structural and thermal behaviour of insulated frp

STRUCTURAL AND THERMAL BEHAVIOUR OF INSULATED

FRP-STRENGTHENED REINFORCED CONCRETE BEAMS AND

SLABS IN FIRE

by

Masoud Adelzadeh

A thesis submitted to the Department of Civil Engineering

in conformity with the requirements for

the degree of Doctor of Philosophy

Queen’s University

Kingston, Ontario, Canada

(September, 2013)

Copyright ©Masoud Adelzadeh, 2013

ii

Abstract

Despite the superior properties of Fibre Reinforced Polymer (FRP) materials, the use of

FRPs in buildings is limited. A key cause of concern for their use in buildings arises from

their poor performance in fire occurrences. This thesis presents the results of fire

performance of Reinforced Concrete (RC) beams and slabs strengthened with externally

bonded FRP sheets. The performance and effectiveness of insulation materials and

techniques are also investigated in this thesis. Two full-scale reinforced concrete T-beams

and two intermediate-scale slabs were strengthened in flexure with carbon and glass fibre

reinforced polymer sheets and insulated with a layer of spray-on material. The T-beams

and slabs were then exposed to a standard fire. Fire test results show that fire endurances of

more than 4 h can be achieved using an appropriate insulation system. Tests were

performed in order to understand the behaviour of FRP concrete bond at high

temperatures. An empirical model was then formulated to describe the bond strength

deterioration due to temperature rise. Innovative measurement techniques were employed

throughout the experiments to measure important observables like strain and temperature.

Meanwhile, the effectiveness and practicality of techniques such as Fibre Optic Sensing

(FOS) and Particle Image Velocimetry (PIV) for high temperature applications were

investigated.

A numerical finite-volume heat transfer model was developed to simulate the heat

transfer phenomenon. The validity of the numerical model was verified by comparing the

results with the results from the fire tests. By using this model, parametric analyses were

performed to investigate the effect of different fire scenarios on the performance of the

insulated beams. To simulate the structural performance of the T-beams a numerical model

which was capable of predicting stresses and strains and deflections of a heated beam was

developed. The model is capable of incorporating the effects of axial forces in the response

of a restrained beam. This model was verified and used in combination with the thermal

model to simulate the deflections of T-beams in fire.

iii

Acknowledgements

Numerous people contributed to the completion of this thesis. First I would like to

express my gratitude to Dr. Mark Green. I would also like to thank the industrial

partners who provided financial and technical support during the experiments. Thanks

go to Sika and Sika Canada and Richard Sherping. Most of the tests have been

conducted at Fire Risk Management testing facility at the National Research Council of

Canada. I would like to Thank Dr. Noureddine Bénichou of the National Research

Council of Canada, also the technical officers and staff at the National Research Council

of Canada. I would also like to thank the faculty and staff at the Civil Engineering

Department of Queen’s University, among them Dr. Andy Take, Dr Duncan Cree,

Maxine Wilson, Fiona Froats, Dave Tyron, Lloyd Rhymer, Jamie Escobar, Paul Thrasher

and Neil Porter. Also my friends and colleagues, Dr. Ershad Chowdhury and Tarek

Khalifa. And Finally I would like to thank Minoo, Reza And Sattar Adelzadeh, Parvin

Navadeye Razi and Shadi Ghazimoradi for their support and encouragement.

iv

Statement of Originality

I hereby certify that all of the work described within this thesis is the original work of

the author. Any published (or unpublished) ideas and/or techniques from the work of

others are fully acknowledged in accordance with the standard referencing practices.

Masoud Adelzadeh

July, 2013

v

Table of Contents

Abstract ...................................................................................................................................... ii

Acknowledgements .................................................................................................................iii

Statement of Originality .......................................................................................................... iv

Table of Contents ...................................................................................................................... v

List of Tables ............................................................................................................................ xii

List of Figures .........................................................................................................................xiv

Chapter 1 : Introduction ............................................................................................................... 1

1.1 Concrete structures and need for rehabilitation ............................................................. 2

1.2 FRP materials ....................................................................................................................... 3

1.3 Research objectives ............................................................................................................. 4

1.4 Contributions ....................................................................................................................... 6

1.5 Thesis outline ....................................................................................................................... 7

Chapter 2 : Literature review .................................................................................................... 10

2.1 Effects of fire on structures and fire test procedures ................................................... 10

2.2 Material behaviour at high temperatures ...................................................................... 12

2.2.1 Concrete ....................................................................................................................... 12

2.2.2 Steel .............................................................................................................................. 14

2.2.3 FRP ............................................................................................................................... 17

2.3 Fire performance of strengthened beams and slabs ..................................................... 19

2.4 Bond behaviour at high temperature for externally bonded FRP sheets .................. 20

vi

2.5 Insulation techniques........................................................................................................ 21

2.5.1 Concrete ....................................................................................................................... 22

2.5.2 Sprayed insulation ..................................................................................................... 22

2.5.3 Board insulation systems .......................................................................................... 23

2.5.4 Intumescent coating ................................................................................................... 23

2.6 Fire safety and sensing at high temperatures ............................................................... 24

2.6.1 Stimulated Brillouin scattering for fibre optic sensors ......................................... 25

Chapter 3: Experimental program ............................................................................................ 28

3.1 General.......................................................................................................................... 28

3.2 Fire Tests, T-beams and Slabs .................................................................................... 28

3.2.1 Test specimens ..................................................................................................... 28

3.2.1.1 Dimensions ...................................................................................................... 28

3.2.2 Materials ............................................................................................................... 31

3.2.2.1 Concrete ............................................................................................................ 31

3.2.2.2 Steel ................................................................................................................... 31

3.2.3 Fabrication ............................................................................................................ 32

3.2.3.1 Reinforcing bars .............................................................................................. 32

3.2.3.2 Instrumentation ............................................................................................... 35

3.2.3.3 Curing ............................................................................................................... 38

3.2.4 FRP strengthening ............................................................................................... 39

3.2.4.1 Slab-A ................................................................................................................ 39

3.2.4.2 Slab-B ................................................................................................................ 40

vii

3.2.4.3 Beam-A ............................................................................................................. 44

3.2.4.4 Beam-B .............................................................................................................. 45

3.2.5 Fire proofing ........................................................................................................ 49

3.2.6 Test apparatus ..................................................................................................... 50

3.2.7 Test conditions and procedures ........................................................................ 53

3.2.7.1 End conditions ................................................................................................. 53

3.2.7.2 Loading ............................................................................................................. 53

3.2.7.3 Failure criteria .................................................................................................. 55

3.3 Fire test results and discussion ................................................................................. 56

3.3.1 Temperatures ....................................................................................................... 58

3.3.2 Performance of the insulation system .............................................................. 65

3.3.3 Deflections ............................................................................................................ 68

3.3.4 Summary .............................................................................................................. 71

3.4 FRP-concrete bond tests ............................................................................................. 71

3.4.1 Bond tests results and discussion ..................................................................... 74

3.4.2 Proposed analytical model ................................................................................ 77

3.4.3 Discussion ............................................................................................................ 81

3.4.4 Summary bond tests ........................................................................................... 82

3.5 FRP coupon tests and FOS results ............................................................................ 83

3.5.1 Instrumentation ................................................................................................... 84

3.5.1.1 Results ............................................................................................................... 87

Chapter 4 : Numerical heat transfer simulation ..................................................................... 95

viii

4.1 Finite volume formulation ............................................................................................... 96

4.1.1 Stability criterion ...................................................................................................... 100

4.1.2 Free convection ......................................................................................................... 101

4.1.3 Moisture effect .......................................................................................................... 102

4.1.4 Verification ................................................................................................................ 107

4.2 Model results for slabs and T-beams ............................................................................ 108

4.3 Finite element simulation using ABAQUS .................................................................. 113

4.4 Different fire scenarios ................................................................................................... 116

4.5 Sample design charts ...................................................................................................... 122

4.6 Summary .......................................................................................................................... 131

Chapter 5 : Structural modelling ............................................................................................ 133

5.1 General.............................................................................................................................. 133

5.2 Generating moment-curvature curves ......................................................................... 136

5.3 Beam analysis .................................................................................................................. 137

5.4 Verification ....................................................................................................................... 138

5.4.1 RC Beam 1 (typical RC beam) ................................................................................ 138

5.4.2 RC Beam 2 ................................................................................................................. 141

5.4.3 FRP-RC Beam 1......................................................................................................... 144

5.4.4 FRP-RC Beam 2......................................................................................................... 149

5.5 Deflections simulation in fire exposed T-beams ......................................................... 153

5.5.1 T-Beam C ................................................................................................................... 153

5.5.2 T-Beam A and B ........................................................................................................ 156

ix

5.6 Different fire scenarios ................................................................................................... 160

5.7 Summary .......................................................................................................................... 162

Chapter 6 : Conclusions and Future Research ...................................................................... 165

6.1 General.............................................................................................................................. 165

6.2 Key findings ..................................................................................................................... 166

6.3 Detailed conclusions ....................................................................................................... 167

6.3.1 Fire tests ..................................................................................................................... 167

6.3.2 Bond tests .................................................................................................................. 168

6.3.3 Material testing and Fibre Optic Sensors .............................................................. 169

6.3.4 Numerical models .................................................................................................... 169

6.3.4.1 Heat transfer models ........................................................................................ 169

6.3.4.2 Strength model .................................................................................................. 170

6.4 Recommendations for future work .............................................................................. 171

References .............................................................................................................................. 174

A. Appendix A: Detailed experimental results .............................................................. 180

A.1 Temperature readings for Slabs .............................................................................. 180

A.2 Temperatures and deflections of T-beams ............................................................ 184

A.2.1 Beam-A temperature data ................................................................................ 184

A.2.2 Beam-B temperature data ................................................................................ 190

A.2.3 Deflection Results .............................................................................................. 196

B. APPENDIX-B: T-beam Load Calculation and Design ................................................. 202

B.1 Assumptions, Dimensions and Material properties ............................................ 202

x

B.1.1 Material properties............................................................................................ 203

B.2 Design Flexural Strength of Reinforced Concrete Beam ..................................... 205

B.2.1 Design Flexural Strength according to CSA A23.3-04 ................................. 206

B.2.2 Design Flexural Strength according to ACI 318/318R-05 ............................ 208

B.3 Flexural Capacity of FRP-Strengthened Reinforced Concrete Beam ................. 210

B.3.1 Beam-A FRP-Strengthened load calculation ................................................. 210

B.3.1.1 Flexural Capacity according to CSA S806-02 ............................................ 210

B.3.1.2 Flexural Capacity according to ACI 440.2R-08 ......................................... 212

B.3.1.3 Beam-A design summary ............................................................................. 217

B.3.2 Beam-B FRP-Strengthened load calculation .................................................. 219

B.3.2.1 Flexural Capacity according to CSA S806-02 ............................................ 219

B.3.2.2 Flexural Capacity according to ACI 440.2R-08 ......................................... 221

B.3.2.3 Beam-B design summary ............................................................................. 225

B.4 Superimposed Fire Test Loads ................................................................................ 228

B.4.1 Required Jack Stress during Fire Test ............................................................ 230

C. Appendix C: Material properties at high temperature ................................................ 232

C.1 Concrete ...................................................................................................................... 232

C.1.1 Thermal properties ........................................................................................... 232

C.1.1.1 Thermal conductivity ................................................................................... 232

C.1.1.2 Specific heat ................................................................................................... 234

C.1.2 Mechanical properties ...................................................................................... 237

C.1.2.1 Stress strain relation ...................................................................................... 237

xi

C.1.2.2 Thermal expansion ........................................................................................ 242

C.1.2.3 Creep and Transient strain .......................................................................... 243

C.2 Reinforcing steel ........................................................................................................ 244

C.2.1.1 Stress strain relation ...................................................................................... 244

C.2.1.2 Thermal elongation of reinforcing steel ..................................................... 246

C.3 FRP .............................................................................................................................. 247

C.3.1.1 Thermal properties ....................................................................................... 247

C.3.1.2 Mechanical properties .................................................................................. 248

C.4 Insulation .................................................................................................................... 248

C.4.1.1 Sikacrete 213F ................................................................................................ 248

C.4.1.2 Other Insulation materials ........................................................................... 249

C.4.1.3 Tyfo® Vermiculite-Gypsum (VG) Insulation ............................................ 249

C.4.1.4 Promat-H and Promatect-L ......................................................................... 251

xii

List of Tables

Table 3-1 FRP and insulation details for intermediate-scale slabs. ...................................... 42

Table 3-2 Summary of FRP-Insulation system used for T-beams. ....................................... 44

Table 3-3 Summary of test results ............................................................................................. 57

Table 3-4 General observation during test of T-beams. ......................................................... 57

Table 3-5 Strength results for steady state tests. ..................................................................... 75

Table 3-6 Failure temperatures for transient tests at different sustained load levels. ....... 78

Table 3-7 Specimen information and test regime. .................................................................. 83

Table 3-8 Modulus calculation results for room temperature test at different load levels;

strain is calculated using PIV analysis. .................................................................................... 88

Table 3-9 Steady-state tension test results for FRP at high temperature. ............................ 89

Table 4-1 Coefficients for laminar and turbulent free convection (Bayazıtoğlu, Özışık

1988). ........................................................................................................................................... 102

Table 4-2 Parameters used to produce fire curves. .............................................................. 117

Table 5-1: Properties of the typical RC beam used in the verfication (RC Beam1). ......... 139

Table 5-2: Description of the typical RC beam used in the verification (RC Beam2). ..... 142

Table 5-3. Summary of Properties for FRP-RC Beam1 ........................................................ 147

Table 5-4: Summary of Properties for FRP-RC Beam 2. ...................................................... 151

Table B-1 load factor calculation. ............................................................................................ 229

Table C-1 Values for the main parameters of the stress-strain relationships of normal

weight concrete with siliceous or calcareous aggregates concrete at elevated

temperatures, from Eurocode2. .............................................................................................. 241

xiii

Table C-2 values for the parameters of the stress-strain relationship of hot rolled and

cold worked reinforcing steel at elevated temperatures ..................................................... 245

Table C-3: Coefficient of thermal expansion for FRPs, Ahmad (2010). ............................. 248

xiv

List of Figures

Figure 1-1 FRP consumption share per industry,(Berreur, de Maillard et al. 2002). ........... 4

Figure 2-1 Stress-strain relationship for normal concrete derived in strain-rate controlled

tests (Schneider 1988). ................................................................................................................ 13

Figure 2-2 Stress-strain curves for steel at different temperatures (fy=300 MPa), (Lie

1992) .............................................................................................................................................. 15

Figure 2-3 Variation of strength of (a) reinforcing and (b) pre-stressing steels with

temperature (Holmes, Anchor et al. 1982). .............................................................................. 16

Figure 3-1 Dimensions and reinforcement details of SLAB-A and SLAB-B (dimensions in

mm) ............................................................................................................................................... 29

Figure 3-2 Dimensions and reinforcement details of BEAM-A and BEAM-B (All steel

bars are 10M) ............................................................................................................................... 30

Figure 3-3 Formwork and reinforcement layout for slabs (Williams, 2004). ...................... 33

Figure 3-4 Steel reinforcement for T-beams ............................................................................ 34

Figure 3-5 Formwork and reinforcement layout for T-beams .............................................. 34

Figure 3-6 Location of thermocouples in slab specimens (all dimensions in mm) ............ 36

Figure 3-7 Location of thermocouples in T-beams (all dimensions in mm) ....................... 37

Figure 3-8 Location of displacement gauges (all dimensions in mm). ................................ 38

Figure 3-9: CFRP strips on Slab A. ............................................................................................ 42

Figure 3-10: CFRP Wraps on Slab B.......................................................................................... 43

Figure 3-11 Surface thermocouples and surface preperation T-beams. .............................. 46

Figure 3-12 CFRP plate installation Beam-A. .......................................................................... 47

xv

Figure 3-13 CFRP plate installation Beam-B. .......................................................................... 47

Figure 3-14U-wrap installation Beam-B................................................................................... 48

Figure 3-15 U-wrap installation Beam-A. ................................................................................ 48

Figure 3-16 Thermocouples at FRP-insulation interfce and insulation surface (before

spraying insulation). ................................................................................................................... 49

Figure 3-17 Spraying insulation layer. ..................................................................................... 50

Figure 3-18 Measuring insulation thickness T-Beams. .......................................................... 50

Figure 3-19 ASTM E119 standard time temperture curve. ................................................... 51

Figure 3-20 Intermediate-scale furnace for slabs. .................................................................. 52

Figure 3-21 Full-scale floor furnace for beams. ....................................................................... 52

Figure 3-22 Test setup and instrumentation for slabs. ........................................................... 54

Figure 3-23 Instrumentation at unexposed surface T-beams. ............................................... 55

Figure 3-24 Temperatures vs. exposure time for slab A. ...................................................... 58

Figure 3-25 Temperatures vs. exposure time for slab B. ........................................................ 59

Figure 3-26 Temperatures vs. exposure time comparison for slabs A and B at FRP-

concrete bond line and steel reinforcement locations. ........................................................... 59

Figure 3-27 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A. .... 61

Figure 3-28 Steel reinforcement temperatures (web) Beam-A. ............................................. 62

Figure 3-29 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B. .... 63

Figure 3-30 Steel reinforcement temperatures (web) Beam-B. ............................................. 64

Figure 3-31 Shrinkage cracks in insulation, T-beams before fire test. ................................. 65

xvi

Figure 3-32 Spalling of un-insulated concrete (flange). Note, insulation layer was

removed manually after fire test. .............................................................................................. 66

Figure 3-33 Flames are visible at cracks in the U-wrap location, Beam-B after 1 hour and

53 minutes of fire exposure........................................................................................................ 66

Figure 3-34 Cracks at insulation surface after fire test Beam-B. .......................................... 67

Figure 3-35 Slab-B after test. ...................................................................................................... 67

Figure 3-36 T-beams after fire test in the loading frame. ...................................................... 68

Figure 3-37 Comparison of mid span deflection of Beam-A and Beam-B. ........................ 70

Figure 3-38 Bond test setup. ...................................................................................................... 73

Figure 3-39 Sample preparation. ............................................................................................... 73

Figure 3-40 Strength vs. temperature for steady-state tests. ................................................. 75

Figure 3-41, Room temperature steady state specimen before and after failure.

Debonding happens inside concrete very close to the interface. ......................................... 76

Figure 3-42 Steady state specimen, T=105C, before and after failure. Debonding happens

inside epoxy layer. ...................................................................................................................... 77

Figure 3-44 Transient test results failure temp. vs load level. .............................................. 79

Figure 3-45 Transient test specimens before and after failure and debonded surface for

20% (top) and 80% load level (bottom). ................................................................................... 80

Figure 3-46: CFRP coupon dimensions and fibre optic sensor location (all dimensions in

mm). .............................................................................................................................................. 84

Figure 3-47 Square pixel patches on FRP sheet used in PIV analysis (yellow squares). ... 85

xvii

Figure 3-48 Damage progress during test for specimen 2.1. Temperatures are 28, 77, 183,

200, 210 and 256 ˚C from left to right. ...................................................................................... 86

Figure 3-49 Fibre optic sensor and protective cover installation details. ............................ 87

Figure 3-50 OTDR style curve shows the reflectivity along the fibre length and the right

side curve is a 3-D (top view) of the fibre section under stress. These curves are obtained

from specimen 1.1. ...................................................................................................................... 87

Figure 3-51 CFRP specimen 2.1, transient test, before and after the test. ........................... 89

Figure 3-52 Secant modulus for specimen 2.1 vs. temperature. ........................................... 89

Figure 3-53 Comparison of strain reading using PIV method (dotted line) and FOS (solid

lines) specimen 1.1 at room temperature. ................................................................................ 91


lines) specimen 1.3 at 90°C. ........................................................................................................ 91


lines) specimen 1.2 at 110°C. ...................................................................................................... 92


lines) specimen 1.4 at 130°C. ...................................................................................................... 93

Figure 4-1 Spatial discretization. ............................................................................................... 97

Figure 4-2 Descritization and effective length for different finite volumes ........................ 99

Figure 4-3 Predicted and measured temperatures as a function of exposure time for

different depths within the concrete specimen (experimental data obtained from (Lie,

Woollerton 1988). ...................................................................................................................... 108

xviii

Figure 4-4 Predicted and measured temperatures as a function of exposure time for slabs

at, (a) unexposed surface slab-A (40 mm insulation thickness), (b) FRP-concrete interface

slab-A, (c) unexposed surface slab-B and (d) FRP-concrete interface slab-B.................... 110

Figure 4-5 Predicted and measured temperatures vs. exposure time for T-beams at (a)

unexposed surface, (b) on the centreline with concrete cover of 155 mm, (c) longitudinal

steel, and (d) FRP-concrete interface. ..................................................................................... 111

Figure 4-6 Measured steel temperature (mean ±1 standard deviation) compared to

predicted temperature. ............................................................................................................. 112

Figure 4-7 Steel simulation temperature erorr compared to standard deviation of

measured temperature. ............................................................................................................ 112

Figure 4-8 Temperature contour from FE simulation at the cross section of the recangular

column after 180 min of standard fire exposure (temperatures in °C ). ............................ 113

Figure 4-9 Predicted temperatures for different depths within the concrete specimen

using FV and FE simulations (experimental data obtained from (Lie, Woollerton 1988).

..................................................................................................................................................... 114

Figure 4-10 FE results vs. FV and experimantal results. Temperature is measured at the

bottom longitudinal bar of T-beam A. ................................................................................... 115

Figure 4-11 3D temperature isotherm surfaces from FE simulation at the cross section of

T-Beam-A after 240 min of standard fire exposure (temperatures in °C ). ....................... 116

Figure 4-12 Time temperature curves for four different fire scenarios. ............................ 118

xix

Figure 4-13 Time-Temperature curve in Dalmarnock real compartment fire (mean ± 1

standard deviation) in comparison with ASTM standard fire curve and “fireIV” curve

used here(Stratford, Gillie et al. 2009). ................................................................................... 118

Figure 4-14 Longitudinal steel temperature in beams subjected to Fires I to IV. ............ 119

Figure 4-15 FRP-concrete interface temperature in beams subjected to Fires I to IV. ..... 119

Figure 4-16 Predicted moment capacity of T-beams exposed to different fire curves and

applied maximum moment during the fire test. .................................................................. 121

Figure 4-17: Temperature vs. exposure time at FRP-concrete interface for different

insulation thicknesses (Depth is insulation thickness in mm). ........................................... 123

Figure 4-18: Temperature vs. exposure time with 20 mm concrete cover for different

insulation thicknesses. .............................................................................................................. 124











xx

Figure 4-24: Temperature vs. exposure at unexposed surface of concrete slab (thickness

150 mm) for different insulation thicknesses (Depth is insulation thickness in mm). .... 130

Figure 5-1 Free thermal strain vs temperature for various concretes from EuroCode 2. 135

Figure 5-2 Strain compatibility and load equilibrium at a typical section of the T-beam.

..................................................................................................................................................... 137

Figure 5-3 Time temperature curves data points are from Dwaikat and Kodur 2008 and

lines are results of the current model. .................................................................................... 140

Figure 5-4 Mid-span deflection vs. time, dotted line is from Dwaikat and Kodur 2008

and the solid line is current model. ........................................................................................ 140

Figure 5-5 Details of the cross section and loading for RC Beam 2, Dotreppe (1985). .... 141

Figure 5-6: Tension steel temperature vs. time, dotted line is model prediction and solid

line is the test result. ................................................................................................................. 143

Figure 5-7 Mid-span deflection vs. time, dotted line is model prediction and solid line is

the test result. ............................................................................................................................. 144

Figure 5-8 Details of the cross section and loading for FRP-RC Beam 1, Blontrock (2003).

..................................................................................................................................................... 146

Figure 5-9 Tension steel temperature vs. time, dotted line is model prediction and solid



the test result. ............................................................................................................................. 149

Figure 5-11 details of the cross section and loading for FRP-RC Beam 2, Blontrock (2003).

..................................................................................................................................................... 150

xxi




the test result. ............................................................................................................................. 152


the test result. ............................................................................................................................. 156

Figure 5-15 Assumed axial load time curves for the T-beams used in the simulation. .. 157

Figure 5-16 Mid-span deflection vs. time for T-beam A, dotted lines are model

predictions for deflection assuming different axial loads, solid line is the test result. ... 158

Figure 5-17 Mid-span deflection vs. time for T-beam B, dotted lines are model

predictions for deflection assuming different axial loads, solid line is the test result. ... 160

Figure 5-18 Longitudinal steel temperatures for Beam-C under different fires. ............. 161

Figure 5-19 Mid-span deflections for Beam-C exposed to different fires, beam fails under

Fire-IV in less than four hours. ............................................................................................... 162

Figure A-1 Temperatures vs. exposure time for slab A. ..................................................... 180

Figure A-2 Temperatures vs. exposure time for slab B. ...................................................... 181

Figure A-3 Interior concrete temperatures Slab-A. .............................................................. 181

Figure A-4 Interior concrete temperatures Slab-B. ............................................................... 182

Figure A-5 Temperatures vs. exposure time comparison for slabs A and B at FRP-

concrete bond line and steel reinforcement locations. ......................................................... 182

Figure A-6 Steel rebar temperatures Slab-A.......................................................................... 183

Figure A-7 Steel rebar temperatures Slab-B. ......................................................................... 183

xxii

Figure A-8 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A. ... 184

Figure A-9 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-A.

..................................................................................................................................................... 185

Figure A-10 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-A.

..................................................................................................................................................... 186

Figure A-11 Steel reinforcement temperatures (web) Beam-A........................................... 187

Figure A-12 Unexposed surface temperature (centerline) Beam-A. .................................. 188

Figure A-13 Unexposed surface temperature (flange) Beam-A. ........................................ 189

Figure A-14 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B. . 190

Figure A-15 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-B.

..................................................................................................................................................... 191

Figure A-16 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-B.

