STRUCTURAL BEHAVIOUR OF STEEL COLUMNS AND STEEL-CONCRETE …

STRUCTURAL BEHAVIOUR OF STEEL COLUMNS AND STEEL-CONCRETE COMPOSITE GIRDERS

RETROFITTED USING CFRP

By

Amr Abdel Salam Shaat

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

November, 2007

Copyright © Amr A. Shaat, 2007

Abstract

i

Abstract

Steel bridges and structures often need strengthening due to increased life loads, or repair

due to corrosion or fatigue cracking. This study explored the use of adhesively bonded

Carbon Fibre Reinforced Polymers (CFRP) flexible sheets and rigid plates in retrofitting

steel columns and girders, through experimental and analytical investigations. The first

part of the research program investigated the behaviour of CFRP-strengthened steel

columns comprised of square Hollow Structural Sections (HSS). Fifty columns, 175 mm

to 2380 mm long (i.e. with slenderness ratios ranging from 4 to 93), were tested under

axial compression loads to examine the effects of number and type of CFRP layers, fibre

orientation, and slenderness ratio. Transverse wrapping was shown to be suitable for

controlling outwards local buckling in HSS short columns, while longitudinal layers were

more effective in controlling overall buckling in slender columns. The maximum

increases in axial strength observed in the experiments were 18 and 71 percent, for short

and slender columns, respectively. An analytical fibre-element model and a non-linear

finite element model were developed for slender columns. The models account for steel

plasticity, geometric non-linearities, and residual stresses. The models were verified

using experimental results, and used in a parametric study. It was shown that CFRP

effectiveness increases for columns with larger out-of-straightness imperfections and

higher slenderness ratios.

The second part of the research program investigated w-section steel-concrete composite

girders retrofitted using CFRP materials. Three girders, 6100 mm long, were tested to

study strengthening of intact girders using CFRP plates. Eleven girders, 2030 mm long,

Abstract

ii

including girders artificially damaged by completely cutting their tension flanges at mid-

span, were tested to study the effectiveness of repair using CFRP sheets. The parameters

considered were the CFRP type, number of layers, number of retrofitted sides of the

tension flange, and the length of CFRP repair patch. The strength and stiffness of the

intact girders have increased by 51 and 19 percent, respectively. For the repaired girders,

the strength and stiffness recovery ranged from 6 to 116 percent and from 40 to 126

percent, respectively. Unlike flexural strength, the stiffness was not much affected by the

bond length. Analytical models were developed, verified, and used in a parametric study,

which showed that the higher the CFRP modulus, the larger the gain in stiffness and

yielding moment, but the lower the gain in strength and ductility. In general, this study

demonstrated that steel structures can indeed be successfully strengthened or repaired

using CFRP material.

Acknowledgements

iii

Acknowledgements

First and foremost, I thank God through whom all things are possible. I would also like to

recognize and thank all the people who made my time at Queen's University during the

past four years unforgettable.

I would like to express my deepest gratitude to my supervisor, Dr. Amir Fam, for his

unwavering support and guidance throughout this research project. His patience,

leadership, and never ending encouragement gave me the confidence to focus and

proceed. I owe him an unbelievable amount of gratitude for his prominent role in helping

me to achieve one of the greatest accomplishments in my life.

The support of the staff has been a vital part of my success. Thanks go to Fiona Froats,

Cathy Wagar, Maxine Wilson, Lloyd Rhymer, Neil Porter, Paul Thrasher, Jamie Escobar,

and Bill Boulton. Special thanks go to Dave Tryon, who provided great technical

experience and guidance to make the experimental part of this research runs efficiently.

I would also like to acknowledge my fellow graduate students, who helped me along the

way. Thanks go to Abdul Chehab, Andrew Kong, Britton Cole, Hart Honickman, Jeff

Mitchell, Siddwatha Mandal, Tarek Sharaf, Wojciech Mierzejewski, and Yazan Qasrawi.

I wish to acknowledge the financial support provided by the Natural Sciences and

Engineering Research Council of Canada (NSERC). Thanks also go to Mr. Richard

Shirping Sika Inc. for providing his experience in bonding the CFRP plates of phase II. I

Acknowledgements

iv

also wish to thank Fyfe.Co.LLC, Mitsubishi Chemical, and Sika INC. for providing the

FRP materials.

I could not have survived the duration of this study without my family. I would like to

thank my parents, brother, and sisters for their on-going love, support and encouragement

throughout my entire life. Special thanks go to my uncle, Dr. Fathy Saleh, whose

example showed me the value of pursuing an academic career. Also, love and prayers of

my mother-in-law will never be forgotten; to her soul I am truly thankful.

Finally, I would like to thank my wife, Dalia, for believing in me and for all her support

throughout these years. For all your love, patience and dedication, I am grateful. I would

also like to acknowledge my son, Ibrahim, who enlightened my life with his smile.

Table of Contents

v

Table of Contents Abstract ....................................................................................................... i

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

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

List of Figures ................................................................................................... xiii

List of Tables .................................................................................................. xxv

Notation ................................................................................................. xxvi

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

1.1 General ...........................................................................................................1

1.2 Research Objectives .....................................................................................3

1.3 Scope and Contents ......................................................................................6

Chapter 2 Background and Literature Review…………………….………..11

2.1 Introduction..................................................................................................11

2.2 Metallic Materials .........................................................................................12

2.2.1 Cast iron.................................................................................................12

2.2.2 Steel .......................................................................................................12

2.2.3 Buckling strength of steel members .......................................................13

2.2.4 Residual stresses in steel sections ........................................................14

2.3 Conventional Retrofit Techniques of Metallic Structures........................15

2.4 Retrofit of Steel Structures using FRP Materials .....................................17

2.4.1 Bond and force transfer..........................................................................18

2.4.2 Brief review of retrofit applications .........................................................20

2.4.2.1 Repair of naturally deteriorated I-girders...................................................21

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vi

2.4.2.2 Repair of artificially damaged I-girders......................................................22

2.4.2.2.1 Non-composite I-girders ..................................................................22

2.4.2.2.2 Steel-concrete composite girders ....................................................24

2.4.2.3 Flexural strengthening of intact I-girders ...................................................26

2.4.2.3.1 Non-composite I-girders ..................................................................26

2.4.2.3.2 Steel-concrete composite girders ....................................................29

2.4.2.4 Retrofit of I-girders in shear.......................................................................31

2.4.2.5 Flexural strengthening of tubular sections.................................................32

2.4.2.6 Other special cases of strengthening and repair studies ..........................35

2.4.2.7 Fatigue and cyclic load behaviour of retrofitted members.........................36

2.5 Surface Preparation and Bond Issues.......................................................38

2.6 Analysis and Design ...................................................................................40

2.6.1 Analysis of bonded joints .......................................................................40

2.6.2 Analysis of steel girders strengthened with FRP bonded material .........42

2.6.3 Design of bonded joints..........................................................................44

2.6.4 Flexural design of CFRP strengthening of steel structures....................45

2.7 Durability of Steel Structures Retrofitted with FRP .................................46

2.8 Field Applications........................................................................................51

Chapter 3 Experimental Program ........................................................ 65

3.1 Introduction..................................................................................................65

3.2 Materials .......................................................................................................66

3.2.1 Structural steel .......................................................................................67

3.2.1.1 Cold-formed HSS ......................................................................................67

3.2.1.2 Hot-rolled W-sections ................................................................................69

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vii

3.2.2 Fibre Reinforced Polymer (FRP)............................................................70

3.2.2.1 FRP sheets................................................................................................70

3.2.2.2 FRP plates.................................................................................................70

3.2.2.3 Epoxy resins..............................................................................................71

3.2.2.4 Coupon tests of FRP sheets and plates....................................................71

3.2.3 Concrete.................................................................................................72

3.3 Experimental Phase I – Strengthening HSS Columns .............................73

3.3.1 Test specimens ......................................................................................73

3.3.2 Fabrication of column specimens...........................................................75

3.3.3 Test setup ..............................................................................................79

3.3.4 Instrumentation ......................................................................................80

3.4 Experimental Phase II – Strengthening of Intact Composite Girders.....82

3.4.1 Test specimens ......................................................................................82

3.4.2 Fabrication of girders .............................................................................83

3.4.3 Test setup ..............................................................................................86


3.5 Experimental Phase III – Repair of Artificially–Damaged Composite

Beams ......................................................................................................................88

3.5.1 Test specimens ......................................................................................88

3.5.2 Fabrication of beam specimens .............................................................90

3.5.3 Test setup ..............................................................................................93


Chapter 4 Experimental Results and Discussion of Phase I:

Axial Compression Members ......................................... 120

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viii

4.1 Introduction................................................................................................120

4.2 Results of Group A (Slender Column Sets 1 to 6) ..................................121

4.2.1 Effect of slenderness ratio on effectiveness of CFRP..........................123

4.2.2 Failure modes ......................................................................................124

4.3 Results of Group B (Slender Column sets 7 to 11) ................................126

4.3.1 Effect of out-of-straightness imperfection on the effectiveness of CFRP-

strengthening..........................................................................................................126

