finite element analysis of a prestressed concrete beam using frp tendon

APPENDIX 1

A PROJECT REPORT on

FINITE ELEMENT ANALYSIS OF A PRESTRESSED

CONCRETE BEAM USING FRP TENDON Submitted By

GIRISH KUMAR SINGH 1011020021

in the partial fulfillment for the award of the degree

of

BACHELOR OF TECHNOLOGY (FULL TIME) In

CIVIL ENGINEERING Under the guidance of

Mr. SELVA CHANDRAN PANDIAN (Engineering Manager, Parson Brinckerhoff)

SRM UNIVERSITY RAMAPURAM

APRIL, 2014

CONTENTS CHAPTER NO. TITLE PAGE

NO. TABLE OF CONTENT ii

ACKNOWLEDGEMENT vi

ABSTRACT vii

LIST OF TABLE ix

LIST OF FIGURES x

LIST OF ABBREVIATION xii

METHODOLOGY xiii

1. INTRODUCTION 1.1 General 1

1.2 Material Introduction 4

1.2.1 Glass 4

1.2.2 Aramid 4

1.2.3 Carbon 4

1.2.4 Carbon Fibre Composite Cable 5

(CFCC)

1.3 Finite element method

1.3.1 General 6

1.3.2 Ansys 6

1.3.2.1 Finite Element Model Of 6

Concrete


Steel Beam


Reinforcement

ii


External Prestressed

Tendon


Steel Plates


Interface Surface

1.3.2.7 Representation Of Shear 9

Connectors

2. LITERATURE SURVEY

2.1 General 11

2.2 Serviceability Of Concrete Beams Prestressed 11

By Fiber Reinforced Plastic Shells

2.3 Finite Element Analysis Of Prestressed 12

Concrete Beams

2.4 Element Used In Prestressed Members In Ansys 13

2.4.1 Solid65 Description 14

2.4.2 Link8 Description 17

3. ANSYS MODEL

3.1 General

3.1.1 Element Types 18

3.2 Model No. 1

3.2.1 Material Properties 18

3.2.2 Modelling 24

3.2.3 Meshing 26

3.2.4 Numbering Controls 27

3.2.5 Boundary conditions 28

3.2.6 Analysis type 28

3

3.2.7 Load step method 29

3.2.8 Results 34

3.3 Model No. 2

3.3.1 Beam Property 39 3.3.2 Real Constants 40 3.3.3 Material Properties 42 3.3.4 Modelling 45 3.3.5 Meshing 46 3.3.6 Numbering controls 47 3.3.7 Boundary conditions 48 3.3.8 Analysis type 48 3.3.9 Load step method 49 3.3.10 Results 56

3.4 Model No. 3

3.4.1 Beam Property 60 3.4.2 Real constants 60 3.4.3 Material Properties 62 3.4.4 Modelling 65 3.4.5 Meshing 66 3.4.6 Numbering controls 67 3.4.7 Boundary conditions 68 3.4.8 Analysis type 68 3.4.9 Load step method 69 3.4.10 Results 76

4. EXPERIMENTAL RESULTS

4.1 General 79

4.2 Test Specimen 79

4.3 Testing Scheme 82

4

4.4 Material Properties 82

4.5 Results Of The Experimental Program 85

5. CONCLUSION 89

REFERENCES 90

5

ACKNOWLEDGEMENT

I would like to acknowledge all the people who have helped me in the completion

of this dissertation. First and foremost I would like to express my deepest gratitude to my

advisors Selva Chandran Pandian, Engineering Manager, Parson Brinckerhoff for all his

guidance, advice, suggestion and friendship.

I have been incredibly to have the advisors who gave me the freedom to discover

on my own. I would also like to thanks my HOD Mrs. T.CH. Madhavi For all her support

and suggestion. I am also thankful to the department of civil engineering for their support.

Lastly I would like to give a hearty gratitude to my internal guide Mr.

Sivaramakrishanan Asst. Professor of SRM University for all his support, without his help

and suggestions this project work would not have been possible.

6

ABSTRACT

Concrete prestressed structural components exist in buildings and bridges in

different forms. Understanding the response of these components during loading is

crucial to the development of an overall efficient and safe structure. Different

methods have been utilized to study the response of structural components.

Experimental based testing has been widely used as a means to analyse individual

elements and the effects of concrete strength under loading.

While this is a method that produces real life response, it is extremely time

consuming, and the use of materials can be quite costly. In this paper we used finite

element analysis to study behaviour of these components. The use of computer

software (Ansys) to model these elements is much faster, and extremely cost-

effective. To fully understand the capabilities of finite element computer software

(Ansys), we look back to experimental data and simple analysis.

Data obtained from a finite element analysis package is not useful unless the

necessary steps are taken to understand what is happening within the model that is

created using the software. Also, executing the necessary checks along the way, is

key to make sure that what is being output by the Ansys is valid.

This paper is a study of prestressed concrete beams using finite element

analysis to understand the response of prestressed concrete beams due to transverse

loading and to analyse the behaviour of FRP material under these circumstances.

vii

This paper also includes the comparison of steel and FRP on the same module and

also gives the final load v/s deflection curve under the both linear and non-linear

properties of the materials.

8

LIST OF TABLES

SR. NO.

1.1

TITLE OF THE TABLE

Typical Fibre Properties

PAGE NO.

2

1.2 Material Type of specimen - 1 18

1.3 Real Constants of specimen - 1 19

1.4 Material Properties of specimen - 1 21

1.5 Result Comparison of specimen -1 38

1.6 Material Type of specimen – 2 39

1.7 Real Constants of specimen – 2 41

1.8 Material Properties of specimen – 2 43


1.10 Material Type of specimen – 3 60

1.11 Real Constants of specimen – 3 61

1.12 Material Properties of specimen – 3 63


1.14 Test Program 82

1.15 Tensile Properties of Leadline 83

1.16 Concrete Properties 83

1.17 Prestressing Force in the Tested Beams 84

9

LIST OF FIGURES

SR.NO.

1.

NAME OF THE FIGURE

Geometry of Solid 65

PAGE NO.

6

2. Geometry of Shell 43 7

3. Geometry of Link 8 8

4. Geometry of Link 45 8

5. Geometry of Contra 173 and Target 170 9

6. Geometry of Combin 39 10

7. Stress-Strain curve of concrete 23

8. Cross and Reinforcement Details 24

9. Line Diagram of the R-2-.5V 25

10. Line Diagram showing Tendons 25

11. Cross-Sectional View of Elements 26

12. Isometric View of Element 26

13. Behavior of Beam 34

14. Bursting Zone due to prestressing 34

15. Y-Component Displacement 35

16. Load vs. Midspan Deflection with no prestressing 35

17. Load vs. Midspan Deflection with 30% prestressing 36




21. Stress- Strain Curve of Concrete 44

22. Line Diagram of Beam 45

23. Outline of Beam In Ansys 45

24. Cross-Sectional View of Elements 46

25. Isometric View of Element 46

26. Elements of Beam 54

1

27. Stress Distribution in beam 54

28. Stress in X-Direction 55

29. Stress in Y-Direction 55

30. Deflection for Sr. No. 2 57




34. Stress Strain curve of concrete 65

35. Outline of beam in Ansys 65

36. Front line view 66

37. Elements after Meshing 66

38. Elements of Beam 74

39. Stress Pattern 74

40. Deflection of beam 75

41. Line Diagram 75

42. Final Graph for Load v/s Deflection 76

43. Load v/s Deflection For Sr. No. 1 77




47. Cross Section of the Tested Beams 81

48. Details of End Zone of the Beam 81

49. Stress-Strain Relationship of Lead line Bar 84

50. Load-Deflection graph with different number of 87

Lead line Bars

51. Stress Strain Behavior of beams 88

1

List of Abbreviations

SR. NO.