..................................................................................................................................................... 192

Figure A-17 Steel reinforcement temperatures (web) Beam-B. .......................................... 193

Figure A-18 Unexposed surface temperature (centerline) Beam-B. .................................. 194

Figure A-19 Unexposed surface temperature (flange) Beam-B. ......................................... 195

Figure A-20 Deflection at midspan and quatre points for Beam-A. .................................. 196

Figure A-21 Deflection at midspan and quatre points for Beam-B. ................................... 197

Figure A-22 Comparison of mid span deflection of Beam-A and Beam-B. ..................... 198

Figure A-23 load deflection curve Beam-A. .......................................................................... 199

Figure A-24 load deflection curve Beam-B. ........................................................................... 200

Figure A-25 Load deflection comparison for Beam-A and B. ............................................. 201

xxiii

Figure B-1 T-beam cross section. ............................................................................................. 206

Figure C-1 Thermal conductivity of normal weight concrete based on Eurocode 2 (EN

2004) and (Lie 1992). ................................................................................................................. 234

Figure C-2 Eurocode2 compressive stress strain curve for concrete. ................................ 239

Figure C-3 model for stress-strain relationships of reinforcing steel at elevated

temperatures .............................................................................................................................. 244

1

Chapter 1: Introduction

Composites in civil engineering have been used increasingly in past decades. Early

applications of fibre reinforced polymer (FRP) composites go back to the 1970’s (Parkyn

1970). Although early application results were not satisfactory, the FRP application

techniques have been vastly improved. FRPs are used in the construction of new

structures as well as in the rehabilitation and strengthening of existing structures.

Deteriorating infrastructure is also in need of retrofit and rehabilitation. FRPs have been

adapted to address these problems. High strength, light weight, resistance to

electrochemical corrosion, and ease of installation are advantages that make FRPs

attractive for engineering applications.

While FRPs have superior thermal and mechanical properties in comparison to

conventional construction materials, they are susceptible to degradation in high

temperatures. This makes their application in residential buildings to a certain extent

problematic. The National Fire Protection Association reported that there were over

500,000 structural fires annually in the United States (Karter 2009). While conventional

construction materials are also susceptible to degradation due to fire exposure, their

behaviour has been adequately investigated and researched during the past decades.

The results of these efforts are reflected in several fire safety codes and building codes.

2

The behaviour of FRP materials, on the other hand, has not been thoroughly

investigated and their behaviour at elevated temperatures is rather unknown.

1.1 Concrete structures and need for rehabilitation

Reinforced concrete has been widely used as a construction material during the last

century. The superior characteristics of reinforced concrete and the increasing need for

construction has led to the mass consumption of concrete in infrastructure; however the

continuation of this trend of production and consumption of concrete needs to be

considered attentively. The production of 1.6 billion tons of cement each year is

responsible for about 7% of the global carbon dioxide emission into the atmosphere,

(Mehta 2001). In order to produce one tonne of Portland cement an amount of energy

approximately equal to 4 GJ is needed, (Malhotra 1999). Addressing these concerns,

Freyermuth (2001) has suggested a service life of 100 to 150 years should be

implemented for the design of structures. Keeping in mind the necessity of extending

the service life of existing structures for sustainability, the need for strengthening is

further emphasized considering the economic and environmental aspects of the

problem.

Other than the need for the extension of service life, structures experience

deterioration throughout their designed service life. For example, the American Society

of Civil Engineers (ASCE 2005) estimated the total investment needed to upgrade

3

existing infrastructure to be about $1.6 trillion. Canada’s infrastructure needs $49 billion

for rehabilitation, (Mufti 2003). Further, the Bureau of Transportation reports that there

are approximately 150,000 deficient bridges in the United States, (National

Transportation Statistics 2005). In Canada, it is estimated that about 30,000 bridges are

structurally or functionally deficient (Mufti 2003). Clearly, the existing engineering

technology in construction and materials is not sufficient to address this infrastructure

crisis. Use of FRP strengthening techniques could help alleviate this problem, especially

considering the use of green composites, natural fibres and recycling. A quick overview

of FRP Materials which are the subject of this research will be presented in the following

section.

1.2 FRP materials

It is hard to accurately evaluate global composite production; it was estimated to be 7

million tonnes in year 2000 and 10 million tonnes in year 2006, with over 10% of

production being consumed in Civil engineering and construction industry (Berreur, de

Maillard et al. 2002), Figure 2-1.

4

Figure 1-1 FRP consumption share per industry,(Berreur, de Maillard et al. 2002).

Fibre reinforced polymers have a large share in the composite industry and they have

been commonly used in the aerospace and, automotive industries. FRP is a composite

material made of a polymer matrix which is reinforced by fibres. The fibres are usually

carbon, glass, aramid or basalt (Patnaik et al.2010 ) and the polymer is usually an epoxy,

a vinylester, or a polyester thermosetting plastic. In order to fulfill the design

requirement there is a need to know the behaviour of material at elevated temperatures.

1.3 Research objectives

The objectives of the research presented in this thesis could be summarized in three

main sections:

1. To investigate the behaviour of reinforced concrete beams strengthened

externally with FRP in fire. Specifically,

5

o To evaluate the behaviour of insulated FRP-strengthened intermediate-

scale reinforced concrete slabs exposed to standard fire through fire test

experiments.

o To evaluate the behaviour of insulated FRP-strengthened full-scale

reinforced concrete T-beam exposed to standard fire through fire test

experiments.

o To develop and validate numerical models to predict heat transfer and

thermally-induced strength degradation in FRP-strengthened flexural

members exposed to fire.

2. To investigate material behaviour and load transfer mechanism at bond between

FRP and concrete, specifically,

o To experimentally evaluate the bond behaviour between FRP and

concrete at elevated temperatures.

o To experimentally evaluate the behaviour of FRP materials at elevated

temperatures.

o To develop an empirical FRP-concrete bond behaviour model based on

experiment results.

3. To study the feasibility and effectiveness of instrumentation and sensing at

elevated temperatures, specifically,

6

o To experimentally evaluate the effectiveness of fibre optic sensor (FOS) at

elevated temperatures.

o To investigates the effectiveness and feasibility of particle image

velocimetry imaging (PIV) techniques at measuring strain during high

temperature testing.

1.4 Contributions

This thesis makes several important and original contributions to the understanding of

the performance of FRP strengthened concrete flexural members in fire. The full-scale

fire tests examine FRP materials and insulation systems that have not been previously

studied. The FRP-concrete bond study is particularly novel because no other researchers

have studied this performance at high temperature. Since the bond of FRP to concrete is

critically susceptible to high temperature, this information is vital in understanding the

performance of FRP strengthened concrete structures in fire. Additional innovation was

achieved through the study of FOS at high temperature because such sensors have not

previously been used at such high temperatures. In terms of numerical modelling,

original contributions include the incorporation of transient creep and axial thrust into

the flexural structural modelling, and the investigation of the performance of FRP

strengthened concrete beams when subjected to several different fire scenarios.

7

1.5 Thesis outline

This thesis has 6 chapters. Chapter 2 covers the background information on fire safety

and FRP materials. It also reviews the existing literature on the fire behaviour of FRP-

strengthened reinforced concrete structures, sensing technologies, and other relevant

information. Chapter 3 describes the experimental program and testing procedures

conducted for this thesis. It includes the details of the testing instrumentation and the

equipment used during the tests, and information on intermediate scale and full scale

fire tests. Chapter 3 also presents the experimental procedure, material properties,

testing schemes, and results for FRP concrete bond tests. Chapter 4 gives the details of

the numerical heat transfer model developed for simulation of the experiments. It

includes theoretical details of the model as well as the results of the developed model.

Model verification information is also included in this chapter. Parametric analysis is

also performed to demonstrate the capabilities of the developed model. Chapter 5

presents the numerical simulation results for strength simulation. It includes the details

of the model verification procedure. The effect of axial restraint is also studied in this

chapter. Chapter 6 summarizes the research and presents the conclusions derived from

this thesis and gives recommendations for future work. Detailed temperature and

deflection readings from the fire tests are presented in Appendix A, while load

calculations and design of the beams based on CSA and ACI are presented in Appendix

B, and finally Appendix C summarizes material properties at elevated temperatures.

10

Chapter 2: Literature review

2.1 Effects of fire on structures and fire test procedures

When considering structural fire safety it is assumed that the fire happens in a room or

an enclosed section of the building. These fires are called compartment fires. When a fire

in a compartment starts, it will grow burning the fuel available in the room. Assuming

sufficient combustible materials exist; temperatures will rise especially in the upper air

layers in the room. If the temperature is high enough, the ambient heat flux reaches a

critical level where all combustible items in the compartment will begin to burn. This

leads to a sharp rise in both heat release rate and temperature. This transition is called

“flashover” and the fire is called “post flashover fire” or a “fully developed fire”

(Feasey, Buchanan 2002).

The rate of fire spread and growth depends on many factors (Gewain, Iwankiw et al.

2003),

• Ventilation of the compartment

• Type of combustible materials and their availability

• Geometry of the compartment and its configuration

• Fire detection systems and subsequent fire suppression systems

• Efficiency of fire barriers

11

The behaviour of the fire will be less predictable in rooms which have large floor areas,

high ceilings or irregular arrangement of fuel or openings. Maximum temperature of a

post-flashover fire will rarely exceed 1000ºC (Alfawakhiri, Hewitt et al. 2002), while in

the case of not fully developed fires the temperature will not exceed 550 °C.

The elevated temperature during the fire is the major factor affecting the safety and

performance of the structure.

Simulation of temperatures in a realistic fire is very complicated due to the multiplicity

of variables involved. Design codes and standards, however, use standard fire tests to

measure the performance of the structural members in fire. Although they may not

represent a real fire incident, standard fire tests could be used to assess and compare the

level of performance of structural members in fire. An actual fire will have a slower

growth phase and will experience temperature fluctuations, thus the standard

temperature-time curve is somewhat conservative because it corresponds to a severe

fire, but not the severest possible fire event (Khoury 2000).

Once the standard temperature-time curves have been established to simulate fire

behaviour, the fire endurance of a member could be measured in a standard fire test.

Fire endurance is typically determined by exposing a structural element to fire in a

specially constructed furnace. The purpose of the fire test is to define a structure’s

ability to withstand fire exposure without losing its function as a load-bearing element

or a barrier to the spread of fire. In North America ASTM E119 describes the standard

12

fire test procedure and standard fire time-temperature curve. A very similar document

“Standard Methods of Fire Endurance Tests of Building Construction and Materials” is

used in Canada. In Europe, ISO 834, Fire Resistance Tests-Elements of Building

Construction defines the standard fire test.

Test specimens for a fire test should be constructed in a similar manner to the building

elements they represent. During the fire test, the temperature in the specimen must be

measured at exposed and unexposed faces. Fire endurance is determined once the

specimen reaches one of the failure criteria. Fire endurance is the duration of fire

exposure until this failure point.

2.2 Material behaviour at high temperatures

Fairly adequate information is available about the behaviour of concrete and steel at

high temperatures; while there is limited data on behaviour of FRP, insulation and

adhesive. Appendix C covers the material models in detail.

2.2.1 Concrete

Rise in temperature affects the stress strain behaviour of concrete. Experimental results

reported by Schneider (1988) for concrete in uniaxial compression at different

temperatures are plotted in Figure 2-1. It could be observed from the diagram that a rise

in temperature results in a degradation of compressive strength and stiffness of the

concrete. Meanwhile the increase in temperature affects the ductility of the concrete.

13

Figure 2-1 Stress-strain relationship for normal concrete derived in strain-rate controlled

tests (Schneider 1988).

Concrete response to uniaxial loading at high temperature is dependent on many factors

like aggregate type, water content etc. and concrete response is also dependant on the

applied compressive stress during heating (Schneider, Kassel 1985) or in other words the

loading history has an effect in behaviour of the concrete. To account for this

phenomenon, an additional strain component is defined in heated concrete. This strain

is called “transient creep strain” or “transient strain” or “load induced thermal strain

(LITS)”.

20 °C 150 °C

350 °C

450 °C

750 °C

550 °C

0

0.2

0.4

0.6

0.8

1

1.2

0 0.0005 0.001

Nor

mal

ized

stre

ss, σ

/f'c

(20)

Strain

14

2.2.2 Steel

A glance at literature suggests that models for yield and ultimate strength of steel vary

considerably because these properties depend on steel composition and the definition of

yield strength (Buchanan 2002). Curves for the stress-strain relation of mild steel at

various temperatures are shown in Figure 2-2. It can be seen that the yield strength

decreases with temperature and there is a yield plateau at lower temperatures which

disappears at higher temperatures. Considering the residual strength of the reinforcing

steel, the reinforcing steel recovers most of its original yield strength after cooling when

the maximum strength experienced by it remains below 500°C (Neves, Rodrigues et al.

1996). The percentage of strength and modulus recovery depends on the highest

temperature experienced by reinforcing steel. When steel is subjected to temperatures

above 500°C a gradual decrease in residual strength is observed.

Extensive research has been performed to evaluate the performance of structural steel at

fire. In general, at approximately 1000 °F (538 °C), steel loses approximately 50 % of its

room-temperature strength and modulus of elasticity (ASCE-78, 1992), see Figure 2-3.

15

Figure 2-2 Stress-strain curves for steel at different temperatures (fy=300 MPa), (Lie

1992)

16

Figure 2-3 Variation of strength of (a) reinforcing and (b) pre-stressing steels with

temperature (Holmes, Anchor et al. 1982).

17

2.2.3 FRP

Thermal and mechanical properties of FRPs are dependent on the properties of their

constituents i.e. fibre and matrix. Volume fraction of fibres and matrix also influences

the behaviour of the FRPs (Sorathia, Rollhauser et al. 1992). Glass and carbon FRPs

generally produce less smoke than aramid fibre. Fibre type also considerably influences

thermal conductivity of FRPs. Carbon FRPs have higher thermal conductivity than glass

and aramid FRPs.

Studies show that carbon fibres experience little to no change in their tensile strength up

1000 °C (Rostasy, Hankers et al. 1992), and they have better performance at high

temperatures than steel. Glass fibres lose almost 50% of their original tensile strength at

550°C (Dimitrienko 1999) and (Sen, Mariscal et al. 1993), which is similar to steel

behaviour at high temperatures. According to Sumida (2001) aramid fibres experience a

linear decline in strength at temperatures above 50°C with 50% loss of strength at 300°C.

FRP on the other hand loses most of its strength when the temperature reaches the glass

transition temperature (Tg) of its adhesive/matrix. At this temperature, the resin softens

and the resin will no longer be as effective in transferring stresses between fibres. As far

as fire behaviour of FRP is concerned, glass transition temperature is the most important

property of any FRP.

There are a couple of techniques for determining Tg of a composite. Among them two

are more popular:

18

• DSC, differential scanning calorimetry (ASTM-E1356) and,

• DMA, Dynamic mechanical analysis (ASTM-D7028).

DSC determines the glass transition temperature based on changes in heat capacity of

the material while DMA does so by measuring changes in the dynamic stress-strain

behaviour. Since DMA measures Tg based on mechanical behaviour of the material

rather than thermal properties, it is more accurate in predicting mechanical behaviour of

FRP in fire.

Another method that determines charring temperature or the temperature at which

thermal decomposition of the constituent materials occurs is TGA or thermogravimetic

analysis (ASTM-E1131). TGA determines Tg by monitoring mass loss with increasing

temperature.

Manufacturers sometimes report Heat Deflection Temperature (HDT) instead of Tg.

Although Tg and HDT are highly correlated they are not the same. Tg is the temperature

at which a polymer structure shifts from a “glassy state” to a “rubbery state”. According

to ASTM-D648, HDT is a temperature at which a polymer sample deflects a certain

amount under heat and load. Measuring HDT is a time consuming procedure. In

addition, HDT is a function of the temperature, stress and strain rate. Due to

inconsistencies in results, methods and interpretation, HDT is not used as commonly as

Tg.

19

2.3 Fire performance of strengthened beams and slabs

There are very few studies in literature concerning the fire behaviour of externally FRP-

strengthened beams. (Deuring 1994) tested six beams (300mm by 400mm by 5m) where

four of them were strengthened with CFRP sheets and were subjected to sustained

loading. Insulated beams showed satisfactory fire endurance in the tests. The un-

insulated beams had a fire endurance of 81minutes while the insulated beams gave an

endurance of 146 minutes. Interestingly the endurance of insulated CFRP plated beam

was larger than that of the un-strengthened RC beam. Blontrock, Taerwe et al. (2000)

tested CFRP plated beams using multiple insulation schemes. During the experiments

once the temperature of FRP reached Tg, the load bearing contribution of FRP was

significantly reduced. Overall the fire endurance observed in the tests was not sufficient.

Williams (2004) and Chowdhury (2005) tested full scale insulated T-beams and

intermediate scale slabs. Beams were subjected to sustained load but slabs were tested

without loading (Williams, Kodur et al. 2008). Length of the beams was 3.81m and the

web and flange width were 1220 and 300 mm respectively. Beam depth was 400mm.

Dimensions of the intermediate slabs were 954 by 1331mm. They concluded that beams

and slabs with sufficient insulation could achieve fire endurances of more than 4 hours.

Stratford, Gillie et al. (2009), studied the performance of bonded FRP strengthening in

real compartment fire (the Dalmarnock Fire Tests). They applied near surface mounted

and externally bonded FRPs. They also used intumescent coating and gypsum boards as

20

insulation materials. They concluded that FRP reinforcements are vulnerable during a

real compartment fire. Palmieri, Matthys et al. (2011) performed fire tests on six near

surface mounted FRP strengthened concrete beams with different insulation systems.

They achieved 2-hour fire endurance in their experiments.

2.4 Bond behaviour at high temperature for externally bonded FRP sheets

The effectiveness of FRP strengthening methods in reinforced concrete (RC) applications

is usually dependant on the effectiveness of the FRP-Concrete Bond (FCB). However

FRP-Concrete bond is susceptible to fracture and environmental factors like

temperature, corrosive materials and humidity (Tuakta, Büyüköztürk 2011, Leone 2009).

Thermosetting epoxies are usually used for attaching FRP plates to the concrete surface.

Structural characteristics of epoxies degrade very rapidly with increase of temperature

beyond the glass transition temperature (Tg) which is in the range of 60°C to 82°C for

most civil engineering applications (ACI-440-2R-08). High temperatures could occur

because of fire or service condition of the bond. There a few studies characterizing FRP

bar concrete bond behaviour at elevated temperatures. Katz, Berman (2000) performed

pull-out tests on FRP bars. They concluded that bond loses about 90% of strength when

temperature reaches 150-200°C. There are limited studies addressing the behaviour of

externally bonded FRP-Concrete behaviour at elevated temperatures in the literature.

Masmoudi et al.( 2011) studied the long-term bond performance of GFRP bars in

21

concrete at temperature ranging from 20 °C to 80 °C . They performed pull-out tests on

heat treated specimens subjected to high temperatures up to 80 °C for a duration of 4 -8

months. They reported 14% reduction of bond strength for the specimen subjected to

80°C (above Tg). Chowdhury (2011) tested lap splice tests on FRP sheets at temperatures

ranging from 20 to 200°C and proposed an analytical model for FRP-FRP bond strength

degradation. Tadeu, Branco (2000) studied the steel concrete bond behaviour at high

temperature. Leone (2009) analysed the behaviour of FRP–concrete interface at elevated

service temperatures ranging from 20°C to 80 °C. They performed double face shear

tests on CFRP and GFRP strengthened specimen. Specimen dimensions were 150 by 150

by 800mm. They observed a decrease of 25% to 75% in bond strength and an increase of

2.5 to 3 times in bond transfer length in temperatures beyond Tg of the

resin. They also derived experimental bond-slip curves. Ahmed, Kodur (2011)

established a numerical model to study the bond behaviour on fire resistance of FRP-

strengthened reinforced concrete beams using a bond-slip model.

2.5 Insulation techniques

Fire proofing is essential for structural elements with low fire resistance. This could be

done by applying a coating of fire suppressing materials or materials with low thermal

conductivity. The insulation materials could be applied as pre-made boards or they

could be sprayed on the structural member. Different types of fire proofing are

22

available. Performance of a number of common insulating materials will be discussed

below.

2.5.1 Concrete

Concrete among construction material is a good insulator however the use of concrete as

insulation has been reduced recently while lighter and more cost effective insulation

techniques are prevalent. Concrete encasing is time consuming and adds considerable

weight to the member. Another problem could be the possibility of explosive spalling.

Despite disadvantages concrete is durable and resistant to impact, abrasions, and

weather exposure.

2.5.2 Sprayed insulation

There are two major types of spray applied insulation materials, cementitious and

mineral fibre. The mineral-fibre mixture combines fibres, mineral binders, air and water.

In its final cured form, the mineral-fibre coating is lightweight, non-combustible,

chemically inert and a poor conductor of heat. Cementitious coating usually

incorporates lightweight aggregates, like vermiculite, in a heat-absorbing matrix of

gypsum or Portland cement. Some formulations also use magnesium oxysulfate,

magnesium oxychloride or calcium aluminate (Gewain, Iwankiw et al. 2003). The

sprayed insulation is cost effective compared to most other systems.

23

2.5.3 Board insulation systems

Gypsum boards are considered the most common type of fire protection boards. Their

fire resistance greatly relies on the chemically-combined water, which is approximately

one fifth of the weight of the boards. When the board system is exposed to fire, the water

gradually evaporates in a process that consumes heat, and thus keeps the temperature of

the protected structural element relatively low. When all the water evaporates, the

temperature of the structural element starts to increase slowly based on the thermal

conductivity of the dry gypsum boards. Less common types of boards include

vermiculite boards. Vermiculite boards are made by pressing vermiculite particles into

board form. These boards can withstand thermal shocks and temperatures up to 1100

°C.

2.5.4 Intumescent coating

Intumescent coating is a paint-like material. When exposed to high temperature (200 to

250 ºC) it swells and produces a charred layer with very low conductivity. Despite its

low conductivity intumescent coating usually provides limited fire resistance of 1 hour

or less. In the charring process a series of decomposition reactions happens. Initially the

inorganic salt in the presence of an amide is decomposed. Following this, the carbonific

agent is decomposed which produces a large amount of char. Eventually the char

24

expands due to temperature as the blowing agent starts to expand. The final result of

these reactions is a solidified material with a very low thermal conductivity.

2.6 Fire safety and sensing at high temperatures

In 2008, the National Fire Protection Association reported that there were over 500,000

structural fires annually in the United States causing 2,900 civilian deaths and $12.4

billion in property damage (Karter 2009). In addition to the direct costs of fires, recent

collapses such as the World Trade Center disaster and other tall buildings in Madrid

and Delft due to fire have emphasized the importance of fire safety. Although fire safety

design of buildings has improved the behaviour of structures in fire, it has not

eliminated the hazards of building fires. Current approaches to reducing fire losses

employ a more holistic view to fire safety by combining and integrating different

technologies. This integration provides early forecasts of the chain of events after the

start of a fire. In the forefront of these technologies is sensing. Sensing technology can

help emergency responders make critical decisions by detecting fire location and

severity, extent of fire spread, and structural integrity.

In addition to fires, structures are prone to other types of damage. Earthquake, aging

and fatigue, and vandalism can all cause problems for structures. To detect these types

of damage and preserve the health of structures, there is a need for sensors.

Conventionally used sensors such as smoke detectors, thermocouples, and electrical

25

resistance strain gauges are among these sensors. However, having multiple types of

sensors in structures is costly and difficult to incorporate. As a result, sensors with the

capacity to sense multiple variables simultaneously are gaining popularity. Fibre optic

sensors (FOS) are capable of sensing many useful variables such as temperature, strain,

displacement, pressure, acceleration, integrity, and cracking extent (Ravet, Briffod et al.

2009, Kersey, Dandridge 1990).

2.6.1 Stimulated Brillouin scattering for fibre optic sensors

Stimulated Brillouin Scattering (SBS)-based sensor systems are distributed sensors that

can measure temperature and strain along the entire length of the fibre. Unlike other

sensors the fibre used to transfer the light to the sensing point is also the sensing

medium. Thus, continuous temperature and strain distributions can be obtained. SBS is

a nonlinear process and the Brillouin frequency shift (BFS) is linearly related to the

temperature and strain in the fibre allowing the measurement of strain and temperature

simultaneously. Recently, most of the strain sensing using Brillouin scattering has been

based on a standard single mode fibre (SMF28) with an acrylate coating, which can only

sustain temperatures of 80°C. Obviously, this limitation is insufficient for sensing in fire

situations, but sensing fibres with a carbon/polyimide coating have been used to

overcome this shortcoming. The temperature limitations are in the range 400~500°C for

this type of fibre.

26

Zeng, Bao et al. (2002) successfully used (SBS)-based sensors to function as a distributed

strain sensor in a reinforced concrete beam with a spatial resolution of 500 mm along a

1650 mm long beam. Additionally, Zou, Bao et al. (2004) have reported temperature and

strain measurement accuracy of 1.3 ±˚C and15 με using (SBS)-based sensors. They

reached a spatial resolution of 150 mm.

28

Chapter 3: Experimental program

3.1 General

The experimental program presented here consisted of two parts, the first part

consisting of full-scale fire tests and the second part consisting of material tests on FRP

material and FRP-concrete bond tests at high temperatures. Alongside these tests, fibre

optic sensors (FOS) were used in both full-scale tests and material tests in order to

measure strain and temperature.

3.2 Fire Tests, T-beams and Slabs

3.2.1 Test specimens

The experimental program consisted of fire tests on two intermediate-scale reinforced

concrete slabs and two full-scale reinforced concrete T-beams, all of which were

strengthened with Sika FRP materials applied externally to the specimens. The slabs

were designated as Slab-A and Slab-B and the T-beams were designated as Beam-A and

Beam-B. Details of the reinforced concrete slabs and reinforced concrete T-beams are

shown in Figure 3-1 and Figure 3-2, respectively.

3.2.1.1 Dimensions

The slabs dimensions were 1331 mm by 954 mm and 152 mm. The reinforcement details

are shown in Figure 3-1.

29

Figure 3-1 Dimensions and reinforcement details of SLAB-A and SLAB-B (dimensions in

mm)

305

305

305

305 305

25152

208

208

1331

172 172

954

SECTION A-A:

A A

NTS

15M steel rebar 10M steel rebar

30

The T- beams had a span of 3.9 m (12.7 ft.) and overall height of 400 mm (15.7 in.). The

flange was 1220 mm (48 in.) wide and 150 mm (5.9 in.) thick. The web was 300 mm

(11.8 in.) wide. The reinforcement details are shown in Figure 3-2.

Figure 3-2 Dimensions and reinforcement details of BEAM-A and BEAM-B (All steel

bars are 10M)

31

3.2.2 Materials

3.2.2.1 Concrete

Portland cement Type I was used for fabricating the reinforced concrete slabs and T-

beams. The aggregate type for all specimens was carbonated aggregate. The maximum

aggregate size used in the slabs and T-beams was 13 mm. The concrete for slabs and

beams was supplied by Lafarge, Kingston, Canada. The concrete for the slabs was

designed to have a specified compressive strength of 28 MPa. The concrete for the beams

was designed to have a specified compressive strength of 30 MPa. The 28-day

compressive strength of the slab concrete was 27 ±3 MPa and the compressive strength

on the day of fire test was 26±4 MPa. The average 28-day compressive strength of the T-

beam concrete was 32±2 MPa and the test day strength was 28.5±3 MPa.