4.3.2 Failure modes ......................................................................................129

4.4 Results of Group C (Short Column sets 12 to 20) ..................................130

4.4.1 Effect of CFRP strengthening on the short column specimens............130

4.4.2 Effect of fibre orientation ......................................................................132

4.4.3 Effect of CFRP type, thickness, and number of layers.........................132

4.4.4 Failure modes ......................................................................................133

Chapter 5 Experimental Results and Discussion of Phases II

and III: Flexural Members................................................. 155

5.1 Introduction................................................................................................155

5.2 Results of Phase II – Strengthening of Intact Girders ...........................155

5.2.1 Effectiveness of the CFRP strengthening system................................156

5.2.2 Effect of CFRP elastic modulus ...........................................................158

5.2.3 Effect of bonded length of CFRP plates...............................................160

5.2.4 Failure modes ......................................................................................161

5.3 Results of Phase III – Repair of Artificially Damaged Beams................162

5.3.1 Effect of cutting the tension flange at mid-span ...................................163

5.3.1.1 Flexural behaviour...................................................................................163

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ix

5.3.1.2 Failure modes..........................................................................................165

5.3.2 Effect of type of CFRP .........................................................................166


5.3.2.2 Failure modes..........................................................................................168

5.3.3 Effect of number of repaired sides of flange.........................................169


5.3.3.2 Failure modes..........................................................................................170

5.3.4 Effect of CFRP force equivalence index ..............................................171


5.3.4.2 Failure modes..........................................................................................172

5.3.5 Effect of bonded length of CFRP .........................................................172


5.3.5.2 Failure Modes..........................................................................................176

Chapter 6 Analytical and Numerical Modeling of CFRP-

Strengthened HSS Slender Columns........................... 202

6.1 Introduction................................................................................................202

6.2 Fibre Model (Model 1)................................................................................203

6.2.1 Residual stresses in HSS sections ......................................................204

6.2.2 Meshing system ...................................................................................204

6.2.3 Force equilibrium and moments...........................................................205

6.2.4 Lateral displacement ............................................................................207

6.2.4.1 Effective moment of inertia (Ieff) ...............................................................210

6.2.4.1.1 Bare steel column ..........................................................................210

6.2.4.1.2 FRP-strengthened steel column ....................................................213

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x

6.2.5 Axial displacement ...............................................................................215

6.2.6 Failure criteria ......................................................................................216

6.2.7 Generation of full load-displacement responses ..................................218

6.2.8 Illustration of key features of the fibre model .......................................220

6.3 Finite-Element Model (FEM) (Model 2).....................................................221

6.3.1 Material properties ...............................................................................222

6.3.2 Elements’ types and mesh density.......................................................223

6.3.3 Loading and boundary conditions ........................................................225

6.3.4 Geometric imperfections ......................................................................225

6.3.5 Residual stresses.................................................................................225

6.4 Verification of Models 1 and 2 ..................................................................226

6.5 Parametric Study on CFRP–Strengthened HSS Slender Columns.......229

6.5.1 Effect of number of CFRP layers .........................................................230

6.5.2 Effect of initial out-of-straightness (e’) ..................................................231

6.5.3 Effect of residual stresses ....................................................................231

6.5.4 Effect of slenderness ratio....................................................................232

6.6 Comparison between models 1 and 2 .....................................................232

Chapter 7 Analytical Modeling of CFRP-Retrofitted Steel-

Concrete Composite Girders.......................................... 267

7.1 Introduction................................................................................................267

7.2 Intact Steel-Concrete Composite Girders Strengthened using CFRP

Materials ...................................................................................................................268

7.2.1 Moment-curvature relationship.............................................................269

7.2.2 Load-deflection behaviour....................................................................271

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xi

7.2.3 Verification of the model.......................................................................271

7.3 Parametric Study on Girder Strengthening ............................................272

7.3.1 Effect of CFRP elastic modulus ...........................................................273

7.3.2 Effect of CFRP reinforcement ratio ......................................................274

7.3.3 Effect of rupture strain of CFRP ...........................................................275

7.4 Damaged Steel-Concrete Composite Girders Repaired using CFRP

Materials ...................................................................................................................275

7.4.1 Ultimate moment capacity....................................................................276

7.4.1.1 Intact cross section..................................................................................276

7.4.1.2 Damaged cross section (but not repaired) ..............................................277

7.4.1.3 Damaged and repaired cross sections....................................................277

7.4.1.3.1 Cross section repaired using HM-CFRP........................................278

7.4.1.3.2 Cross section repaired using SM-CFRP ........................................278

7.4.1.4 Calibration of parameter for the neglected part of the steel web .........279

7.4.2 Deflection at service load .....................................................................280

7.4.2.1 Effect of stress flow in the vicinity of the crack ........................................283

7.4.2.2 Calibration of the slope (z:1) ...................................................................285

Chapter 8 Summary and Conclusions............................................. 301

Summary and Conclusions ............................................................................... 301

8.1 Summary ....................................................................................................301

8.2 Conclusions ...............................................................................................302

8.2.1 Axially loaded members .......................................................................302

8.2.1.1 Slender columns......................................................................................302

8.2.1.2 Short columns .........................................................................................304

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xii

8.2.2 Flexural members ................................................................................305

8.2.2.1 Strengthening of intact girders ................................................................305

8.2.2.2 Repair of damaged girders......................................................................306

8.3 Recommendations for Future Work ........................................................309

References................................................................................................................311

Appendix A Measurements of Out-of-Straightness Profiles for Column

Sets 1 to 6................................................................................. 326

A.1 General .......................................................................................................326

Appendix B Estimated Out-of-Straightness Imperfections at Mid-Height for

Column Sets 1 to 11 ................................................................ 336

B.1 General .......................................................................................................336

List of Figures

xiii

List of Figures Figure 1.1 CFRP-strengthening of HSS columns. ............................................................9

Figure 1.2 CFRP-retrofitted steel-concrete composite girders. .......................................10

Figure 2.1 Residual stresses in hot-rolled and cold-formed sections..............................54

Figure 2.2 Typical stress-strain curves for CFRP, GFRP, and steel. ..............................54

Figure 2.3 Measured and predicted strain distributions along the bonded length of a

double lap joint. [Miller et al., 2001] ..........................................................................55

Figure 2.4 Test setup for bonded FRP plates in flexure..................................................55

Figure 2.5 Various techniques of introducing artificial damage to steel girders. .............56

Figure 2.6 Load-deflection responses of artificially damaged non-composite girders.....56

Figure 2.7 Failure modes of artificially damaged steel-concrete composite girders........57

Figure 2.8 Different strengthening schemes of steel beams...........................................58

Figure 2.9 Load-deflection response of a composite girder strengthened with HM-CFRP

plates. [Tavakkolizadeh and Saadatmanesh, 2003a] ...............................................58

Figure 2.10 Failure mode of web-strengthened beams...................................................59

Figure 2.11 Load-deflection response and failure mode of a tubular pole. .....................59

Figure 2.12 Effective bond length for steel tube strengthened with HM-CFRP...............60

Figure 2.13 Different strengthening schemes of rectangular HSS against bearing

stresses. [Zhao et al., 2006] .....................................................................................60

Figure 2.14 Installation of CFRP sheets on cracked aluminum truss k-joint. ..................61

Figure 2.15 Degradation of mean deflection of beams under fatigue loading.................61

Figure 2.16 Different techniques used to reduce peeling stresses. ................................62

Figure 2.17 Stress distribution in adhesively bonded double-sided joints.......................62

Figure 2.18 Comparisons of shear and peel stresses for plates with and without taper

under UDL. [Deng et al., 2004] .................................................................................63

List of Figures

xiv

Figure 2.19 Finite element analysis versus experimental load-deflection responses. ....63

Figure 2.20 Design guidelines for steel–concrete composite beams strengthened with

HM-CFRP materials. [Schnerch et al., 2007]............................................................64

Figure 2.21 Installation of CFRP plate on the Christina Creek bridge (I-704). ................64

Figure 3.1 Different steel cross sections used in the experimental investigation. .........101

Figure 3.2 Test setup of HSS stub-column. ..................................................................101

Figure 3.3 Compressive stress-strain responses of HSS stub-columns. ......................102

Figure 3.4 Tensile stress-strain response of a coupon cut from W250x25 ...................103

Figure 3.5 Sample coupon cut from W150x22. .............................................................103

Figure 3.6 Tensile stress-strain responses of coupons cut from W150x22...................104

Figure 3.7 Tension coupons and test setup of FRP materials. .....................................104

Figure 3.8 Tensile stress-strain responses of different FRP materials..........................105

Figure 3.9 Test setup for concrete cylinders. ................................................................105

Figure 3.10 Effect of FRP on local and overall buckling of short and slender HSS

columns. .................................................................................................................106

Figure 3.11 Details of FRP strengthening configurations of HSS columns in Phase I. .106

Figure 3.12 Various preparation measures of the HSS columns in Phase I. ................107

Figure 3.13 A typical out-of-straightness geometric imperfection profile of slender

columns (specimen 6-3). ........................................................................................108

Figure 3.14 FRP installation on the HSS columns in Phase I. ......................................108

Figure 3.15 Test setup A of columns in group A of Phase I. .........................................109

Figure 3.16 Test setup B of columns in group B of Phase I. .........................................110

Figure 3.17 Test setup C of columns in group C of Phase I..........................................111

Figure 3.18 A schematic and fabrication process of girders tested in Phase II.............112

Figure 3.19 Casting concrete slabs of the girders tested in Phase II. ...........................113

Figure 3.20 Test setup of girders tested in Phase II. ....................................................114

List of Figures

xv

Figure 3.21 Schematic of test setup and instrumentations of girders tested in Phase II.

