002440.00027,

and an ultimate strength of 73919 MPa. The corresponding stress-strain curves of the

steel bars from each batch are presented in Figures C-6 to C-8. It should be mentioned

that after yielding the strain gauges installed on the specimens were damaged in most

cases and therefore the curves were terminated in Figures C-6 to C-8.

499

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Str

es

s (

MP

a)

Strain

15M Specimen 1

15M Specimen 2

15M Specimen 3

Figure C-6: Stress-strain curve of 15M steel bars in batch #1.

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Str

es

s (

MP

a)

Strain

10M Specimen 1

10M Specimen 2

10M Specimen 3


500

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Str

ess (

MP

a)

Strain

15M Specimen 1

15M Specimen 2


501

Appendix D: ANSYS Logs

D.1 Introduction

In this appendix, the files related to ANSYS model generated for the prestressed

NSM-CFRP strengthened beam, BS-P2-R, are printed.

D.2 ANSYS Logs for BS-P2-R

D.2.1 BS-P2-R.mntr

SOLUTION HISTORY INFORMATION FOR JOB: BS-P2-R.mntr

ANSYS RELEASE 12.0 .1 14:54:00 04/13/2011

LOAD STEP

SUB-STEP

NO. ATTM

P

NO. ITER

TOTL ITER

INCREMENT TIME/LFACT

TOTAL TIME/LFA

CT

VARIAB 1 MONITOR

CPU

VARIAB 2 MONITOR

MxDs

VARIAB 3 MONITOR

MxPl

1 1 1 7 7 1.00E-04 1.00E-04 46.598 0.84115 1.93E-02

2 1 1 3 10 0.11999 0.12009 21.481 0.21545 3.59E-04

2 2 1 2 12 0.11999 0.24008 35.381 -0.26924 1.17E-04

2 3 1 2 14 0.17999 0.42007 49.343 -0.45912 1.23E-04

2 4 1 2 16 0.23998 0.66004 63.508 -0.7123 1.33E-04

2 5 1 2 18 0.23998 0.90002 77.548 -0.96547 1.30E-04

2 6 1 2 20 0.14999 1.05 91.495 -1.1237 1.11E-04

2 7 1 2 22 0.14999 1.2 105.57 -1.2819 1.06E-04

3 1 1 2 24 3.50E-02 1.235 14.742 -1.3188 7.47E-05

3 2 1 2 26 3.50E-02 1.27 28.829 -1.3558 7.08E-05

3 3 1 2 28 5.25E-02 1.3225 43.025 -1.4111 7.29E-05

3 4 1 2 30 5.60E-02 1.3785 57.346 -1.4702 7.27E-05

3 5 1 2 32 5.60E-02 1.4345 71.448 -1.5293 7.14E-05

3 6 1 2 34 5.60E-02 1.4905 85.489 -1.5884 6.89E-05

3 7 1 2 36 5.60E-02 1.5465 99.482 -1.6474 6.62E-05

3 8 1 2 38 5.60E-02 1.6025 113.99 -1.7066 6.60E-05

3 9 1 2 40 5.60E-02 1.6585 128.23 -1.766 6.53E-05

3 10 1 18 58 5.60E-02 1.7145 257.14 -1.8718 7.27E-04

3 11 1 2 60 5.60E-02 1.7705 272.56 -1.9327 5.33E-05

3 12 1 2 62 5.60E-02 1.8265 289.16 -1.9937 5.48E-05

3 13 1 3 65 5.60E-02 1.8825 312.06 -2.0551 8.87E-05

502

3 14 1 4 69 5.60E-02 1.9385 341.22 -2.1166 1.19E-04

3 15 1 2 71 5.60E-02 1.9945 356.37 -2.1777 5.13E-05

3 16 1 2 73 5.60E-02 2.0505 371.5 -2.2386 5.23E-05

3 17 1 2 75 5.60E-02 2.1065 386.57 -2.2997 5.23E-05

3 18 1 2 77 5.60E-02 2.1625 401.31 -2.3609 5.17E-05

3 19 1 2 79 5.60E-02 2.2185 415.85 -2.4219 5.16E-05