3.2.2.2 Steel

Deformed bars were used for reinforcing both the slabs and T-beams (Figures 3-1 and

3-2). In the slabs, four 10M steel bars were along the direction of the 954 mm edge and

three 15M steel bars were placed along the direction of the 1331 mm edge. The clear

cover for 15M steel bars was 25 mm from the bottom. All reinforcements in the slabs had

specified yield strengths of 400MPa. The longitudinal reinforcement in the T-beams

consisted of six 10M steel bars in the flange and two 15M steel bars in the web. For

lateral reinforcement, twenty-six 10M steel ties placed every150mm. Additional lateral

32

bars were placed in the flange. The tested yield strengths of the steel bars were 470 MPa

for the 10M and 15M bars.

3.2.3 Fabrication

The slabs and T-beams were fabricated and cured in the Structures Testing Laboratory at

Queen’s University, Kingston, Canada and then shipped to the Fire Testing Facility of

the National Research Council, Ottawa, Canada. Both slabs and beam-slabs were cast in

plywood formwork.

3.2.3.1 Reinforcing bars

The 15M longitudinal reinforcing bars were placed into holes drilled into the plywood to

maintain a consistent concrete clear cover of 25 mm (1.0 in.). The longitudinal

reinforcements were subsequently tied together using steel ties. Figure 3-3 shows the

formwork and reinforcement layout during fabrication of the slabs.

33

Figure 3-3 Formwork and reinforcement layout for slabs (Williams, 2004).

The stirrups for the T-beams were arc-welded together to form the steel cage (minimal

welding was performed just to keep the cage strong enough for concrete pouring). The

cage was placed on small concrete blocks to maintain a consistent concrete clear of 40

mm to the steel ties. Figure 3-4 and Figure 3-5 show the steel cage for the beam-slabs

during fabrication.

34

Figure 3-4 Steel reinforcement for T-beams

Figure 3-5 Formwork and reinforcement layout for T-beams

35

3.2.3.2 Instrumentation

Chromel-alumel (Type K) thermocouples were used in order to record the temperatures

during the fire endurance tests. Figure 3-6 shows the locations of the thermocouples

within the slabs. Figure 3-7 shows the location of the internal and surface thermocouples

within the T-beams and on the unexposed surfaces of the T-beams. Displacement gauges

were also used during the fire tests to monitor beam deflection, as shown in Figure 3-8.

36

Figure 3-6 Location of thermocouples in slab specimens (all dimensions in mm)

51

51

A

B

LOCATION A

18

1716

CL

Insulation

EpoxyFRPEpoxy

125

100

75

5030

22 15

45

2423

44

43

19

20

21

LOCATION B

LC

CL

LCNTS NTS

37

Figure 3-7 Location of thermocouples in T-beams (all dimensions in mm)

TCs

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5720

7

40

77

35 35 35

400

150

607

460

40

U-W

rap 46

4748

434445

End

Jcl

ose

to

sect

ion

G

End

Icl

ose

to

sec

tion

D

38

Figure 3-8 Location of displacement gauges (all dimensions in mm).

3.2.3.3 Curing

The slabs and T-beams were cured under wet burlap and plastic sheets at room

temperature and 100% humidity for seven days, after which the formwork was removed

11681168

500123

4

678

5

Location of displacement gauge

39

and the samples were cured in the Structures Testing Laboratory at Queen’s University

at room temperature for at least six months before they were transported to the National

Research Council of Canada, Ottawa.

3.2.4 FRP strengthening

Three strips of Sika® CarboDur S512 CFRP plates were installed side by side to cover a

width of approximately 150 mm on Slab A, Figure 3-9. The FRP on Slab B consisted of

two layers of SikaWrap Hex 103C unidirectional carbon/epoxy FRP strengthening

system Figure 3-10. The FRP was bonded to the tension face of both slabs in the

longitudinal direction. A summary of the strengthening system for the slabs is presented

in Table 3-1.

Installation steps for the installation of FRP sheets or plates for the intermediate-scale

slabs were as follows:

3.2.4.1 Slab-A

1. The concrete surface was prepared using hand grinders to roughen the surface

and create the desired texture.

2. The dust removed by vacuuming the surface.

3. An even layer of SikaDur®-30 epoxy was applied to the prepared concrete

surface where the Sika CarboDur® S512 plates were going to be applied.

40

4. A layer of SikaDur®-30 epoxy was placed on one side of CarboDur plates.

5. The plates were placed on the prepared concrete surface.

6. Even pressure applied to the plated using a roller to assure proper adhesion and

to control the adhesive thickness.

7. Excess epoxy was removed from the specimen

8. Another layer of SikaDur®-30 epoxy was applied on top of the installed plates.

9. Another layer of SikaDur®-300 epoxy was applied to the final surface and special

sand was sprinkled to the saturated surface to increase the bond of insulation to

the FRP surface.

3.2.4.2 Slab-B

1. The concrete surface was prepared using hand grinders to roughen the surface

and create the desired texture.

2. The dust removed by vacuuming the surface.

3. SikaWrap® Hex 103C sheet was cut to the desired length and impregnated using

SikaDur®-300 epoxy.

4. An even layer of SikaDur®-300 epoxy was applied using a nap roller to the

prepared concrete surface where the FRP wrap were going to be applied.

5. The resin-saturated sheet of FRP was placed on the prepared concrete surface.

6. The plates were placed on the prepared concrete surface.

41

7. Even pressure applied to the sheet using a roller to remove air bubbles beneath

the wrap.

8. Another layer of SikaDur®-300 epoxy was applied to the final surface and special

sand was sprinkled to the saturated surface to increase the bond of insulation to

the FRP surface.

42

Table 3-1 FRP and insulation details for intermediate-scale slabs.

Slab A Slab B

FRP Type Sika CarboDur® S512 SikaWrap® Hex 103C

No. Layers/strips 3 side by side 2

FRP Width (mm) 3×50 635

Epoxy SikaDur®-30 SikaDur®-300

Insulation Type Sikacrete®-213F Sikacrete®-213F

Insulation Thickness 40 mm 60 mm

Figure 3-9: CFRP strips on Slab A.

43

Figure 3-10: CFRP Wraps on Slab B.

Beam-A was strengthened by CFRP Sika® CarboDur S812 in flexure and Beam-B was

strengthened by one layer of CFRP SikaWrap® Hex 103C on the bottom of the beam

web. Two different CFRP U-wraps are selected for Beam-A. The U-wrap at one end

consisted of two 635 mm wide layers of SikaWrap® Hex 103C and the other U-wrap had

four 600 mm wide layers of SikaWrap® Hex 230C. In the case of Beam-B, U-wrap at one

end consisted of two 610 mm wide layers of SikaWrap® Hex 100G and the other U-wrap

has four 610 mm wide layers of SikaWrap® Hex 430G. A summary of the strengthening

systems for the T-beams is presented in Table 3-2. Installation specialists from Sika®

installed the strengthening system at the National Research Council of Canada.

44

Table 3-2 Summary of FRP-Insulation system used for T-beams.

Beam A Beam B

Flexural FRP Type Sika CarboDur® S812 SikaWrap® Hex 103C

No. Layers/strips 1 1 FRP Width (mm) 80 200

Insulation Type Sikacrete®-213F

Insulation Thickness 36.0 mm 36.0 mm U-wrap END I Type SikaWrap® Hex 103C SikaWrap® Hex 100G

No. Layers 2 2 Wrap Width (mm) 635 610

U-wrap ENDJ Type SikaWrap® Hex 230C SikaWrap® Hex 430G No. Layers 4 4 Wrap Width (mm) 600 610

Installation steps for the installation of FRP sheets or plates for the beams were as

follows:

3.2.4.3 Beam-A

• The concrete surface was prepared using hand grinders to roughen the surface and

create the desired texture where the longitudinal FRP and U-wraps were going to be

applied.

• A thin layer of SikaDur®-30 epoxy was applied to the prepared concrete surface

where the Sika CarboDur® S812 plate was going to be applied.

• A layer of SikaDur®-30 epoxy was placed on one side of CarboDur plates

45

• The plates were placed on the prepared concrete surface.

• Even pressure applied to the plated using a roller to assure proper adhesion and to

control the adhesive thickness.

• SikaWrap® Hex 103C and SikaWrap® Hex 230C sheets were cut to the required

length for U-wraps and impregnated in SikaDur®-300 epoxy.

• Concrete surface was saturated by a layer of SikaDur®-330 epoxy for U-wraps.

• U-wraps were applied in layers.

• Another layer of SikaDur®-300 epoxy was applied to the final surface and special

sand was sprinkled to the saturated surface to increase the bond of insulation to the

FRP surface.

3.2.4.4 Beam-B

• The concrete surface was prepared using hand grinders to create the desired

texture. And dust removed by vacuuming the surface.

• An even layer of SikaDur®-330 epoxy was applied using a nap roller to the

prepared concrete surface where the FRP wraps were going to be applied.

• SikaWrap® Hex 103C sheet was cut to the desired length and impregnated using

SikaDur®-300 epoxy.

• The resin-saturated sheet of SikaWrap® Hex 103C was placed on the prepared

concrete surface on the bottom of the beam.

46

• Even pressure applied to the sheet using a roller to remove air bubbles beneath the

wrap.

• SikaWrap® Hex 100G and SikaWrap® Hex 430G sheets were cut to the required

length for U-wraps and impregnated in SikaDur®-300 epoxy.

• U-wraps were applied in layers.

• Another layer of SikaDur®-330 epoxy was applied to the final surface and special

sand was sprinkled to the saturated surface to increase the bond of insulation to the

FRP surface.

Figure 3-11 Surface thermocouples and surface preperation T-beams.

47

Figure 3-12 CFRP plate installation Beam-A.

Figure 3-13 CFRP plate installation Beam-B.

48

Figure 3-14U-wrap installation Beam-B.

Figure 3-15 U-wrap installation Beam-A.

49

Figure 3-16 Thermocouples at FRP-insulation interfce and insulation surface (before

spraying insulation).

3.2.5 Fire proofing

In order to provide supplemental fire insulation over the FRP on beams and slabs

Sikacrete®-213F was used as insulation. Sikacrete®-213F is a cement-based, dry mix fire

protection mortar for wet sprayed application. It contains phyllosilicate aggregates,

which are highly effective in resisting the heat of hydrocarbon fires. A 40 mm layer of

Sikacrete®-213F was spray-applied to Slab-A, Beam-A and Beam-B. The insulation

thickness for Slab-B was 60 mm. A steel mesh was installed on the FRP strengthened

surface in the slabs in order to reinforce the bond of the insulation to the slabs. The

sprayed insulation was allowed to cure in the Fire Testing Laboratory at the National

Research Council of Canada (NRC) until the date of the test.

50

Figure 3-17 Spraying insulation layer.

Figure 3-18 Measuring insulation thickness T-Beams.

3.2.6 Test apparatus

During the fire endurance tests, the specimens were exposed to elevated temperatures

on their soffits. The two slabs were tested in the intermediate-scale furnace at NRC, and

the two beam-slabs were tested in the full-scale floor furnace, also at NRC. These

51

furnaces were designed to produce temperature and loading conditions as prescribed in

ASTM E119 and CAN/ULC S101 (Figure 3-19).

Figure 3-19 ASTM E119 standard time temperture curve.

The Intermediate-Scale Furnace can tests specimens up to a maximum size of 1.35m by

1.98m (Figure 3-20). While it is possible to apply load during the fire test, no load was

applied to the slabs in this study. The full-scale floor furnace can test samples to a

maximum size of 4.9 m by 4.0 m. (Figure 3-21).

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (minutes)

ASTM E119

52

Figure 3-20 Intermediate-scale furnace for slabs.

Figure 3-21 Full-scale floor furnace for beams.

The T-beams were subjected to a load from above using 30 distributed hydraulic jacks.

Each jack had a maximum load capacity of 13 kN (refer to Figure 3-21 and Figure 3-23).

Layers of insulation were provided between the two slabs and two beam specimens to

make sure they are thermally independent as shown in Figure 3-22 and Figure 3-36.

The temperatures in the furnaces were measured using Type K thermocouples.

53

3.2.7 Test conditions and procedures

Both the intermediate-scale and full-scale furnaces can produce the conditions described

in ASTM E119, which are similar to those prescribed by CAN/ULC S101.

The two slabs were tested side by side in furnace. Each slab was supported on three

sides. As mentioned earlier, no load was applied to the slabs during the fire exposure

Figure 3-22. The beams were placed in a movable frame and fixed to the frame by steel

mounts at both ends. Then the frame was placed on the furnace and all openings were

filled with ceramic-insulated panels. The relative humidity of each specimen at the time

of testing is given in Table 3-3.

3.2.7.1 End conditions

The intermediate-scale slabs were not subjected to applied load during fire exposure and

therefore their end conditions are not discussed here. The slabs of the T-beams were

axially restrained during the fire test by placing steel shims at their ends prior to testing.

The support conditions were selected to meet the conditions described in ASTM E119

and CAN/ULC S101 corresponding to an axially-restrained flexural assembly.

3.2.7.2 Loading

The purpose of fire testing the intermediate-scale slabs was to evaluate the thermal

performance of the two insulation thicknesses. Thus, the slab experienced no load other

than its self-weight during the fire endurance test.

54

During the full-scale T-beam fire tests, the assemblies were tested under a sustained

uniformly distributed load. The sustained applied load was 25.7 kN/m, which

represented 71% of the ultimate strengthened capacity according to ACI 440.2R-08, and

73% according to CSA S806-02. Details of the load calculations are presented in

Appendix A. The preloading of the T-beam specimens began 45 minutes prior to the

start of the fire exposure. Upon reaching the required load level, the heating in the

furnace was started. The required load level was maintained at a constant value

throughout the fire test.

Figure 3-22 Test setup and instrumentation for slabs.

55

Figure 3-23 Instrumentation at unexposed surface T-beams.

3.2.7.3 Failure criteria

In a fire test, the structural member must not fail under applied load for the required

duration. Because there was no load applied to the slabs, no load-bearing failure criteria

was applicable. Since the purpose of the slab tests was to investigate the performance of

the thermal insulation, the temperatures during the slab fire endurance were compared

with the thermal criteria stated in ASTM E119 and ULC S101. Thus, the slab specimens

were assumed to have failed if any of the following limits were reached:

Slab Criterion 1: Steel temperature reaches 593°C,

Slab Criterion 2: Unexposed surface temperature reaches 140°C,

Slab Criterion 3: Any individual point at unexposed face reaches 180°C.

T-beams were subjected to their service load during fire testing. The beams were

assumed to have failed if any of the following criteria were reached:

56

T-beam Criterion 1: Steel temperature 593°C

T-beam Criterion 2: Average unexposed face temperature reaches 140°C,

T-beam Criterion 3: Any individual point at unexposed face reaches 180°C.

T-beam Criterion 4: Load-bearing capacity of the beam reaches the applied service load

Both T-beams successfully resisted the sustained applied load of 27.7 kN/m for more

than four hours of fire exposure without structural failure. Close the end of the fire

endurance test, the applied load was increased to 39 kN/m but the beams did not fail

even at that load level. After 4.5 hrs the fire test was stopped to prevent any damage to

the floor furnace. Since the T-beams were restrained axially, they were not required to

satisfy the specified temperature limits stated in ASTM E119 to achieve a fire endurance

rating. Thus, the beams achieved a 4-hour fire endurance rating.

3.3 Fire test results and discussion

A summary of results of the fire endurance tests is given in Table 3-3. General

observations recorded during the beams fire tests are presented in Table 3-4. The

temperatures of the furnace, concrete, steel, FRP and insulation, and the vertical

deflections were recorded during the fire endurance tests. The recorded temperatures

for the slabs and beams are given in Appendix-A.

57

Table 3-3 Summary of test results

Relative Humidity (%)

Ambient Temp. (° C)

Ultimate Load Capacity (kN/m)

Applied Load (kN/m)

Failure Load (kN)

Fire Endurance (min.)

Failure Mode

Slab-A 63 23 - - - > 240 N/A Slab-B 63 23 - - - > 240 N/A Beam-A 61 22 38.6 25.7 N/A > 255 N/A Beam-B 61 22 40.4 25.7 N/A >255 N/A

Table 3-4 General observation during test of T-beams.

Time (hr:min) Observations /Actions

Before test Small cracks was observed on the Insulation surface

0:45 earlier Beam was loaded to 25.7 kN/m

0:00 Furnace turned on

0:14 Moisture and emission of steam noted at unexposed surface

0:36 Flaming observed at the at U-warps both beams

0:45 Flaming observed at mid-span, cracks start to widen

4:02 Load increase from 25.7 kN/m to 39 kN/m

4:15 No failure observed, loading stopped

58

3.3.1 Temperatures

Results of thermocouple temperature readings for slabs are given in detail in Appendix

A. These graphs show temperatures at the FRP-concrete bond line and steel

reinforcement during the fire tests. These data indicate that it will be difficult to

maintain the FRP temperature below the glass transition temperature (Tg) of the matrix

for prolonged periods of time during fire. Temperatures in Slab-B are lower compared to

Slab-A temperatures, because of the thicker layer of insulation, but the FRP is still not

fully protected for the full duration of the fire. In both cases, the FRP-concrete

temperature exceeds glass transition temperature in less than 30 minutes. The average

unexposed surface temperature after 4 hours of fire exposure reached 88˚C and 62˚C in

slab A and B, respectively (Figure 3-24, Figure 3-25 and Figure 3-26).

Figure 3-24 Temperatures vs. exposure time for slab A.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Furnace avg.

TC-45 Insulation Surface

TC-44 FRP-Insulation

TC-43 FRP-Concrete

Avg. Unexposed Face

59

Figure 3-25 Temperatures vs. exposure time for slab B.

Figure 3-26 Temperatures vs. exposure time comparison for slabs A and B at FRP-

concrete bond line and steel reinforcement locations.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Furnace avg.



TC-43 FRP-Concrete

Avg. Unexposed Face

0

100

200

300

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

FRP-Concrete Slab-AFRP-Concrete Slab-BRebar Bottom Slab-ARebar Bottom Slab-B

60

Detailed temperature readings for T-beams are given in Appendix A. Similar to the

slabs; FRP-concrete bond temperature exceeds glass transition temperature in less than

30 minutes. Steel temperatures in all tests are below 250 ˚C . Figures 3-27 to Figure 3-30

illustrates temperature recordings in various sections of the T-beams A and B.

61

Figure 3-27 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.

Concrete-Insulation sec-B TC-28

Insulation Surface sec-B TC-30

FRP-Insulation sec-B TC-29

62

Figure 3-28 Steel reinforcement temperatures (web) Beam-A.

0

50

100

150

200

250

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

Longitudinal Steel sec-A TC-2


Longitudinal Steel sec-B TC-25


63

Results for Beam-B are as follows.

Figure 3-29 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.




64

Figure 3-30 Steel reinforcement temperatures (web) Beam-B.

0

50

100

150

200

250

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)





65

3.3.2 Performance of the insulation system

There were minor shrinkage cracks in all samples which contributed to further cracking

later during the fire test (Figure 3-31). These cracks gradually widened as the test

progressed, likely due to thermally-induced shrinkage of the insulation material. Wider

cracks accelerated heating of resin impregnated FRP layer to heat up faster at the

location of the cracks. Subsequently stable flames were created at crack locations, see

Figure 3-33. Theses cracks and residual charring are visible for Beam-B in Figure 3-34

and Slab-B in Figure 3-31. The insulation layer protected the concrete from spalling. As

depicted in Figure 3-32, spalling of concrete is visible where there was no fire protection.

There was no separation or spalling of the insulation layer during either of the fire tests,

see Figure 3-35 and Figure 3-36.

Figure 3-31 Shrinkage cracks in insulation, T-beams before fire test.

66

Figure 3-32 Spalling of un-insulated concrete (flange). Note, insulation layer was

removed manually after fire test.

Figure 3-33 Flames are visible at cracks in the U-wrap location, Beam-B after 1 hour and

53 minutes of fire exposure.

67

Figure 3-34 Cracks at insulation surface after fire test Beam-B.

Figure 3-35 Slab-B after test.

68

Figure 3-36 T-beams after fire test in the loading frame.

3.3.3 Deflections

Figure 3-37 illustrates the mid span deflection of Beam-A and Beam-B; it also gives the

magnitude of the superimposed load vs. time. While preloading the distributed load on

the beams increases linearly until it reaches the predefined superimposed load of 25.6

kN/m. The load was then kept constant for approximately 30min before heating started.

The deflections in the preloading sections increased nearly linearly with time. The

subsequent increase in deflection is the result of fire exposure since the load is kept

constant for the first 4 hours of fire exposure. The large jump in the deflections in the

69

first hour of the fire exposure is most likely due to the differential temperature

distribution in the height of the beams. This differential temperature distribution creates

larger thermal strains at the soffit of the beams and results in increase of curvature and

deflection of the beams. Since the dimensions and material used in the beams are similar

(except FRP), it is expected that the final deflections of the beams to be similar in

magnitude to each other. Of course the effect of FRP would be diminished in the first

hour of fire exposure. Nevertheless, as it is apparent from Figure 3-37, Beam-B has a

larger deflection compared to Beam-A. This could be the result of measuring error

during the tests. It is also possible that the loading frame against which the

displacements are measured is deformed unevenly or the load distribution was uneven.

Detailed results of beam deflections are presented in Appendix A.

70

Figure 3-37 Comparison of mid span deflection of Beam-A and Beam-B.

71

3.3.4 Summary

Fire endurance tests were conducted on two intermediate-scale slabs and two full-scale

T-beams. Both T-beams and slabs were strengthened with externally-bonded FRP in

flexure and both were protected using a layer of supplemental fire insulation materials.

From the experimental program, the following conclusions can be drawn:

• Reinforced concrete T-beams strengthened with externally-bonded FRP achieved

fire endurance ratings of more than 4-hours.

• Slabs and T-beams with 40mm and 60mm thickness of the insulation material

satisfied the thermal criteria stated in the ASTM E119 and ULC-S101 standards

for more than 4-hours.

• Insulation material protected concrete and internal steel from adverse effects of

fire, thus preventing the failure of T-beam sand slabs.

3.4 FRP-concrete bond tests

The configuration of the pull-off test for the study of FRP-concrete behaviour at elevated

temperatures is shown in Figure 3-38. An FRP sheet or plate is attached to a concrete

block and the concrete block is clamped by two steel plates at top and bottom. During

the test, FRP and the bottom rod are pulled apart causing a shearing force exactly at the

interface. For high temperature tests the whole setup is placed in an environmental

chamber which controls the testing temperature to the desired testing condition. Internal

72

dimensions of the chamber are 250 mm in width, 250 mm in depth and 300 mm in height

and the machine has a maximum load capacity of 600 kN. Concrete block dimensions

were 6 inches/152 mm in height, 4 inches/102 mm in width and 3 inches/76 mm in depth;

see Figure 3-39. The 28-day compressive strength of the concrete was 30MPa. Concrete

blocks had aged for at least 6 months before the test. Concrete bond surfaces were sand

blasted prior to application of FRP plates. The CFRP plates were Sika® CarboDur S512

but they were cut in half lengthwise to make the width of the FRP plates equal to 25±1

mm. The adhesive used for attaching the plate to the concrete surface was Sikadur30

with a Tg value of 60°C. Glass beads were placed between concrete surface and FRP

sheets to achieve a uniform 1.5 mm adhesive thickness along the bond. Sikadur30 will

reach its design strength after 7 days based on manufacturer’s data sheet. All samples

were aged at room temperature for at least 60 days after application of the FRP.

73

Figure 3-38 Bond test setup.

Figure 3-39 Sample preparation.

There are numerous variables that affect the bond behaviour such as bond length, FRP

width, type of FRP, etc. In this study most variables were kept constant and the main

74

variable was the exposure temperature. For example bond length and adhesive

thickness and material type were identical for all tests.

Two types of thermal tests have been performed: steady state and transient. In steady-

state thermal tests, samples were heated up to the determined temperatures. Tests were

performed at room temperature, 60, 80, 105, 150 and 200°C. The rate of heating was

10°C/min. Four samples were tested in each temperature group. Samples were kept at

the target temperature for 60 minutes to achieve a uniform temperature distribution.

Heated specimens were then exposed to tensile loading while the temperature was kept

constant. The tensile force was increased until failure or debonding at the interface. In

transient temperature testing, samples were loaded to a determined tensile loading that

was maintained throughout the test. Then, the temperature was increased until the

sample failed. Loading levels during the transient tests were 20%, 40%, 60% and 80% of

the room temperature strength determined during the tests. Three samples were tested

for each load level. Temperature was measured on the FRP surface by standard type K

thermocouples inside the environmental chamber.

3.4.1 Bond tests results and discussion

The steady -state test results are presented in Table 3-5. Figure 3-40 depicts the

degradation of bond at higher temperatures; the solid line presents the average value.

As could be seen the bond loses about 50 percent of its strength at approximately 100 °C,

75

which is approximately 40 °C higher than Tg for the adhesive. For the case where the

temperature was 200°C failure happened during the heating process approximately 30

minutes through steady-state heating. The strength value of zero is entered for them.

Table 3-5 Strength results for steady state tests.

Test Temperature, T (°C)

Reduced Strength at Temp. T (kN)

Average Strength (kN)

STD (kN) Strength loss %

Residual strength %

23 (room temp.) 13.6 14.1 13.7 14.6 14.0 0.4 0% 100% 60 (Tg) 12.9 12.9 12.3 16.0 12.7 1.7 9% 91% 80 8.9 8.5 9.7 9.1 9.0 0.5 36% 64% 105 6.5 5.0 6.2 5.7 5.8 0.7 58% 42% 150 2.2 2.7 2.9 3.0 2.7 0.3 81% 19% 200 0.0 0.0 0.0 0.0 0.0 0 100% 0%

Figure 3-40 Strength vs. temperature for steady-state tests.

0.02.04.06.08.0

10.012.014.016.018.0

0 50 100 150 200 250

Stre

ngth

(kN

)

Temperature (°C)

Average

76

In design practices the FRP contribution to load carrying capacity of the structure is

assumed to be zero once its temperature reaches Tg of the adhesive. Based on these

results, this assumption is conservative because the FRP-concrete has retained 90% of its

maximum capacity at Tg. A notable observation is that in high temperature tests, unlike

room temperature tests, failure does not happen in concrete substrate but the failure

surface occurs within the epoxy adhesive layer; Figure 3-41 and Figure 3-42 . The room

temperature failure mode can be described as cohesive concrete failure while the failures

at higher temperatures are adhesive failures. As the failure temperature rises the failure

is less abrupt. It seems that the adhesive material behaves in a brittle manner at lower

temperatures but a more elasto-plastic manner at elevated temperatures.