................................................................................................................................115

Figure 3.22 A schematic and fabrication process of artificially-damaged beams tested in

Phase III..................................................................................................................116

Figure 3.23 Sandblasting the tension steel flanges of beams tested in Phase III. ........117

Figure 3.24 Installation process of FRP sheets on beams tested in Phase III. .............118

Figure 3.25 Test setup and instrumentations of beams tested in Phase III. .................119

Figure 4.1 Load-axial displacement responses of column sets 1 and 2 of group A. .....137



Figure 4.4 Load-lateral displacement of column sets 1 and 2 of group A. ....................138



Figure 4.7 Load-axial strain responses based on strain gauge S1 of column sets 1 and 2

of group A. ..............................................................................................................140


of group A. ..............................................................................................................140


of group A. ..............................................................................................................141

Figure 4.10 Load-axial strain responses based on strain gauge S2 of column sets 1 and

2 of group A. ...........................................................................................................141


4 of group A. ...........................................................................................................142


6 of group A. ...........................................................................................................142

Figure 4.13 Variation of axial strength with slenderness ratio of group A columns.......143

List of Figures

xvi

Figure 4.14 Effect of slenderness ratio on the CFRP effectiveness in group A columns.

................................................................................................................................143

Figure 4.15 Failure modes of group A columns. ...........................................................144

Figure 4.16 Variation of the compressive strain of CFRP at ultimate with slenderness

ratio.........................................................................................................................145

Figure 4.17 Load-axial displacement responses of column sets 7 to 11 of group B. ....145

Figure 4.18 Load-lateral displacement responses of column sets 7 to 11 of group B...146

Figure 4.19 Load-axial strain responses of specimen 7 of group B. .............................146



Figure 4.22 Load-axial strain responses of specimen 10 of group B. ...........................148

Figure 4.23 Load-axial strain responses of specimen 11 of group B. ...........................148

Figure 4.24 Mid-height imperfection of specimen 7 of group B versus the applied load.

................................................................................................................................149

Figure 4.25 Failure modes of group B columns. ...........................................................150

Figure 4.26 Load-axial displacement responses of column sets 12 to 20 of group C...151

Figure 4.27 Load-axial strain response of control specimen 12-1 of group C...............152

Figure 4.28 Effect of using SM-CFRP on load-axial displacement responses in group C

columns. .................................................................................................................152

Figure 4.29 Effect of using HM-CFRP on load-axial displacement responses in group C

columns. .................................................................................................................153

Figure 4.30 Effect of using two types of CFRP on strengthening short specimens. .....153

Figure 4.31 Failure modes of group C columns. ...........................................................154

Figure 5.1 Load-deflection responses of specimens tested in Phase II. .......................178

Figure 5.2 Load-strain responses of the lower flange of the control specimen G1. ......178

Figure 5.3 Load-steel strain responses at the web of specimens tested in Phase II. ...179

List of Figures

xvii

Figure 5.4 Load-strain responses along the CFRP plates of specimen G2 in Phase II.179

Figure 5.5 Load-strain responses along the CFRP plates of specimen G3 in Phase II.180

Figure 5.6 Load-average shear stress responses along the CFRP plates of specimen G2

in Phase II...............................................................................................................180

Figure 5.7 Load-average shear stress responses along the CFRP plates of specimen G3

in Phase II...............................................................................................................181

Figure 5.8 Load-concrete strain responses of specimens tested in Phase II................181

Figure 5.9 Failure modes of girders in Phase II. ...........................................................182

Figure 5.10 Load-deflection responses of specimens B1 and B2 in Phase III. .............183

Figure 5.11 Load-strain responses of the upper steel flanges of specimens B1 and B2 in

Phase III..................................................................................................................183

Figure 5.12 Load-strain responses of the lower steel flanges of specimens B1 and B2 in

Phase III..................................................................................................................184

Figure 5.13 Load-strain responses along the mid-span cross section of specimen B2 in

Phase III..................................................................................................................184

Figure 5.14 Load-strain responses at a distance of 20 mm and 80 mm above the

underside of the lower flange of specimen B2........................................................185

Figure 5.15 Failure modes of specimens B1 and B2 in Phase III. ................................185



Figure 5.18 Strain distributions along the CFRP sheets of specimen B3 in Phase III...187




Figure 5.22 Load-strain responses of CFRP at mid-span of specimens B3, B4, and B6 in

Phase III..................................................................................................................189

List of Figures

xviii

Figure 5.23 Load-strain responses of the upper steel flange at mid-span of specimens

B3, B4, and B6 in Phase III.....................................................................................189

Figure 5.24 Failure modes of specimens B3 to B6 in Phase III. ...................................190


Figure 5.26 Strain distributions along the lower CFRP sheets of specimen B7 in Phase

III.............................................................................................................................191

Figure 5.27 Strain distributions along the upper CFRP sheets of specimen B7 in Phase

III.............................................................................................................................192

Figure 5.28 Failure mode of specimen B7 in Phase III. ................................................193


Figure 5.30 Effect of force equivalence index (ω) on the strength of the repaired beams.

................................................................................................................................194

Figure 5.31 Failure mode of specimen B8. ...................................................................195

Figure 5.32 Load-deflection responses of specimens B8 to B11 in Phase III. ..............195

Figure 5.33 Effect of bonded length of CFRP on ultimate load. ....................................196


III.............................................................................................................................196


III.............................................................................................................................197


III.............................................................................................................................197


III.............................................................................................................................198

Figure 5.38 Load-strain responses of CFRP at mid-span of specimens B8 to B11 in

Phase III..................................................................................................................198

Figure 5.39 Load versus slip of concrete slab of specimen B9 in Phase III. .................199

List of Figures

xix

Figure 5.40 Maximum strains versus the bonded length of the CFRP sheets. .............199

Figure 5.41 Load-average shear stress responses along the lower CFRP sheets of

specimen B8 in Phase III. .......................................................................................200


specimen B9 in Phase III. .......................................................................................200


specimen B10 in Phase III. .....................................................................................201


specimen B11 in Phase III. .....................................................................................201

Figure 6.1 Meshing system for stress integration. ........................................................237

Figure 6.2 Stress and strain distributions within the cross section of slender column at

mid-height. ..............................................................................................................237

Figure 6.3 Lateral and axial displacements of slender columns....................................238

Figure 6.4 Summary of the finite difference model and convergence study. ................238

Figure 6.5 Illustration of the superposition concept in predicting load-axial displacement

response. ................................................................................................................239

Figure 6.6 Variation of ultimate compressive-to-tensile strain ratio of CFRP at failure with

slenderness ratio. ...................................................................................................239

Figure 6.7 Illustration of significance of various features of the fibre model..................240

Figure 6.8 Eigenvalue elastic buckling analysis. ...........................................................240

Figure 6.9 Stress-strain curves used in the FEM. .........................................................241

Figure 6.10 Elements used in the FEM.........................................................................241

Figure 6.11 Mesh refinement and results......................................................................242

Figure 6.12 Verification of models 1 and 2 using test results on HSS 203 x 203 x 6.3

mm..........................................................................................................................242

List of Figures

xx

Figure 6.13 Verification of models 1 and 2 using test results on HSS 152 x 152 x 4.9

mm..........................................................................................................................243

Figure 6.14 Measured and predicted load-lateral displacement responses of set 1. ....243






Figure 6.20 Measured and predicted load-lateral displacement responses of specimen 7.

................................................................................................................................246


................................................................................................................................247


................................................................................................................................247

Figure 6.23 Measured and predicted load-lateral displacement responses of specimen

10............................................................................................................................248

Figure 6.24 Measured and predicted load-lateral displacement responses of specimen

11............................................................................................................................248

Figure 6.25 Measured and predicted load-axial displacement responses of set 1. ......249






Figure 6.31 Measured and predicted load-axial displacement responses of specimen 7.

................................................................................................................................252

List of Figures

xxi


................................................................................................................................252


................................................................................................................................253


................................................................................................................................253


................................................................................................................................254

Figure 6.36 Measured and predicted load-axial strain responses of set 1....................254






Figure 6.42 Measured and predicted load-axial strain responses of specimen 7. ........257



Figure 6.45 Measured and predicted load-axial strain responses of specimen 10. ......259

Figure 6.46 Measured and predicted load-axial strain responses of specimen 11. ......259

Figure 6.47 Comparison between the deformed shapes in experiments and FEM (Model

2). ...........................................................................................................................260

Figure 6.48 Load-lateral displacement responses for specimens with e’=L/500...........261



Figure 6.51 Load-lateral displacement responses for specimens with e’=L/1000.........262

Figure 6.52 Load-lateral displacement responses for specimens with e’=L/2000.........263

List of Figures

xxii

Figure 6.53 Load-lateral displacement responses for specimens with Frs = 0.50 Fy. ....263

Figure 6.54 Load-lateral displacement responses for specimens with kL/r =160. ........264

Figure 6.55 Summary of results of parametric study. ...................................................265

Figure 6.56 Strength comparison between Models 1 and 2..........................................266

Figure 6.57 Stiffness comparison between Models 1 and 2. ........................................266

Figure 7.1 Steel-concrete composite girder strengthened with FRP and subjected to pure

bending. ..................................................................................................................288

Figure 7.2 Constructing the load-deflection diagram. ...................................................288

Figure 7.3 Predicted versus experimental moment-curvature behaviour of control girder

G1 in Phase II. ........................................................................................................289

Figure 7.4 Predicted versus experimental moment-curvature behaviour of girder G2 in

Phase II. .................................................................................................................289

Figure 7.5 Predicted versus experimental moment-curvature behaviour of girder G3 in

Phase II. .................................................................................................................290