3 20 1 2 81 5.60E-02 2.2745 430.44 -2.4829 5.14E-05

3 21 1 4 85 5.60E-02 2.3305 458.99 -2.5444 1.14E-04

3 22 1 2 87 5.60E-02 2.3865 473.67 -2.6056 4.78E-05

3 23 1 5 92 5.60E-02 2.4425 509.47 -2.6697 1.39E-04

3 24 1 3 95 5.60E-02 2.4985 531.96 -2.7319 7.61E-05

3 25 1 4 99 5.60E-02 2.5545 560.76 -2.7966 1.00E-04

3 26 1 3 102 5.60E-02 2.6105 582.73 -2.859 7.33E-05

3 27 1 2 104 5.60E-02 2.6665 597.45 -2.9202 4.42E-05

3 28 1 2 106 5.60E-02 2.7225 611.85 -2.9816 4.47E-05

3 29 1 2 108 5.60E-02 2.7785 626.34 -3.0428 4.55E-05

3 30 1 2 110 5.60E-02 2.8345 641.37 -3.1039 4.53E-05

3 31 1 2 112 5.60E-02 2.8905 655.97 -3.1652 4.52E-05

3 32 1 3 115 5.60E-02 2.9465 677.39 -3.2266 7.34E-05

3 33 1 2 117 5.60E-02 3.0025 692.47 -3.2877 4.32E-05

3 34 1 5 122 5.60E-02 3.0585 728.45 -3.3499 1.27E-04

3 35 1 2 124 5.60E-02 3.1145 743.22 -3.4111 4.26E-05

3 36 1 2 126 5.60E-02 3.1705 757.73 -3.4724 4.41E-05

3 37 1 2 128 5.60E-02 3.2265 772.33 -3.5333 4.36E-05

3 38 1 11 139 5.60E-02 3.2825 850.44 -3.5569 3.35E-04

3 39 1 5 144 5.60E-02 3.3385 886.66 -3.6152 1.16E-04

3 40 1 4 148 5.60E-02 3.3945 915.1 -3.6738 9.23E-05

3 41 1 2 150 5.60E-02 3.4505 929.81 -3.7341 4.02E-05

3 42 1 2 152 5.60E-02 3.5065 944.4 -3.7944 4.14E-05

3 43 1 2 154 5.60E-02 3.5625 959.11 -3.8548 4.13E-05

3 44 1 2 156 5.60E-02 3.6185 974.3 -3.9147 4.03E-05

3 45 1 2 158 5.60E-02 3.6745 988.94 -3.9742 3.98E-05

3 46 1 3 161 5.60E-02 3.7305 1010.3 -4.0336 6.68E-05

3 47 1 2 163 5.60E-02 3.7865 1025.1 -4.0936 3.95E-05

3 48 1 7 170 5.60E-02 3.8425 1074.8 -4.1495 1.63E-04

3 49 1 4 174 5.60E-02 3.8985 1103.2 -4.2099 8.64E-05

3 50 1 2 176 5.60E-02 3.9545 1117.7 -4.2702 3.84E-05

3 51 1 2 178 4.55E-02 4 1132.6 -4.3191 3.83E-05

4 1 1 7 185 0.8 4.8 52.073 -5.1716 2.23E-04

4 2 1 18 203 0.8 5.6 184 -5.9885 4.38E-04

503

4 3 1 5 208 0.8 6.4 220.96 -6.8395 2.78E-04

4 4 1 5 213 1.2 7.6 258.28 -8.1193 2.06E-04

4 5 1 14 227 1.6 9.2 360.83 -9.7927 4.50E-04

4 6 1 7 234 1.6 10.8 413.22 -11.49 2.62E-04

4 7 1 35 269 1.6 12.4 671.02 -13.167 9.91E-04

4 8 7 3 512 1.88E-02 12.419 2454.5 -13.187 7.08E-05

4 9 1 16 528 1.88E-02 12.438 2572.3 -13.206 3.59E-04

4 10 1 2 530 1.88E-02 12.456 2587.6 -13.226 8.22E-05

4 11 1 2 532 2.81E-02 12.484 2603.3 -13.255 3.32E-05

4 12 1 4 536 4.22E-02 12.527 2633.6 -13.299 7.35E-05

4 13 1 2 538 4.22E-02 12.569 2648.9 -13.344 3.05E-05

4 14 1 2 540 6.33E-02 12.632 2664.1 -13.411 3.27E-05

4 15 1 5 545 9.49E-02 12.727 2701.3 -13.511 1.00E-04

4 16 1 2 547 9.49E-02 12.822 2716.8 -13.611 3.33E-05

4 17 1 2 549 0.14238 12.964 2733.3 -13.762 3.91E-05

4 18 1 2 551 0.21357 13.178 2750 -13.988 4.73E-05

4 19 1 4 555 0.32036 13.498 2780.8 -14.328 1.04E-04