Figure 3-41, Room temperature steady state specimen before and after failure. Debonding happens inside concrete very close to the interface.

77

Figure 3-42 Steady state specimen, T=105C, before and after failure. Debonding happens inside epoxy layer.

3.4.2 Proposed analytical model

An analytical model of the form,

𝑆(𝑇) = 𝑆𝑟2

+ 𝑆𝑟2�𝑡𝑎𝑛ℎ�−𝑤(𝑇 − 𝑇𝑐)�� (3-2)

could be used to model the mechanical properties of the FRP-concrete bond where S(T)

is the remaining strength at temperature T, Sr is the room temperature strength, Tc is the

central temperature and w is an empirical constant. For current tests Tc is taken as Tg +34

and w is 0.018. Fitted curve and experimental data are shown in Figure 3-43.

78

Figure 3-43 Analytical model vs experimental results dotted lines are 95% confidance interval of the curve. Transient test results are given in Table 3-5 and Figure 3-44. The FRP-concrete bond

could survive higher temperatures at lower sustained load level. At 20% of maximum

capacity the bond could be functional up to approximately 250 °C in a transient thermal

loading as described above. This temperature is significantly higher than Tg for the

adhesive. However the critical temperature is lower for the case of a much higher load

level of 80% (150°C at 80% load level compared to 250°C in the 20% load level case).

Table 3-6 Failure temperatures for transient tests at different sustained load levels.

Load level %

Sustained load (kN)

Failure Temp. (°C)

Mean Failure Temp. (°C)

STD

80% 11.2 137 146 154 146 6.4 60% 8.4 159 169 159 162 7.1 40% 5.6 209 238 211 219 16.2 20% 2.8 287 256 283 275 16.9

0.0

5.0

10.0

15.0

20.0

0 50 100 150 200

Stre

ngth

(kN

)

Temperature (°C)

ProposedModel

79

Figure 3-434 Transient test results failure temp. vs load level.

As mentioned above the failure at high temperatures happens in the adhesive layer

therefore the debonding mechanism is different and development length assumptions

which are derived from Linear Elastic Fracture Mechanics (LEFM) concepts may no

longer be valid. Further investigation in this regard is needed to establish proper

development length criteria.

120140160180200220240260280300

0% 50% 100%

Failu

re te

mpe

ratu

re (°

C)

Load level

80

Figure 3-445 Transient test specimens before and after failure and debonded surface for

20% (top) and 80% load level (bottom).

81

3.4.3 Discussion

The results of the steady-state tests are particularly important for high temperature

environments such as hot climates or high operating temperatures in industrial

applications. In such cases, the FRP-concrete bond will need to retain its full room

temperature strength since an overload could be expected at any time during prolonged

high temperature exposure. Thus, an operating temperature limit close to Tg (60°C)

would be reasonable for this application. Therefore, this finding supports the ACI

4402R-08 limit of Tg – 15 °C for maximum service (operating) temperature for FRP (Xian,

Karbhari 2007, Luo, Wong 2002). On the other hand, in a fire scenario, temperatures

increase rapidly and thus correspond more closely to the transient temperature test

conditions. Additionally, loads in a fire are not expected to be at ultimate conditions

because the maximum loading condition is not expected to occur at the same time as a

fire. Typically, the expected loads in a fire are at the service load level or lower (ULC

S101-07). For service load levels, the stresses in the FRP would be approximately 20 to

30% of ultimate. At these low stress levels, the FRP-concrete bond may be structurally

effective at temperatures as high as 200 to 250°C.

82

3.4.4 Summary bond tests

• Testing was performed to evaluate the behaviour of FRP concrete bond at

elevated temperatures. Based on the results of these tests, the following

conclusions can be drawn,

• FRP concrete bonds are sensitive to elevated temperatures and there has been a

50% loss of strength at temperature 40°C above glass transition temperature of

the adhesive.

• Widely accepted rule of ignoring the FRP contribution to carrying capacity once

it reaches Tg is safe and conservatively accounts for the bond behaviour.

• In transient heating cases the FCB could withstand much higher temperatures

than Tg, at 80 % of maximum load this temperature was 150 °C at 10°C/min

heating rate.

• Unlike room temperature debonding failure happens in the adhesive layer rather

than concrete substrate.

• The analytical model presented here is able to describe the mechanical property

degradation adequately.

• Additional testing is required to establish a proper development length of FCB at

higher temperatures.

83

3.5 FRP coupon tests and FOS results

To investigate the mechanical behaviour of carbon fibre reinforced polymer CFRP

material at elevated temperatures, two different types of tests were considered. Four

samples were tested under a steady-state regime and one sample was tested in a

transient regime (Table 3-7) as described in section 3.4. The mechanical behaviour of the

FRP at higher temperatures is dependent on the behaviour of both constituents, i.e. resin

and fibre. The mechanical properties of the resin degrade drastically at a temperature

known as the glass transition temperature (Tg) which is usually between 50 to 120˚C.

Since the FRP may experience significant loss in its mechanical properties near Tg,

steady-state tests were conducted at Tg, Tg +20 and Tg -20 °C (Table 3-7).

Table 3-7 Specimen information and test regime.

Specimen ID

Test Regime Temperature (˚C) Load Level (kN)

1.1 Steady-State 20 1.2 Steady-State Resin Tg (110) 1.3 Steady-State Resin Tg – 20 (90) 1.4 Steady-State Resin Tg + 20 (130)

2.1 Transient 60 % of ultimate (54.6)

Samples were exposed to heating in the middle of the sample; the heated length was

approximately 300 mm. The temperature variance in the furnace was less than ±5˚C. The

rate of temperature increase was 10˚C/min for all steady-state tests. The same rate was

84

used in the transient tests, but to achieve more stable reading by the FOS, temperature

was kept constant for approximately 5 minutes at 100 and 200˚C. Load was applied at a

constant rate of 2.5 mm/min in all tests. To prepare more stable reading situations for

FOS in steady-state tests, load was kept constant for approximately 5 minutes at some

load levels of 20, 40, 60, 70, 75 and 80 kN.1

Figure 3-456: CFRP coupon dimensions and fibre optic sensor location (all dimensions in

mm).

3.5.1 Instrumentation

The important variables were axial deformation and strain, load in the CFRP specimen,

and finally temperature of the furnace. Load was captured by the internal load cell of the

Universal Testing Machine (UTM). Temperature was recorded by two type K

1 Not all load levels were used for all the tests.

700

50 25 FOS

Protection

CFRP tabs

85

thermocouples located inside the furnace. The thermocouple readings were in

agreement with furnace’s target temperature.

The axial strain of FRP samples was measured using particle image velocimetry (PIV)

(White et al. 2003). High resolution images were taken during various stages of the test

procedure. PIV is capable of tracking the movement of any pixel patches in a sequence

of images. This allows for measuring the displacement field in the sample during the

test. To measure the axial strain, the displacement of pixel patches similar to those in

Figure 3-46 were tracked. The difference in axial displacement of the patches divided by

their axial distance gives the strain in that direction. Figure 3-48 shows a sequence of

pictures taken during the transient test. Since the PIV analysis tracks the pixel pattern

around a certain point, difficulties arise when the surface texture changes due to thermal

effects.

Figure 3-467 Square pixel patches on FRP sheet used in PIV analysis (yellow squares).

Pixel Patches

86

Figure 3-478 Damage progress during test for specimen 2.1. Temperatures are 28, 77, 183, 200, 210 and 256 ˚C from left to right. SBS-based2 FOSs were installed on the specimen along their longitudinal axis of

symmetry as shown in Figure 3-46. The fibre was attached to the FRP sample at the ends

using epoxy glue. The glued parts were kept outside the furnace. To further protect the

bond between FOS and the coupon, a protective cover was placed on top of the glued

fibre (Figure 3-49).

2 SBS stands for stimulated Brillouin scattering.

87

Figure 3-489 Fibre optic sensor and protective cover installation details.

3.5.1.1 Results

Based on dynamic mechanical analysis (DMA) tests on the FRP material, Tg was

determined to be 110˚C. Figure 3-50 shows a sample FOS reading from specimen 1.1.

Figure 3-49 OTDR style curve shows the reflectivity along the fibre length and the right

side curve is a 3-D (top view) of the fibre section under stress. These curves are obtained

88

from specimen 1.1.

PIV analysis was performed to calculate the strain at several load levels for the test

sample 1.1. Knowing the load level and the sample dimensions, these strain values were

used to calculate the secant elastic modulus as reported in Table 3-8. Table 3-9 shows

the results of the steady-state tests. No significant loss of strength was observed in tests

performed at temperatures below Tg. The elastic modulus as reported by the

manufacturer is 165 GPa which is in good agreement with the obtained results.

Figure 3-52 shows the secant modulus versus temperature during the transient test. The

modulus of the material decreases as the temperature rises. The rate of reduction

increases dramatically just above the glass transition temperature (110 ˚C).

Table 3-8 Modulus calculation results for room temperature test at different load levels;

strain is calculated using PIV analysis.

Load (kN) Strain PIV Stress (MPa) Secant Modulus (GPa) 40 0.92% 1388 151 60 1.32% 2082 158 80 1.70% 2777 163

89

Table 3-9 Steady-state tension test results for FRP at high temperature.

Specimen ID Temperature (˚C)

Width (mm)

Peak load (kN)

Strength (MPa)

Strength Loss %

1.1 27 24.0 81.6 2830 0.0

1.2 110 24.0 73.1 2540 11.6

1.3 90 24.6 82.1 2780 0.7

1.4 130 23.4 55.3 1970 47.5

Figure 3-50 CFRP specimen 2.1, transient test, before and after the test.

Figure 3-51 Secant modulus for specimen 2.1 vs. temperature.

1.65

1.70

1.75

1.80

1.85

0 50 100 150 200

Seca

nt E

last

ic M

odul

us

(GPa

)

Temperature (˚ C)

90

A comparison between strain readings using PIV method and FOS readings are

presented in Figure 3-53 to Figure 3-56. Since the FOS readings were taken only at

constant load levels the strain readings from FOSs are discontinuous. As is evident in

these figures strain readings from FOSs match the PIV results (with a maximum error of

13%) and FOSs could be used as a reliable strain measurement technique at high

temperature testing. Currently, since the FOS is not refined for commercial purposes

strain readings are very labour intensive especially at post processing stage. Having said

that, FOS has advantages over PIV method, where charring happens at the surface of the

specimen (Figure 3-55 ).

02000400060008000

1000012000140001600018000

0 5 10 15 20 25 30

Stra

in

Time (min) strain FOS (με)

strain PIV (με)

91

Figure 3-523 Comparison of strain reading using PIV method (dotted line) and FOS

(solid lines) specimen 1.1 at room temperature.


(solid lines) specimen 1.3 at 90°C.

-5000

0

5000

10000

15000

20000

25000

20 30 40 50 60

Stra

in

Time (min)

strain FOS (με)

strain PIV (με)

92



02000400060008000

1000012000140001600018000

0.0 10.0 20.0 30.0 40.0 50.0 60.0

Stra

in


strain PIV (με)

93



0

2000

4000

6000

8000

10000

12000

14000

16000

0 10 20 30 40 50

Stra

in


strain PIV (με)

95

Chapter 4: Numerical heat transfer simulation

High temperatures cause severe damage to concrete, steel, and FRP. Therefore,

predicting the temperature distribution in a structural member is a crucial step in

understanding the behaviour of the member. A major challenge is the simulation of the

concrete behaviour due to its complicated chemical and structural composition.

Portland cement paste may undergo various changes such as dehydration, porosity

increase, thermal cracking, spalling and many others. Several models have been

proposed for hygrothermo-mechanical simulation of concrete. Some existing models

account for a coupled field heat and mass transfer problem. These models are capable of

predicting temperature and pore pressure during exposure to elevated temperatures

(Gawin, Majorana et al. 1999, Mounajed, Obeid 2004). If only temperatures are required,

several simplifications can be made, which lead to the solution of a de-coupled field

equation. The following assumptions are usually made for decoupling the problem:

- Temperature of the fluid and the solid are the same at each point

- The amount of heat transferred by mass diffusion is negligible

- Evaporation of chemically and physically bound water is negligible (Capua, Mari

2007).

96

Even more simplified methods for predicting temperature distribution in a concrete

section which use a pre-determined temperature variation in the concrete section are

available (Wickstrom 1986, Malhotra 1982). Although these methods provide a

reasonable approximation in some problems, they are not suitable for complex

geometries.

4.1 Finite volume formulation

The model developed here is a finite-volume (FV) code that is capable of predicting

temperature in an insulated concrete section; refer to (Patankar 1980) for further

information on the finite volume method.

The partial differential equation of heat conduction can be expressed as (Arpaci, Arpaci

1966)

𝜌𝑐 𝜕𝑇𝜕𝑡

= ∇. (𝑘∇𝑇) = 𝜕𝜕𝑥�𝑘 𝜕𝑇

𝜕𝑥� + 𝜕

𝜕𝑦�𝑘 𝜕𝑇

𝜕𝑦� (4-1)

where 𝑘 is thermal conductivity, 𝜌 is density, 𝑐 is heat capacity, T is temperature, t is

time, and x and y are spatial coordinates. In general, k and c.ρ are functions of

temperature and spatial variables. Explicit discretization in time domain is

ii

yTk

yxTk

xtTc

∂∂

∂∂

+∂∂

∂∂

=

∂∂ )()(ρ ( 4-2)

[ ]iii

i

yTk

yxTk

xtTTc

∂∂

∂∂

+∂∂

∂∂

=∆−+

)()(1

ρ ( 4-3)

97

Where the spatial discretization and material properties belong to the current time step

i.e. t=ti. In spatial discretization , the integral form of the heat equation is obtained by

using the Gauss theorem:

∫∫ =∇SV

dSdV n.FF. ( 4-4)

dRTkdRtTc

RR∫∫ ∇∇=

∂∂ ).(ρ ( 4-5)

Applying Gauss theorem

∫∫∫∫ ∂∂

=∇=∇=∇∇CCCR

dCnTkdCTkdCTkdRTk )().().().( nn ( 4-6)

∫∫ ∂∂

=∂∂

CR

dCnTkdR

tTc )(ρ (4-7)

Figure 4-1 Spatial discretization.

pl r

d

u

ld rd

rulu

98

For a two-dimensional rectangular grid (Figure 4-1), the discretized field equation is,

∫∫ ∂∂

=∂∂

CR

dCnTkdR

tTc )(ρ ( 4-8)

∫∫∫∫∫−−−− ∂

∂+

∂∂

+∂∂

+∂∂

=∂∂

rulu udurd rluld lrdld dp

dxnTkdx

nTkdx

nTkdx

nTkdxdy

tTcρ ( 4-9)

∫∫∫∫∫−−−− ∂

∂+

∂∂

+∂∂

−∂∂

−=∂∂

rulururdluldrdldp

dxyTkdy

xTkdy

xTkdx

yTkdxdy

tTcρ ( 4-10)

xyTky

xTky

xTkx

yTkyx

tTc

puprplpdp

∆

∂∂

−∆

∂∂

−∆

∂∂

−∆

∂∂

−=∆∆

∂∂ρ ( 4-11)

xyTT

kyxTT

kyxTT

kxyTT

kyxtTc pu

pupr

prlp

pldp

pdp

∆∆

−+∆

∆

−+∆

∆

−−∆

∆

−−=∆∆

∂∂ρ ( 4-12)

+=

dp

dppd kk

kkk

2or

+=

2dp

pd

kkk both for uniform grid (Patankar 1980),

Finally finite volume discretization equations will be

[ ]i

pupu

prpr

plpl

pdpd

ip

ipi

p xyTT

kyxTT

kyxTT

kxyTT

kyxt

TTc

∆

∆

−+∆

∆

−+∆

∆

−+∆

∆

−=∆∆

∆

−+1

ρ (4-13

)

99

Figure 4-2 Descritization and effective length for different finite volumes

Accounting for Convection and Radiation Boundary Conditions explicit discretization

is, Figure 4-2,

[ ]

⋅∆−+∆−+∆∆

−+∆

∆

−

+∆∆

−+∆

∆

−=∆∆

∆

−+

cip

iacr

ip

ifre

ip

iui

pue

ip

iri

pr

e

ip

ili

ple

ip

idi

pdee

ip

ipi

p

LTThLTThxyTT

kyxTT

k

yxTT

kxyTT

kyxt

TTc

)()(

1

ρ ( 4-14)

Where hr and hc are radiation and convection heat transfer coefficients, by

assuming,

−𝑎p0 = [ρc]pi∆xe∆ye∆t

(4-15)

1 2 3

4

100

yx

ka eipdd ∆∆

=0 xy

ka eipll ∆∆

=0 xy

ka eiprr ∆∆

=0 yx

ka eipuu ∆∆

=0 ( 4-16)

We have,

⋅∆−+∆−

+−+−+−+−=−+

cip

ic

icr

ip

if

if

ip

iuu

ip

irr

ip

ill

ip

idd

ip

ipp

LTThLTTh

TTaTTaTTaTTaTTa

)()(

)()()()()( 000010

( 4-17)

assuming

𝑎∗0 = −�−𝑎p0 + 𝑎d0 + 𝑎l0 + 𝑎r0 + 𝑎u0 + ℎfi∆Lr + ℎci ∆Lc� (4-18)

𝑏0 = ℎfi𝑇fi∆Lr + ℎci 𝑇ci∆Lc (4-19)

By rearranging the equation,

⋅+++++=+ 0000000*

10 bTaTaTaTaTaTa iuu

irr

ill

iddp

ipp ( 4-20)

𝑇𝑝𝑖+1 = �𝑎∗0𝑇𝑝𝑖 + 𝑎𝑑0𝑇𝑑𝑖 + 𝑎𝑙0𝑇𝑙𝑖 + 𝑎𝑟0𝑇𝑟𝑖 + 𝑎𝑢0𝑇𝑢𝑖 + 𝑏0� 𝑎𝑝0� ( 4-21)

Where 𝑇𝑝𝑖+1 is the temperature at point p at time step 𝑡 = 𝑡𝑖+1.

4.1.1 Stability criterion

The explicit finite volume method is not unconditionally stable (Patankar 1980); that is, if

the time step is larger than a specific limit then the order of magnitude of errors are

comparable to the magnitude of the variables. Although the method can be

101

mathematically convergent, it presents no physically meaningful results. Therefore, the

largest permissible value of the time step is limited by the stability criteria given by the

equations below. These equations were determined based on the theory described in

(Cengel, Klein et al. 1998) and (Lie 1992). The stability criteria are satisfied if 000* >paa .

The radiation heat flow can be estimated using

)( 44pfcf TTq −= εσε ( 4-22)

where σ is the Stefan-Boltzmann constant, and εf and εc are the emissivities of fire and

concrete respectively, for the ease of iterative programming the following manipulations

could be done.

))()(( 22pfpfpfcf TTTTTTq −++= εσε (4-23)

)( pfr TThq −= (4-24)

))(( 22pfpfcfr TTTTh ++= εσε (4-25)

4.1.2 Free convection

The amount of free convection heat transfer rate from a horizontal plate when the hot

surface is upward is calculated from following equation.

)( pac TThq −= (4-26)

Where the convection heat transfer coefficient is

102

LkNu=hc. (4-27)

𝑁𝑢 = 𝑐(𝐺𝑟.𝑃𝑟)𝑛𝑙 (4-28)

in which Pr is the material property of air. Pr is a temperature dependant property, and

n and c are given in Table 4-1 for laminar and turbulent convection over heated surface.

Gr is readily calculated as

as

ap

+TT)L-Tg(T

Gr=2

3

ν ( 4-29)

in which Ta and Tp are the air and surface temperatures respectively and L is the

representative length of the surface, g is the acceleration of gravity and ν is the dynamic

viscosity of air which is temperature dependent (Bayazıtoğlu, Özışık 1988).

Table 4-1 Coefficients for laminar and turbulent free convection (Bayazıtoğlu, Özışık

1988).

c n laminar 0.54 1/4 Turbulant 0.14 1/3

4.1.3 Moisture effect

This model assumes there is no moisture migration. The effect of moisture in simulation

would be the increase in heat capacity of moist concrete and also the amount of heat

103

absorbed when the temperature reaches the boiling temperature of water. The former

can easily been accounted by changing the heat capacity of moist concrete as follows

( ) ( ) ( )wcmc ccc ρϕρρ += (4-30)

where,

( )mccρ the density and heat capacity of moist concrete

( )ccρ the density and heat capacity of dry concrete

( )wcρ the density and heat capacity of water

𝜑 volume fraction of moisture with respect to concrete

The evaporation of water needs to be treated more carefully, especially because this

approach may be grid/mesh dependent.

Following the notation used before, for a concrete element with the average moisture

content of pϕ the energy balance would be as

[ ]

⋅∆−+∆−+∆∆

−+∆

∆

−

+∆∆

−+∆

∆

−=∆∆

∆

−+

cip

iacr

ip

ifre

ip

iui

pue

ip

iri

pr

e

ip

ili

ple

ip

idi

pdee

ip

ipi

p

LTThLTThxyTT

kyxTT

k

yxTT

kxyTT

kyxt

TTc

)()(

1

ρ (4-31)

In this case [ ]ipcρ is the properties of moist concrete at time t=ti.

The right hand side in above equation is the amount of entering heat/energy rate so

104

⋅∆−+∆−+∆∆

−

+∆∆

−+∆

∆

−+∆

∆

−==

cip

iacr

ip

ifre

ip

iui

pu

e

ip

iri

pre

ip

ili

ple

ip

idi

pdin

LTThLTThxyTT

k

yxTT

kyxTT

kxyTT

kE

)()(

rateenergy Entering

(4-32)

⋅∆−+∆−

+−+−+−+−=

cip

ic

icr

ip

if

if

ip

iuu

ip

irr

ip

ill

ip

iddin

LTThLTTh

TTaTTaTTaTTaE

)()(

)()()()( 0000 ( 4-33)

⋅∆+∆

+∆+∆++++−+++=

ci

cicr

if

if

ipc

icr

ifurld

iuu

irr

ill

iddin

LThLTh

TLhLhaaaaTaTaTaTaE )( 00000000 ( 4-34)

000*

0000 )( bTaaTaTaTaTaE ipp

iuu

irr

ill

iddin ++−+++=

(4-35)

[ ]tyx

ca eeipp ∆

∆∆= ρ0

yx

ka eipdd ∆∆

=0 xy

ka eipll ∆∆

=0 xy

ka eiprr ∆∆

=0 yx

ka eipuu ∆∆

=0 (4-36)

)( 000000* c

icr

ifurldp LhLhaaaaaa ∆+∆++++−= (4-37)

ci

cicr

if

if LThLThb ∆+∆=0 (4-38)

The mass of water in the form of moisture in the element is equal to

)1( ×∆∆== eeipwwww yxVm ϕρρ (4-39)

Introducing Lh latent heat of water vaporization the amount of heat needed to evaporate

all the water will be

105

)1( ×∆∆== eeipwhwhevp yxLmLE ϕρ (4-40)

The amount of the heat needed to increase the element’s temperature to 100° C is

[ ] ( )

><×∆∆−

=CTCTyxTc

E ip

ipee

ip

ip

10001001100

100

ρ. (4-41)

noting that [ ] ipcρ is the property for moist concrete.

If in step i the representative temperature of the element , Tp, 3 is below boiling

temperature of water i.e. 100° C and the amount of entering heat is enough to increase

the elements temperature to 100° C the excess heat will instead cause the moisture to

evaporate and meanwhile this keeps the temperature constant and equal to 100° C.

Based on the preceding scenario one the following cases will happen,

1- 100EtEE inin <∆= ,the element’s temperature is below 100° C and the amount of

entering heat is not enough to increase the temperature to 100° C which is

obviously does not change the previous formulation.

3 This temperature is not necessarily the temperature at point p and it should represent the thermal capacity of the whole element.

106

2- evpin EEEE +<< 100100 , the element’s temperature is below or equal to 100° C and

the amount of entering heat is more than the required energy to increase the

temperature to 100° C. In this case the excess heat will cause the moisture to

evaporate and meanwhile this keeps the temperature constant and equal to

100°C until all the moisture evaporates. The moisture volume fraction at the end

of the current step would be,

ϕϕϕ ∆+=+ i

pip

1 (4-42)

[ ]11

/)(1

/ 100100

×∆∆−∆

−=×∆∆

−−=

×∆∆∆

=∆

=∆eehw

in

ee

whin

ee

ww

e

w

yxLEtE

yxLEE

yxm

VV

ρρρϕ

(4-43)

In a case that the element's temperature is equal to 100° C, 0100 =E and we have,

1×∆∆∆

−=∆eehw

in

yxLtE

ρϕ

. (4-44)

3- evpin EEE +> 100 , the amount of entering heat will evaporate all the moisture, so

01 =+ipϕ , and the temperature will reach a value larger than 100° C.

[ ] evpineei

pi

pip EEEyxTTc −−=×∆∆−+

1001 1)(ρ ( 4-45)

[ ] 11001

×∆∆

−−+=+

eeip

evpinip

ip yxc

EEETT

ρ, (4-46)

107

[ ] 11001

×∆∆

−−∆+=+

eeip

evpinip

ip yxc

EEtETT

ρ

(4-47)

Noting that [ ] ipcρ here is the properties of dry concrete. Similar to case 2 if the

initial temperature is 100°C then

[ ] 11

×∆∆

−∆+=+

eeip

evpinip

ip yxc

EtETT

ρ

(4-48)

4.1.4 Verification

The model developed here is used to simulate a rectangular concrete section similar to

the one tested by (Lie, Woollerton 1988); the column is subjected to the ASTM E119

standard fire from all four sides. The cross-sectional dimensions of the section are 305 by

305 mm. The model prediction is compared with measured temperatures in Figure 4-3.

Three points A, B, and C with concrete covers of 6, 63, and 152 mm, respectively, are

selected for comparison. For point A (near the surface), the model predicts the

experimental results with a maximum deviation of approximately 50 °C up to just over

400 °C. At that point, larger discrepancies are noted, but the predicted temperatures are

higher than those measured in the test. For points B and C, the temperatures are

underestimated at the early stages (below 100 °C) and then slightly overestimated

afterwards. These discrepancies near 100 °C occur because the model does not account

for moisture migration away from the heated surface. Sources of error could be because

108

of concrete spalling, inaccuracy in measuring the thermocouple location, inability to

follow ASTM temperature curve during the test and inaccuracy or incompatibility of the

material models and numerical errors.