1.

Abbreviation

FRP

Full Form

Fibre Reinforced Polymer

2. GFRP Glass Fibre Reinforced Polymer

3. AFRP Aramid Fibre Reinforced Polymer

4. CFRP Carbon Fibre Reinforced Polymer

5. CFCC Carbon Fibre Composite Cable

6. FEM Finite Element Modelling

7. UX Degree in freedom X- direction

8. UY Degree of freedom in Y-direction

9. UZ Degree of freedom in Z-direction

10. MAT Material

11. EX Modulus of Rigidity

12. PRXY Poisson’s Ratio

xii

METHODOLOGY 3.1 RESEARCH METHODOLOGY

Finite element method was used to study the behavior of pre-stressed beam

using FRP Tendons. Linear and non-linear analyses were carried out to evaluate the stress

in the beam. The finite element modeling of beam was validated with the results available

from literature. The results of experimental investigation were used for validation of the

finite element model. Finite element analyses on the simply supported beam were carried

out and the results are presented. From the analytical investigation, the behavior of FRP

Tendons can be studied.

13

Methodology flow chart

14

CHAPTER 1

INTRODUCTION

1.1 GENERAL

(REFER ACI440-04R)

Fibre-reinforced polymer (FRP) composites have been proposed for use as

prestressing tendons in concrete structures. The promise of FRP materials lies in their high-

strength lightweight, noncorrosive, non-conducting, and nonmagnetic properties. In

addition, FRP manufacturing, using various cross-sectional shapes and material

combinations, offers unique opportunities for the development of shapes and forms that

would be difficult or impossible with conventional steel materials. Lighter-weight

materials and preassembly of complex shapes can boost constructability and efficiency of

construction.

At present, the higher cost of FRP materials suggests that FRP use will be confined

to applications where the unique characteristics of the material are most appropriate.

Efficiencies in construction and reduction in fabrication costs will expand their potential

market. FRP reinforcement is available in the form of bars, grids, plates, and tendons. This

document examines both internal and external prestressed reinforcement in the form of

tendons.

One of the principal advantages of FRP tendons for prestressing is the ability to

configure the reinforcement to meet specific performance and design objectives. FRP

tendons may be configured as rods, bars, and strands as shown in Table. 1.1. The surface

texture of FRP tendons may vary, resulting in bond with the surrounding concrete that

varies from one tendon configuration to another. Unlike conventional steel reinforcement,

there are no standardized shapes, surface configurations, fibre orientation, constituent

materials, and proportions for the final products.

Similarly, there is no standardization of the methods of production, such as

pultrusion, braiding, filament winding, or FRP preparation for a specific application. Thus,

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FRP materials require considerable engineering effort to use properly. Bakis (1993) has

outlined manufacturing processes. FRP tendons are typically made from one of three basic

fibres. These fibres are aramid, carbon, and glass. Aramid fibres consist of a semi crystalline

polymer known as aromatic polyamide. Carbon fibres are based on the layered grapheme

(hexagonal) networks present in graphite, while glass generally uses either E-glass or S-

glass fibres. E-glass is a low-cost calcium-alumino boro silicate glass used where strength,

low conductivity, and acid resistance are important. S-glass is a magnesium- alumino

silicate glass that has higher strength, stiffness, and ultimate strain than E-glass. S- glass

costs more than E-glass, and both are susceptible to degradation in alkaline

environments. Table 1.1 gives properties of typical fibres.

The selection of the fibre is primarily based on consideration of cost, strength,

stiffness, and long-term stability. Within these fibre groups, different performance and

material characteristics may be achieved. For example, aramids may come in low, high,

and very high modulus configurations. Carbon fibres are also available with moduli

ranging from below that of steel to several multiples of that of steel. Of the several fibre

types, glass-based FRP reinforcement is least expensive and generally uses either E-glass

or S-glass fibres. The resins used for fibre impregnation are usually thermosetting and may

be polyester, vinyl ester, epoxy, phenolic, or polyurethane.

The formulation, grade, and physical-chemical characteristics of resins are

practically limitless. The possible combinations of fibres, resins, additives, and fillers make

generalization of the properties of FRP tendons very difficult. Additionally, FRP

composites are heterogeneous and anisotropic. Final characteristics of an FRP tendon are

dependent on fibre and resin properties, as well as the manufacturing process. Specific

details of a particular tendon should be obtained from the manufacturer of the tendon.

The advantages of FRP reinforcement in comparison to steel reinforcement are as follows:

I. High ratio of strength to mass density (10 to 15 times greater than steel)

II. Carbon and Aramid fibre reinforcements have excellent fatigue characteristics(as

much as three times higher than steel) However, the fatigue strength ofglass FRP

reinforcement may be significantly below steel's

III. Excellent corrosion resistance and electromagnetic neutrality

IV. Low axial coefficient of thermal expansion, especially for carbon fibre reinforced

composite materials.

The disadvantages of FRP reinforcement include:

I. High cost (5 to 50 times more than steel)

II. Low modulus of elasticity (for Aramid and glass FRP)

III. Low ultimate failure strain

IV. High ratio of axial to lateral strength causing concern for anchorages when using

FRP reinforcement for prestressing

V. Long term strength can be lower than the short-term strength for

FRPreinforcement due to creep rupture phenomenon

VI. Susceptibility of FRP to damage by ultra-violet radiation

VII. Aramid fibres can deteriorate due to water absorption

VIII. High transverse thermal expansion coefficient in comparison to concrete

The tensile characteristics of reinforcement made from Carbon Fibre Reinforced

Plastic (CFRP) , Aramid Fibre Reinforced Plastic (AFRP), and Glass Fibre Reinforced

Plastic (GFRP), are compared to steel.

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1.2 Material Introduction

1.2.1 Glass:

Two types of glass fibres are commonly used in the construction industry, namely-

glass and S-glass. E-glass type is the most widely used GFRP due to its lower cost

as compared to S-glass type, however S-glass has a higher tensile strength. Fresh

drawn glass fibres exhibit a tensile strength in the order of 3450 Mpa, but surface flaws

produced by abrasion tend to reduce the strength to 1700 Mpa. This strength is

furthered graded under fatigue loading due to the growth of flaws and also degrades in

the presence of water. Commercially GFRP prestressing tendons and rods are available

underthe brand names of Isopod by Pulpal Inc. (Canada), IMCa by Imia Reinforced

PlasticsInc. (USA), Jute by Cousin Frere (France), Kodiak by IGI International Grating

(USA),Plalloy by Asahi Glass Matrex (Japan), Polystal by Bayer AG and StragBau-

AG(Germany), and C-bar by Marshell Ind. (USA).

1.2.2 Aramid:

Aramid (abbreviation for aromatic polyamide) based FRP products have a

tensile strength in the range of 2650 to 3400 MPa and an elastic modulus of from 73 to

165GPa. AFRP prestressing tendons are produced in different shapes such as spiral

wound,braided, and rectangular rods. It has been reported that there is no fatigue limit

for Aramid fibres, however creep-rupture phenomenon has been observed. Aramid fibres

are also quite sensitive to ultra-violet radiation. Commercially, AFRP prestressing tendons

androds are available under the brand names of Technora by Teijin (Japan), Fibre by Mitsui

(Japan), Arapree by AKZO and Hollands cheBetonGroep (Holland), Phillystran by United

Ropeworks (USA), and Parafil Ropes by ICI Linear Composites (UK).