4 20 1 4 559 0.32036 13.819 2811.3 -14.667 9.99E-05

4 21 1 14 573 0.48054 14.299 2917.7 -15.172 3.57E-04

4 22 1 7 580 0.48054 14.78 2973 -15.679 2.02E-04

4 23 1 13 593 0.72081 15.5 3072 -16.439 6.04E-04

4 24 1 25 618 0.72081 16.221 3266.3 -17.192 2.60E-03

4 25 1 6 624 0.72081 16.942 3311.5 -17.955 4.80E-04

4 26 1 25 649 1.0812 18.023 3510.3 -19.09 1.63E-03

4 27 1 16 665 1.0812 19.105 3636.3 -20.23 7.91E-04

4 28 1 6 671 0.89548 20 3681 -21.176 4.65E-04

5 1 1 2 673 0.15 20.15 14.851 -21.335 8.25E-05

5 2 1 17 690 0.15 20.3 134.66 -21.508 7.17E-04

5 3 1 2 692 0.15 20.45 149.29 -21.666 8.06E-05

5 4 1 5 697 0.225 20.675 185.56 -21.904 2.28E-04

5 5 1 2 699 0.225 20.9 201.68 -22.142 9.88E-05

5 6 1 3 702 0.3375 21.237 224.24 -22.499 1.80E-04

5 7 1 3 705 0.4 21.637 247.7 -22.921 2.16E-04

5 8 1 3 708 0.4 22.037 269.65 -23.344 2.08E-04

5 9 1 4 712 0.4 22.437 299.66 -23.766 2.52E-04

5 10 1 4 716 0.4 22.837 331.42 -24.188 2.16E-04

5 11 1 5 721 0.4 23.237 368.04 -24.61 3.10E-04

5 12 1 14 735 0.4 23.637 467.07 -25.031 5.32E-04

5 13 1 3 738 0.4 24.037 489.17 -25.454 1.76E-04

5 14 1 5 743 0.4 24.437 524.44 -25.876 2.30E-04

504

5 15 1 3 746 0.4 24.837 546.63 -26.3 1.76E-04

5 16 1 13 759 0.4 25.237 637.05 -26.746 5.53E-04

5 17 1 14 773 0.4 25.637 735.25 -27.196 6.17E-04

5 18 1 14 787 0.3625 26 832.5 -27.604 5.40E-04

6 1 1 13 800 1.7 27.7 89.997 -29.484 1.27E-03

6 2 1 15 815 1.7 29.4 192.38 -31.383 1.38E-03

6 3 1 13 828 1.7 31.1 281.83 -33.259 1.09E-03

6 4 1 13 841 1.7 32.8 371.42 -35.143 1.01E-03

6 5 1 14 855 1.7 34.5 467.74 -37.016 1.00E-03

6 6 1 16 871 1.7 36.2 578.7 -38.887 1.31E-03

6 7 1 12 883 1.7 37.9 662.91 -40.762 1.02E-03

6 8 1 20 903 1.7 39.6 800.77 -42.638 1.67E-03

6 9 1 12 915 1.7 41.3 884.96 -44.521 1.21E-03

6 10 1 15 930 1.7 43 989.98 -46.39 1.50E-03

6 11 1 21 951 1.7 44.7 1135.6 -48.239 1.69E-03

6 12 1 10 961 1.7 46.4 1205.8 -50.114 9.88E-04

6 13 1 17 978 1.7 48.1 1323.7 -51.985 1.60E-03

6 14 1 13 991 1.7 49.8 1414.4 -53.845 2.00E-03

6 15 1 12 1003 1.7 51.5 1497.8 -55.718 1.18E-03

6 16 1 15 1018 1.7 53.2 1602.4 -57.574 1.24E-03

6 17 1 30 1048 1.7 54.9 1810.5 -59.401 2.80E-03

6 18 1 17 1065 1.7 56.6 1928.5 -61.234 1.25E-03

6 19 1 14 1079 1.7 58.3 2027.1 -63.082 1.15E-03

6 20 1 10 1089 1.7 60 2097.9 -64.93 8.16E-04

7 1 2 6 1155 1.5 61.5 546.49 -66.556 7.84E-04

7 2 2 15 1230 0.75 62.25 1166.7 -67.346 2.67E-03

7 3 1 7 1237 0.75 63 1219.5 -68.156 8.10E-04

7 4 3 5 1362 0.28125 63.281 2264.8 -68.456 4.56E-04

7 5 1 5 1367 0.28125 63.562 2299.8 -68.756 6.39E-04

7 6 1 7 1374 0.42188 63.984 2348.4 -69.212 9.81E-04

7 7 1 5 1379 0.42188 64.406 2384.4 -69.667 2.16E-03

7 8 1 4 1383 0.63281 65.039 2415 -70.362 4.29E-04