Figure 4-3 Predicted and measured temperatures as a function of exposure time for

different depths within the concrete specimen (experimental data obtained from (Lie,

Woollerton 1988).

4.2 Model results for slabs and T-beams

Two different insulation thicknesses were used in slab A and slab B. Figure 4-4

illustrates a comparison between model results and test data. Temperatures from the

unexposed surface and FRP concrete interface are compared. The model predicts the

temperature at the unexposed surface with a maximum discrepancy of 5 °C. For the

temperature at the FRP concrete interface, the model prediction is not quite as close to

109

the measurement. Once again the discrepancy occurs close to 100 °C and is related to the

lack of modelling moisture migration. The maximum deviation between the prediction

and the measured results is approximately 25 °C.

Figure 4-5 shows the temperature calculation from the model compared to temperatures

measured in fire tests for the T-beams. The dotted line is the average of temperatures

obtained from beam-A and beam-B. The model successfully predicts temperatures on

the longitudinal steel and FRP/concrete interface, which are crucial to predicting the

structural behaviour of the strengthened member. The model is conservative in that it

predicts higher temperatures than those measured in the tests. The maximum error in

predicting steel temperature is 13 °C; see Figure 4-6. This error is within the range of

experimental results obtained from 12 thermocouples installed at various locations

along the longitudinal steel. Figure 4-7 compares the model error with standard

deviation of measured data. This figure demonstrates the discrepancy between

modelling and measurement is within the observed experimental error. Thus, the model

is sufficiently accurate.

110

Figure 4-4 Predicted and measured temperatures as a function of exposure time for slabs

at, (a) unexposed surface slab-A (40 mm insulation thickness), (b) FRP-concrete interface

slab-A, (c) unexposed surface slab-B and (d) FRP-concrete interface slab-B.

111

Figure 4-5 Predicted and measured temperatures vs. exposure time for T-beams at (a)

unexposed surface, (b) on the centreline with concrete cover of 155 mm, (c) longitudinal

steel, and (d) FRP-concrete interface.

112

Figure 4-6 Measured steel temperature (mean ±1 standard deviation) compared to

predicted temperature.

Figure 4-7 Steel simulation temperature erorr compared to standard deviation of

measured temperature.

113

4.3 Finite element simulation using ABAQUS

In order to compare finite volume (FV) results with a finite element (FE) simulation, 2D

and 3D models were simulated using the commercially available finite element package

ABAQUS. Experimental data from fire test of a recangular RC column from (Lie,

Woollerton 1988)) is compared against FV and FE simulations in Figure 4-9. Figure 4-8

shows the temperature contour inside the column at t=180 min.

Figure 4-8 Temperature contour from FE simulation at the cross section of the recangular

column after 180 min of standard fire exposure (temperatures in °C ).

114

Figure 4-9 Predicted temperatures for different depths within the concrete specimen

using FV and FE simulations (experimental data obtained from (Lie, Woollerton 1988).

Figure 4-10 compares the 3D FE and 2D FV predictions vs. experimental values for T-

beam-A at bottom steel after 4 hours of standard fire exposure. It is clear that 2D FV

predictions are very close to 3D FE predictions. Figure 4-11 gives the isotherms for T-

Beam-A. Thus, for this problem, 2D simulations appear to be sufficient.

115

Figure 4-10 FE results vs. FV and experimantal results. Temperature is measured at the

bottom longitudinal bar of T-beam A.

0

50

100

150

200

250

0 60 120 180 240

Tem

pera

ture

(˚C

)

Time (min)

FE Abaqus

FV Model

Test Data

116

Figure 4-11 3D temperature isotherm surfaces from FE simulation at the cross section of

T-Beam-A after 240 min of standard fire exposure (temperatures in °C ).

4.4 Different fire scenarios

Although standard fire curves are widely used for determining the fire resistance of

structural members, the intensity and duration of building fires may vary widely.

Several parameters such as amount of combustible material and ventilation affect the

severity and duration of compartment fires. In some cases, standard fire curves have

serious deficiencies in presenting realistic fire situations (Stratford, Gillie et al. 2009,

117

Leone, Matthys et al. 2009). To investigate the effects of different time temperature

curves on the response of T-beams, four different fire scenarios were selected. Fire time

temperature curves were calculated using the following equation, proposed by (Lie

1992).

𝑇𝑓 = 250(10𝐹)0.1

𝐹0.3� 𝑒−𝐹2𝑡[3(1− 𝑒−0.6𝑡)− (1 − 𝑒−3𝑡) + 4(1 − 𝑒−12𝑡)] + C �600𝐹�0.5

(4-49)

where 𝑇𝑓 is fire temperature, t is time in hours and C is a constant related to the

boundary materials. Different fire loads (Q) and opening factors (F) for different fires

scenarios are given in Table 4-2. Figure 4-12 shows the time temperature curves for Fires

I to IV. Figure 4-13 gives a comparison between actual temperature variation captured in

Dalmarnock fire tests and temperature curves used here. The temperature increase

during the flash-over period is sharper than both ASTM and “FIRE IV” curves, but

temperatures remain below both curves.

Table 4-2 Parameters used to produce fire curves.

𝑭 (√𝒎) 𝑸 (𝒌𝒈/𝒎𝟐) 𝑪 Fire I 0.01 30 0.0 Fire II 0.05 30 0.0 Fire III 0.10 30 0.0 Fire IV 0.10 100 1.0

118

Figure 4-12 Time temperature curves for four different fire scenarios.

Figure 4-13 Time-Temperature curve in Dalmarnock real compartment fire (mean ± 1

standard deviation) in comparison with ASTM standard fire curve and “fireIV” curve

used here(Stratford, Gillie et al. 2009).

119

Figure 4-14 Longitudinal steel temperature in beams subjected to Fires I to IV.

Figure 4-15 FRP-concrete interface temperature in beams subjected to Fires I to IV.

120

According to Figure 4-14, after four hours of exposure to fires I to IV, the longitudinal

steel temperature in all scenarios remains below 250 °C. Under these scenarios, the steel

retains most of its tensile strength after fire exposure (approximately 90 percent). Given

the fact that the temperature of the compression concrete (close to unexposed surface) is

lower than the steel temperature, concrete will suffer negligible losses in strength. As a

result, the reduction in the moment capacity of the un-strengthened section will be

minimal. The predicted strength of T-beams exposed to standard fire is given in

Figure 4-16. These calculations are based on based on CSA A23.3-04 and ACI 318/318R-

08 for reinforced concrete section and CSA S806-02 and ACI 440.2R-08 for FRP

strengthened sections. In the calculation of strength, it is assumed that FRP does not

contribute to moment capacity of the section once FRP-concrete temperature reaches Tg.

The predicted capacity of the section even after 4 h is still larger than the applied service

load. While insulation provides limited protection for FRP in fire situations (less than 30

minutes, Figure 4-15), it plays a major role in protecting the reinforcing steel and

concrete.

121

Figure 4-16 Predicted moment capacity of T-beams exposed to different fire curves and

applied maximum moment during the fire test.

122

4.5 Sample design charts

This section presents temperature predictions based on the numerical model developed

to simulate temperature distribution in a composite concrete-insulation system. A slab

with 150 mm thickness is chosen and temperature-time curves at various locations are

given. The slab is made of normal density concrete and it is exposed to ASTM or ULC

standard fire. The insulation material is SikaCrete-213F. Insulation thicknesses of 20, 30,

40 and 60 mm are chosen for simulation. Temperature curves are given below. These

curves could be used as an estimate to predict the steel temperature inside the slab with

equivalent cover. For example if steel cover (from centre of the bar to fire exposed

surface) is 40 mm and insulation thickness is 30 mm, Figure 4-20 should be used. This

temperature can be used to estimate the residual strength of the reinforcing steel.

Figure 4-24 gives the unexposed surface temperatures for various insulation thicknesses.

This value should be compared with requirements of the fire code. Since the unexposed

surface temperature represents the compression concrete temperature, the reduction in

concrete strength could also be estimated.

123

Figure 4-17: Temperature vs. exposure time at FRP-concrete interface for different

insulation thicknesses (Depth is insulation thickness in mm).

20

60

100

140

180

220

260

300

340

380

0.0 30.0 60.0 90.0 120.0

Tem

pera

ture

(˚C

)

Time (min)

FRP- Con Ins. Depth 60,




124


insulation thicknesses.

20

40

60

80

100

120

140

160

180

200

220

240

0.0 30.0 60.0 90.0 120.0

Tem

pera

ture

(˚C

)

Time (min)

cover 20, Ins. Depth 60,




125



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100

120

140

160

180

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220

0.0 30.0 60.0 90.0 120.0

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)

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126



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127



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128



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129



20

40

60

80

100

120

0.0 30.0 60.0 90.0 120.0

Tem

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ture

(˚C

)

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130

Figure 4-24: Temperature vs. exposure at unexposed surface of concrete slab (thickness

150 mm) for different insulation thicknesses (Depth is insulation thickness in mm).

20

25

30

35

40

45

50

55

60

0.0 30.0 60.0 90.0 120.0

Tem

pera

ture

(˚C

)

Time (min)

Unexposed surface Ins. Depth 60,




131

4.6 Summary

The preceding chapter presented procedures and results of the model developed to

simulate the thermal behaviour of FRP-strengthened concrete beams and slabs exposed

to fire. The heat transfer model was verified against the results of fire endurance tests on

concrete columns and beams available in literature and the results of the fire tests

presented in this thesis. Furthermore the results of the FV model developed here were

compared with the predictions of finite element method. Also the 2D and 3D finite

element simulations were performed using the commercially available FEA package

ABAQUS. The comparison of 2D and 3D simulations proved that 2D models adequately

simulate the thermal behaviour of flexural members. Parametric analyses were

performed using the FV model to understand the behaviour of the insulated beam under

different fire scenarios. These simulations showed the level of effectiveness and

reliability of the insulation system. Structural failure of the beam was investigated using

the temperature predictions of the thermal model to showcase the capability of the

model. And finally sample design charts were developed to be used for the design of

concrete slabs with varying insulation thicknesses.

133

Chapter 5: Structural modelling

5.1 General

The object of the mechanical model is to determine the strain and stress distribution at

all the points inside the specimen and to also calculate the deformations under load. In

an uncoupled field problem, the mechanical behaviour of the materials can be

determined using the temperature history at different points of the member. Material

properties parameters at high temperature for concrete, steel and FRP are discussed in

Chapter 2 and Appendix C.

Previously, Bernoulli’s hypothesis has been used in a simplified model for

determination of mechanical behaviour ((Blontrock, Taerwe et al. 2000, Kodur, Dwaikat

2007, Williams 2004, Capua, Mari 2007, Ahmed, Kodur 2011), which satisfactorily

predicts member behaviour. Cai, Burgess et al. (2003) developed a generalized steel/RC

beam column element model for fire conditions, which accounts for large deformation

which produces a better prediction; see also (Bratina, Čas et al. 2005). Pearce, Nielsen et

al. (2004) used a damage model to model thermal and mechanical damage of the

concrete in fire.

Since the final deformations of the beam are small compared to the size of the structure,

using the simplified Euler-Bernoulli beam seems reasonable for the structural

134

simulation. The main assumptions required for defining the relation between forces and

strains in a section are the following:

1. The Bernoulli hypothesis applies (plane sections remain plane during

deformation)

2. The elements have a uniaxial state of stress.

Using these assumptions the ultimate strain at each point inside concrete and steel

element can be determined considering equilibrium of internal and external forces. This

total strain εt can be divided into four components, εσ stress related strain, εthermal

unconstrained thermal strain, εtransient the transient creep strain or load induced thermal

strain and εcreep time dependant creep strain.

εt = εσ +εthermal +εtransient +εcreep (5-1)

Thermal strain can be simulated as, [ ]θε mthermal = , where [ ] ( )Tm 000111α= ,

following Voigt notation. α is the thermal expansion coefficient of concrete; see

Figure 5-1.

135

Figure 5-1 Free thermal strain vs temperature for various concretes from EuroCode 2.

In an unloaded transient test the concrete specimen will expand by increase in

temperature (εthermal). The strain in a loaded case is significantly different (excluding the

elastic deformation). This difference is called “transient creep” or “load induced thermal

strain” and only happens during the first heating of concrete;(Schneider 1988, Khoury,

Grainger et al. 1985, Thelandersson 1987). This irrecoverable strain has a critical effect in

the response of heated member because it may result is severe tensile forces in the

member. The model used by Williams (2004) did not address transient strain in the

structural model. While there are different models proposed to simulate this transient

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

0 200 400 600 800 1000 1200 1400

Free

ther

mal

stra

in

Temperature (°C)

Siliceous

Calcareous

136

effect, Pearce, Nielsen et al. (2004) gives a three dimensional formulation that can be

implemented in finite element simulations.

A similar formulation is used for steel elements except for the fact that there is no

transient creep strain in steel so the stress component for steel would be

εt = εσ +εthermal +εcreep (5-2)

Likewise for FRP elements, the total strain is discretized as thermal mechanical and

creep although the important factor in simulation of a strengthened beam is the

behaviour of bond between FRP and concrete. In the current model experimental results

from bond test performed as a part of this research has been implemented in the model

to account for the behaviour of the FRP- concrete bond.

5.2 Generating moment-curvature curves

Knowing the temperature and external loading on the beam i.e. axial forces and loading

history at any section (residual transient strain components), moment curvature M-κ

diagrams are created at each time step anywhere in the beam as demonstrated in Figure

5-2.

137

Figure 5-2 Strain compatibility and load equilibrium at a typical section of the T-beam.

In order to calculate a point in the M-κ curve, a value for curvature is selected, and an

initial guess for the strain at top fibre of the concrete is chosen. At this point knowing the

curvature and the strain at top concrete fibre, total strain everywhere in the section can

be calculated assuming plain sections remain plain. Once the total strain is found, forces

can be calculated for every element of concrete steel and FRP as discussed previously.

Once the stresses are calculated, forces are summed up in the section. If the equilibrium

criterion is satisfied (i.e., F_ext=Cc+Cs+Ts+Tfrp see Figure 5-2 above), then the assumed

strain at the top fibre is correct. If equilibrium is not satisfied, then an iterative

procedure is employed until convergences is obtained. The resisting moment is then

derived from the forces and stress in the section to determine a point in the M-κ curve.

Similarly, coordinates of different points are calculated using different curvature values.

5.3 Beam analysis

In order to determine the deflection of the beam and stresses during fire exposure, the

beam is discretized into segments longitudinally. After mesh sensitivity analysis number

138

of longitudinal segments were chosen to be 21. For each segment at each time step, the

temperature field is first determined. Using the results of thermal analysis, M-κ curves

are calculated for each segment of the beam at every time step. Knowing the external

load distribution, M-κ curves at each time step are used to calculate the deflection of the

beam.

5.4 Verification

In order to verify the strength model, four different fire exposed beams were chosen.

Two of them were RC beams reinforced with steel bars and the other two were RC

beams strengthened with steel reinforcing bars inside and externally reinforced by FRP.

Subsequently the model results are compared with the experimental results of T-beams

exposed to fire conducted in this study.

5.4.1 RC Beam 1 (typical RC beam)

In this section results from thermal and strength model is compared to the results of

Dwaikat and Kodur’s Model (Dwaikat, Kodur 2008). Material properties and

dimensions of the beam are tabulated in Table 5-1 below. Beam is subjected to ASTM

E119 Standard fire.

139

Table 5-1: Properties of the typical RC beam used in the verfication (RC Beam1).

Description Dwaikat et. al.( 2008) Cross section Dimensions 300mm x 500mm Length (m) 6 Top reinforcements 2ɸ14 mm Bottom reinforcement 3ɸ20 mm f'c (MPa) 30 fy (MPa) 400 Applied total load (kN) 120 Concrete cover thickness (mm) 40 Aggregate type Carbonate

To compare the thermal predictions from the current model to Dwaikat et.al. model,

the temperature variation is plotted as a function of fire exposure time at various

locations of the beam cross section in Figure 5-3 below. Solid lines are the predictions of

Dwaikat and the dots are temperature predictions of the current model. The

temperature results match closely with results from (Dwaikat, Kodur 2008). After

temperature comparison the mid-span deflection is compared in both models in

Figure 5-4. Deflection predictions from the two models match closely. Dwaikat et.al.

model predicts slightly higher deflection than the current model after 150 min fire

exposure, while the deflections are lower before 150 min mark. Overall behaviour of the

beam predicted by both models is very similar. The difference between the deflection

predictions of the models vary from 25% where t<120min to less than 10% for t>120 min.

140

Figure 5-3 Time temperature curves data points are from Dwaikat and Kodur 2008 and

lines are results of the current model.

Figure 5-4 Mid-span deflection vs. time, dotted line is from Dwaikat and Kodur 2008

and the solid line is current model.

0

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400

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800

1000

1200

0 60 120 180 240

Tem

pera

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(°C)

Time (min)

Corner barMid depth (center)125 mm from bottomCentrl Rebar375 mm from bottom

0100200300400500600700800900

1000

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Defle

ctio

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m)

Time (min)

ModelKodur 2008Dwaikat and Kodur (2008)

141

5.4.2 RC Beam 2

For further verification of the model the temperature and deflection prediction of the

model is compared with experimental results of a RC beam tested by(Dotreppe,

Franssen 1985). The dimensions and material properties of the beam are reported in

Figure 5-5 and Table 5-2. The beam is exposed to the ISO 834 fire that is very similar to

the ASTM E119 fire.

Figure 5-5 Details of the cross section and loading for RC Beam 2, Dotreppe (1985).

6500

1625 3250 1625

600

P P

3 12mm

2 12mm

200

600

40

40

27

142

Table 5-2: Description of the typical RC beam used in the verification (RC Beam2).

Description Dotreppe JC, Franssen JM. 1985 Cross section Dimensions 200mm x 600mm Length (m) 6.5 Reinforcements top 2ɸ12 mm Reinforcements bottom 3ɸ22 mm f'c (MPa) 15 fy (MPa) 300 Applied total load (kN) 65 Concrete cover thickness (mm)

40

Aggregate type Siliceous

Temperature prediction of the computer model for the steel rebar located at the bottom

of the beam is compared with the reported temperatures obtained in the experiment

Figure 5-6. The temperature predictions are in good agreement with the test

measurements. The difference in the beginning of the test between predicted and

experimental results are most likely because of moisture migration effect which is not

included in the thermal model. In this section t<40min maximum error is less than 50°C

and for t>40 maximum discrepancy is less than 20°C.

143

Figure 5-6: Tension steel temperature vs. time, dotted line is model prediction and solid

line is the test result.

The predicted and measured mid-span deflections for RC Beam2 are compared in

Figure 5-7. The predicted results are in good agreement with the experimental

measurements (maximum 10 mm deviation).

0

100

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300

400

500

600

0 20 40 60 80 100 120

Tem

pera

ture

(°C)

Time (min)

Steel temp. Model

Steel temp. test

144


the test result.

Results of comparison of the model with other model and experimental results at this

stage indicate that the current model is capable of prediction the thermal and

mechanical behaviour of RC concrete beams exposed to fire. This means the material

models used for simulation of steel and concrete are appropriate and the numerical and

simulation techniques properly capture the physics of the problem.

5.4.3 FRP-RC Beam 1

In previous verification cases the model was used to simulate the behaviour of steel

reinforced RC beams. In order to verify the results of the model for an FRP strengthened

0

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Defle

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Deflection Test

Deflection Model

145

beam, the results of the computer model is compared with the test results for two FRP

strengthened beam tested by (Blontrock, Taerwe et al. 2000). These tests were performed

at the University of Ghent.

The cross-sectional dimensions of the beam were 200 mm by 300 mm and the length was

approximately 3 m. Steel reinforcements were two ɸ10 mm steel bars at top and two ɸ16

mm bars at the bottom. Concrete clear cover of the steel bars was 25mm. There was a

layer of Promat-H insulation over the FRP laminate at the bottom to protect the FRP

from fire. The thickness of the insulation layer was 25mm and it was mechanically

fastened to the beam. One layer of SIKA Carbodur S1012 CFRP plate was attached to the

soffit of the beam for strengthening purpose. The beam was subjected to four-point

bending of 2x38.6kN loads at 1/3 and 2/3 of its span. Aggregate type of the concrete was

siliceous and the 28-day strength was 15MPa. Yield strength of the steel bars was

300MPa. Figure 5-8 and Table 5-3 give an overall description of the dimensions,

reinforcement details, and the loading condition of the beam.

146

Figure 5-8 Details of the cross section and loading for FRP-RC Beam 1, Blontrock (2003).

2850

950 950 950

P P

3150

300

2 10mm

2 16mm

Insulation

200

300

25

30

30

147

Table 5-3. Summary of Properties for FRP-RC Beam1

Description Blontrock 2003 (BV-B-5)

Cross section Dimensions 200mm x 300mm

Length (m) 3150 mm

Reinforcements top 2ɸ10 mm

Reinforcements bottom 2ɸ16 mm

f'c (MPa) 15

FRP SIKA Carbodur S1012

Insulation Promat-H 25mm mechanically attached

fy (MPa) 300

Applied total load (kN) 2x38.6kN at 1/3 and 2/3 of the beam span

Concrete cover thickness

(mm) 25


148



During the test of this beam, debonding of the fibre composite laminate happened very

soon after the start of the fire test, as a result of the premature debonding of glued

protection. A sharp increase in deflection can be observed at 7 minutes after fire starts.

After this point, the beam is unprotected against fire. The test is stopped at 76 minutes

due to excessive deformation of 58 mm in the mid-span. Figure 5-10 shows the model

prediction of the mid span deflection against the experimental measurements.

Maximum discrepancy in the deflection is less than 10% except for first 10 minutes.

0

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0 20 40 60 80 100

Tem

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(°C)

Time (min)

Steel Temp.Test BV-B-5

Model

149


the test result.

5.4.4 FRP-RC Beam 2

Similar to FRP_RC Beam1 cross section dimensions were 200 mm by 300 mm and the

length of the beam was approximately 3 m. Steel reinforcements were two ɸ10 mm steel

bars at top and two ɸ16 mm bars at the bottom. Concrete clear cover was 25mm. There

was a 25 mm thick glued layer of Promatect-100 insulation over a SIKA Carbodur S1012

CFRP laminate. Beam was subjected to four points bending of 2x38.6kN loads at 1/3 and

2/3 of the beam span. Aggregate type of the concrete was siliceous and the 28-day

strength was 15 MPa. Yield strength of the steel bars was 300 MPa. Figure 5-11 and

Table 5-4 give an overall description of the dimensions, reinforcement details, and the

loading condition of the beam.

0

20

40

60

80

100

0 20 40 60 80 100

Defle

ctio

n (m

m)

Time (min)

Test BV-B-5

Model

150

Figure 5-11 details of the cross section and loading for FRP-RC Beam 2, Blontrock (2003).

3000

925 1000 925

P P

3150

300

2 10mm

2 16mm

Insulation

200

300

25

30

30

151

Table 5-4: Summary of Properties for FRP-RC Beam 2.

Description Blontrock 2003 (BV-B-4) Cross section Dimensions 200mm x 300mm Length (m) 3 Reinforcements top 2ɸ10 mm Reinforcements bottom 2ɸ16 mm f'c (MPa) 15 FRP SIKA Carbodur S1012 Insulation Promatect-100 25mm glued fy (MPa) 300 Applied total load (kN) 2x38.6kN at 1/3 and 2/3 of the beam span Concrete cover thickness (mm)

25




0

100

200

300

400

500

0 20 40 60 80 100

Tem

pera

ture

(°C)

Time (min)

Steel temp. testBV-B-4Model

152

Debonding of the insulation happens 19 min after heating starts. The loss of insulation

layer protecting FRP caused subsequent debonding of the FRP laminate and a sharp

increase in the deflection. Figure 5-13 shows the model prediction of the mid span

deflection against the experimental measurements.


the test result.

Results of temperature and deflection predictions of the model match closely with

experimental results from the literature, which proves the accuracy and validity of the

numerical model developed here. Deflections are predicted within 5 mm of the

experimental results.

0

10

20

30

40

50

0 30 60 90 120

Defle

ctio

n (m

m)

Time (min)

Test BV-B-4

Model

153

5.5 Deflections simulation in fire exposed T-beams

Results of thermal modelling for the T-beam have been presented Chapter 4. The goal in

this section is to simulate the mechanical behaviour of the tested T-beams. Using the

temperature results of the heat transfer model as input for the mechanical model and the

boundary conditions of the T-beam, the model can predict stresses, strains and the

deflection of the beam at any point during fire exposure. Having verified the mechanical

model for various RC and FRP strengthened RC beams this could be easily done by

feeding the material properties and the dimensions of the T-beam to the thermal and

mechanical model. Defining the proper boundary conditions is of critical importance

since the existence of the axial restraints during fire could influence the mechanical

behaviour of the test beams. For a simply supported beam with no axial restraint, the

boundary conditions are very easy to define as will be demonstrated in the case of

Beam-C in the following section. However for beams with partial axial restraint, the

implementation of the end conditions is more complicated.

5.5.1 T-Beam C

To simulate the mechanical behaviour of a T-beam with no axial constraint, results from

a fire test for Beam-C reported by Hollingshead (2012) is used. T-beam dimensions and

steel reinforcement details are the same as the T-beams A and B. Beam-C was chosen to

be 400 mm deep, with flange being 1220 mm wide by 150 mm deep. 6-10M bars were

154

placed in the flange and 2-15M bars in the web as tensile reinforcement. A single layer of

(Tyfo SCH-41) CFRP was attached to the soffit of T-beam, the width of the CFRP wrap

was to 100 mm (4”). Both ends of the beam were wrapped with 600 mm (24”) wide

GFRP (Tyfo SEH-51A) U-wraps. The concrete had an average compressive strength of

35.7 MPa measured before the test. WR-AFP insulation (Tyfo-VG) was specified to be

applied over the FRP to a thickness of 13 mm. The insulation covered the entire web and

100 mm (4”) along the bottom of the flange on either side of the web. Limestone course

aggregate with a maximum size of 14 mm and Type I Portland cement were used in the

concrete mix. All 10M bars had yield strength of 460MPa, while the 15M bars had a yield

strength of 406MPa.

During fire test, Beam C suffered only minor insulation loss, occurring after 214 minutes

along the bottom of the web. The beams were subjected to a uniformly distributed

service load of 24.1 kN/m as per CAN/ULC S101-07, which translated into an applied

bending moment of 43.6 kN.m.