1.2.3 Carbon:

Carbon fibres can be produced from two materials, namely textile (PAN-based)and

PITCH-based material. The most common textile material is poly-acrylonitrile

(PAN).PITCH-based material is a by-product of petroleum refining or coal coking. Carbon

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Fibres have exceptionally high tensile strength to weight ratios with strength ranging

from 1970to 3200 MPaand tensile modulus ranging from 270 to 517 GPa. These fibres

also have a low coefficient of linear expansion on the order of 0.2x 10-6 mimiC, and

high fatigue strength. However, disadvantages are their low impact resistance, high

electrical conductivity, and high cost. Commercially available CFRP prestressing tendons

are available under the brand names of Carbon Fibre Composite Cable (CFCC) by

TokyoRope (Japan), Leadline by Mitsubishi Kasai (Japan), Jitec by Cousin Frere (France),

and Bri-Ten by British Ropes (UK).

1.2.4 Carbon Fibre Composite Cable (CFCC):

Carbon Fibre Composite Cables (CFCC) made in Japan by Tokyo

RopeManufacturing Co. use PAN (polyacrylonite) type carbon fibres supplied by Toho

Rayon.Individual wires are manufactured by a roving prepreg process where the epoxy

resin is heat cured. The prepreg is twisted to create a fibre core and then wrapped by

synthetic yarns. The purpose of the yarn is to protect the fibres from ultra-violet radiation

and mechanical abrasion, and also improves the bond properties of the wire to

concrete.Cables are then made from one, seven, nineteen, or thirty-seven wires and are

twisted to allow better stress distribution through the cross-section.

Tokyo Rope currently produces cables with diameters from 3 to 40 mm in any length

up to 600 metres. For 12.5 and 15.2 mm diameter CFCC cables the ultimate tensile strengths

are 2100 and 2150 MPa respectively. Both sizes have a tensile elastic modulus of 137 GPa

and an ultimate tensile failure strain of 1.5 to 1.6%. The thermal coefficient of expansion is

approximately 0.6xl0-6 /C which is about 1/20 that of steel. The relaxation is about 3.5%

after 30 years at 80% of the ultimate load, this is about 50% less than that of steel. Also

pull-out tests show that CFCC has a bond strength to concrete of6.67 MPa, which is more

than twice that of steel.

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1.3 Finite element method

1.3.1 General :

There are many software which is use for analysis but Ansys gives more accurate

results compared to other software.

1.3.2 Ansys:

The ANSYS computer program is utilized for analyzing structural components

encountered throughout the current study. Finite element representation and corresponding

elements designation in ANSYS used in this study are discussed:-

1.3.2.1 Finite element model of concrete

The finite element idealization of concrete should be able to represent the concrete

cracking, crushing, the interaction between concrete and reinforcement and the capability

of concrete to transfer shear after cracking by aggregate interlock. In order to investigate

the failure in concrete for prestressed composite steel-concrete beams, three dimensional

elements are to be used.

In the current study, three-dimensional brick element with 8 nodes is used to model

the concrete (SOLID65 in ANSYS). The element is defined by eight nodes having three

degrees of freedom at each node: translations of the nodes in x, y, and z-directions. The

geometry, node locations, and the coordinate system for this element are shown in Figure

1.

Fig: 1. Geometry Of SOLID65

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1.3.2.2 Finite element model of steel beam

To represent the steel beam in finite element, 4-node shell element is needed

with three translations in x, y and z in each node to achieve the compatibility condition

with translation in x, y and z in adjacent brick element to it. For this purpose, three-

dimensional 4-node shell element, which is represented as (SHELL43 in ANSYS) is used,

regardless of the rotations in each nodes. The element has plasticity, creep, stress

stiffening, large deflection, and large strain capabilities. The geometry, node locations,

and the coordinate system for this element are shown in Figure 2.

Fig: 2. Geometry Of SHELL43

1.3.2.3Finite element model of reinforcement

To model steel reinforcement in finite element. Three techniques exist these are

discrete, embedded, and smeared. The discrete model (LINK8) is used in this study. The

LINK8 is a spar (or truss) element. This element can be used to model trusses, sagging

cables, links, springs, etc. The 3-D spar element is a uniaxial tension-compression

element with three degrees of freedom at each node: translations of the nodes in

x, y, and z-directions. No bending of the element is considered. The geometry, node

locations, and the coordinate system for this element are shown in Figure 3.

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1.3.2.4 Finite element model of external prestressed tendon

In the present study the prestressing stress was taken as the initial value and

equal to the effective stress .It appears in the analysis as initial strain in link element.

Link8 is used to represent the external cable. Since the cable is located outside the steel

section and the prestressing force is transferred to composite beam through end anchorages

and stiffeners, the cable is connected to beam only at the anchorage or stiffeners.

1.3.2.5 Finite element model of steel plates

Steel plates are added at the loading location to avoid stress concentration

problems. This provides a more even stress distribution over the load area. The solid

element (SOLID45 in program) was used for the steel plates. The element is used for the

3-D modelling of solid structures. The element is defined by eight nodes having three

degrees of freedom at each node translations in the nodal x, y, and z directions as shown

in Figure (4).

Fig: 4. Geometry Of SOLID45

Fig: 3. Geometry Of LINK8

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1.3.2.6 Finite element model of interface surface

A three-dimensional nonlinear surface-to-surface “contact-pair” element (CONTA-

173& TARGE170) was used to model the nonlinear behaviour of the interface

surface between concrete and steel beam. The contact-pair consists of the contact

between two boundaries, one of the boundaries represents contact, slid and deformable

surface taken as contact surface (CONTA-173 in ANSYS) and the other represents rigid

surface taken as a target surface

(TARGE-170 in ANSYS). Figure 5 shows the geometry of (CONTA173& TARGE170).

Fig: 5.Geometry of CONTA173 and TARGET170

1.3.2.7Representation of shear connectors

A nonlinear spring element (COMBIN39 in ANSYS) and (Link8) are used to

represent the shear connectors behaviour. COMBIN39 is used to resist the normal

force between the concrete and steel beam while Link8 works as stirrups in resisting

the vertical shear at concrete layer.

COMBIN39 is a unidirectional element (or nonlinear spring) with nonlinear

generalized force-deflection capability that can be used in any analysis.

The element has longitudinal or torsional capability in 1-D, 2-D, or 3-D

applications. The geometry, node locations, and the coordinate system for this element are

shown in Figure 6.

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Fig: 6. Geometry of COMBIN39

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CHAPTER 2

LITERATURE SURVEY

2.1 General

To provide a detailed review of the body of literature related to reinforce and prestressed

concrete in its entirety would be too immense to address in this paper. However, there are

many good references that can be used as a starting point for research (ACI

1978,MacGregor 1992, Nawy 2000). This literature review and introduction will focus

on recent contributions related to FEA and past efforts most closely related to the needs

of the present work.

The use of FEA has been the preferred method to study the behavior of concrete

(For economic reasons). William and Tanabe (2001) contains a collection of papers

concerning finite element analysis of reinforced concrete structures. This collection

contains areas of study such as: seismic behavior of structures, cyclic loading of

reinforced concrete columns, shear failure of reinforced concrete beams, and concrete

steel bond models.

Shing and Tanabe (2001) also put together a collection of papers dealing with

In-elastic behavior of reinforced concrete structures under seismic loads. The

monograph contains contributions that outline applications of the finite element method for

studying post-peak cyclic behavior and ductility of reinforced concrete beam, the analysis

of reinforced concrete components in bridge seismic design, the analysis of reinforced

concrete beam-column bridge connections, and the modeling of the shear behavior of

reinforced concrete bridge structures.

The focus of these most recent efforts is with bridges, columns, and seismic design.

The focus of this thesis is the study of non-prestressed and prestressed flexural members.

AMR A. ABDELRAHMAN(1995) give the basic behavior of prestressed member

with full experimental data and the specification of the section with its dimension and the

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number of strands used in every section during casting. He also provides the property of

FRP material used in the section and the results obtained after the testing of the section.