Figure 7.6 Predicted versus experimental moment-strain behaviour of control girder G1

in Phase II...............................................................................................................290

Figure 7.7 Predicted versus experimental moment-strain behaviour of girder G2 in

Phase II. .................................................................................................................291

Figure 7.8 Predicted versus experimental moment-strain behaviour of girder G3 in

Phase II. .................................................................................................................291

Figure 7.9 Predicted versus experimental load-deflection behaviour of control girder G1

in Phase II...............................................................................................................292

Figure 7.10 Predicted versus experimental load-deflection behaviour of girder G2 in

Phase II. .................................................................................................................292

Figure 7.11 Predicted versus experimental load-deflection behaviour of girder G3 in

Phase II. .................................................................................................................293

List of Figures

xxiii

Figure 7.12 Moment-curvature responses of composite sections strengthened using SM-

CFRP. .....................................................................................................................293

Figure 7.13 Moment-curvature responses of composite sections strengthened using HM-

CFRP. .....................................................................................................................294

Figure 7.14 Moment-curvature responses of composite sections strengthened using

UHM-CFRP.............................................................................................................294

Figure 7.15 Effect of the modulus of CFRP on percentage increase in stiffness for

different reinforcement ratios. .................................................................................295

Figure 7.16 Effect of the modulus of CFRP on percentage increase in yielding moment

for different reinforcement ratios.............................................................................295

Figure 7.17 Effect of the modulus of CFRP on percentage reduction in ductility. .........296

Figure 7.18 Effect of CFRP rupture strain on percentage increase in strength for different

reinforcement ratios. ...............................................................................................296

Figure 7.19 Effective cross sections and corresponding stress and strain distributions in

intact, damaged, and repaired girders. ...................................................................297

Figure 7.20 Effect of parameter η on the predicted-to-measured ultimate moment ratio.

................................................................................................................................298

Figure 7.21 Schematic to illustrate the effect of damage and CFRP-repair on variation of

moment of inertia of girders. ...................................................................................299

Figure 7.22 Effect of slope z on the predicted-to-measured deflection ratio. ................300

Figure A.1 Out-of-straightness geometric imperfection profile of specimen 1-1. ..........327






List of Figures

xxiv




Figure A.10 Out-of-straightness geometric imperfection profile of specimen 4-1. ........331








Figure B.1 Mid-height imperfections of column sets 3 and 4 versus the applied load. .337

Figure B.2 Mid-height imperfections of column sets 5 and 6 versus the applied load. .337

Figure B.3 Mid-height imperfections of specimens 7 to 11 versus the applied load. ....338

List of Tables

xxv

List of Tables Table 3.1 Material properties of the W150x22 steel section used in Phase III...............95

Table 3.2 FRP material properties based on coupon tests. ............................................96

Table 3.3 Concrete strengths of the three batches. ........................................................97

Table 3.4 Test matrix of HSS column specimens tested in Phase I................................98

Table 3.5 Test matrix of composite girders tested in Phase II. .......................................99

Table 3.6 Test matrix of repair of artificially damaged composite beams tested in Phase

III.............................................................................................................................100

Table 4.1 Summary of test results of slender columns in group A of Phase I...............134

Table 4.2 Summary of test results of slender columns in group B of Phase I...............135

Table 4.3 Summary of test results of short columns in group C of Phase I. .................136

Table 5.1 Summary of test results of Phase II. .............................................................177

Table 5.2 Summary of test results of Phase III. ............................................................177

Table 6.1 Comparison between both methods of estimating imperfection....................234

Table 6.2 Comparison between experimental and predicted results using Models 1 and

2..............................................................................................................................235

Table 6.3 Summary of the parametric study on slender CFRP-strengthened HSS

columns ..................................................................................................................236

Table 7.1 Summary of parametric study on strengthening steel-concrete composite

girders.....................................................................................................................286

Table 7.2 Calibration of the neglected part of the steel web in repair applications. ......286

Table 7.3 Calibration of the slope (z:1). ........................................................................287

Notation

xxvi

Notation if

A Area of FRP element

isA Area of steel element

At Transformed cross sectional area

ai Fourier components of out-of-straightness profile of an unloaded column

ia Fourier components of out-of-straightness profile of a loaded column

b Flat breadth of HSS section

bc Breadth of concrete element

ceqb Equivalent breadth for concrete

feqb Equivalent breadth for FRP

bf Breadth of FRP element

bs Breadth of steel element

c neutral axis depth

d depth of the W-section

e’ Initial out-of-straightness

Ect Initial tangent modulus of concrete

Efi Young’s modulus of FRP element i

Esi Young’s modulus of steel element i

Et Tangent modulus

Frs Residual stress

Fsi Stress of steel element i

rssiF + Total stress of any steel element i

Notation

xxvii

Fy yield stress of steel

Gs Elastic shear modulus of steel

h Depth of HSS section

I moment of inertia

i element number

Ieff effective moment of inertia of the cross section

effsI Effective moment of inertia of a steel cross section

GsI Gross moment of inertia of steel cross section

efftI Transformed effective moment of inertia of a steel section retrofitted by FRP

k Axial stiffness of column or factor to account for boundary conditions of columns

L Length of steel member

M Bending moment

m number of internal nodes in the finite difference method or internal virtual

moment

MD Dead moment

Mexp Experimental bending moment

Mf Total factored moment

ML Live moment

Mpred Predicted bending moment

n Number of shear connectors required for full composite action

n’ Actual number of shear connectors

P External applied load

Pcr Euler buckling load

Notation

xxviii

Pexp Experimental load

Pi Critical load of buckling mode i

Ppred Predicted load

Pu Ultimate load

R Radius of curvature for a loaded column

Ro Radius of curvature for an unloaded column

Rx Rotational degree of freedom about x-axis

Ry Rotational degree of freedom about y-axis

Rz Rotational degree of freedom about z-axis

r Radius of gyration.

S chord length of the deformed shape of slender column

t Thickness of steel element

tc Thickness of concrete slab

Ux Translational degree of freedom in x-direction

Uy Translational degree of freedom in y-direction

Uz Translational degree of freedom in z-direction

v Internal virtual shear force

V Shear force

w Total lateral displacement of a loaded column due to out-of-straightness

wo Lateral displacement of an unloaded column due to out-of-straightness

w’ First derivative of the lateral displacement function w(z)

yc Distance between the extreme fibre and the effective centroid of the cross section

Notation

xxix

yi Distance from the center of the element to the effective centroid of the cross

section

z Distance along the length of the column or slope of stress flow in damaged girders

∆ Total axial displacement

∆a Displacements due to axial shortening

∆b Displacements due to curvature from P-δ effect

∆L Length of segment of column in the finite difference method

αD Dead load factor

αL Live load factor

δexp Experimental deflection

δpred Predicted deflection

δ Lateral deflection at mid-height

ε Strain level at the extreme compression side

εf cu Compressive strains of CFRP at failure

εf tu Tensile strains of CFRP at failure

εi Strain in element i located at a distance yi from the centroid

εrs Residual strain

γ Eigenvalue in the finite difference method

η Percentage of the damaged height in steel w-sections

ρ FRP reinforcement ratio or fraction of full shear connection in steel-concrete

composite girders

ω Force equivalence index

Notation

xxx

ψ Curvature of cross section

Chapter 1

1

Chapter 1

Introduction

1.1 General

Aging and overburdened infrastructure are increasingly becoming a threat to public

safety, economy and quality of life. Steel structures comprise a large portion of the

existing infrastructure worldwide. A number of factors can potentially cause major

problems in steel structures in general and steel bridges in particular. These include

corrosion, fatigue, design errors, sub-standard materials, vehicle-caused accidental

damage, and lack of proper maintenance. In other cases, steel bridges may not be

deteriorated or damaged but are rather in need of upgrading to carry larger loads and

increasing traffic volumes. In most cases, the cost of retrofitting is far less than the cost of

replacement. In addition, retrofitting usually takes less construction time and therefore

reduces service interruption time.

Conventional repair methods of steel structures generally involve bolting or welding

heavy steel plates to the existing structures. This may require heavy lifting equipment and

Chapter 1

2

shoring systems in the site, which may cause delays and traffic interruptions. Also,

adding heavy steel plates increases the dead load of the structure, which limits the target

increase of live load carrying capacity. The continuous process of corrosion and the

reduced fatigue life associated with the welded steel plates may reduce the durability, and

limit the effectiveness, of conventional repair methods.

The need for adopting durable materials and cost-effective retrofit techniques is evident.

One of the possible solutions is the use of high performance non-metallic materials such

as Fibre Reinforced Polymers (FRPs). Despite the higher cost of FRP materials,

compared to steel, the material cost alone generally comprises a very small portion of the

overall project cost. The superior mechanical and physical properties of FRP materials

make them quite promising for both repair and strengthening applications. They also

have a minimum visual impact on aesthetic appearance and almost no effect on

clearances underneath the retrofitted girders.

The use of FRP systems for retrofit of concrete structures has been quite successful (ACI

440, 2002). Today, the use of glass- and carbon-FRP materials (GFRP and CFRP) in

retrofitting concrete bridges and structures is becoming widely accepted in practice. FRP

is used in the form of sheets or plates attached to the concrete surface for flexural and

shear retrofitting or as sheets for wrapping columns to increase their ductility and axial

strength.