7 9 1 5 1388 0.94922 65.988 2454.7 -71.395 4.76E-04

7 10 1 8 1396 1.4238 67.412 2513 -72.959 9.88E-04

7 11 1 12 1408 1.4238 68.836 2604.2 -74.504 1.61E-03

7 12 1 21 1429 1.4238 70.26 2772.5 -76.024 3.50E-03

7 13 1 12 1441 1.4238 71.684 2866 -77.559 1.80E-03

7 14 2 9 1510 0.71191 72.396 3456.9 -78.32 1.03E-03

7 15 2 6 1576 0.35596 72.751 4055.1 -78.698 1.44E-03

7 16 1 6 1582 0.35596 73.107 4098.6 -79.082 6.00E-04

505

7 17 4 3 1765 6.67E-02 73.174 5723.6 -79.153 7.18E-04

7 18 1 4 1769 6.67E-02 73.241 5755.8 -79.223 1.40E-02

D.2.2 BS-P2-R.BSC

=========================== = multifrontal statistics = =========================== number of equations = 42060 no. of nonzeroes in lower triangle of a = 1097883 number of compressed nodes = 14791 no. of compressed nonzeroes in l. tri. = 165588 amount of workspace currently in use = 14502137 max. amt. of workspace used = 59562212 no. of nonzeroes in the factor l = 11428652. number of super nodes = 2056 number of compressed subscripts = 285253 size of stack storage = 1000055 maximum order of a front matrix = 1124 maximum size of a front matrix = 632250 maximum size of a front trapezoid = 69856 no. of floating point ops for factor = 4.6494D+09 no. of floating point ops for solve = 4.5925D+07 actual no. of nonzeroes in the factor l = 11428652. actual number of compressed subscripts = 285253 actual size of stack storage used = 1095494 near zero pivot monitoring activated number of pivots adjusted = 0. negative pivot monitoring activated number of negative pivots encountered = 0. factorization panel size = 64 factorization update panel size = 32 solution block size = 2 time (cpu & wall) for structure input = 0.124023 0.139528 time (cpu & wall) for ordering = 0.375000 0.376673 time (cpu & wall) for symbolic factor = 0.015625 0.015230 time (cpu & wall) for value input = 0.155273 0.154428 time (cpu & wall) for numeric factor = 2.636719 1.344835 computational rate (mflops) for factor = 1763.334716 3457.240852 condition number estimate = 0.0000D+00 time (cpu & wall) for numeric solve = 0.078125 0.040978 computational rate (mflops) for solve = 587.838822 1120.723815 effective I/O rate (MB/sec) for solve = 2239.665880 4269.957671

no input or output performed

D.2.3 BS-P2-R.stat

Sparse Solver : curEqn= 42060 totEqn= 42060 Job CP sec= 8345.788 Factor done= 100% Factor Wall sec= 0.0 rate= 0.0 Mflops

506

D.2.4 BS-P2-R.s01

/COM,ANSYS RELEASE 12.0.1 UP20090415 14:53:41 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 1 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 1, 1, 1, KUSE, 0 TIME, 1.000000000E-04 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 1.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000