The following is a review and synthesis of efforts most relevant to this thesis

discussing FEA applications, experimental testing, and concrete material models.

2.2 Serviceability of concrete beams prestressed by fibre reinforced plastic tendons

by Amr a. abdelrahman

Use of carbon fibre reinforced plastic, CFRP, as prestressing reinforcement

for Concrete structures, has increased rapidly for the last ten years. The non-corrosive

Characteristics, high strength-to-weight ratio and good fatigue properties of CFRP

Reinforcement significantly increase the service life of structures. However, the high cost

and low ductility of CFRP reinforcement due to its limited strain at failure are problems yet

to be solved for widespread use of this new material. Use of partially prestressed concrete

members has the advantages of reducing cost and improving deform ability.

However, the deflection and cracking of concrete beams partially prestressed by

CFRP reinforcement should be investigated.An experimental program undertaken at the

University of Manitoba to study the serviceability of concrete beams prestressed by CFRP

reinforcements is reported. Testsare described of eight concrete beams prestressed by

Leadline CFRP bars, produced by Mitsubishi Kasei, Japan, and two beams prestressed by

conventional steel strands. The beams are 6.2 meters long and 330 mm in depth. The

various parameters considered are the prestressing ratio, degree of prestressing, and

distribution of CFRP rods in the tension zone. The thesis examines the various limit states

and flexural behavior of concrete beams prestressed by CFRP bars, including different

modes of failure. The behavior of beams prestressed by CFRP bars is compared to similar

beams prestressed by conventional steel strands.

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Theoretical models are proposed to predict the deflection prior and after cracking

and the crack width of concrete beams prestressed by Lead lineCFRP bars under service

loading conditions. Crack width is predicted using appropriate bond factors for this type of

reinforcement. A procedure is formulated for predicting the location of the centroidal axis

of the cracked sections prestressed by CFRP bars. In addition, a method is proposed to

calculate the deflection and the crack width of beams partially prestressed by CFRP bars

under repeated load cycles within the service loading range. The deform ability of concrete

beams prestressed by CFRP reinforcement is also discussed. A model is proposed to

quantify the deform ability of beams prestressed by fiber reinforced plastic

reinforcements.The reliability of the proposed methods and the other methods used from

the literature to predict the deflection and the crack width is examined by comparing the

measured and the computed values of the tested beams and beams tested by others.

An excellent agreement is found for the methods predicting the deflection and a good

agreement is found for the crack width prediction. Design guidelines for prestressed

concrete beams with CFRP reinforcement are also presented.

2.3 Finite Element Analysis of Prestressed Concrete Beams By Abhinav S.Kasat &

Alsson varghese

Finite element analysis is an effective method of determining the static

performance of structures for the reasons which are saving in design time cost effective in

construction and increase the safety of the structure. Previously it is necessary to use

advanced mathematical methods in analysis large structures, such as bridges tall buildings

and other more accuracy generally required more elaborate techniques and therefore a

large friction of the designer’s time could be devoted to mathematical analysis. Finite

element methods free designer’s from the need to concentrate on mathematical calculation

and allow them to spend more time on accurate representation of the intended

structure and review of the calculated performance (Smith, 1988). Furthermore by using

the programs with interactive graphical facilities it is possible to generate finite element

models of complex structures with considerable ease and to obtain the results in a

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convenient readily assimilated form.This may save valuable design time. More accurate

analysis of structure is possible by the finite element method leading to economics in

materials and construction also in enhancing the overall safety (DeSalvoand

Swanson,1985).

However in order to use computer time and design time effectively it is important to

plan the analysis strategy carefully. Before a series of dynamic tests carry out in the field

a complete three-dimensional finite element models are developed for a bridges prior to

its testing. The results from these dynamic analyses are used to select instrument positions

on the bridge and predict static displacement. Then, they are calibrated using the

experimental frequencies and mode shapes. The frequencies and mode shapes mainly are

used to provide a basis for the study of the influence of certain parameters on the dynamic

response of the structure the influence of secondary structural elements the cracking of the

deck slabs the effects of long-term concrete creep and shrinkage and soon (Paultre and

Proulx, 1995). Besides more sophisticated methods based on finite element or finite strip

representation have been used by some researchers to study the dynamic behaviour of

bridges Fam(1973) and Tabba (1972)studied the behaviour of curved box section bridges

using the finite element method for applied static and dynamic loads. A three-

dimensional finite element analysis program was developed for curved cellular structures.

Solutions of several problems involving static and dynamic responses were presented

using the proposed and others sophisticated methods of analysis. An experimental study

conducted on two curved box girder Plexiglas models confirmed here liability of the

proposed methods of analysis.

2.4 Element Used In Prestressed MemberANSYS 2012

2.4.1 SOLID65 Description:

SOLID65 is used for the 3-D modeling of solids with or without reinforcing

bars (rebar). The solid is capable of cracking in tension and crushing in compression. In

concrete applications, for example, the solid capability of the element may be used to

model the concrete while the rebar capability is available for modeling reinforcement

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behavior. Other cases for which the element is also applicable would be reinforced

composites (such as fiberglass), and geological materials (such as rock). The element is

defined by eight nodes having three degrees of freedom at each node: translations in the

nodal x, y, and z directions. Up to three different rebar specifications may be defined.The

concrete element is similar to the SOLID45 (3-D Structural Solid) element with the

addition of special cracking and crushing capabilities. The most important aspect of this

element is the treatment of nonlinear material properties. The concrete is capable of

cracking (in three orthogonal directions), crushing, plastic deformation, and creep. The

rebar are capable of tension and compression, but not shear. They are also capable of plastic

deformation and creep. See SOLID65 in the ANSYS, Inc. Theory Reference for more details

about this element.

Solid 65 Geometry

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SOLID65

Input Summary

Nodes:-I, J, K, L, M, N, O, P

Degrees of Freedom:-UX, UY, UZ

Real Constants:-MAT1, VR1, THETA1, PHI1, MAT2, VR2,THETA2, PHI2, MAT3,

VR3, THETA3, PHI3, CSTIF

(where MATn is material number, VRn is volume ratio, and THETAn and PHIn are

orientation angles for up to 3 rebar materials)

Material Properties

EX, ALPX (or CTEX or THSX), DENS (for each rebar) EX, ALPX (or CTEX or

THSX), PRXY or NUXY, DENS (for concrete)

Supply DAMP only once for the element (use MAT command to assign material

property set). REFT may be supplied once for the element, or may be assigned on a per

rebar basis. See the discussion in "SOLID65 Input Data" for more details.

Special Features

Plasticity

Creep

Cracking

Crushing

Large deflection

Large strain

Stress stiffening

Birth and death

Adaptive descent

16 | P a g e

2.4.2 LINK8 Description:

LINK8 is a spar which may be used in a variety of engineering applications. This

element can be used to model trusses, sagging cables, links, springs, etc. The 3-D spar

element is a uniaxial tension-compression element with three degrees of freedom at each

node: translations in the nodal x, y, and z directions. As in a pin-jointed structure, no

bending of the element is considered. Plasticity, creep, swelling, stress stiffening, and large

deflection capabilities are included. See LINK8 in the ANSYS, Inc. Theory Reference for

more details about this element. See LINK10 for a tension-only/compression-only element.