Chapter 1

3

The inherent high strength and stiffness of steel makes it a more challenging material to

strengthen, compared to other materials such as concrete and wood. If steel is retrofitted

using a material with a lower Young’s modulus, load transfer and hence load sharing of

the strengthening material will only be significant after the steel yields. Therefore, the

relatively low tensile modulus of glass fibres (72 GPa) makes them less desirable for

retrofitting steel structures. On the other hand, carbon fibres have outstanding mechanical

properties that could be superior to those of steel. The tensile strength and modulus of

carbon fibres could reach up to 4020 MPa and 640 GPa, respectively (Cadei et al., 2004).

In addition, a CFRP plate weighs less than one fifth the weight of a similar size steel plate

and is also corrosion resistant.

A case study was performed to examine the economical advantages of rehabilitation of

damaged steel girders using CFRP pultruded laminates, as compared to replacement of

the girders (Gillespie et al., 1996a). In Delaware, USA, bridge girders with a total length

of 180 meters, were replaced due to severe and extensive damage. The replacement cost

was compared with the cost of rehabilitation using CFRP, at an assumed 25 percent

section loss. It was concluded that the total replacement cost was 3.65 times higher than

the cost of rehabilitation using CFRP.

1.2 Research Objectives

The research program carried out in this thesis is focused on retrofit of two types of steel

structures, namely, Hollow Structural Section (HSS) short and slender columns, and

girders made of W-sections acting compositely with concrete slabs.

Chapter 1

4

(a) Strengthening HSS columns:

In the case of short columns, it is hypothesized that CFRP sheets attached to the surface

in the transverse and longitudinal directions could help control the outwards local

buckling of two opposite faces of the column, and thereby increase its axial strength and

stiffness, as shown in Figure 1.1(a and c).

In the case of HSS slender columns, it is hypothesized that CFRP sheets or plates

attached in the longitudinal direction could delay the overall buckling of the column,

particularly when using high modulus CFRP. This would enhance the axial strength of

the column, as shown in Figure 1.1(b and c).

The specific objectives of the study are:

1. Evaluating the load-deformation responses of axially loaded HSS columns

strengthened using CFRP materials with emphasis on the gains in strength and

stiffness [Figure 1.1(c)].

2. Examining the effects of slenderness ratio, CFRP type, fibre orientation, and

number of layers on the behaviour of HSS columns strengthened using CFRP

materials.

3. Examining the different potential failure modes of CFRP-strengthened HSS

columns of different slenderness ratios and CFRP configurations.

4. Develop analytical and numerical models to predict the behaviour and axial

strength of HSS slender columns strengthened using CFRP.

Chapter 1

5

(b) Strengthening and repair of steel-concrete composite girders:

In the case of strengthening, the goal is to increase the flexural strength and stiffness of

intact girders, beyond their original capacities, using CFRP materials adhesively bonded

to the tension flange, as shown in Figure 1.2(a and c). This simulates upgrading bridge

girders to meet an increased demand of live loads.

In the case of repair, the tension flange is saw-cut at mid-span to simulate section loss

due to a fatigue crack or a localized severe corrosion. CFRP material is then adhesively

bonded to the tension flange, as shown in Figure 1.2(b and c), in order to recover and

possibly exceed the original strength and stiffness.

The objectives of the study are:

1. Evaluating the load-deflection responses of CFRP-strengthened steel-concrete

composite girders scaled down (4:1) from an actual bridge.

2. Evaluating the load-deflection responses of simulated fatigue-damaged steel-

concrete composite girders repaired using CFRP sheets.

3. Examining the effects of elastic modulus, number of layers, and bonded length of

CFRP material used in repair of the damaged steel-concrete composite girders.

4. Develop simplified analytical models to predict the behaviour and strength of

CFRP-strengthened and repaired steel-concrete composite girders.

Chapter 1

6

1.3 Scope and Contents

The scope of this study consists of extensive experimental investigations as well as

analytical and numerical modeling. The experimental program is planned to address the

use of CFRP composite materials in different retrofitting applications of various steel

elements (i.e. columns and beams), as mentioned in the previous section. The

experimental results of this study and other studies are used to verify the proposed

analytical and numerical models. The models are then used in parametric studies to

examine a wider range of parameters.

The experimental program includes three phases. Phase I is focused on evaluating the

behaviour of axially loaded HSS columns strengthened using CFRP sheets and plates.

This was achieved by testing 50 HSS columns of lengths varying from 175 mm to 2380

mm (i.e. slenderness ratios ranging from 4 to 93). Phase II is intended to evaluate the

effectiveness of CFRP plates in strengthening intact steel-concrete composite girders.

Three large-scale (6100 mm long) girders have been tested in four-point bending in this

phase. Phase III is designed to evaluate the effectiveness of using CFRP sheets to repair

artificially damaged steel-concrete composite beams with a simulated section loss in the

tension flange. In this phase, a total of 11 beams, 2040 mm long, have been tested in

four-point bending configurations.

Four analytical and numerical models have been developed for both the axially loaded

and flexural members. The first model is an analytical fibre-element model for HSS

slender columns. The model is based on the concepts of strain compatibility and force

Chapter 1

7

equilibrium and is capable of predicting the full response of axially loaded HSS slender

columns strengthened using FRP materials. The second model is a numerical non-linear

Finite Element Model (FEM), developed as an alternative model for the HSS slender

columns. Both models were verified using experimental results and were used in

comprehensive parametric studies. The third model is a fibre-element analytical model,

developed to predict the effect of FRP materials on strengthening intact steel-concrete

composite girders. The model is based on developing and integrating the moment-

curvature relationship of the composite cross section to predict the full load-deflection

response. Finally, a fourth simplified fibre-element model analytical model is developed

to predict the ultimate moment capacity of steel-concrete composite girders, with a cut in

their tension flanges, and repaired using FRP materials. The model also predicts

deflection at service load.

The following is a brief description of the contents of this thesis:

Chapter 2 presents background of the fundamental characteristics of both metallic and

composite materials. Also, a literature review related to retrofit of steel structures is

presented.

Chapter 3 describes the experimental program conducted at Queen’s University,

including Phase I for column tests and Phases II and III for beam tests. The mechanical

properties of steel, concrete, and FRP materials are also presented.

Chapter 4 presents the results of the columns tests (Phase I) of the experimental

program, including the effects of various parameters as well as different failure modes.

Chapter 1

8

Chapter 5 presents the results of the flexural members tests (Phases II and III) of the

experimental program, including the effects of various parameters as well as different

failure modes.

Chapter 6 presents both the analytical and numerical models developed to predict the

responses of axially loaded slender HSS columns. The models are verified using

experimental results. A comparison study of both models, as well a parametric study is

also presented in this chapter.

Chapter 7 presents the analytical model developed to predict the responses of intact

steel-concrete composite girders strengthened using FRP materials. The chapter also

presents the simplified analytical model developed to predict the ultimate moment and

service load deflection of damaged steel-concrete composite girders repaired using FRP

materials.

Chapter 8 provides a summary of the thesis as well as conclusions based on both the

experimental and theoretical studies. The chapter also presents recommendations for

future work.

Chapter 1

9

Figure 1.1 CFRP-strengthening of HSS columns.

T

T

Longitudinal FRP layers

T

C

C

(b) Slender Column(a) Short Column

TT

TT

Longitudinal FRP layer

Transverse FRP layer

?

CFRP-strengthened

Original

displacement

Load

(c) Load-displacement responses

Local buckling

[Key et al., 1988]

?

T

T


T

C

C

(b) Slender Column(a) Short Column

TT

TT



??

CFRP-strengthened

Original

displacement

Load

(c) Load-displacement responses

Local buckling

[Key et al., 1988]

??

Chapter 1

10

Figure 1.2 CFRP-retrofitted steel-concrete composite girders.

(b) Repair of damaged girders

(c) Load-deflection responses of intact, damaged, and strengthened girders

CFRP

Cracklost

CFRP

(a) Strengthening (upgrading) of intact girders

CFRP

W-section

CFRP

Concrete slab

Fatigue crack

[Boyd, 1970]

CFRP failure

Upgraded

Original (intact)

deflection

Load

Damaged (cracked)

Repair (recovery)

Strengthening (gain)

?

?

(b) Repair of damaged girders

(c) Load-deflection responses of intact, damaged, and strengthened girders

CFRP

Cracklost

CFRP CFRP

Cracklost

CFRP


CFRP

W-section

CFRP

Concrete slab


CFRP

W-section

CFRP

Concrete slab

Fatigue crack

[Boyd, 1970]

Fatigue crack

[Boyd, 1970]

CFRP failure

Upgraded

Original (intact)

deflection

Load

Damaged (cracked)

Repair (recovery)


?

?CFRP failure

Upgraded

Original (intact)

deflection

Load

Damaged (cracked)

Repair (recovery)


??

??

Chapter 2

11

Chapter 2

Background and Literature Review

2.1 Introduction

The development of metallic structures has evolved significantly over the years, from the

19th century era of construction using cast or wrought iron, to modern steel construction.

In general, the steel construction industry involves two types of steel structural members.

The first includes the hot-rolled shapes and members built-up of plates, and the second

includes cold-formed sections fabricated using steel sheets, strips, or plates.

Many of the old cast iron and steel structures and bridges that remained in service are

increasingly becoming in urgent need of retrofitting. This is attributed to a number of

reasons; including deterioration due to corrosion, fatigue cracking, increased loading, and

change in design loads over the years. In most cases, maintaining this infrastructure

through retrofit to extend their service life is far more economical than replacing them.

Chapter 2

12

This chapter first presents an overview of metallic structural materials, followed by a

brief summary of conventional methods currently used in retrofitting steel structures. A

more detailed discussion on Fibre Reinforced Polymer (FRP) materials and their use in

retrofitting metallic structures, along with recent research advances in this field will

follow.