Figure 5-14 shows the measured and predicted midspan deflection of Beam-C. The

model results are in good agreement with the experimental results with a maximum

discrepancy of 10 mm. Deformation before t=0 is preheating deflection of the beam due

to applied uniformly distributed load. Heating starts at t=0. The initial sharp increase in

deflection is due to thermal expansion of the heated area of the beam. The discrepancy

between model prediction and the test results at this section (0<t<90min) mostly relates

155

to the unconstrained thermal expansion model used for concrete. The sharp increase in

deflection in the first 30 to 60min slows down once the rate of temperature gradient

increase slows down. The subsequent increase in deflection is mainly due to loss of

strength and decrease in modulus of steel. In less than 60 min FRP-concrete bond

temperature moves far beyond Tg or Tc (refer to section 3.4.2) of the adhesive (epoxy)

and as a result FRP is not carrying any load at this point. This loss in itself translates into

increased deflection of the beam in the first hour of the fire exposure. Of course the

source of this deflection is the differential thermal expansion of the beam, but loss of

FRP-concrete bond allows for this internal force to translate into deflection. In other

word FRP is no longer resisting the thermal expansion. After the first hour, difference

between an FRP strengthened and un-strengthened beam response in terms of

deflections and stresses would be insignificant (provided that they both have the same

insulation layer which is unlikely).

156


the test result.

5.5.2 T-Beam A and B

The exact end forces of the T-beams A and B are not known in terms of the axial

restraint. Also there was no measurement of the axial load during the test due to space

and test apparatus limitations. To simulate these partially restrained T-beams, ,

assumptions must be made for the axial restraining force. To do this, a load-time curve is

determined by trial and error. Figure 5-15 shows the shape of these load-time curves.

Axial load before fire exposure increases from linearly to a value of 100kN as the

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

-90 -60 -30 0 30 60 90 120 150 180 210 240 270

Defle

ctio

n (m

m)

Time(min)

Beam_C_test

Beam_C_Model

157

distributed load increases on the beam. Since the web of the T-beam was restrained in

the test, rotation of the end of the beam under load was prevented and thus an axial load

would be induced. For the next phase (i.e. fire exposure phase), the axial load increase is

set to increase from 0 to 300 kN for different curves. This makes the final axial load 100,

200, 300 and 400 kN for different curves. For simplicity these curves are name using two

numbers for example in “axial-100-200” curve, axial load increases linearly to 100 kN

before fire and the increase after fire is 200 kN which makes the final axial load the sum

of the two numbers i.e. 300 kN. The increases in axial load during the fire are caused by

the restraint of axial expansion due to thermal effects during the fire.

Figure 5-15 Assumed axial load time curves for the T-beams used in the simulation.

0

100

200

300

400

-60 0 60 120 180 240 300

Axia

l Loa

d (k

N)

Time(min)

Axial-100-0

Axial-100-100

Axial-100-200

Axial-100-300

158

Simulation has been performed using the axial load curves shown above. Deflection

results for Beam A and Beam B are shown in Figure 5-16 and Figure 5-17. There are three

phases in this curve. The preloading phase happens at t<0min where there is no thermal

loading and the mechanical load increases from zero to the service load level (super

imposed load). The second phase is the fire exposure phase where the distributed load

on the beam is constant but the beam is subjected to ASTM E119 thermal loading.

Finally, since the beam did not fail under fire loading the service load was increased to

the maximum capacity of the hydraulic jacks to attempt to reach failure during which

ASTM E119 curve was followed for furnace temperature.

Figure 5-16 Mid-span deflection vs. time for T-beam A, dotted lines are model

predictions for deflection assuming different axial loads, solid line is the test result.

0

5

10

15

20

25

30

-60 0 60 120 180 240 300

Defle

ctio

n (m

m)

Time(min)

Model Axial=100-0Model Axial=100-100Model Axial=100-200Model Axial=100-300Beam_A_Test

159

As can be observed in Figure 5-16, the measured deflection for Beam-A from the

experiment (solid line) falls between the “axial-100-100” and “axial-100-200” curves.

Thus, the axial load should follow a curve between “axial-100-100” and “axial-100-200”

curves. In the first phase, there is an increase in deflection due to quasi-static load

increase on the beam. Model predictions match very well with experimental results in

this phase with maximum discrepancies of 2 mm. During the second phase (i.e. fire

exposure) there is a sharp increase in the deflection due to differential thermal

expansion. Both the axial load and unconstrained thermal expansion models used for

concrete have important effects for estimating deflection of the beam in this phase, but

as discussed for Beam C, the effect of the thermal expansion model is likely more

important. In this portion (0<t<60min), the models underestimate deflections by

approximately 2 to 5 mm. As discussed earlier and based on experimental bond test

results presented in Chapter 3 the FRP-concrete bond is completely deteriorated within

the first hour of fire exposure. As could be seen the deflection curve reaches a plateau

after the first hour due to existence of axial load. Similar results could be seen in

Figure 5-17 for T-beam B. In this case choosing “Axial-100-200” for axial load seems

reasonable. As discussed before in Chapter 3 the discrepancy between the displacement

readings for Beam-A and Beam-B is most likely due to measurement errors, otherwise

axial loads for beams A and B should be similar since they have the same dimensions

160

and the materials in both beams are comparable. Again similar to T-beam A, there is a

sharp increase in deflection in the first hour of fire exposure followed by a plateau.

Figure 5-17 Mid-span deflection vs. time for T-beam B, dotted lines are model

predictions for deflection assuming different axial loads, solid line is the test result.

5.6 Different fire scenarios

In order to simulate the behaviour of an insulated T-beam under various fire scenarios,

simulations have been done using different time temperature curves introduced

previously in Chapter 3 i.e. Fire-I to Fire- IV. As a reminder this beam has a layer of WR-

AFP insulation and the thickness of this layer is 13 mm. Temperature predictions for

longitudinal steel are presented in Figure 5-18. In all fire scenarios except for Fire-IV, the

0

5

10

15

20

25

30

-60 0 60 120 180 240 300

Defle

ctio

n (m

m)

Time(min)

Model Axial=100-0Model Axial=100-100Model Axial=100-200Model Axial=100-300Beam_B_Test

161

steel temperature remains below 593°C even after 5 hours of fire exposure. However, the

steel temperature reaches the limiting failure temperature of 593°C in 222 min when the

beam is subjected to Fire-IV. This failure is also evident in Figure 5-19 where the slope of

mid-span deflection becomes very sharp as it approaches t=222 min where the beam

fails. These results suggest that the model could successfully simulate a realistic fire

scenario. Also, the performance of the FRP strengthened concrete beams is adequate for

most fire situations under a range of fire scenarios. Fire IV is very severe and represents

conditions similar to that of a hydrocarbon fire. Even in this severe scenario, the FRP

strengthened beam has a fire endurance of over 3 hours.

Figure 5-18 Longitudinal steel temperatures for Beam-C under different fires.

0

200

400

600

800

0 60 120 180 240 300

Tem

pera

ture

(°C)

Time(min)

Steel Temp. Fire I

Steel Temp. Fire II

Steel Temp. Fire III

Steel Temp. Fire IV

Steel Temp. E119

162

Figure 5-19 Mid-span deflections for Beam-C exposed to different fires, beam fails under

Fire-IV in less than four hours.

5.7 Summary

The preceding chapter presented procedures and results of the model developed to

simulate the structural behaviour of FRP-strengthened concrete beams exposed to fire.

The model is capable of predicting stresses and deflections. The model was verified

against the results of various fire endurance tests from literature. After verifying the

model it was successfully used to simulate the deflections of a simply supported T-

beam. The model then was used to simulate the deflections of the partially restrained T-

beams in fire where the effect of axial restraint was taken into consideration. And finally

parametric analyses were performed using the strength model to understand the

0

50

100

150

200

0 60 120 180 240 300

Defle

ctio

n (m

m)

Time(min)

Deflection Fire I

Deflection Fire II

Deflection Fire III

Deflection Fire IV

Deflection E119

163

behaviour of the insulated beam under different fire scenarios by predicting their

deflections.

165

Chapter 6: Conclusions and Future Research

6.1 General

The main objective of this thesis was to investigate the fire performance of FRP

strengthened RC flexural members through experimental and numerical methods. In an

experimental study, intermediate scale slabs were tested to evaluate the thermal

behaviour of the insulation system. Full scale fire tests were later performed on T-beams

under sustained load in order to realistically simulate the T-beams at fire. This thesis has

also helped obtain a better insight in the bond behaviour of externally bonded FRP

strengthening systems at elevated temperatures. A simplified model was proposed for

FRP-concrete bond strength at high temperature. The model determines the bond

strength degradation at high temperatures. Several innovative techniques such as FOS

and PIV methods were used to measure strain and temperature during the experimental

program. Fibre optic sensors were used in full scale and material tests, and their

accuracy and effectiveness were investigated and compared with other methods. FOS

application in material testing successfully predicted strain at high temperature. A

numerical model was developed in order to trace the thermal and mechanical response

of FRP-strengthened RC beams which takes into account fire, loading and axial restraint

conditions. The model consists of two separate modules: a thermal simulation module

and a structural modelling module. The thermal simulation takes into account radiation

166

conduction and convective heat transfer mechanisms. The underlying numerical

approach for the model is the finite volume method. The mechanical model uses time-

dependent moment-curvature relationships to trace the response of the beam under fire

conditions. The model effectively incorporates several factors such as high temperature

material models, different strain components, FRP concrete bond degradation, and axial

restraint forces.

6.2 Key findings

The main conclusions are:

• With sufficient insulation, FRP strengthened beams and slabs can be safely used

in buildings and structures where fire exposure is a concern, and can achieve fire

resistances of up to 4 hours under exposure to a range of practical fire scenarios.

• Both FOS and PIV sensing systems can be applied for measuring strains at

elevated temperatures.

• FRP to concrete bonds are sensitive to elevated temperatures. There has been a

50% loss of strength at temperature 40 °C above glass transition temperature of

the adhesive.

• New numerical models have been developed that incorporate transient creep

and axial thrust, and have been validated against experimental results.

167

6.3 Detailed conclusions

6.3.1 Fire tests

• Based on the experimental results, none of the slabs or beams failed during the

fire tests, which suggests that with sufficient insulation, FRP strengthened beams

and slabs could be safely used in buildings and structures where fire exposure is

a concern.

• All specimens achieved 4-hour fire endurance according to ASTM E119

specifications.

• The results confirm the vulnerability of the FRP/Concrete bond during a fire.

Results confirm that FRP reached its glass transition temperature in all

specimens in less than 30 min., which means FRP does not contribute to the load

carrying capacity of the beam beyond this point.

• Despite the fact that FRP-concrete bond degrades rapidly even in an insulated

beam, the insulation system used in all cases effectively protected T-beams and

slabs mainly by keeping internal steel temperatures below 250 ˚C.

• Despite initial shrinkage cracks in the insulation, there was no spalling or

debonding of the insulation material in the fire tests. Localized cracking was

observed during the fire tests, which likely caused localized areas to be

susceptible to rapid heat ingress.

168

6.3.2 Bond tests

Based on FRP-concrete bond test results at elevated temperature, the following

conclusions can be drawn.

• FRP to concrete bonds are sensitive to elevated temperatures and there has been

a 50% loss of strength at temperature 40 °C above glass transition temperature of

the adhesive.

• The widely accepted rule of ignoring the FRP contribution to load carrying

capacity once it reaches Tg is safe, and conservatively accounts for the bond

behaviour.

• In transient heating cases the FRP-concrete bond could withstand much higher

temperatures than Tg. For example, at 80 % of room temperature strength, the

failure temperature was 150 °C at a 10C/min heating rate. This was higher than

the Tg=60°C of the adhesive.

• Unlike the room temperature debonding mechanism where failure happens in

concrete substrate, at higher temperatures the debonding face is within the

adhesive layer.

• Bond failure at high temperatures is ductile compared to brittle fracture in

concrete at room temperature.

• The analytical model presented is able to describe the mechanical bond strength

degradation adequately.

169

6.3.3 Material testing and Fibre Optic Sensors

• For FRP coupon testing for tensile strength, no significant loss of strength

occurred at temperatures below Tg, and the CFRP coupons preserved slightly

more than half of their room temperature strength even at temperatures above

their Tg. This residual strength exceeds the strength requirements in most

flexural strengthening applications, provided that adequate bond can be

maintained between the FRP and concrete.

• Results showed that PIV analysis is a convenient and accurate method of strain

measurement, but the analysis will not be suitable where the surface texture of

the material is damaged.

• Fibre optic sensors used in the experiments successfully predicted the strain at

high temperatures and matched the PIV strain measurements. Thus, FOSs are

suitable for high-temperature strain measurements.

• The computational cost of PIV strain measurement (where applicable) is

considerably lower than FOS method.

6.3.4 Numerical models

6.3.4.1 Heat transfer models

• The two-dimensional FV thermal model, developed in this thesis, is capable of

predicting internal temperature in insulated concrete beams with adequate

170

precision. Model predictions were verified using existing test data from the

literature for RC and insulated members. The crucial steel temperature was

predicted with a maximum error of ±13˚C.

• A similar numerical model was developed to allow prediction of temperatures in

FRP-strengthened and insulated reinforced concrete slabs. The model was

validated against test data, and was found to adequately predict temperatures

within the member.

• Using the numerical models, parametric studies were performed on the effect of

different realistic fire scenarios on the response of insulated T-beams.

6.3.4.2 Strength model

• The numerical model developed here could predict the stress strain fields and

subsequently calculate the deflection of insulated/un-insulated RC beams. The

model uses time-dependent moment-curvature relationships to trace the

response of the beam under fire conditions.

• The model considers multiple strain components such as thermal, transient, and

creep components to achieve a realistic prediction.

• The model was successfully verified by comparing the results of several fire test

results from the literature. The model is capable of predicting the structural

behaviour of un-strengthened and FRP-strengthened beams.

171

• The model is capable of incorporating the axial restraint forces in the response of

the beam. A trial and error method was used to predict the response of the

beams with partial axial restraint.

6.4 Recommendations for future work

While this research has made many contributions in the experimental and numerical

characterization of FRP-strengthened members, more research is needed to further

investigate the behaviour of FRP materials and FRP-strengthened structures at elevated

temperatures. The following are some recommendations for further research:

• Accurate measurement of the end restraints during the fire tests are needed in

order to further investigate the effect of end conditions where partial or full

restraints are present.

• Full-scale fire testing of insulation systems other than the one studied in this

program should be performed in order to achieve an optimum insulation

thickness at critical locations. One such scenario could be the use of more

insulation materials at U-wraps or corners.

• Improving the thermal model to include moisture migration and evaporation in

concrete and insulation could result in better temperature predictions. The effects

of moisture migration were apparent in the recorded temperature data.

172

• Numerical models developed here could be used to simulate a frame including

beams and columns to achieve realistic loading and end-conditions.

• More tests are needed to further understand the FRP-concrete bond behaviour in

order to address the effect of additional variables such as material type, bond

length, loading rate, and moisture.

174

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A. Appendix A: Detailed experimental results

In this chapter the temperature and deflection readings from the fire tests are reported in

detail.

A.1 Temperature readings for Slabs

Figure A-1 Temperatures vs. exposure time for slab A.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Furnace avg.



TC-43 FRP-Concrete

Avg. Unexposed Face

181

Figure A-2 Temperatures vs. exposure time for slab B.

Figure A-3 Interior concrete temperatures Slab-A.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Furnace avg.



TC-43 FRP-Concrete

Avg. Unexposed Face

0

50

100

150

200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

TC-34 Cover 15 mm

TC-33 Cover 30 mm

TC-32 Cover 50 mm

TC-31 Cover 75 mm

TC-30 Cover 100 mm

TC-29 Cover 125 mm

Avg. Unexposed Face

182

Figure A-4 Interior concrete temperatures Slab-B.

Figure A-5 Temperatures vs. exposure time comparison for slabs A and B at FRP-

concrete bond line and steel reinforcement locations.

0

50

100

150

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

TC-34 Cover 15 mm

TC-33 Cover 30 mm

TC-32 Cover 50 mm

TC-31 Cover 75 mm

TC-30 Cover 100 mm

TC-29 Cover 125 mm

Avg. Unexposed Face

0

100

200

300

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

FRP-Concrete Slab-AFRP-Concrete Slab-BRebar Bottom Slab-ARebar Bottom Slab-B

183

Figure A-6 Steel rebar temperatures Slab-A.

Figure A-7 Steel rebar temperatures Slab-B.

0

50

100

150

200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

TC-26 Top of Rebar

TC-28 Base of Rebar

TC-27 Middle of Rebar

0

50

100

150

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

TC-26 Top of Rebar

TC-28 Base of Rebar

TC-27 Middle of Rebar

184

A.2 Temperatures and deflections of T-beams

A.2.1 Beam-A temperature data

Results for Beam-A are as follows.

Figure A-8 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.



Insulation Surface sec-B TC-30

185

Figure A-9 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-A.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.

Concrete-Insulation U-wrap End J (secG) TC-43

FRP-Insulation U-wrap End J (secG) TC-44

Insulation Surface U-wrap End J (secG) TC-45

186

Figure A-10 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-A.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.

Concrete-Insulation U-wrap End I (secD) TC-46

FRP-Insulation U-wrap End I (secD) TC-47

Insulation Surface U-wrap End I (secD) TC-48

187

Figure A-11 Steel reinforcement temperatures (web) Beam-A.

0

50

100

150

200

250

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)





188

Figure A-12 Unexposed surface temperature (centerline) Beam-A.

15

20

25

30

35

40

45

50

55

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

Un-exposed Surface sec-D TC-1

Un-exposed Surface sec-E TC-7

Un-exposed Surface sec-B TC-9

Un-exposed Surface sec-F TC-32

Un-exposed Surface sec-G TC-39

189

Figure A-13 Unexposed surface temperature (flange) Beam-A.

0

20

40

60

80

100

120

140

160

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)





190

A.2.2 Beam-B temperature data

Results for Beam-B are as follows.

Figure A-14 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.




191

Figure A-15 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-B.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.

Concrete-Insulation U-wrap End J (secG) TC-43

FRP-Insulation U-wrap End J (secG) TC-44

Insulation Surface U-wrap End J (secG) TC-45

192

Figure A-16 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-B.

0

200

400

600

800

1000

1200

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

ASTM E119

Ave. furnace temp.

Concrete-Insulation U-wrap End I (secD) TC-46

FRP-Insulation U-wrap End I (secD) TC-47

Insulation Surface U-wrap End I (secD) TC-48

193

Figure A-17 Steel reinforcement temperatures (web) Beam-B.

0

50

100

150

200

250

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)





194

Figure A-18 Unexposed surface temperature (centerline) Beam-B.

15

20

25

30

35

40

45

50

55

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)

Un-exposed Surface sec-D TC-1

Un-exposed Surface sec-E TC-7



Un-exposed Surface sec-G TC-39

195

Figure A-19 Unexposed surface temperature (flange) Beam-B.

0

20

40

60

80

100

120

140

0 60 120 180 240

Tem

pera

ture

(˚C)

Time (min)





196

A.2.3 Deflection Results

Figure A-20 Deflection at midspan and quatre points for Beam-A.

197

Figure A-21 Deflection at midspan and quatre points for Beam-B.

198

Figure A-22 Comparison of mid span deflection of Beam-A and Beam-B.

199

Figure A-23 load deflection curve Beam-A.

200

Figure A-24 load deflection curve Beam-B.

201

Figure A-25 Load deflection comparison for Beam-A and B.

202

B. APPENDIX-B: T-beam Load Calculation and Design

This chapter presents detailed load calculations for T-beams tested at the National

Research Council, Ottawa, Canada. Load calculations are based on CSA A23.3-04 and

ACI 318-02/318R-05 for un-strengthened beams. ACI 440.2R-08 design guide and CSA

S806-02 are used in addition for strengthened load calculations. And finally test

superimposed load calculators are performed in accordance with ULC-S101-07.

B.1 Assumptions, Dimensions and Material properties

T-beams are 3900mm in length, and their height is 400mm, web and flange width are 300

and 1220mm respectively.

The initial live load for the design of un-strengthened beam is assumed to be 2.4kPa, and

the dead load is the self-weight plus an additional 1kPa for partition load. An increase in

live load is assumed as a practical strengthening scenario. Beams are subjected to an

increased live load of 4.8kPa. After initial design the maximum capacity of the beam is

the basis for the calculation of superimposed test load (it is assumed that in the worst

case the beam is subjected to maximum allowable load which can be larger than the

initial design loads).

One of the T-beams is strengthened by CFRP Sika® CarboDur S812 in flexure and the

other one is strengthened by 1 layer of CFRP SikaWrap® Hex 103C on the bottom of the

203

beam web. A summary of strengthening system for T-beams are presented earlier in

Chapter 3.

B.1.1 Material properties

Material properties of steel, concrete and FRP is as listed below,

Longitudinal Steel Elastic Modulus, Es= 200000 MPa Yield Strength of Longitudinal Reinforcing Steel, 𝑓𝑦 =400 MPa

Concrete 28-day Concrete Compressive Strength, 𝑓𝑐′ =30 MPa Desity, γc= 2400 Kg/m3 Elastic Modulus, Ec= 26621 MPa

CFRP SikaWrap® Hex 103C Cured Laminate Properties with Sikadur® Hex 300 Epoxy [21° - 24°C (70° - 75°F)/5 days and 48 hrs post cure at 60°C (140°F)]

Elastic Modulus, Ef= 70552 MPa Ultimate Strain, 𝜀𝑓𝑢∗ = 1.12% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ =849 MPa Thickness of the FRP, 𝑡𝑓 = 1.016 mm

CFRP Sika® CarboDur S812 Cross section area flexural FRP, Afrp=96 mm2 Elastic Modulus, Ef= 165000 MPa Ultimate Strain, 𝜀𝑓𝑢∗ = 0.017 Ultimate Tensile Strength, 𝑓𝑓𝑢∗ = 2800 MPa Thickness of the FRP, 𝑡𝑓 =1.2 mm

204

SikaWrap® Hex 100G Cured Laminate Properties with Sikadur® Hex 300 Epoxy [21° - 24°C (70° - 75°F)/5 days and 48 hrs post cure at 60°C (140°F)]

Elastic Modulus, Ef= 26119 MPa Ultimate Strain, 𝜀𝑓𝑢∗ =2.34% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ =612 MPa Thickness of the FRP, 𝑡𝑓 =1.016 mm

CFRP, SikaWrap® Hex 230C Cured Laminate Properties with Sikadur® 330 Epoxy Properties after standard cure at 21° - 24°C (70° - 75°F)/5 days

Elastic Modulus, Ef = 65402 MPa Ultimate Strain, 𝜀𝑓𝑢∗ =1.37% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ = 894 MPa Thickness of the FRP, 𝑡𝑓 = 0.381 mm

GFRP, SikaWrap® Hex 430G Cured Laminate Properties with Sikadur® 330 Epoxy Properties after standard cure [21° - 24°C (70° - 75°F)/5 days and 48 hrs post-cure at 4°C (39°F)]

Elastic Modulus, 𝐸𝑓 = 26493 MPa Ultimate Strain, 𝜀𝑓𝑢∗ = 2.03% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ = 537 MPa Thickness of the FRP, 𝑡𝑓 = 0.508 mm

205

B.2 Design Flexural Strength of Reinforced Concrete Beam

The reinforced concrete specimens had two layers of flexural reinforcements: 6 No. 10M

bars in the flange on top and 2 No. 15M bars as tension steel in the bottom of the web,

see Figure 1. Flexural strength contribution of steel in the flange is neglected; therefore

design is based on flexural strength contribution from the two 15M reinforcing bars in

tension and two 10M reinforcing bars on the top of the web.

Area of primary tension steel is (two 15M bars) 𝐴𝑠 = 2(200) = 400 𝑚𝑚2 and the distance

from extreme compression fibre to the centroid of the primary longitudinal tension steel,

𝑑, is:

𝑑 = ℎ − 𝑐𝑜𝑣𝑒𝑟 − 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑡𝑖𝑟𝑟𝑢𝑝 − 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑠𝑡𝑒𝑒𝑙 (15𝑀)

= 400− 40 − 11 − 162� ≅ 341 𝑚𝑚

Area of top steel4 (two 10M bars), 𝐴𝑠′ = 2(100) = 200 𝑚𝑚2 and the distance from

extreme compression fibre, 𝑑′, is:

𝑑′ = 𝑐𝑜𝑣𝑒𝑟 + 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑡𝑖𝑟𝑟𝑢𝑝 + 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑠𝑡𝑒𝑒𝑙 (10𝑀) = 40 + 11 + 112�

≅ 56.5 𝑚𝑚

4 This steel will be in tension see calculation results below.

206

Figure B-1 T-beam cross section.

B.2.1 Design Flexural Strength according to CSA A23.3-04

According to Clause 10.3.3, the overhanging flange width on each side is the lesser of:

a) One fifth the span length = 38065� = 761.2 𝑚𝑚

b) 12 times the flange thickness= 12 × 150 = 1440 𝑚𝑚

c) One-half of the clear distance to the next web= (1220 − 300) 2⁄ = 460

Therefore the effective flange width, 𝑏𝑓 = 2[min (761, 1440, 460)] + 300 = 1220 𝑚𝑚 .

Assuming,

• strain distribution in linear in the section depth,

• Neural axis is within the flange

• Primary tension steel has yielded

• Section will fail by concrete crushing in compression

We have:

150

400

300

15M bars

56.5

341

207

Strain at the extreme compression concrete fibre 𝜀𝑐 is equal to ultimate concrete

strain 𝜀𝑐𝑢 = 0.0035 (Clause 10.1.3).

By trial and error depth of neutral axis, 𝑐 = 11.90 𝑚𝑚 , will satisfy the equilibrium of

forces in the section.

Strain at the bottom steel 𝜀𝑠 and strain at the top steel 𝜀𝑠′ will be:

𝜀𝑠 = 𝜀𝑐𝑢 �𝑑 − 𝑐𝑐

� = 0.0035 �341− 11.9

11.9� = 0.09678

𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐𝑐 � = 0.0035 �

56.5− 11.911.9

� = 0.01311

And the stresses at steel reinforcement will be

𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 0000(0.09678)� = 400 MPa

𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 0000(0.09678)� = 400 MPa

The forces in steels will be

𝑇𝑠 = 𝜙𝑠𝐴𝑠𝜎𝑠 = 0.85(400)(400) = 136000 𝑁

𝑇′𝑠 = 𝜙𝑠𝐴′𝑠𝜎𝑠 = 0.85(200)(400) = 68000 𝑁

𝜙𝑠, the resistance factor for steel is equal to 0.85 according to Clause 8.4.3.