LINK8 Input Summary

Nodes:-I, J

Degrees of Freedom:-UX, UY, UZ

Real Constants:- REA - Cross-sectional areaISTRN - Initial strain

Material Properties EX, ALPX (or CTEX or THSX), DENS, DAMP

Special Features

Large deflection ,Creep,Large deflection, Plasticity, Stress

stiffening, Swelling , Birth and death

LINK8 GEOMETRY

17 | P a g e

CHAPTER 3

ANSYS MODEL

3.1 General

3.1.1Element Types

Table: 1.2- Material Type

Material Type ANSYS Element

Concrete Solid 65

Steel Plates and Supports Solid 45

Reinforcement Link 8

The element types for this model are shown in Table 1.2. The Solid65 element was

used to model the concrete. This element has eight nodes with three degrees of freedom at

each node – translations in the nodal x, y, and z directions. This element is capable of

plastic deformation, cracking in three orthogonal directions, and crushing.

A Solid45 element was used for steel plates at the supports for the beam. This

element has eight nodes with three degrees of freedom at each node – translations in the

nodal x, y, and z directions.

A Link8 element was used to model steel reinforcement. This element is a 3D spar

element and it has two nodes with three degrees of freedom – translations in the nodal x,

y, and z directions. This element is also capable of plastic deformation.

3.2 Real Constants

The real constants for this model are shown in Table: 1.3. Note that individual

elements contain different real constants. No real constant set exists for the Solid45

element. Real Constant Set 1 is used for the Solid65 element. It requires real constants for

18 | P a g e

rebar assuming a smeared model. Values can be entered for Material Number, Volume

Ratio, and Orientation Angles. The material number refers to the type of material for the

reinforcement. The volume ratio refers to the ratio of steel to concrete in the element. The

orientation angles refer to the orientation of the reinforcement in the smeared model.

ANSYS allows the user to enter three rebar materials in the concrete.

Each material corresponds to x, y, and z directions in the element. The

reinforcement has uniaxial stiffness and the directional orientation is defined by the user.

In the present study the beam is modelled using discrete reinforcement.

Therefore, a value of zero was entered for all real constants which turned the

smeared reinforcement capability of the Solid65 element off. Real Constant Sets 2 is

defined for the Link8 element. Values for cross-sectional area and initial strain were

entered.

Table:1.3- Real Constants

Real Constant Element Type Constants

Real

Constants

for Rebar

1

Real

Constants

for Rebar

2

Real

Constants

for Rebar

3

Material

Number

0 0 0

Volume

Ratio

0 0 0

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1. Solid 65 Orientation

Angle

0 0 0

Orientation 0 0 0

Angle

Cross- 50.26

sectional

Area

(mm2)

2. Link 8 Initial 0.0088874

Strain

(mm/mm)

3.2.1 Material Properties

Three material models were given:

1. Material 1 for Concrete

a. Linear Isotropic

b. Concrete

c. Multilinear Elastic

2. Material 2 for Steel Plates

a. Linear Isotropic

3. Material 3 for FRP

a. Linear Isotropic

b. Bilinear Isotropic

The values of Material Properties is shown in Table 1.4

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Table: 1.4- Material Properties

Material Model No. Element Type Material Properties

Linear Isotropic

EX 38,480

PRXY 0.2

Multilinear Isotropic 1. Solid 65

Point 1

Strain

0.00036

Stress

9.8023 Point 2 0.0006 15.396 Point 3 0.0013 27.517

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Point 4 0.0019 32.102

Point 5 0.00243 33.095

Concrete

ShrCf-Op 0.3

ShrCf-Cl 1

UnTensSt 5.3872

UnTensSt -1

BiCompSt 0

HydroPrs 0

BiCompSt 0

UnTensSt 0

TenCrFac 0

Linear Isotropic

2. Solid 45 EX 2,00,000 PRXY 0.3

Linear Isotropic

EX 1,87,000

PRXY 0.65

3. Link 8 Bilinear Isotropic

Yield Stress 2050

Tang Mod 0.65

22 | P a g e

Fig: 7. Stress- Strain Curve of Concrete

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3.2.2Modelling

3.2.2.1Model 1

Fig: 8. Cross and Reinforcement Details

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Fig: 9. Line Diagram of the R-2-.5V

Fig: 10. Line Diagram showing Tendons

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3.2.3Meshing

Fig: 11. Cross-Sectional View of Elements

Fig: 12. Isometric View of Element

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3.2.4 Numbering Controls

The command merge items merges separate entities that have the same

location. These items will then be merged into single entities. Caution must be taken when

merging entities in a model that has already been meshed because the order in which

merging occurs is significant. Merging keypoints before nodes can result in some of the

nodes becoming “orphaned” that is, the nodes lose their association with the solid model.

The orphaned nodes can cause certain operations (such as boundary condition transfers,

surface load transfers, and so on) to fail. Care must be taken to always merge in the order

that the entities appear. All precautions were taken to ensure that everything was merged

in the proper order. Also, the lowest number was retained during merging.

Commands Used

NUMMRG,NODE – To merge all nodes

NUMMRG,KP – To merge all keypoints

27 | P a g e

3.2.5 Boundary Conditions

Displacement boundary conditions are needed to constrain the model to get a unique

solution. To ensure that the model acts the same way as the experimental beam, boundary

conditions need to be applied at points of symmetry, and where the supports and loadings

exist. The symmetry boundary conditions were set first.

(Go To Main Menu)

Solution

Define Loads

Apply

Structural

Displacement

On Lines

(Pick lines) & OK

(Lab2) All DOF (DOFs to be constrained)

(Value) 0

OK

3.2.6 Analysis Type

The finite element model for this analysis is a simple beam under transverse loading.

For the purposes of this model, the Static analysis type is utilized. The Restart command

is utilized to restart an analysis after the initial run or load step has been completed. The

use of the restart option will be detailed in the analysis portion of the discussion.

28 | P a g e

(Go To Main Menu)

Solution

Analysis Type

Static & OK

3.2.7 Load Step Method

Step 1

(Go To Main Menu)

Solution

Solution Controls

Basic – Enter the values as shown below.

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Step 2

(Go To Main Menu)

Solution

Solution Controls

Nonlinear - Enter the values as shown below.

Step 3

(Go To Main Menu)

Solution

Define Loads

Apply

Structural

Force/Moment Value On Nodes

30 | P a g e

Step 4

(Go To Main Menu)

Solution

Load Step Opts

Write LS File

(Value) Load Step file number n, 1 &OK

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Step 5

(Go To Main Menu)

Solution

Define Loads

Delete

Structural

Force/Moment Value

On Nodes- Pick All

Step 6

Repeat the procedure from step 1 to step 5 with different load values.

Step 7

(Go To Main Menu)

Solution

Solve

From LS File

(Value) LSMIN- 1, LSMAX- 6, LSINC- 1

32 | P a g e

Step 8

(Go To Main Menu)

General Post Processor

Read Results

By Pick- Read

Step 9

(Go To Main Menu)

Time History Processor

Add

Nodal Solution

DOF

Choose Y- Component Displacement

Pick middle node & OK

Plot graph

33 | P a g e

3.2.8 Results

Fig: 13.Behaviour of Beam

Fig: 14. Bursting Zone due to prestressing

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Fig: 15. Y-Component Displacement

Fig: 16. Load vs. Midspan Deflection with no prestressing

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Fig: 17. Load vs. Midspan Deflection with 30% prestressing


36 | P a g e



37 | P a g e

Table: 1.5-Result Comparison:

SNO. Pre-stressing

Force, KN

Percentage Pre-

stressing, %

Midspan

Deflection At

35KN Load(mm)

1. 0 0 160

2. 50.12 30 62

3. 83.53 50 20

4. 116.94 70 12

5. 167.06 100 11

3.Model No. 2

Beam Dimensions:

38 | P a g e

Total number of Tendons: - 4

Spacing between tendons: - 25mm

Total Span length :- 6200mm

3.3.1. Beam Property

Table 1.6- Material Type


Concrete Solid 65



The element types for this model are shown in Table 1.6. The Solid65 element was

used to model the concrete. This element has eight nodes with three degrees of freedom at

each node – translations in the nodal x, y, and z directions. This element is capable of

plastic deformation, cracking in three orthogonal directions, and crushing.