2.2 Metallic Materials

A wide range of metallic materials has been used in construction. This section briefly

describes two of the most commonly used structural metals, namely, cast iron and steel.

2.2.1 Cast iron

Structural cast iron was developed at the end of the 18th century and the first cast iron

bridge was built in 1779 (Cadei et al., 2004). Cast iron typically has non-linear stress-

strain relationship with low values of secant modulus ranging between 100 GPa and 145

GPa. It also has a higher compressive strength than its tensile strength. The maximum

compressive strength can reach 772 MPa, while the maximum tensile strength is limited

to 280 MPa.

2.2.2 Steel

Commercial steel has been produced since 1860; however, it is rare to find steel

structures built before 1890. Steel has become the backbone of the structural engineering

infrastructure and has remained the material of choice for various projects by engineers

due to its light weight, and favourable strength and ductility. Steel is also an ideal

Chapter 2

13

material for short, medium, and long span bridges because of its durability, ease of

maintenance, and ease of use in construction. Typically, steel has similar mechanical

properties in tension and compression, including an elastic modulus of 200 to 210 GPa

and a yield strength ranging between 230 MPa and 700 MPa (Kulak and Grondin, 2002).

2.2.3 Buckling strength of steel members

An important phenomenon to be considered by designers is the buckling strength of steel.

Two types of buckling may occur to compression steel elements, namely, local buckling,

which occurs within the thin elements comprising the cross section of a member, and

overall buckling that takes place in slender compression members.

Although there are no definite boundaries between short and long columns, it is believed

that columns with slenderness ratio values less than 20 (Fy = 300 MPa) may be

considered as short columns and will not undergo the overall buckling type of failure

(Kulak and Grondin, 2002). Local buckling of the walls of a cross section depends on the

width-to-thickness ratio and the type of support provided to the wall. For example, in

short columns consisting of rectangular Hollow Structural Sections (HSS), two opposite

sides would typically buckle outwards and the other two sides would buckle inwards

(Dawe et al., 1985 and Key et al., 1988). In thin-walled sections, this type of buckling

occurs before reaching the cross-sectional yielding capacity, whereas in thick-walled

sections, it occurs after yielding.

Chapter 2

14

Steel columns of medium to high slenderness ratios are rather susceptible to overall

buckling failure, before developing their full plastic capacity. Due to some unavoidable

disturbances during the rolling and cooling processes, the steel sections produced can

never be perfectly straight. As such, when these sections with their imperfect shapes (also

known as out-of-straightness) are used as columns, overall buckling will be introduced.

2.2.4 Residual stresses in steel sections

Another characteristic of interest to steel designers is residual stresses. These are

essentially the stresses remaining in an unloaded member after it has been formed into a

finished product. Examples of such stresses include but are not limited to: those induced

by cooling after rolling (as in the case of hot-rolled section) and cold bending (as in the

case of cold-formed sections). Residual stresses are of particular importance in column

design as they result in reduction of flexural stiffness of the columns and consequently in

a lower buckling strength (Weng, 1984 and Key and Hancock, 1993). Although residual

stresses are self-equilibrating, the effective moment of inertia of the cross section will be

changed when parts of the section, which have residual compressive stresses, are yielded.

The studies conducted by Beedle and Tall (1960), Tebedge et al. (1973), among other

researchers, found that the magnitude of maximum residual stresses in hot-rolled sections

of a moderate steel strength is approximately equal to 30 percent of the yield strength and

are uniformly distributed across the thickness of the plate. A typical idealized residual

stress distribution in a hot-rolled I-section is shown in Figure 2.1(a), in which the shown

stresses are normal to the cross sectional plane. An extensive experimental investigation

of residual stresses in cold-formed HSS sections was performed by Davison and

Chapter 2

15

Birkemoe (1983) and Key and Hancock (1985). The investigations revealed that two

longitudinal residual stress gradients can in fact be found in cold-formed HSS tubes. One

gradient is known as the perimeter (membrane) residual stress and is developed parallel

to the tube wall, as shown in Figure 2.1(b). The other gradient is known as the through-

thickness residual stress and is developed across the tube wall face and along the cross

sectional perimeter, as shown in Figure 2.1(c). It was found, however, that the through-

thickness residual stress gradient is the most dominant parameter that affects the tangent

modulus and ultimate strength of HSS columns (Davison and Birkemoe, 1983). The

magnitude of this type of residual stresses varies from 25 to 70 percent of the material

yield strength (Weng and Pekoz, 1990).

2.3 Conventional Retrofit Techniques of Metallic Structures

Retrofit of existing structures is typically needed when live loads increase beyond those

the structures were originally designed for. It may also be required because of an

inadequate design, damage, fatigue cracking, or deterioration such as corrosion. The

following steps are recommended for upgrading steel bridges (Bakht et al., 1979):

1. Welding cover plates to the critical flange areas of the bridge floor beams.

2. When flange material is added, the existing bolting system may become

insufficient. This should be corrected by adding more bolts or substituting larger

bolts.

3. Bearing stiffeners may be reinforced by bolting or welding angles or by welding

plates.

4. Intermediate stiffeners may also be added by bolting or welding plates.

Chapter 2

16

5. If the web was not originally spliced to resist moment, it may be spliced by

adding side plates.

6. Tension truss members can be reinforced by the addition of adjustable bars or

cover plates. Cover plates must, however, be welded to the gusset plates.

7. Compression truss members can also be strengthened by adding cover plates,

either to convert unsymmetric cross sections to a symmetric geometry, or to

reduce the width-to-thickness ratio of the plates that comprise the cross section, in

order to avoid local bucking and fully utilize their yield strength.

The previously mentioned methods of retrofitting steel bridges (and structures) typically

involve bolting or welding additional steel plates to the structure. These methods,

however, have a number of constructability and durability drawbacks. In many cases,

welding is not a desirable solution due to fatigue problems associated with weld defects

(Kulak and Grondin, 2002). On the other hand, mechanical (bolted) connections, which

have better fatigue life, are time consuming and costly. Drilling holes for bolted

connections also results in a cross sectional loss as well as the introduction of stress

raisers. Additionally, steel plates require heavy lifting equipment and may add

considerable dead loads to the structure, which reduces their strengthening effectiveness.

The added steel plates are also susceptible to corrosion, which could lead to an increase

in future maintenance costs.

Chapter 2

17

2.4 Retrofit of Steel Structures using FRP Materials

There is a need for adopting durable materials and cost-effective retrofit techniques to

overcome some of the drawbacks of conventional techniques stated earlier. One of the

possible solutions is to use high performance non-metallic materials such as FRPs. In

general, FRP materials provide superior strength-to-weight ratios for retrofit of structures.

FRP rigid plates and flexible sheets are available and can easily be applied to the metallic

surface. FRP flexible sheets in particular offer a unique advantage of being able to

conform to complex and curved surfaces.

Bonded FRP materials result in reducing stress concentrations as compared to mechanical

fastening of steel plates and do not generate thermally-induced stresses or heat-affected

areas in the metal as typically occurs in welding (Grabovac et al., 1991). Bonding FRP

materials to metallic structures was first used in aerospace and mechanical engineering

applications. CFRP laminates have been successfully used to repair damaged aluminum

and steel aircraft structures (Armstrong, 1983 and Karbhari and Shully, 1995). Bonding

of composite laminates was also shown to have many advantages for marine structures

(Allan et al., 1988 and Hashim, 1999).

Carbon-FRP (CFRP) materials are available in a variety of grades, according to the

process by which they are manufactured. In the context of this thesis, CFRP material will

be referred to according to its elastic modulus. CFRP material with an elastic modulus

value less than that of steel (i.e. ECFRP < 200 GPa) will be referred to as Standard

Modulus-CFRP (SM-CFRP), whereas CFRP having elastic modulus ranging between

Chapter 2

18

200 GPa and 400 GPa will be referred to as High Modulus-CFRP (HM-CFRP). CFRP

material with high value of elastic modulus larger than 400 GPa will be referred to as

Ultra High Modulus-CFRP (UHM-CFRP). A detailed review of the different types of

fibres and resins used to develop FRP materials is reported elsewhere (Cadei et al., 2004).

Figure 2.2 shows typical stress-strain curves of commercially available SM-, HM-, and

UHM-CFRP, compared to mild steel and Glass-FRP (GFRP).

2.4.1 Bond and force transfer

Force transfer between FRP and steel is controlled by bond at the interface between the

two materials. Bond performance is influenced by several factors such as the bonded

length and width, type of fibres and adhesive (resin), surface preparation, thickness of

adhesive, and thickness of FRP laminate. One of the simplest test configurations for

investigating bond strength and behaviour between either similar or dissimilar materials

is the single- or double-lap shear joint test (ASTM, D5868-01). Lam et al. (2004)

investigated the tensile strength of double lap joints using SM-CFRP plates. Four

different lap lengths of 50, 75, 100, and 150 mm were employed. Although debonding

was the typical mode of failure for all lap lengths, an increase in load was obtained by

increasing the lap length. In addition, large displacement at failure was observed for

joints with longer lap lengths. Photiou et al. (2006b) investigated the behaviour of

double-lap joints using both SM-CFRP and HM-CFRP plates. The study showed that the

low value of ultimate strain of the HM-CFRP resulted in joints with lower strength

compared to using the SM-CFRP plates, which have a higher ultimate strain. Moreover,

inserting a layer of GFRP with a low value of elastic modulus (softer) between steel and

Chapter 2

19

HM-CFRP resulted in a more gradual load transfer (i.e. better shear stress distribution)

and increased the joint capacity by 26 percent. The previous lap tests attempted to

simulate a typical bonded CFRP system used for repair applications.