507

BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR

D.2.5 BS-P2-R.s02

/COM,ANSYS RELEASE 12.0.1 UP20090415 14:57:06 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 2 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 10, 40, 5, KUSE, 0 TIME, 1.20000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 1.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000

508

. D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -1.20000000 , 0.00000000 D, 14830,UY , -1.20000000 , 0.00000000 D, 14839,UY , -1.20000000 , 0.00000000 D, 14842,UY , -1.20000000 , 0.00000000 D, 14851,UY , -1.20000000 , 0.00000000 D, 14854,UY , -1.20000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR

D.2.6 BS-P2-R.s03

/COM,ANSYS RELEASE 12.0.1 UP20090415 15:04:30 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 3 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 80, 100, 50, KUSE, 0 TIME, 4.00000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL,

509

OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -4.00000000 , 0.00000000 D, 14830,UY , -4.00000000 , 0.00000000 D, 14839,UY , -4.00000000 , 0.00000000 D, 14842,UY , -4.00000000 , 0.00000000 D, 14851,UY , -4.00000000 , 0.00000000 D, 14854,UY , -4.00000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR

D.2.7 BS-P2-R.s04

/COM,ANSYS RELEASE 12.0.1 UP20090415 15:24:09 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 4 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1

510

BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 20, 10000, 10, KUSE, 0 TIME, 20.0000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -20.0000000 , 0.00000000 D, 14830,UY , -20.0000000 , 0.00000000 D, 14839,UY , -20.0000000 , 0.00000000 D, 14842,UY , -20.0000000 , 0.00000000 D, 14851,UY , -20.0000000 , 0.00000000 D, 14854,UY , -20.0000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000

511

BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR

D.2.8 BS-P2-R.s05

/COM,ANSYS RELEASE 12.0.1 UP20090415 16:59:46 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 5 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 40, 10000, 15, KUSE, 0 TIME, 26.0000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000

512

. D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -26.0000000 , 0.00000000 D, 14830,UY , -26.0000000 , 0.00000000 D, 14839,UY , -26.0000000 , 0.00000000 D, 14842,UY , -26.0000000 , 0.00000000 D, 14851,UY , -26.0000000 , 0.00000000 D, 14854,UY , -26.0000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR

D.2.9 BS-P2-R.s06

/COM,ANSYS RELEASE 12.0.1 UP20090415 17:14:44 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 6 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 20, 10000, 10, KUSE, 0 TIME, 60.0000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 60 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL,

513

OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -60.0000000 , 0.00000000 D, 14830,UY , -60.0000000 , 0.00000000 D, 14839,UY , -60.0000000 , 0.00000000 D, 14842,UY , -60.0000000 , 0.00000000 D, 14851,UY , -60.0000000 , 0.00000000 D, 14854,UY , -60.0000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000

D.2.10 BS-P2-R.s07

/COM,ANSYS RELEASE 12.0.1 UP20090415 17:50:07 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 7 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 20, 10000, 10, KUSE, 0

514

TIME, 120.000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 60 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -120.000000 , 0.00000000 D, 14830,UY , -120.000000 , 0.00000000 D, 14839,UY , -120.000000 , 0.00000000 D, 14842,UY , -120.000000 , 0.00000000 D, 14851,UY , -120.000000 , 0.00000000 D, 14854,UY , -120.000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000

515

BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000

516

Appendix E: Developed Computational Source Code in Mathematica

E.1 Introduction

The developed code for calculation of the load-deflection response of the exposed

beams explained in Section 5.5 is presented in this section. The first step is to define the

stress-strain curve of the exposed concrete as a function so that it can be used by the

source code for calculation of the load-deflection response.

E.2 Calculation of the Exposed Concrete Stress-Strain Curve

The concepts and procedure for the calculation of the exposed concrete stress-

stress curve is presented in Section 5.5.3.1. To facilitate the trend of the analysis the

described procedure was performed by developing a small code in Mathematica as

below:

517

E.3 Computational Source Code

The computational source code for calculation of the load-deflection response of

the RC beams strengthened using NSM CFRP reinforcements subjected to the freeze-

thaw exposure is similar to the one presented in Appendix A excepts that the inputs are

different. For instance, the solution for beams BS-P3-F is presented in this section.

518

518

519

519

520

520

521

521

1 university of calgary long-term flexural performance of prestressed-nsm-cfrp

Documents