Compression force in concrete can be calculated using the Whitney's equivalent stress

block,

𝐶𝑐 = −(𝛼1𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝑎);

𝑎 = 𝛽1𝑐

According to clause 10.1.7,

208

𝛼1 = max�(0.85− 0.0015𝑓𝑐′), 0.67� = max�(0.85 − 0.0015 × 30), 0.67� = 0.81

𝛽1 = max�(0.97− 0.0025𝑓𝑐′), 0.67� = max�(0.97− 0.0025 × 30), 0.67� = 0.90

𝐶𝑐 = −(𝛼1𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.81(. 65)(30)] ∙ (1220) ∙ [0.90(11.90)] = −204000 𝑁

𝜙𝑐, the resistance factor for concrete is equal to 0.65 according to Clause 8.4.2.

Sum of the forces is equal to zero,

𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 = −204000 + 68000 + 136000 = 0

The sectional moment resistance is:

𝑀𝑟 = 𝐶𝑐𝛽1𝑐

2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ = −204000

0.90(11.9)2

+ 341(136000) + 56.5(68000)

= 49.1 𝑘𝑁.𝑚

B.2.2 Design Flexural Strength according to ACI 318/318R-05

According to Clause 8.10.2, the width of slab effective as a T-beam flange on each side is

the lesser of:

a) One-quarter of the span length = 38064� = 951 𝑚𝑚

b) 8 times the slab thickness= 8 × 150 = 1200 𝑚𝑚

c) One-half of the clear distance to the next web= (1220 − 300) 2⁄ = 460

Therefore the effective flange width, 𝑏𝑓 = 2[min (951, 1200, 460)] + 300 = 1220 𝑚𝑚 .

Strain at the extreme compression concrete fibre 𝜀𝑐 is assumed to be equal to ultimate

concrete strain 𝜀𝑐𝑢 = 0.003 (Clause 10.2.3).

Taking neutral axis, 𝑐 = 9.076 𝑚𝑚 , will satisfy the equilibrium of forces in the section.

209

Strain at the bottom steel 𝜀𝑠 and strain at the top steel 𝜀𝑠′ will be:

𝜀𝑠 = 𝜀𝑐𝑢 �𝑑 − 𝑐𝑐

� = 0.003 �341 − 9.08

9.08� = 0.10972

𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐𝑐 � = 0.003 �

56.5− 9.089.08

� = 0.01568

And the stresses at steel reinforcement will be


𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.01568)� = 400 MPa


𝑇𝑠 = 𝐴𝑠𝜎𝑠 = (400)(400) = 160000 𝑁

𝑇′𝑠 = 𝐴′𝑠𝜎𝑠 = (200)(400) = 80000 𝑁


block,

𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝑎);

𝑎 = 𝛽1𝑐

According to clause 10.2.7.3,

𝛽1 = max��0.85− 0.05�𝑓𝑐′ − 30

7 �� , 0.65� = max�(0.85− 0.05 × 0), 0.65� = 0.85

𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.85(30)] ∙ (1220) ∙ [0.85(9.08)] = −240000 𝑁


𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 = −240000 + 80000 + 160000 = 0


210

𝑀𝑟 = 𝜙 𝑀𝑛

According to Clause 9.3.2.1 𝜙 in a tension-controlled section is equal to 0.90.

𝑀𝑟 = 𝜙 � 𝐶𝑐𝛽1𝑐

2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′�

= 0.90 �−2400000.85(9.08)

2+ 341(160000) + 56.5(80000)� = 52.3 𝑘𝑁.𝑚

B.3 Flexural Capacity of FRP-Strengthened Reinforced Concrete Beam

Detailed calculation for FRP strengthened will be presented in this section. Calculations

for Beam-A and Beam-B will be presented separately.

B.3.1 Beam-A FRP-Strengthened load calculation

Beam-A is strengthened with one strip of Sika CarboDur® S812 bonded to the soffit of

the beam.

B.3.1.1 Flexural Capacity according to CSA S806-02

According to Clause 7.1.6.2, FRP resistance factor is 𝜙𝐹 = 0.75. Also CSA-S806 limits the

strain in the FRP to 0.007 (Cl. 11.3.1.1). Similar to un-strengthened section a linear strain

distribution is assumed.

By trial and error taking neutral axis, 𝑐 = 35.3 𝑚𝑚 , will satisfy the equilibrium of forces

in the section.

Assuming strain in FRP, 𝜀𝑓, reaches 0.007 before crushing happens in concrete, strain

values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:

211

𝜀𝑓 = 0.007, 𝜀𝑐 < 𝜀𝑐𝑢

𝜀𝑠 = 𝜀𝑓 �𝑑 − 𝑐ℎ − 𝑐

� = 0.007 �341 − 35.3400 − 35.3

� = 0.00587

𝜀𝑠′ = 𝜀𝑓 �𝑑′ − 𝑐ℎ − 𝑐 �

= 0.007 �56.5− 35.3400 − 35.3

� = 0.00041

And the stresses at steel and FRP reinforcement will be


𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00041)� = 81.55 MPa

𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.007(165000) = 1155 MPa < fFu = 2800 MPa


𝑇𝑠 = 𝜙𝑠𝐴𝑠𝜎𝑠 = 0.85(400)(400) = 136000 𝑁

𝑇′𝑠 = 𝜙𝑠𝐴′𝑠𝜎𝑠 = 0.85(200)(81.55) = 13863 𝑁

𝑇𝑓 = 𝜙𝑓𝐴𝑓𝜎𝑓 = 0.75(96)(1155) = 83160 𝑁

Compression force in concrete can be calculated by direct integration of concrete stress-

strain curve or by using the Whitney's equivalent stress block. Here since strain at top

fibre of concrete does not reach concrete’s ultimate strain, stress block coefficients

should be adjusted accordingly. In the modified stress block the height of stress block is

assumed to be 𝑎 = 𝛽𝑐 and the stress is 𝛼𝑓𝑐′.

Knowing the strain distribution and stress-strain distribution of concrete then stress can

be determined by knowing the position of the fibre in the section ∴ 𝜎𝑐 = 𝜎𝑐(𝑦).

𝛼𝛽 = � �𝜎𝑐(𝑦)𝑓𝑐′

�𝑑𝑦1

0

212

𝛼𝛽2 = 2� �𝜎𝑐(𝑦)𝑓𝑐′

� (1 − 𝑦)𝑑𝑦1

0

By evaluating the two integrals 𝛼 and 𝛽 can be determined.

𝜀𝑐 = 𝜀𝑓 �𝑐

ℎ − 𝑐� = 0.007 �

35.3400− 35.3

� = 0.000677

𝛼 = 0.4134

𝛽 = 0.6721

𝐶𝑐 = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝑎) = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝛽𝑐);

𝐶𝑐 = −[0.41(0.65)(30)](1220)[0.67(35.3)] = −233023 𝑁


𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −233023 + 13863 + 136000 + 83160 = 0


𝑀𝑟 = 𝐶𝑐𝛽𝑐2

+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝑇𝑓ℎ

= −2330230.67(35.3)

2+ 341(136000) + 56.5(13863) + 400(83160)

= 77.7 𝑘𝑁.𝑚

B.3.1.2 Flexural Capacity according to ACI 440.2R-08

The effective ultimate strength of the FRP wrap is taken as the product of the ultimate

strength and an environmental reduction coefficient 𝐶𝐸 as follows, (CL. 9.4):

𝑓𝑓𝑢 = 𝐶𝐸 ∙ 𝑓𝑓𝑢∗

𝑓𝑓𝑢 = 0.95 ∙ 2800 = 2660 𝑀𝑃𝑎

Similarly, the design rupture strain is:

213

𝜀𝑓𝑢 = 𝐶𝐸 ∙ 𝜀𝑓𝑢∗

𝜀𝑓𝑢 = 0.95 ∙ 1.7% = 1.62%.

In order to prevent intermediate crack-induced debonding failure, ACI 440.2R-08 Clause

10.1.1 limits the stress in FRP to 𝜀𝑓𝑑. 𝜀𝑓𝑑, the effective strain in FRP reinforcement is the

strain level at which debonding may occur

𝜀𝑓𝑑 = 0.41�𝑓𝑐′

𝑛𝐸𝑓𝑡𝑓≤ 0.9𝜀𝑓𝑢 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠

Where,

𝐸𝑓 = tensile modulus of elasticity of FRP (MPa)

𝑛 = number of plies of FRP reinforcement

𝑡𝑓 = nominal thickness of one ply of FRP reinforcement (mm)

𝜀𝑓𝑑 = 0.41�30

1(165000)(1.2) = 0.00505 ≤ 0.9(0.01615) = 0.015


Strain values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:

𝜀𝑓 = 𝜀𝑓𝑑 = 0.00505, 𝜀𝑐 < 𝜀𝑐𝑢


� = 0.00505 �341− 9.98400− 9.98

� = 0.004283

𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐ℎ − 𝑐�

= 0.00505 �56.5− 9.98400 − 9.98

� = 0.000602


𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.004283)� = 400 MPa

214

𝜎𝑠′ = min�𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.000602)� = 120.4 MPa

𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.00505(165000) = 832.7 MPa


𝑇𝑠 = 𝐴𝑠𝜎𝑠 = (400)(400) = 160000 𝑁

𝑇′𝑠 = 𝐴′𝑠𝜎𝑠 = (200)(120.4) = 24076 𝑁

𝑇𝑓 = 𝐴𝑓𝜎𝑓 = �1.2(80)�(832.7) = 79941 𝑁


ℎ − 𝑐� = 0.00505 �

9.98400− 9.98

� = 0.000192


block,

𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝑎);

𝑎 = 𝛽1𝑐

According to ACI 318-05 Clause 10.2.7.3,

𝛽1 = max��0.85− 0.05�𝑓𝑐′ − 30

7 �� , 0.65� = max�(0.85− 0.05 × 0), 0.65� = 0.85

𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.85(30)] ∙ (1220) ∙ [0.85(9.98)] = −264017 𝑁


𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −264017 + 24076 + 160000 + 79941 = 0

Clause 10.2.10 reduces the contribution of FRP in the nominal flexural strength by

introducing a reduction factor 𝜓𝑓= 0.85.

215

𝑀𝑛 = 𝐶𝑐𝛽1𝑐

2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝜓𝑓𝑇𝑓ℎ

= −2640170.85(9.98)

2+ 341(160000) + 56.5(24076) + 0.85(400)(79941)

= 82.0 𝑘𝑁.𝑚



According to Clause 10.2.7, 𝜙 in defined as:

𝜙 =

⎩⎪⎨

⎪⎧ 0.9 𝜀𝑡 ≥ 0.005

0.65 +0.25�𝜀𝑡 − 𝜀𝑠𝑦�

0.005− 𝜀𝑠𝑦 𝜀𝑠𝑦 < 𝜀𝑡 < 0.005

0. 65 𝜀𝑡 ≤ 𝜀𝑠𝑦

𝜀𝑡 is the net tensile strain in extreme tension steel. Here 𝜀𝑡 = 𝜀𝑠 = 0.004283 therefore,

𝜙 = 0.65 +0.25(0.004283− 0.002)

0.005− 0.002= 0.852

And finally,

𝑀𝑟 = 𝜙 𝑀𝑛 = 0.852(82.0) = 69.9 𝑘𝑁.𝑚

B.3.1.2.1 Serviceability criterion

Clause 10.2.7 requires the following limits,

• The stress in the steel reinforcement under service load should be limited to 80%

of the yield strength

• compressive stress in concrete under service load should be limited to 45% of the

compressive strength

216

Assuming steel 𝜎𝑠 = 0.8𝑓𝑦 strains and stresses and forces in steel FRP and concrete are:

𝑐 = 43.50 𝑚𝑚

𝜀𝑓 = 𝜀𝑠 �ℎ − 𝑐𝑑 − 𝑐

� = 0.0016 �400 − 43.5341 − 43.5

� = 0.0019

𝜀𝑐 = 𝜀𝑐𝑢 �𝑐

𝑑 − 𝑐� = 0.0016 �

43.5341 − 43.5

� = 0.00023

𝜎𝑐 = 5.82 𝑀𝑃𝑎 < 0.45𝑓𝑐′ = 0.45(30) = 13.5 𝑀𝑃𝑎

Corresponding service and factored moments are

𝑀𝑠 = 53.4 𝑘𝑁.𝑚

𝑀𝐹 = 𝑀𝑠(𝛼𝐷 + 𝛼𝐿)

2= 53.4

(1.2 + 1.6)2

= 74.8 𝑘𝑁.𝑚

B.3.1.2.2 Strengthening Limits

The existing strength of the structure should be sufficient to resist a level of load as

described by (Cl. 9.2),

(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ (1.1𝑆𝐷𝐿 + 0.75𝑆𝐿𝐿)𝑛𝑒𝑤

Assuming DL=LL,

(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ �1.85

2(𝑆𝐷𝐿 + 𝑆𝐿𝐿)�

𝑛𝑒𝑤

= 0.925 𝑆𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤

(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 = 52.3 𝑘𝑁.𝑚

𝑀𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤 =(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔

0.925=

52.30.925

= 56.5 𝑀𝑃𝑎

The corresponding factored moment will be,


2= 56.5

(1.2 + 1.6)2

= 79.2 𝑘𝑁.𝑚

217

B.3.1.3 Beam-A design summary

Considering the strengthening limit and serviceability limit and section nominal

strength, the maximum strengthening limit according to ACI is:

𝑀𝐹 = 69.9 𝑘𝑁.𝑚

𝑀𝑠 = 49.9 𝑘𝑁.𝑚

This limit according to CSA is:

𝑀𝐹 = 77.7 𝑘𝑁.𝑚

𝑀𝑠 = 56.5 𝑘𝑁.𝑚

B.3.1.3.1 U-wrap design

Two different CFRP U-wraps are selected for this beam. The U-wrap at one end consists

of two 635 mm wide layers of SikaWrap® Hex 103C and the other U-wrap has four 600

mm wide layers of SikaWrap® Hex 230C.

According to ACI 440.2R-08 Clause 13.1.2 when the factored shear force at the

termination point is greater than 2/3 the concrete shear strength (𝑉𝑢 > 0.67𝑉𝑐), the FRP

laminates should be anchored with transverse reinforcement (U-wrap) to prevent FRP

end peeling or cover delamination. The area of the U-wrap reinforcement 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 is:

𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =�𝐴𝑓𝑓𝑓𝑢�𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙�𝐸𝑓𝜅𝜈𝜀𝑓𝑢�𝑎𝑛𝑐ℎ𝑜𝑟

𝜅𝜈 is bond-dependent coefficient for shear and is calculated using:

218

𝜅𝜈 =𝑘1 𝑘2 𝐿𝑒

11900 𝜀𝑓𝑢 ≤ 0.75 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠

The active bond length 𝐿𝑒 and bond reduction factors, 𝑘1 and 𝑘2 are defined as:

𝐿𝑒 =23300

�𝑛𝑓 𝑡𝑓 𝐸𝑓�0.58

𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠 ( 𝐸𝑓in MPa 𝑡𝑓 in mm)

𝑘1 = �𝑓𝑐′

27�

23

(𝑓𝑐′ 𝑖𝑛 𝑀𝑃𝑎)

𝑘2 =𝑑𝑓𝑣 − 𝐿𝑒𝑑𝑓𝑣

𝑓𝑜𝑟 𝑈 − 𝑤𝑟𝑎𝑝𝑠

𝑑𝑓𝑣 is the effective depth of FRP shear reinforcement (mm). Le in mm

B.3.1.3.1.1 SikaWrap® Hex 103C U-wrap

𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚

𝐿𝑒 =23300

�2 (1.016)(70552)�0.58

= 24 𝑚𝑚

𝑘1 = �3027�23

= 1.07

𝑘2 =211 − 24

211= 0.89

𝜅𝜈 =1.07 (0.89)(24)11900(0.0106)

= 0.18 ≤ 0.75

𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =96(2660)

70552(0.17)(0.0106) = 1901 𝑚𝑚2

Area of two layers of SikaWrap® Hex 103C is:

𝐴𝑓𝑟𝑝𝑣 = 2(2)�635(1.016)� = 2581 𝑚𝑚2 > 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟

219

B.3.1.3.1.2 SikaWrap® Hex 230C U-wrap

𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚

𝐿𝑒 =23300

�4 (0.381)(65402)�0.58

= 29 𝑚𝑚

𝑘1 = �3027�23

= 1.07

𝑘2 =211 − 29

211= 0.86

𝜅𝜈 =1.07 (0.86)(29)11900(0.0137)

= 0.17 ≤ 0.75


65402(0.17)(0.0137) = 1712 𝑚𝑚2

Area of two layers of SikaWrap® Hex 230C is: 𝐴𝑓𝑟𝑝𝑣 = 2(2)�610(0.381)� = 1859 𝑚𝑚2 > 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟

B.3.2 Beam-B FRP-Strengthened load calculation

Beam-B is strengthened with one 200 mm wide layer of SikaWrap®Hex-103C bonded to

the soffit of the beam.

B.3.2.1 Flexural Capacity according to CSA S806-02

According to Clause 7.1.6.2, FRP resistance factor is 𝜙𝐹 = 0.75. Also CSA-S806 limits the

strain in the FRP to 0.007 (Cl. 11.3.1.1). Similar to un-strengthened section a linear strain

distribution is assumed.

By trial and error taking neutral axis, 𝑐 = 34.7 𝑚𝑚 , will satisfy the equilibrium of forces

in the section.

Assuming strain in FRP, 𝜀𝑓, reaches 0.007 before crushing happens in concrete, strain

values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:

220

𝜀𝑓 = 0.007, 𝜀𝑐 < 𝜀𝑐𝑢


� = 0.007 �341 − 34.7400 − 34.7

� = 0.00587

𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐ℎ − 𝑐�

= 0.007 �56.5− 34.7400 − 34.7

� = 0.00042



𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00042)� = 83.58 MPa

𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.007(70552) = 494 MPa < fFu = 849 MPa


𝑇𝑠 = 𝜙𝑠𝐴𝑠𝜎𝑠 = 0.85(400)(400) = 136000 𝑁

𝑇′𝑠 = 𝜙𝑠𝐴′𝑠𝜎𝑠 = 0.85(200)(83.58) = 14209 𝑁

𝑇𝑓 = 𝜙𝑓𝐴𝑓𝜎𝑓 = 0.75�1.016(200)�(494) = 75265 𝑁


ℎ − 𝑐� = 0.007 �

34.7400− 34.7

� = 0.000665

𝛼 = 0.4066

𝛽 = 0.6719

𝐶𝑐 = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝑎) = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝛽𝑐);

𝐶𝑐 = −[0.41(0.65)(30)](1220)[0.67(34.7)] = −225473 𝑁


𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −225474 + 14209 + 136000 + 75265 = 0


221

𝑀𝑟 = 𝐶𝑐𝛽𝑐2

+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝑇𝑓ℎ

= −2254730.67(34.7)

2+ 341(136000) + 56.5(14209) + 400(75265)

= 74.7 𝑘𝑁.𝑚

B.3.2.2 Flexural Capacity according to ACI 440.2R-08

The effective ultimate strength of the FRP wrap is taken as the product of the ultimate

strength and an environmental reduction coefficient 𝐶𝐸 as follows, (CL. 9.4):

𝑓𝑓𝑢 = 𝐶𝐸 ∙ 𝑓𝑓𝑢∗

𝑓𝑓𝑢 = 0.95 ∙ 849 = 806.55 𝑀𝑃𝑎

Similarly, the design rupture strain is:

𝜀𝑓𝑢 = 𝐶𝐸 ∙ 𝜀𝑓𝑢∗

𝑓𝑓𝑢 = 0.95 ∙ 1.12% = 1.06%.

In order to prevent intermediate crack-induced debonding failure, ACI 440.2R-08 Clause

10.1.1 limits the stress in FRP to 𝜀𝑓𝑑. 𝜀𝑓𝑑, the effective strain in FRP reinforcement is the

strain level at which debonding may occur

𝜀𝑓𝑑 = 0.41�𝑓𝑐′

𝑛𝐸𝑓𝑡𝑓≤ 0.9𝜀𝑓𝑢 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠

Where,

𝐸𝑓 = tensile modulus of elasticity of FRP (MPa)

222

𝑛 = number of plies of FRP reinforcement

𝑡𝑓 = nominal thickness of one ply of FRP reinforcement (mm)

𝜀𝑓𝑑 = 0.41�30

1(70552)(1.016) = 0.0084 ≤ 0.9(0.01064) = 0.0095


Strain values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:

𝜀𝑓 = 𝜀𝑓𝑑 = 0.0084, 𝜀𝑐 < 𝜀𝑐𝑢


� = 0.0084 �341 − 12.05400 − 12.05

� = 0.00711

𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐ℎ − 𝑐 �

= 0.0084 �56.5− 12.05400 − 12.05

� = 0.00096


𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.0071)� = 400 MPa

𝜎𝑠′ = min�𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00096)� = 192.2 MPa

𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.0084(70552) = 592 MPa


𝑇𝑠 = 𝐴𝑠𝜎𝑠 = (400)(400) = 160000 𝑁

𝑇′𝑠 = 𝐴′𝑠𝜎𝑠 = (200)(192.2) = 38440 𝑁

𝑇𝑓 = 𝐴𝑓𝜎𝑓 = �1.016(200)�(592) = 120247 𝑁


ℎ − 𝑐� = 0.0084 �

12.05400 − 12.05

� = 0.00026

223


block,

𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝑎);

𝑎 = 𝛽1𝑐

According to ACI 318-05 Clause 10.2.7.3,

𝛽1 = max��0.85− 0.05�𝑓𝑐′ − 30

7 �� , 0.65� = max�(0.85− 0.05 × 0), 0.65� = 0.85

𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.85(30)] ∙ (1220) ∙ [0.85(12.05)] = −318688 𝑁


𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −318688 + 38440 + 160000 + 120247 = 0

Clause 10.2.10 reduces the contribution of FRP in the nominal flexural strength by

introducing a reduction factor 𝜓𝑓= 0.85.

𝑀𝑛 = 𝐶𝑐𝛽1𝑐

2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝜓𝑓𝑇𝑓ℎ

= −3186880.85(12.05)

2+ 341(160000) + 56.5(38440)

+ 0.85(400)(120247) = 96.0 𝑘𝑁.𝑚



According to Clause 10.2.7, 𝜙 in defined as:

224

𝜙 =

⎩⎪⎨

⎪⎧ 0.9 𝜀𝑡 ≥ 0.005

0.65 +0.25�𝜀𝑡 − 𝜀𝑠𝑦�

0.005− 𝜀𝑠𝑦 𝜀𝑠𝑦 < 𝜀𝑡 < 0.005

0. 65 𝜀𝑡 ≤ 𝜀𝑠𝑦

𝜀𝑡 is the net tensile strain in extreme tension steel. Here 𝜀𝑡 = 𝜀𝑠 = 0.00711 therefore,

𝜙 = 0.9

And finally,

𝑀𝑟 = 𝜙 𝑀𝑛 = 0.9(96.0 ) = 86.4 𝑘𝑁.𝑚

B.3.2.2.1 Serviceability criterion

Clause 10.2.7 requires the following limits,

• The stress in the steel reinforcement under service load should be limited to 80%

of the yield strength

• compressive stress in concrete under service load should be limited to 45% of the

compressive strength

Assuming steel 𝜎𝑠 = 0.8𝑓𝑦 strains and stresses and forces in steel FRP and concrete are:

𝑐 = 43.10 𝑚𝑚

𝜀𝑓 = 𝜀𝑠 �ℎ − 𝑐𝑑 − 𝑐

� = 0.0016 �400 − 43.1341 − 43.1

� = 0.0019

𝜀𝑐 = 𝜀𝑐𝑢 �𝑐

𝑑 − 𝑐� = 0.0016 �

43.1341 − 43.1

� = 0.00023

𝜎𝑐 = 5.79 𝑀𝑃𝑎 < 0.45𝑓𝑐′ = 0.45(30) = 13.5 𝑀𝑃𝑎

Corresponding service and factored moments are

𝑀𝑠 = 52.3 𝑘𝑁.𝑚

225


2= 52.3

(1.2 + 1.6)2

= 73.2 𝑘𝑁.𝑚

B.3.2.2.2 Strengthening Limits

The existing strength of the structure should be sufficient to resist a level of load as

described by (Cl. 9.2),

(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ (1.1𝑆𝐷𝐿 + 0.75𝑆𝐿𝐿)𝑛𝑒𝑤

Assuming DL=LL,

(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ �1.85

2(𝑆𝐷𝐿 + 𝑆𝐿𝐿)�

𝑛𝑒𝑤

= 0.925 𝑆𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤

(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 = 52.3 𝑘𝑁.𝑚

𝑀𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤 =(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔

0.925=

52.30.925

= 56.5 𝑀𝑃𝑎

The corresponding factored moment will be,


2= 56.5

(1.2 + 1.6)2

= 79.2 𝑘𝑁.𝑚

B.3.2.3 Beam-B design summary

Considering the strengthening limit and serviceability limit and section nominal

strength, the maximum strengthening limit according to ACI is:

𝑀𝐹 = 73.2 𝑘𝑁.𝑚

𝑀𝑠 = 52.3 𝑘𝑁.𝑚

This limit according to CSA is:

𝑀𝐹 = 74.7 𝑘𝑁.𝑚

226

𝑀𝑠 = 54.3 𝑘𝑁.𝑚

B.3.2.3.1 U-wrap design

Two different GFRP U-wraps are selected for this beam. The U-wrap at one end consists

of two 610 mm wide layers of SikaWrap® Hex 100G and the other U-wrap has four 610

mm wide layers of SikaWrap® Hex 430G.

The area of the U-wrap reinforcement 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 is:

𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =�𝐴𝑓𝑓𝑓𝑢�𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙�𝐸𝑓𝜅𝜈𝜀𝑓𝑢�𝑎𝑛𝑐ℎ𝑜𝑟

𝜅𝜈 is bond-dependent coefficient for shear and is calculated using:

𝜅𝜈 =𝑘1 𝑘2 𝐿𝑒

11900 𝜀𝑓𝑢 ≤ 0.75 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠

The active bond length 𝐿𝑒 and bond reduction factors, 𝑘1 and 𝑘2 are defined as:

𝐿𝑒 =23300

�𝑛𝑓 𝑡𝑓 𝐸𝑓�0.58

𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠

𝑘1 = �𝑓𝑐′

27�

23

𝑘2 =𝑑𝑓𝑣 − 𝐿𝑒𝑑𝑓𝑣

𝑓𝑜𝑟 𝑈 − 𝑤𝑟𝑎𝑝𝑠

𝑑𝑓𝑣 is the effective depth of FRP shear reinforcement (mm).