39 | P a g e







3.3.2. Real Constants

The real constants for this model are shown in Table 1.7. Note that individual














entered.

40 | P a g e

Table 1.7- Real Constants


Real

Constants

for Rebar

1

Real

Constants

for Rebar

2

Real

Constants

for Rebar

3

Material 0 0 0

Number

Volume 0 0 0

Ratio

1. Solid 65 Orientation

0

0

0

Angle

Orientation 0 0 0

Angle

Cross- 134.52

sectional

Area

(mm2)


Strain

(mm/mm)

41 | P a g e

3.3.3. Material Properties



a. Linear Isotropic

b. Concrete



a. Linear Isotropic


a. Linear Isotropic



42 | P a g e

Table 1.8- Material Properties


Linear Isotropic

EX 38,480

PRXY 0.2

Multilinear Isotropic 1.

Concrete

ShrCf-Op 0.3

ShrCf-Cl 1

UnTensSt 5.3872

UnTensSt -1

BiCompSt 0

HydroPrs 0

BiCompSt 0

Solid 65 Strain

Stress

Point 1 0.00036 9.8023 Point 2 0.0006 15.396 Point 3 0.0013 27.517 Point 4 0.0019 32.102 Point 5 0.00243 33.095

43 | P a g e

Figure 3.1- Stress- Strain Curve of Concrete

UnTensSt 0

TenCrFac 0

Linear Isotropic

2. Solid 45 EX 2,00,000 PRXY 0.3

Linear Isotropic

EX 1,87,000

PRXY 0.65


Yield Stres 2050

Tang Mod 0.65

Fig: 21. Stress- Strain Curve of Concrete

44 | P a g e

3.3.4 Modelling

Fig: 22. Line Diagram of Beam

Fig: 23.Outline of Beam In Ansys

45 | P a g e

3.3.5 Meshing

Fig: 24. Cross-Sectional View of Elements

Fig: 25. Isometric View of Element

46 | P a g e

3.3.6. Numbering Controls





nodes becoming “orphaned”; that is, the nodes lose their association with the solid model.





Commands Used


NUMMRG,KP – To merge all key points

47 | P a g e

3.3.7. Boundary Conditions





(Go To Main Menu)

Solution

Define Loads

Apply

Structural

Displacement

On Lines

(Pick lines) & OK


(Value) 0

OK

3.3.8. Analysis Type


For the purposes of this model, the Static analysis type is utilized.

The Restart command is utilized to restart an analysis after the initial run or load

step has been completed. The use of the restart option will be detailed in the analysis

portion of the discussion.

48 | P a g e

(Go To Main Menu)

Solution

Analysis Type

Static & OK

3.3.9. Load Step Method

Step 1

(Go To Main Menu)

Solution

Solution Controls


49 | P a g e

Step 2

(Go To Main Menu)

Solution

Solution Controls


Step 3 (Go To Main Menu)

Solution

Define Loads

Apply

Structural

Force/Moment Value

On Nodes

50 | P a g e

Step 4

(Go To Main Menu)

Solution

Load Step Opts

Write LS File


51 | P a g e

Step 5

(Go To Main Menu)

Solution

Define Loads

Delete

Structural

Force/Moment Value

On Nodes- Pick All

Step 6


Step 7

(Go To Main Menu)

Solution

Solve

From LS File


52 | P a g e

Step 8

(Go To Main Menu)


Read Results

By Pick- Read

Step 9

(Go To Main Menu)


Add

Nodal Solution

DOF



Plot graph (Graphs are in the end.)

53 | P a g e

3.3.10. Results Fig: 26.Elements of Beam

Fig: 27.Stress Distribution in beam

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4.12 Bending And Stress in beam after prestressing

Fig: 28.Stress in X-Direction.

Fig: 29.Stress in Y-Direction

55 | P a g e

Final Graph For Load v/s Deflection

Conclusion:-

• The failing load for this beam is 95 kN and crack starts developing on the application 0f 24.5 kN load on the beam

• The final deflection in the beam is 169 mm.. • The ultimate load carrying capacity for the beam is 102kN.

Table 1.9- Result Comparison:

Sr. No Prestressing Force Ultimate Load(kN)

Deflection(mm)

1 92 95 169

2 100 104 157

3 105 112 153

4 110 113 148

5 115 117 144

56 | P a g e

Fig: 30. Deflection for Sr. No. 2


57 | P a g e



58 | P a g e

3.4 Model No. 3

Beam Dimensions:

Total number of Tendons: - 4

Spacing between tendons: - 25mm

Total Span length :- 6200mm

59 | P a g e

3.4.1 Beam Property

Table 1.10- Material Type


Concrete Solid 65



The element types for this model are shown in Table 1.10. The Solid65 element

was used to model the concrete. This element has eight nodes with three degrees of

freedom at each node – translations in the nodal x, y, and z directions. This element is

capable of plastic deformation, cracking in three orthogonal directions, and crushing.







3.4.2 Real Constants

The real constants for this model are shown in Table 1.11. Note that individual






60 | P a g e









entered.

Table: 1.11- Real Constants


Real

Constants

for Rebar

1

Real

Constants

for Rebar

2

Real

Constants

for Rebar

3

Material

Number

0 0 0

1. Solid 65

Volume

Ratio

Orientation

Angle

0 0 0

0 0 0

3.4.3 Material Properties


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Orientation

Angle

0 0 0

Cross- 157.45

sectional

Area

(mm2)


Strain

(mm/mm)


a. Linear Isotropic

b. Concrete



a. Linear Isotropic


a. Linear Isotropic



62 | P a g e

Table: 1.12- Material Properties


Linear Isotropic

EX 38,480

PRXY 0.2

Multilinear Isotropic 1. Solid 65

Strain

Stress Point 1 0.00036 9.8023 Point 2 0.0006 15.396 Point 3 0.0013 27.517 Point 4 0.0019 32.102

63 | P a g e

Point 5 0.00243 33.095

Concrete

ShrCf-Op 0.3

ShrCf-Cl 1

UnTensSt 5.3872

UnTensSt -1

BiCompSt 0

HydroPrs 0

BiCompSt 0

UnTensSt 0

TenCrFac 0

Linear Isotropic

2. Solid 45 EX 2,00,000 PRXY 0.3

Linear Isotropic

EX 1,87,000

PRXY 0.65


Yield Stress 2050

Tang Mod 0.65

64 | P a g e

Figure 3.1- Stress- Strain Curve of Concrete

Fig: 34. Stress Strain curve of concrete

3.4.4. Modelling

Fig: 35. Outline of beam in Ansys

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Fig: 36. Front line view

3.4.5Meshing

Fig.37. Elements after Meshing

66 | P a g e

3.4.6 Numbering Controls





nodes becoming “orphaned”; that is, the nodes lose their association with the solid model.





Commands Used


NUMMRG,KP – To merge all keypoints

67 | P a g e

3.4.7 Boundary Conditions





(Go To Main Menu)

Solution

Define Loads

Apply

Structural

Displacement

On Lines

(Pick lines) & OK


(Value) 0

OK

3.4.8 Analysis Type


For the purposes of this model, the Static analysis type is utilized.

The Restart command is utilized to restart an analysis after the initial run or load

step has been completed. The use of the restart option will be detailed in the analysis

portion of the discussion.