Miller (2000) examined the behaviour of a bonded CFRP system using double-lap joints.

Two 457 mm long and 37 mm wide CFRP plates were bonded on both sides of a 914 mm

long steel plate. It was found that approximately 98 percent of the total force is

transferred within the first 100 mm of the bonded plate as shown in Figure 2.3.

Al-Emrani et al. (2005) used a similar test configuration, as that shown in Figure 2.3,

however, the steel plate width was tapered from 90 mm at both ends to 36 mm at the

middle. This specific geometry was introduced to allow for possible steel yielding prior

to failure of CFRP material. The study reported that although using HM-CFRP plates (i.e.

E = 362 - 383 GPa) results in increasing the yield strength of the steel specimen, the

fibres rupture in tension in a brittle manner at low strains. On the other hand, the highest

gain in both strength and ductility was obtained by using SM-CFRP (i.e. E = 155 - 175

GPa). However, in this case, debonding occurred after the steel plate has progressively

yielded near the mid-section and the adhesive layer was no longer able to accommodate

the large difference in deformation between the steel plate and the SM-CFRP.

Although lap joint specimens are simple to investigate the bond behaviour, they examine

the adhesive under shear stresses only, which could be useful for limited number of

applications. Nozaka et al. (2005a and 2005b) developed a special test setup to simulate a

Chapter 2

20

more realistic case where the adhesive is tested while bonded to a flexural member. In

this case, the adhesive is subjected to both shear and peel stresses. The test setup

consisted of a W360 x 101 steel section with a large hole and a slit introduced at mid-

span of the girder, as shown in Figure 2.4, to represent a severe crack in the tension

flange of a fatigued girder. Two steel plates were then bolted to the bottom side of the

notched flange and then FRP strips were applied to connect these two plates together. A

total of 27 specimens were tested to study different factors affecting bond of CFRP strips,

including the CFRP and adhesive types, crack width, bond configuration, and the bonded

length. The experimental results indicated that an adhesive with relatively large ductility

is required to redistribute the stresses successfully within the thickness of the adhesive

layer.

2.4.2 Brief review of retrofit applications

Research efforts to examine the feasibility and effectiveness of retrofitting steel structures

using FRP have generally been focused on the following areas:

1. Repair of naturally deteriorated I-girders.

2. Repair of artificially damaged I-girders.

3. Flexural strengthening of intact I-girders.

4. Retrofit of I-girders in shear.

5. Flexural strengthening of tubular sections.

6. Other special cases of strengthening and repair studies.

7. Fatigue and cyclic load behaviour of retrofitted members.

Chapter 2

21

A brief summary of research activities and findings in each of these areas is given in the

following sections, in light of the available and published literature.

2.4.2.1 Repair of naturally deteriorated I-girders

Corrosion is the most common cause of deterioration in steel structures. FRP repair

techniques can be used to increase the capacity of corroded members as reported by

Gillespie et al. (1996a). In this research program, two full-scale I-girders were removed

from an old and deteriorated bridge, repaired using FRP and then tested. The two

corroded girders were 9754 mm long, 610 mm deep, and had a flange width of 229 mm.

Both girders had uniform corrosion along their length, mostly concentrated within the

tension flange, which is typical in many bridges. Evaluation of the girders indicated,

approximately, a 40 percent loss of the tension flange. This flange loss resulted in a 29

percent reduction in stiffness. Since the webs of the girders were not severely corroded, it

was decided that only the bottom flanges would be retrofitted, along the entire length of

the girders, using a single layer of CFRP strip, 6.4 mm thick and 38 mm wide. The

repaired girders were then tested and the load was increased until local buckling failure

occurred in the compression flange, since no concrete slab was provided. As the

corrosion of the first girder was more severe than that of the second girder, it was found

that the CFRP strips have increased the elastic stiffness of the first and second girders by

10 and 37 percent, respectively. The ultimate capacities of the first and second girders

were also increased by 17 and 25 percent, respectively. These increases are with respect

to the predicted capacities of the unrepaired specimens. It is believed, however, that the

gain in ultimate capacity could have been higher, provided that local buckling of the

Chapter 2

22

compression flange was prevented. Furthermore, it was shown that the inelastic strains in

the tension flange were reduced by 75 percent in comparison to the unrepaired girder, at

the same load level.

2.4.2.2 Repair of artificially damaged I-girders

2.4.2.2.1 Non-composite I-girders

Artificial damage of steel sections has been attempted to simulate corrosion or fatigue

cracks. Section loss due to corrosion is typically simulated by cutting part of the flange or

the web, or machining the tension flange to a reduced thickness throughout the entire

span, as shown in Figure 2.5. Fatigue cracks are simulated by introducing a partial or

complete saw cut in the steel flange thickness. Another method of introducing an

artificial damage is by loading the steel girder beyond yielding and then unloading. These

damaged sections are then repaired with FRP to study the effectiveness of the system in

recovering the strength and stiffness of the member, as discussed in the following

sections.

Three-point bending tests were conducted on four simply supported W310 x 21 beams

with a span of 2438 mm (Liu et al., 2001). Specimen 1, with an intact cross section, was

tested without retrofit as a control specimen. The tension flanges of specimens 2, 3, and 4

were completely cut, as shown in Figure 2.5(a) within a length of 102 mm, at mid-span.

Specimen 2 was tested without CFRP repair to serve as a damaged control specimen.

Specimens 3 and 4 were repaired by bonding a HM-CFRP plate of 100 mm width and 1.4

mm thickness to each specimen. In order to examine the effect of the bond length, the

Chapter 2

23

CFRP plate covered the entire length in specimen 3 and one quarter of the length in

specimen 4. Since no concrete slabs were provided on the compression side, the beams

were laterally braced at the supports as well as two quarter points. Both unrepaired

specimens 1 and 2 failed by lateral torsional buckling of the compression flange. The

failure mode of specimen 3 (full length repair) was due to a gradual debonding of the

CFRP laminate, which initiated at mid-span, and extended to the end as the load

increased. This behaviour was triggered by the high stress concentration and high shear

stresses near the cut part of the flange. Failure of specimen 4 was due to sudden

debonding of the CFRP laminate. Figure 2.6 shows the load versus mid-span deflection

of the four specimens. The figure shows that the strength of the intact specimen has

dropped from 200 kN to 106 kN as a result of cutting the lower tension flange. The figure

also shows that none of the two repaired specimens recovered the strength of the control

intact specimen. Test results showed, however, 56 and 41 percent recovery of the lost

capacity of specimens 3 and 4, respectively.

The effect of partial cutting of the flange, shown in Figure 2.5(c), using different depths

of the cut was also examined, using 1220 mm long S130 x 15 beams (Tavakkolizadeh

and Saadatmanesh, 2001b). Cuts of 3.2 mm (shallow) and 6.4 mm (deep) depths were

introduced in the tension flanges, which represented 40 and 80 percent area losses of the

flange, respectively. The main difference between shallow and deep cuts was the

significant loss of ductility in the case of deep cut. SM-CFRP sheets, 7.6 mm wide and

0.13 mm thick, of different lengths were used (100 mm to 600 mm) to restore both

strength and stiffness of the damaged beams. Results indicated increases of 144 and 63

Chapter 2

24

percent in the ultimate capacities with respect to the counterpart damaged beams of 40

percent and 80 percent loss of tension flange, respectively, regardless of the length of

CFRP.

2.4.2.2.2 Steel-concrete composite girders

Another potential application of bonded FRP materials is the repair of steel-concrete

composite girders, commonly used in buildings and bridges. The presence of a concrete

slab in a composite action with a steel girder provides a continuous reinforcement and

support to the compression steel flange, which prevents the premature lateral torsional

buckling and thereby shifts failure to the tension side, at higher loads. Furthermore, the

location of the neutral axis of a composite section is normally shifted upwards, towards

the concrete slab. Therefore, it is expected that the FRP system applied to the tension

flange of composite sections will be utilized more effectively than in steel girders.

Tavakkolizadeh and Saadatmanesh (2003b) tested three composite girders of 4780 mm

span. The steel sections were W355 x 13.6 and the concrete flanges were 910 mm x 75

mm. The area of the tension flanges of the girders was reduced in a similar fashion to that

shown in Figure 2.5(b), to simulate 25, 50, and 100 percent loss of its tensile capacity.