B.3.2.3.1.1 SikaWrap® Hex 100G U-wrap

𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚

227

𝐿𝑒 =23300

�2 (1.016)(26119)�0.58

= 42 𝑚𝑚

𝑘1 = �3027�23

= 1.07

𝑘2 =211 − 42

211= 0.80

𝜅𝜈 =1.07 (0.80)(42)11900(0.0234)

= 0.13 ≤ 0.75


26119(0.13)(0.0234) = 2056 𝑚𝑚2

Area of two layers of SikaWrap® Hex 100G is:


B.3.2.3.1.2 SikaWrap® Hex 430G U-wrap

𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚

𝐿𝑒 =23300

�4 (0.508)(26493)�0.58

= 42 𝑚𝑚

𝑘1 = �3027�23

= 1.07

𝑘2 =211 − 42

211= 0.80

𝜅𝜈 =1.07 (0.80)(42)11900(0.0203)

= 0.15 ≤ 0.75


26493(0.15)(0.0203) = 2040 𝑚𝑚2

Area of two layers of SikaWrap® Hex 430G is:

228


B.4 Superimposed Fire Test Loads

ULC S101-07 requires a superimposed load to be applied to the test specimens during

the fire test. This load is determined to simulate the total specified load (M) on the T-beams.

Following is a brief definition for some of the terms used in this section:

Md dead load during test (weight of the beam)

M total specified load on the beam

MD dead load

ML live load

Ms required superimposed load on column

Mr factored flexural resistance

α load factor on total specified load

αD dead load factor

αL live load factor

r dead-to-live load ratio

The required superimposed load Ms is calculated as,

Ms=M-Md

Knowing the dead-to-live ratio(r), M can be back calculated from factored flexural

resistance (Mr),

229

𝑟 =𝑀𝐷

𝑀𝐿

M= Mr/ α, where α is,

𝛼 =𝑟𝛼𝐷 + 𝛼𝐿𝑟 + 1

As a results Ms= Mr/ α -Md .

Assuming a dead to live ratio of r= MD/ML =15 , Table 1 give a summary of the

calculations.

𝛼 =𝛼𝐷 + 𝛼𝐿

2

Table B-1 load factor calculation.

αD αL 𝒓 =𝑷𝑫𝑷𝑳

𝜶 =𝒓𝜶𝑫 + 𝜶𝑳𝒓 + 𝟏

ACI 318-05 1.2 1.6 1 1.4 CSA S806-02 1.25 1.5 1 1.375

Considering load calculation summary, sections 0 and 0, maximum moment allowable

for both Beams are selected as:

According to ACI 440.2R-08

𝑀𝑟 = 73.2 𝑘𝑁.𝑚

5 As in example 1 clause C 1.3 of ULC S101-07

230

𝑀 = 52.3 𝑘𝑁.𝑚

According to CSA S806-02

𝑀𝑟 = 77.7 𝑘𝑁.𝑚

𝑀 = 56.5 𝑘𝑁.𝑚

Since CSA S806-02 gives a higher load, for that reason superimposed load calculations

are based on CSA S806-02 values.

Existing dead load Md=11.0 kN.m. So the superimposed load on the beam is

Ms=M-Md=56.5-11.0=45.5 kN.m.

B.4.1 Required Jack Stress during Fire Test

The load is delivered to the beam through a set of 6 jacks. The total load required along

the beam is:

𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑝𝑒𝑟𝑖𝑚𝑝𝑜𝑠𝑒𝑑 𝑗𝑎𝑐ℎ𝑖𝑛𝑔 𝑙𝑜𝑎𝑑 =8𝑀𝑠

𝐿=

8 × 45.53.806

= 95.7 𝑘𝑁

There are 6 jacks and each jack head has a diameter of 2.5in, leading to a jack area of:

𝐽𝑎𝑐𝑘 𝐴𝑟𝑒𝑎 = 𝜋𝐷2

4= 3166 𝑚𝑚2 = 4.91 𝑖𝑛2

Hence, the stress required in each jack during loading is:

𝑱𝒂𝒄𝒌 𝑺𝒕𝒓𝒆𝒔𝒔 =𝑻𝒐𝒕𝒂𝒍 𝒍𝒐𝒂𝒅𝑱𝒂𝒄𝒌 𝑨𝒓𝒆𝒂

= 𝟓.𝟎𝟑 𝑴𝑷𝒂 = 𝟕𝟑𝟎 𝒑𝒔𝒊

232

C. Appendix C: Material properties at high temperature

The fire performance of FRP-strengthened RC beams under fire exposure is governed by

the thermal and mechanical properties of concrete, steel reinforcement, FRP

reinforcement, adhesive and insulation materials. Thermal properties are necessary to

determine the temperature field inside the structural element at any specific time,

specifically where the member exposed to fire. The thermal properties that affect the

thermal behaviour and temperature distribution in the member are thermal

conductivity, specific heat and density. In these chapter thermal and mechanical

properties of material is presented in detail.

C.1 Concrete

C.1.1 Thermal properties

C.1.1.1 Thermal conductivity

(Lie 1992) suggested the following equations for the thermal conductivity of siliceous

aggregate concrete,

CTforkCTforTk

c

c

8000.1

80005.1000625.0

>=

≤≤+−=( C-1)

The temperature, T, has units of ºC and ck has units of W/m-ºC. And for

Calcareous aggregate

233

CTforTkCTfork

c

c

2937162.1001241.0

293355.1

>+−=

≤= ( C-2)

Eurocode 2 (EN 2004) gives the following equations for lower and upper limit of thermal

conductivity of concrete. The upper limit of thermal conductivity of normal weight

concrete is determined using the following equation

CTCformKWTTkc 120020/

1000107.0

1002451.02

2

≤≤

+

−= ( C-3)

And the following equation could be used for the lower limit

CTCformKWTTkc 120020/

1000057.0

100136.036.1

2

≤≤

+

−= ( C-4)

Following figure compares the two models.

234

Figure C-1 Thermal conductivity of normal weight concrete based on Eurocode 2 (EN

2004) and (Lie 1992).

C.1.1.2 Specific heat

(Lie 1992) suggested the following equations for the volumetric specific heat for siliceous

aggregate concrete,

0.00

0.40

0.80

1.20

1.60

2.00

2.40

0 200 400 600 800 1000 1200

Ther

mal

cond

uctiv

ity W

/mK

Temperature °C

EC2 upper limit

Sillicious Lie, TT

Carbonated Lie, TT

EC2 lower limit

235

CTCforccc 400200107.2 6 ≤≤×=⋅ρ

( ) CTCforTccc 500400105.2013.0 6 ≤≤×−=⋅ρ

( ) CTCforTccc 600500105.10013.0 6 ≤≤×+−=⋅ρ

( C-5)

Density, cρ , has units of kg/m3, specific heat, cc , has units of J/kg-ºC, temperature, T,

has units of ºC, and thermal capacity, cc c⋅ρ , has units of J/m3-ºC.

(Lie 1992) suggests the following for Calcareous aggregate,

CTforccc400010566.2 6 ≤≤×=⋅ρ

( ) CTCforTccc 41040010034.681765.0 6 ≤≤×−=⋅ρ

( ) CTCforTccc 4454101000671.2505043.0 6 ≤≤×+−=⋅ρ

CTCforccc 50044510566.2 6 ≤≤×=⋅ρ

( ) CTCforTccc 6355001044881.501603.0 6 ≤≤×−=⋅ρ

( ) CTCforTccc 7857151007343.17622103.0 6 ≤≤×+−=⋅ρ

( C-6)

( ) CTforTccc2000107.1005.0 6 ≤≤×+=⋅ρ

CTforccc600107.2 6 ≥×=⋅ρ

( ) CTCforTccc 7156351090225.10016635.0 6 ≤≤×−=⋅ρ

CTforccc78510566.2 6 ≥×=⋅ρ

236

Lie’s model does not account for moisture content of the concrete and moisture effect

should be accounted for separately.

Eurocode 2 gives the following equations for the specific heat of dry concrete (no

moisture),

100°C T 20°C K) (J/kg 900 =)( ≤≤Tcc

200°C T < 100°Cfor K) (J/kg 100) - (T + 900 =)( ≤Tcc

400°C T < 200°Cfor K) (J/kg 200)/2 - (T + 1000 =)( ≤Tcc

1200°C T < 400°Cfor K) (J/kg 1100 =)( ≤Tcc

( C-7)

When the moisture content of concrete is not accounted for in the calculation method,

the function given for the specific heat of dry concrete should be adjusted to account for

the moisture. For both siliceous and calcareous aggregates this could be modelled by a

constant value, cc.peak, situated between 100°C and 115°C with linear decrease between

115°C and 200°C.

• cc.peak = 900 J/kg K for moisture content of 0 % of concrete weight

• cc.peak = 1470 J/kg K for moisture content of 1,5 % of concrete weight

• cc.peak = 2020 J/kg K for moisture content of 3,0 % of concrete weight

And linear relationship between (115°C, cc.peak) and (200°C, 1000 J/kg K).

237

The variation of density with temperature is influenced by water loss and is defined as

follows,

115°C 20°Cfor (20°C) =)( c ≤≤TTc ρρ

°C002 115°Cfor 85115 - T0.02 - 1(20°C) =)( c ≤<

⋅⋅ TTc ρρ

°C004 200°Cfor 200

200 - T0.03 - 0.98(20°C) =)( c ≤<

⋅⋅ TTc ρρ

°C0021 400°Cfor 800

400 - T0.07 - 0.95(20°C) =)( c ≤<

⋅⋅ TTc ρρ

( C-8)

C.1.2 Mechanical properties

C.1.2.1 Stress strain relation

(Lie 1992) provides an estimate for the stress-strain relationship of concrete at high

temperature. The stress in the concrete is a function of the strain in the material and its

relation to the strain at maximum stress (εcmax).

238

For ascending branch where :max thencc εε ≤

−−⋅=

2

max

max' 1c

cccc ff

εεε

And for the descending branch where :max thencc εε >

⋅−

−⋅=2

max

max'

31

c

cccc ff

εεε

Where:

≥

−

⋅−⋅

<= CTifTf

CTifff

c

c

c º4501000

20353.2011.2

º450'0

'0

'

( C-9)

Here cε is the strain in concrete, maxcε is the concrete strain at maximum stress, fc is the

stress in concrete (MPa) , f’c is the temperature dependent concrete strength (MPa) and

f’c0 is the concrete strength at room temperature (MPa). The concrete strain at

maximum stress, maxcε , is dependent on the temperature and is defined as below.

Temperature is in ºC.

( ) 62max 1004.00.60025.0 −×⋅+⋅+= TTcε ( C-10)

The strain at crushing failure in the concrete is not strictly defined in Lie’s model.

Williams 2005 assumed that at all temperatures, the crushing strain in the concrete (εcult)

239

is related to the strain at maximum stress ( maxcε ) by the same ratio that applies room

temperature.

Eurocode 2 proposes a stress stain curve for uniaxially stressed concrete at elevated

temperatures as could be seen in the figure below.

Figure C-2 Eurocode2 compressive stress strain curve for concrete.

The stress in concrete σ(𝜃) is related to strain 𝜀 using the following equation,

𝜎(𝜽) = �

𝟑𝜺𝒇𝒄,𝜽

𝜺𝒄𝟏,𝜽�𝟐+�𝜺

𝜺𝒄𝟏,𝜽�𝟑�

𝜺 < 𝜺𝒄𝟏,𝜽

Linear or nonlinear descending branch 𝜺𝒄𝟏,𝜽 < 𝜺 < 𝜺𝒄𝒖𝟏,𝜽

( C-11)

240

The stress-strain relationship in ascending branch is defined by two parameters, the

compressive strength 𝒇𝒄,𝜽 and the strain 𝜺𝒄𝟏,𝜽 corresponding to 𝒇𝒄,𝜽. These two

parameters are temperature dependent and could be determined using the following

table. Where fck is Characteristic cylinder strength (MPa). εcu1,θ the ultimate strain. A

descending branch could be adopted for numerical purposes for strains larger than 𝜺𝒄𝟏,𝜽.

241

Table C-1 Values for the main parameters of the stress-strain relationships of normal

weight concrete with siliceous or calcareous aggregates concrete at elevated

temperatures, from Eurocode2.

Concrete temp.θ

Siliceous aggregates Calcareous aggregates

fc,θ / fck εc1,θ εcu1,θ fc,θ / fck εc1,θ εcu1,θ

[°C] [-] [-] [-] [-] [-] [-]

1 2 3 4 5 6 7

20 1.00 0.0025 0.0200 1.00 0.0025 0.0200

100 1.00 0.0040 0.0225 1.00 0.0040 0.0225

200 0.95 0.0055 0.0250 0.97 0.0055 0.0250

300 0.85 0.0070 0.0275 0.91 0.0070 0.0275

400 0.75 0.0100 0.0300 0.85 0.0100 0.0300

500 0.60 0.0150 0.0325 0.74 0.0150 0.0325

600 0.45 0.0250 0.0350 0.60 0.0250 0.0350

700 0.30 0.0250 0.0375 0.43 0.0250 0.0375

800 0.15 0.0250 0.0400 0.27 0.0250 0.0400

900 0.08 0.0250 0.0425 0.15 0.0250 0.0425

1000 0.04 0.0250 0.0450 0.06 0.0250 0.0450

1100 0.01 0.0250 0.0475 0.02 0.0250 0.0475

1200 0.00 - - 0.00 - -

242

C.1.2.2 Thermal expansion

The coefficient of thermal expansion is a function of temperature; Lie (1992) proposed

the following equation for both carbonated and siliceous aggregate concretes.

610)6008.0( −×+= Tcα ( C-12)

The temperature, T, has units of ºC, and αc has units of ºC-1.

Eurocode 2 suggests the following equations to calculate the thermal strain in concrete,

For siliceous aggregates:

εc(θ) = -1,8 × 10-4 + 9 × 10-6θ + 2,3 × 10-11θ 3 for 20°C ≤ θ ≤ 700°C

εc(θ) = 14 × 10-3 for 700°C < θ ≤ 1200°C ( C-13)

and for calcareous aggregates:

εc(θ) = -1,2 × 10-4 + 6 × 10-6θ + 1,4 × 10-11θ 3 for 20°C ≤ θ ≤ 805°C

εc(θ) = 12 × 10-3 for 805°C < θ ≤ 1200°C ( C-14)

Where θ is the concrete temperature (°C). These strains are calculated with reference to

the length at 20°C.

243

C.1.2.3 Creep and Transient strain

Creep deformation in concrete at room temperature is small but at elevated

temperatures creep could be significant for example where concrete is subjected to an

elevated service temperature for prolonged length of time. (Anderberg, Thelandersson

1976) concluded that creep could be ignored at temperatures below 400°C. In the case of

severe compartment fires where the duration of exposure is relatively short, the effect of

creep is minimal and it is usually ignored.

𝜀𝑐𝑟 = 0.00053 𝜎𝑐𝑓𝑐,𝑇

� 𝑡180

𝑒0.00304(𝑇−20) ( C-15)

where 𝑓𝑐,𝑇 is the strength of concrete at temperature T (°C) and t is time in minutes. 𝜎𝑐 is

the applied stress.

In addition to time dependant creep strains in concrete there is another component of

strain which is called transient strain or load induced thermal strain (LITS). LITS

develops in addition to creep during the first heating under load (Khoury 2000). In

Anderberg’s formulation transient strain is related to unconstrained thermal expansion

of concrete 𝜀𝑡ℎ and the stress history of the element as could be seen in the following

equation.

𝜀𝑡𝑟 = −𝑘2𝜎

𝑓𝑐,20𝜀𝑡ℎ ( C-16)

𝑘2 is an empirical constant between 1.8 to 2.35.

244

C.2 Reinforcing steel

C.2.1.1 Stress strain relation

Lie (1992) provides a set a equations for the stress-strain relationship of reinforcing steel

at high temperature as follows.

( )

( ) ( ) ( )

>−+−+⋅

≤⋅=

pspsp

pss

y

TfTfTf

Tf

fεεεεε

εεε

001.0,001.0,001.0

001.0,001.0

001.0,

( C-17)

Where: ( ) ( )( )[ ] 9.603.030exp104.050),( ⋅⋅+−−⋅⋅−= εε TTTf and 06104 yp fx ⋅= −ε .

The variable T is the temperature (ºC) of the steel rebar, and fy0 is the room temperature

yield strength of the steel (MPa).

Eurocode 2 suggests a different equation for the reinforcing bars, as can be seen in the

figure below.

Figure C-3 model for stress-strain relationships of reinforcing steel at elevated

temperatures

245

The following equations determine the state of stress at any temperature given a specific

strain.

𝜎(𝜃) =

⎩⎪⎪⎨

⎪⎪⎧

𝜀𝐸𝑠,𝜃 𝜀 < 𝜀𝑠𝑝,𝜃

𝑓𝑠𝑝,𝜃 − 𝑐 + �𝑏𝑎� �𝑎2 − �𝜀𝑠𝑦,𝜃 − 𝜀�2�

0.5𝜀𝑠𝑝,𝜃 ≤ 𝜀 ≤ 𝜀𝑠𝑦,𝜃

𝑓𝑠𝑦,𝜃 𝜀𝑠,𝜃 ≤ 𝜀 ≤ 𝜀𝑠𝑡,𝜃

𝑓𝑠𝑦,𝜃�1− �𝜀 − 𝜀𝑠𝑡,𝜃� �𝜀𝑠𝑢,𝜃 − 𝜀𝑠𝑡,𝜃�� 𝜀𝑠𝑡,𝜃 ≤ 𝜀 ≤ 𝜀𝑠𝑢,𝜃 0.0 𝜀 > 𝜀𝑠𝑢,𝜃

( C-18)

Where a, b and c are determined using the following equations.

𝑎2 = �𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃��𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃 + 𝑐/𝐸𝑠,𝜃�

𝑏2 = 𝑐�𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃�𝐸𝑠,𝜃 + 𝑐2

𝑐 =�𝑓𝑠𝑦,𝜃 − 𝑓𝑠𝑝,𝜃�

2

�𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃�𝐸𝑠,𝜃 − 2�𝑓𝑠𝑦,𝜃 − 𝑓𝑠𝑝,𝜃�

εsp,θ = fsp,θ / Es,θ , εsy,θ = 0,02, εst,θ = 0,15, εsu,θ = 0,20,

εst,θ = 0,05 and εsu,θ = 0,10

The temperature dependant parameters could be determined using the following table;

fyk is the room temperature yield stress of the reinforcement.

Table C-2 values for the parameters of the stress-strain relationship of hot rolled and

cold worked reinforcing steel at elevated temperatures

246

Steel

Temperature fsyθ / fyk fspθ / fyk Esθ / Es

θ [°C] hot

rolled

cold

worked

hot

rolled

cold

worked

hot

rolled

cold

worked

20.00 1.00 1.00 1.00 1.00 1.00 1.00

100.00 1.00 1.00 1.00 0.96 1.00 1.00

200.00 1.00 1.00 0.81 0.92 0.90 0.87

300.00 1.00 1.00 0.61 0.81 0.80 0.72

400.00 1.00 0.94 0.42 0.63 0.70 0.56

500.00 0.78 0.67 0.36 0.44 0.60 0.40

600.00 0.47 0.40 0.18 0.26 0.31 0.24

700.00 0.23 0.12 0.07 0.08 0.13 0.08

800.00 0.11 0.11 0.05 0.06 0.09 0.06

900.00 0.06 0.08 0.04 0.05 0.07 0.05

1000.00 0.04 0.05 0.02 0.03 0.04 0.03

1100.00 0.02 0.03 0.01 0.02 0.02 0.02

1200.00 0.00 0.00 0.00 0.00 0.00 0.00

C.2.1.2 Thermal elongation of reinforcing steel

Based on Eurocode 2 the thermal strain εs(θ) of steel could be calculated from the

following equation.

247

εs(θ) = -2,416 × 10-4 + 1,2x10-5 θ + 0,4 × 10-8 θ 2 for 20°C ≤ θ ≤ 750°C

εs(θ) = 11 × 10-3 for 750°C < θ ≤ 860°C

εs(θ) = -6,2 × 10-3 + 2 × 10-5 θ for 860°C < θ ≤ 1200°C

( C-19)

where θ is the steel temperature (°C) and strains are measured with reference to state of

deformation at 20°C.

C.3 FRP

C.3.1.1 Thermal properties

Thermal properties of FRP depend on the type of fibres and matrix material used in its

composition and the volume fraction of the constituents. Material used as matrix

generally has lower thermal conductivity compared to the fibres. For example thermal

conductivity of epoxy is 0.346 W/m-°C compared to 50~130 W/m-°C in the case of

Carbon fibres (PK Mallick 1993). This cause directional dependency of thermal

properties in FRPs. Specifically in the case of unidirectional FRPs thermal conductivity is

high in the direction of the fibres which the conductivity in transverse directions is

lower. In transverse directions the defining factor is the thermal conductivity of the

matrix rather than fibres.

248

C.3.1.2 Mechanical properties

Coefficient of thermal expansion of some common FRP composites is reported in

Table C-3 below (Mallik 1988).

Table C-3: Coefficient of thermal expansion for FRPs, Ahmad (2010).

Material Coefficient of Thermal Expansion W/m-°C

Longitudinal Transverse

Glass-Epoxy 6.3 19.8

Aramid-Epoxy -3.6 54

High Modulus Carbon-Epoxy -0.09 27

Ultra-high Modulus Carbon-Epoxy -1.44 30.6

C.4 Insulation

C.4.1.1 Sikacrete 213F

Sikacrete 213F is a cement-based, dry mix fire protection mortar for wet sprayed

application. It contains phyllosilicate aggregates, which could effectively resist the heat

of hydrocarbon fires. The manufacturer reported thermal conductivity for it is

0.23W/mK at 10°C. and the compressive strength of the insulation is approximately 2.0

MPa. In order to determine the specific heat and thermal conductivity of the insulation

the 50 mm by 50mm by 15mm samples of insulation was prepared during the

installation. Later when the moisture content of the samples was stabilized they were

249

tested in Thermal Conductivity Meter (Kyoto Electronics Model TC-31). Using a non-

steady (transient) state measurement technique.

After averaging the results appropriate curves were fitted following equations is the

result of this procedure.

The thermal conductivity of Sikacrete 213F could be approximated using the following

equation.

𝑘𝑐(𝑇) = 0.46 � 𝑇1000

�2− 0.21 � 𝑇

1000�+ 0.32 ( C-20)

And the equation for specific heat of Sikacrete213F is

𝑐𝑐(𝑇) = 14.96 � 𝑇100

�2− 116.4 � 𝑇

100�+ 1611 ( C-21)

Density was calculated to 700kg/m3.

C.4.1.2 Other Insulation materials

C.4.1.3 Tyfo® Vermiculite-Gypsum (VG) Insulation

This insulation product is manufactured by Tyfo®. (Bisby 2003) reported the following

equations for thermal properties based on Thermogravimetric Analysis (TGA) in

addition to material property estimates from litraturte. Tyfo® VG insulation consists of

two components gypsum and vermiculite. Assuming a mixture ratio of 2:1 of

vermiculite and gypsum, Bisby (2003) obtained the following relationships for specific

heat (J/kg-ºC) and temperature (ºC).

250

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

39167.0:690

31663663690

9167.06976.16976.1:690663

31610610663

8509.06976.18509.0:663610

31153153610

8509.00136.10136.1:610153

31137137153

0136.13722.13722.1:153137

31125125137

3722.19066.69066.6:137125

317878125

3058.19066.63058.1:12578

312002078

1763.13058.11763.1:7820

31763.1:200

EcT

ETcT

ETcT

ETcT

ETcT

ETcT

ETcT

ETcT

EcT

VGVG

VGVGVG

VGVGVG

VGVGVG

VGVGVG

VGVGVG

VGVGVG

VGVGVG

VGVG

=≤

⋅

−⋅

−−

−=≤≤

⋅

−⋅

−−

+=≤≤

⋅

−⋅

−−

−=≤≤

⋅

−⋅

−−

−=≤≤

⋅

−⋅

−−

−=≤≤

⋅

−⋅

−−

+=≤≤

⋅

−⋅

−−

+=≤≤

=≤≤

( C-22)

Using a similar method thermal conductivity (W/m-ºC) with temperature was derived

assuming that the thermal conductivity of vermiculite is constant with temperature.

( ) ( )

( ) ( )

( ) ( )8008001000

1224.02087.01224.0:800

400400800

0726.01224.00726.0:800400

0726.0:400101

100100101

0726.01158.01158.0:101100

1158.0:1000

−⋅−−

+=≤

−⋅−−

+=≤≤

=≤≤

−⋅−−

−=≤≤

=≤≤

VGVGVG

VGVGVG

VGVG

VGVGVG

VGVG

TkT

TkT

kT

TkT

kT

( C-23)

And finally for density the following equations could be used.

251

( ) ( )

287:200

100100200287351351:200100

351:1000

=≤

−⋅−−

−=≤≤

=≤≤

VGVG

VGVGVG

VGVG

T

TT

T

ρ

ρ

ρ

( C-24)

C.4.1.4 Promat-H and Promatect-L

Promat H and Promat L are medium and light density calcium silicate boards with a

density at 20 °C of 870 kg/m3 and 500 kg/m3 respectively, (Blontrock, Taerwe et al. 2000).

Thermal conductivity of Promat H as function of temperature (T) is as follows

𝑘𝑝𝑟,𝐻(𝑊/𝑚℃) = 0.196− 0.207 ∙ 10−2 � 𝑇100

�+ 0.131 ∙ 10−2 � 𝑇100

�2 ( C-25)

And for the specific heat this equation could be used.

𝑐𝑝𝑟,𝐻(𝐽/𝑘𝑔℃) = 561 − 101.1 � 𝑇100

�+ 22.4 � 𝑇100

�2

+ 2.5 � 𝑇100

�3( C-26)

Thermal conductivity of Promat L as function of temperature (T) is as follows

𝑘𝑝𝑟,𝐿(𝑊/𝑚℃) = 0.0804− 0.589 ∙ 10−3 � 𝑇100

�+ 1.541 ∙ 10−3 � 𝑇100

�2( C-27)

And for the specific heat this equation could be used.

𝑐𝑝𝑟,𝐿 �𝐽𝑘𝑔℃� = 561 − 101.1 � 𝑇

100� + 22.4 � 𝑇

100�2

+ 2.5 � 𝑇100

�3( C-28)

structural and thermal behaviour of insulated frp

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