68 | P a g e

(Go To Main Menu)

Solution

Analysis Type

Static & OK

3.4.9 Load Step Method

Step 1

(Go To Main Menu)

Solution

Solution Controls


69 | P a g e

Step 2

(Go To Main Menu)

Solution

Solution Controls


Step 3

(Go To Main Menu)

Solution

Define Loads

Apply

Structural

Force/Moment Value

On Nodes

70 | P a g e

Step 4

(Go To Main Menu)

Solution

Load Step Opts

Write LS File


71 | P a g e

Step 5

(Go To Main Menu)

Solution

Define Loads

Delete

Structural

Force/Moment Value

On Nodes- Pick All

Step 6


Step 7

(Go To Main Menu)

Solution

Solve

From LS File


72 | P a g e

Step 8

(Go To Main Menu)


Read Results

By Pick- Read

Step 9

(Go To Main Menu)


Add

Nodal Solution

DOF



Plot graph (Graphs are in the end.)

73 | P a g e

Fig:-38.Elements of Beam

Fig:-39.Stress Pattern

74 | P a g e

Fig:-40.Deflection of beam

Fig:-41.Line Diagram

75 | P a g e

Fig: 42. Final Graph for Load v/s Deflection

3.4.10 Conclusion:-

• The failing load for this beam is 97.5 kN and crack starts developing on the application 0f 31.5 kN load on the beam

• The final deflection in the beam is 174 mm.. • The ultimate load carrying capacity for the beam is 113kN.

Table 1.13- Result comparison

Sr. No. Prestressing Ultimate Deflection(mm) Force(kN) Load(kN)

1 128 113 174

2 135 117 164

3 140 124 154

4 145 130 150

76 | P a g e

Fig: 43. Load v/s Deflection For Sr. No. 1


77 | P a g e

Fig: 45. Loadv/s Deflection For Sr. No. 3


78 | P a g e

CHAPTHER 4

EXPERIMENTAL RESULTS

4.1 GENERAL

The experimental program was undertaken to study the flexural behaviour of

prestressed and partially prestressed concrete beams with carbon fibre-reinforced-plastic

(CFRP) prestressing bars. The serviceability limit states in terms of crack width, crack

spacing and deflection prior to and after cracking were examined. The modes of failure and

the ultimate carrying capacity of the beams were also investigated. The test specimens

consisted of eight beams prestressed by CFRP bars and two additional beams prestressed

by conventional steel strands. The parameters considered in this experimental program

were the prestressing ratio and the degree of prestressing. Several control specimens were

tested to evaluate the material properties of the concrete, CFRP reinforcement, and

prestressing steel. This chapter presents details of jacking, testing setup and different

instrumentations used to measure the response of the beams. This chapter also presents the

properties of the materials used in this study based on testing of the control specimens.

4.2 TEST SPECIMENS

Ten pretensioned prestressed concrete T -beams with a total length of 6.2 m and a

depth of 330 mm were tested. The beams were simply supported with a 5.8-m span and a

200-mm projection from each end. The beams had the same span-to-depth ratio as is

typically used by industry for bridge girders. The beams had a flange width varying from

200 mm to 600 mm, as shown in Fig. 47. Eight of the tested beams were prestressed by 8-

mm Leadline CFRP bars produced by Mitsubishi Kasei, Japan; and two beams were

prestressed by 13-mm conventional steel strands. The beams were reinforced for shear

using double-legged steel stirrups, 6 mm in diameter, uniformly spaced 100 mm apart. The

steel stirrups were tied to two longitudinal steel bars, 6 mm in diameter, 25 mm from the

top surface of the beam. The nominal yield stress of the steel stirrups and longitudinal bars

79 | P a g e

was 400 MPa. The top flange was reinforced by welded wire fabric (WWF) 102xl02, MW

18.7 x MW 18.7 (CPCI Metric Design Manual 1989). The end zone of the beam was

reinforced by two steel plates of 12.5-mm (112") thickness and two steel bars of 10 mm

diameter. The beams had an adequate factor of safety for shear and bond. The variables of

the test program were as follows:

1. Degree of prestressing: two levels of jacking stresses of CFRP bars were used, 50

and 70 percent of the guaranteed ultimate strength of the Leadline as reported by

the manufacturing company

2. Number of Leadline bars: two and four bars were used.

3. Distribution of the Leadline bars in the tension zone: where Leadline bars were

placed in two and four layers, as shown in Fig. 47.

4. Flange width of the beams: two widths were used, 200 mm and 600 mm

Detailed information about the tested beams is given in Table 3.1. The designation

of the beams have the first letter either T, R, or S, refers to T -section of 600-mm flange

width, Rectangular section of 200-mm flange width and beams prestressed by steel

reinforcement, respectively. The first number of the beam designation is either 2 or 4,

which refers to the number of prestressing bars, while the second number, .5 or .7, refers

to the ratio of the jacking stress to the guaranteed ultimate strength. The last letter in the

beam designation, H or V, refers to the configuration of the bars in the tension zone, either

Horizontal or Vertical.

80 | P a g e

Fig: 47. Cross Section of the Tested Beams

Fig: 48. Details of End Zone of the Beam

81 | P a g e

4.3 TESTING SCHEME

The beams were tested using two quasi-static monotonic concentrated loads, 1.0 m

apart. The load was applied under stroke control with a rate of 1.0 mm/min up to the

cracking load and thereafter at a rate of 2.0 mm/min up to failure. The load was cycled

three times between an upper load level of 60 percent of the predicted strength of the

beams, which is equivalent to 1.5 to 2 times the cracking load, depending on the

prestressing level, and a lower load level of 80 percent of the cracking load of the beam.

The second and the third cycles were applied using the same rate of loading as in the initial

cycle. The aim of the repeated loading at the service load limit was to study the deflection,

after loss of beam stiffness due to cracking and the cracking behaviour after stabilization

of cracks.

4.4 MATERIAL PROPERTIES

Table 1.14 – Test Program

82 | P a g e

Table 1.16 – Concrete Properties

Table 1.15 – Tensile Properties of Leadline

83 | P a g e

Table 1.17 – Prestressing Force in the Tested Beams

Fig: 49. Stress-Strain Relationship of Leadline Bar

84 | P a g e

4.5 RESULTS OF THE EXPERIMENTAL PROGRAM

Beam R-2-.5: was prestressed with the same' force and the same location of bars as

beam T-2-.5. The camber of the beam was 7 mm 36 days after casting. The beam cracked

at 12.7 KN and failed at 56.8 kN. Five cracks were observed in the constant moment zone,

as shown in Fig. 6-9; four of them occurred at load levels ranging between 12.7 and 15.9

KN, while the fifth crack occurred at 23.4 kN with a loud noise.

The load was cycled three times between 10.0 and 24.0 kN. Again the beam failed

by rupture of the bottom Leadline bar, accompanied by flexure and flexure-shear cracks

extending to the top flange of the beam. The load dropped to 22.0 KN and the beam carried

more load until the test was stopped. The deflection at failure was 164.6 mm, or 1135 of

the beam span.

Beam R-4-.5-V: had a 200-mm flange width and was prestressed by four Leadline

bars jacked to 50 percent of the guaranteed strength and located as in beam T-4-.5-V. The

camber of beam R-4-.5-V was measured prior to testing, 40 days after casting, and was

found to be 10.0 mm. The beam had a cracking load of 23.1 kN and five cracks occurred

between 23.4 kN and 30.0 kN,

The beam was cycled between lower and upper load levels of 20.0 and 45.0 kN.

The beam failed by rupture of the bottom Leadline bar at a load level of 90.2 kN

accompanied by a horizontal crack at about 50 mm from the bottom surface of the beam.

The load dropped to 50.9 leN. The beam carried more load until crushing of the concrete

at the top surface of the beam between the two concentrated loads occurred at a load level

of 53.7 kN.

The deflectionof the beam was 186.2 mm, or 1/31 of the beam span. This deflection

was the largest observed deflection compared to that of the other beams prestressed by

Leadline and jacked to 50 percent of the guaranteed ultimate strength. This is attributed to

the type of failure where both the concrete and the Leadline were strained to the full

capacity.

85 | P a g e

Beam R-4-.7: had a 200-mm flange width and a prestressing force identical to that

of beam T-4-.7. The beam was prestressed by four Leadline bars located as in beam T-4-

.5-V. The measured camber of the beam. on the day of testing, 36 days after casting, was

13 mm. The beam cracked at 32.1 kN and failed at 98.1 kN by rupture of the bottom

Leadline bar.

Five cracks were observed in the constant moment zone, as shown in Fig. 6-7. The

second to fifth cracks occurred at load levels ranging from 34.2 kN to39.0 kN. The beam

was cycled three times between 25.0 and 50.0 kN. At onset of failure, two cracks in the

constant moment zone extended to the top surface of the flange and the load dropped to

zero. The deflection at failure was 164.5 mm, or 1135 of the span of the beam.

Beam T-4-.5-V: had a flange width of 600 mm and was prestressed by four Leadline

bars located at 50, 78, 100, and 128 mm from the bottom fibres of the beam. The Leadline

bars were jacked to 50 percent of the guaranteed strength. Before testing, the camber was

5.5 mm 33 days after casting. The beam cracked at a load level of 27.3 kN and failed at a

load level of 97.9 kN. Five cracks occurred in the constant moment zone as shown in Fig.

6-4. The first three cracks occurred at a load level of 27.3 kN.

The other two cracks occurred at a load level ranging between 29.0 and 33.0 kN.

The beam was cycled three times between lower and upper load limits of 23.0 and 45.0

kN, respectively. The beam was unloaded at 68.6 kN, which is 70 percent of the measured

failure load, and loaded again to failure to evaluate the released elastic and the consumed

inelastic energy of the beam.

The corresponding deflection of the beam at 68.6 kN, before unloading, was 91.8

mm. The behaviour of the beam was not completely elastic as the residual deflection of the

beam at zero load was 10.5 mm.

The energy released at unloading of the beam was mainly elastic. The inelastic

energy consumed by the beam was very small and occurred mainly due to cracking of

concrete. After reloading, the deflection of the beam at 68.6 kN was only 5 percent higher

86 | P a g e

than that before unloading despite the severe cracking of the beam at this load level. This

is attributed to the elastic behaviour of the Leadline. The beam failed by rupture of the

Leadline bar, which is the closest to the extreme tension fibre of concrete, at a load level

of 97.6 kN.

The load dropped to 58.2 kN and increased until the second Leadline bar from the

bottom failed at a load level of 68.2 kN. The load dropped again to 30.8 kN and increased

until the third Leadline bar failed at 43.0 kN.

The load dropped for the third time to 16.8 kN and the test was stopped at a load of

19.2 kN. Before failure, flexural shear cracks were observed outside the constant moment

zone. The deflection of the beam at failure of the first Leadline bar was 171.4 mm, or 1134

of the beam span.

Fig: 50. Load-Deflection graph with different number of Leadline Bars

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Fig: 51. Stress Strain Behaviour of beams

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CONCLUSION

The final results obtained from Ansys are perfectly matching with the laboratory

test done by Amr A. Abdelrahman in University of Manitoba for Serviceability of

Concrete Beams Prestressed by Fiber Reinforced Plastic Tendons in year 1995.

The model prepared in Ansys is showing the same load deflection curve so now we

can say that the finite element testing of CFRP can be done by Ansys and models that we

prepared are exactly behaving like model that they had prepared in laboratory.

The deflection of FRP material having modulus of elasticity 1, 87,000 and poison

ratio 0.65 is calculated under various load and constrained condition and the output of the

activity is giving the real deflection what we assumed to get in laboratory.

As per the final conclusion the FRP prestressed beam are able to take load like other

available material but the main advantage with FRP material is that they are free from

corrosion so we can use them in underground structure and as well as in those areas where

rusting is a big problem.

The ultimate load carrying capacity of the FRP materials are more that steel and it

also undergo less deformation. The behaviour of steel and FRP is shown in figure below.

89 | P a g e

REFERENCES

1. Analysis Of Reinforced Concrete Structures Usingansys Nonlinear Concrete

Modelantonio F. Barbosa And Gabriel O. Ribeiro federal University Of Minas

Geraisdepartment Of Structural Engineering avenida Do Contorno, 842 – 2o

Andar30110-060 – Belo Horizonte - Mg – Brazil

2. Ansys Problem #1(Beam Deflection) By Nyquist/Haghighi

3. A General Method For Deflections Evaluation Of Fiber reinforced Polymer (Frp)

Reinforced Concrete Members Maria Antonietta Aiello And Luciano Ombres,

University Of Lecce, Lecce, Italy

4. Bond Properties Of CFCC Prestressing Strands In Pretensioned Concrete

Beamsbynolan G. Domenico

5. Deflection Analysis Of Reinforced Concrete T-Beam Prestressed With CFRP

Tendons Externally Byle Huangphd Studentschool Of Civil Engineering wuhan

University china

6. Deflection Of Frp Reinforced Concrete Beamsraed Al-Sunna1,2, Kypros

Pilakoutas2, Peter Waldron2 And Tareqal-Hadeed building Research Centre, Royal

Scientific Society, Amman, Jordan.Centre for Cement and Concrete, Department of

Civil and Structural Engineering,University Of Sheffield, United Kingdom.

7. Ductility Of Pretensioned Concrete Beams With Hybridfrp/Stainless Steel

Reinforcements Dorian P. Tung And T. Ivan Campbell department Of Civil

Engineering, Queen.S University, Kingston, Ontario, Canada

8. Experimental Study Of Influence Of Bond On Flexural behaviour Of Concrete Beams

Pretensioned With Aramid fiber Reinforced Plastics by Janet M. Lees And Chris J.

Burgoyne

9. Finite Element Analysis Of Prestressed Concrete Beams Byabhinav S. Kasat &

Valsson Varghese

10. Flexural BehaviourOf Reinforced Concretebeams Using Finite Element Analysis

(Elastic Analysis) Byr. Srinivasan And K. Sathiya

90 | P a g e

11. Finite Element Modelling Of Composite Steel-Concrete Beams With External

Prestressing Amer M. Ibrahim1, Saad K. Mohaisen2, Qusay W. Ahmed3

1- Professor, College Of Engineering, Diyala University, Iraq

2- Dr.College Of Engineering, Al-Mustansiriya University, Iraq

3- Structure Engineering Diyala University, Iraq

12. Finite Element Analysis Of An Intentionally Damaged Prestressed Reinforced

Concrete Beam Repaired With Carbon Fiber Reinforced Polymers by David A.

Brighton submitted To The Graduate Faculty As Partial Fulfilment Of The

Requirements For The Masters Of Science Degree In Civil Engineering

13. Flexural Behaviour Of Reinforced and Prestressed Concrete Beamsusing Finite

Element Analysis by Anthony J. Wolanski, B.S.

14. Modelling And Behaviour Of Prestressed Concrete Spandrel beamsa Dissertation

submitted To The Faculty Of The Graduate School of The University Of Minnesota

by bulentmercan

15. Nonlinear Analysis Of Rc Beam For Different Shear Reinforcement Patterns By

Finite Element Analysissaifullah, M.A. Hossain, S.M.K.Uddin, M.R.A. Khan And

M.A. Amin

16. Prestressed Concrete Structures Dr. A. K. Senguptadepartment Of Civil

EngineeringIndian Institute Of Technology, Madras

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finite element analysis of a prestressed concrete beam using frp tendon

Engineering

finite element model

finite element method

ansys model

element types

prestressed concrete

material properties

analysis type

prestressed members