The specimens were repaired with SM-CFRP laminates, of 3950 mm long and various

cross sectional areas ranging between 97 mm2 for the girders with 25 percent loss and

483 mm2 for the girders with 100 percent loss, and were then tested to failure. It was

found that the strength was not only restored but also increased by 20, 80, and 10 percent,

using CFRP laminate areas of 97, 290, and 483 mm2, respectively, compared to a

Chapter 2

25

calculated value for the intact (control) specimen. On the other hand, no extra gain in

stiffness was noticed, where the measured stiffness values were 91, 102, and 86 percent,

of that of the intact girder, for the aforementioned girders. It was also found that rupture

of CFRP laminate occurred in the girder having 25 percent loss and repaired with 97 mm2

of CFRP laminate, as shown in Figure 2.7(a). The girder having 50 percent loss in tension

flange and repaired with 290 mm2 of CFRP laminate failed by crushing of the concrete

slab, followed by a limited debonding of the CFRP laminate at mid-span. In the case of

the girder having 100 percent loss in tension flange and repaired with 483 mm2 of CFRP

laminate, complete debonding of CFRP laminate occurred, as shown in Figure 2.7(b). It

should be noted that the change in failure mode of the previous specimens could be

related to both the difference in the degree of damage and the area of CFRP laminate. In

both cases (50 percent and 100 percent loss), the failure of the girders was always

associated with crack propagation, as shown in Figure 2.7(b). In a different study, Al-

Saidy et al. (2004) followed a similar approach by introducing 50 percent and 75 percent

loss of the tension flange of W200 x 22 using the technique shown in Figure 2.5(b). It

was shown that repairing the girders using HM-CFRP plates was able to fully restore the

strength of the original undamaged girders, whereas the stiffness was only partially

restored. The CFRP debonding mode of failure was not observed in this study. Only

crushing of the concrete slab or rupture of the CFRP plates was reported. In fact, this

could be attributed to the HM-CFRP plates used in this particular study, unlike the SM-

CFRP plates used in the previous study by Tavakkolizadeh and Saadatmanesh (2003b).

The higher the elastic modulus of the CFRP material, the lower the rupture strain is.

Chapter 2

26

Sen et al. (2001) used a different approach to simulate severe service distress in 6100 mm

long girders. Six W200 x 36 steel girders acting compositely with concrete slabs (710

mm x 114 mm) were loaded beyond the yield stress, and then unloaded. The girders were

then repaired using SM-CFRP laminates of thicknesses 2 and 5 mm. The increases in

strength were 21 and 52 percent in the specimens repaired with 2 mm and 5 mm thick

SM-CFRP laminates, respectively, relative to the control unrepaired specimen. On the

other hand, stiffness of the repaired specimens was marginally increased. For all repaired

girders in this study, mechanical clamps were used at the CFRP laminate ends to prevent

the debonding failure mode.

2.4.2.3 Flexural strengthening of intact I-girders

FRP materials may not only be used to restore the capacity of damaged or deteriorated

members but can also be used to increase the strength and stiffness of intact members.

This is typically the case in upgrading applications to accommodate an increase in live

load, as demonstrated in the following sections:

2.4.2.3.1 Non-composite I-girders

A number of researchers have tested different sets of non-composite I-beams to explore

the effectiveness of using CFRP plates in strengthening applications. Colombi and Poggi

(2006) tested four HEA140 steel beams of 2500 mm span in three-point bending.

Although the tests were terminated before failure, after excessive deflections were

observed at mid-span, the beam strengthened with two 120 mm x 1.4 mm layers of HM-

CFRP plates achieved 14 and 40 percent increase in stiffness and strength, respectively. It

Chapter 2

27

should be noted that the ends of the CFRP plates were wrapped with CFRP sheets, which

were extended up along the web, to provide anchorage and prevent the debonding failure

mode. Based on the strain distribution along the CFRP plates, the study estimated that a

development length of 100 mm is required to achieve full transfer of the longitudinal

stresses from the tension flange to the bonded CFRP plates. This value agrees with the

observations of the experimental and analytical studies performed by Miller (2000), and

shown in Figure 2.3.

Linghoff et al. (2006) tested five HEA180 steel beams of 1800 mm span in four-point

bending. The beam strengthened with two HM-CFRP strips of 80 mm x 1.2 mm attached

to each of the bottom and top sides of the lower flange achieved 18 percent increase in

strength. The load carrying capacity of the beam was dropped after the bottom layers of

the HM-CFRP ruptured.

Deng and Lee (2007) tested ten 127 x 76UB13 steel beams of 1100 mm span, either in

three- or four- point bending. HM-CFRP plates, 76 mm wide, with different thicknesses

and lengths bonded to the lower flange. It was concluded that increasing the CFRP plate

thickness as well as decreasing its length initiate the debonding mode of failure at lower

load levels. The maximum gain in strength (30 percent) was achieved in the beam with

the longest bonded length (500 mm) and thinnest CFRP plate thickness (3 mm). It should

be noted that for all the previous experimental investigations, the beams were laterally

supported to prevent lateral torsional buckling.

Chapter 2

28

It can be concluded for these studies that the use of CFRP materials with elastic modulus

equivalent to that of steel (i.e. HM-CFRP) and a reasonably high tensile strength would

be most suitable for increasing flexural strength of steel beams. On the other hand, CFRP

with even higher modulus (i.e. UHM-CFRP) or larger cross sectional area would be

required to increase stiffness of steel beams.

Edberg et al. (1996) and Gillespie et al. (1996b) studied four different strengthening

schemes, as shown in Figure 2.8, applied to the tension flange of W200 x 15 steel beams

of 1372 mm span, over the middle 1219 mm. The first scheme [Figure 2.8(a)] consisted

of a 4.6 mm thick CFRP plate, bonded directly to the tension flange of the steel beam.

The second scheme [Figure 2.8(b)] consisted of a similar CFRP plate, but was bonded to

an aluminium honeycomb block, which was bonded to the steel flange. The idea was to

position the CFRP plate further away from the centroid of the steel section, to increase its

moment of inertia. In the third scheme [Figure 2.8(c)], a foam core was attached to the

tension flange, followed by wrapping the whole assembly by a GFRP sheet, which

contains fibres in the ± 45 degree directions. The fourth scheme [Figure 2.8(d)] consisted

of a GFRP pultruded channel, which was both adhesively bonded and mechanically

connected to the tension flange with self-tapping screws. Based on the test results, the

increases in stiffness were 20, 30, 11 and 23 percent, for the schemes shown in Figure

2.8(a, b, c, and d), respectively, whereas, the increases in strength were 42, 71, 41 and 37

percent, respectively. It was concluded that the sandwich CFRP-plated technique [Figure

2.8(b)], was the most efficient, while the GFRP wrapped system [Figure 2.8(c)] was the

least efficient.

Chapter 2

29

El Damatty et al. (2003) studied the effect of bonding 154 mm wide by 19mm thick

GFRP plates to both the top and bottom flanges of W150 x 37 sections. Four-point

bending tests were conducted on beams of 2800 mm span. The reported failure mode was

delamination within the GFRP plate in the tension side. No failure of the adhesive

between steel and GFRP was observed. The reported increases in stiffness, yield and

ultimate load were 15, 23 and 78 percent, respectively.

In the last two studies presented, a 4.6 mm thick CFRP plate, and two 19 mm thick GFRP

plates were bonded to steel beams of comparable sizes to enhance their structural

performance. It is worth noting that the GFRP plate, which is four times thicker than the

CFRP plate, has provided an increase in stiffness, 25 percent lower than that provided by

CFRP. On the other hand, the GFRP plate has provided an increase in strength, 36

percent higher than that provided by CFRP. This suggests that GFRP could be suitable

for strength-controlled applications, provided that a fairly thick plate is used. On the other

hand, CFRP is clearly more effective in stiffness-controlled applications. It is

recommended that future feasibility studies be conducted to compare the effectiveness of

GFRP and CFRP systems in enhancing both the stiffness and strength, especially with

GFRP has the advantage of lower cost and also does not develop galvanic corrosion, as

will be discussed later.

2.4.2.3.2 Steel-concrete composite girders

As mentioned earlier, the presence of a concrete slab above the steel girder adds stability

to the compression steel flange against the lateral torsional buckling. Tavakkolizadeh and

Chapter 2

30

Saadatmanesh (2003a) explored strengthening composite girders using 76 mm wide SM-

CFRP plates. Three 4780 mm long W355 x 13.6 steel girders with 910 mm x 75 mm

concrete slabs were tested in four-point bending. The reported increase in ultimate load

for the girders strengthened with 1.3, 3.9 and 6.4 mm thick CFRP plates were 44, 51 and

76 percent, respectively. All girders failed by crushing of the concrete slab. A sample

load versus mid-span deflection as well as the failure mode of the girder strengthened

with 6.4 mm thick CFRP plate is shown in Figure 2.9. Al-Saidy et al. (2007) followed a

similar approach but bonded an additional HM-CFRP plate on each side of the lower 50

mm of the web. Crushing of concrete slabs was also the observed mode of failure for all

specimens. The achieved increase in strength was 45 percent; however, the increase in

stiffness in the two studies was insignificant.

In all the previous studies introduced in this section, there was no remarkable increase in

the girders’ stiffness observed when CFRP reinforcement of a reasonable amount was

used. This is attributed to the value of elastic modulus of the CFRP materials used, where

only minor improvement in the transformed section properties occurred as a result of the

SM- and HM-CFRP used. A major increase in stiffness can be achieved by using UHM-

CFRP with a significantly higher modulus of elasticity than that of steel. Schnerch (2005)

used externally bonded HM- and UHM-CFRP laminates to strengthen two large-scale

steel-concrete composite beams. The beams consisted of W310 x 45 steel sections and

840 mm x 100 mm concrete slabs. The modulus of elasticity of the HM- and UHM-CFRP

materials was 229 GPa and 457 GPa, respectively. A four-point bending load

configuration was used with a 6400 mm span and a 1000 mm constant moment region.

Chapter 2

31

The CFRP plates were wrapped at their ends with 330 mm wide CFRP sheets, which

were extended up on the web from both sides. The HM-CFRP plates increased both the

elastic stiffness and flexural strength of the beams by 10 and 16 percent, respectively. On

the other hand, the UHM-CFRP strengthening (area of CFRP is 70 percent larger than the

previous case) increased both the elastic stiffness and flexural strength of the beams by

36 and 45 percent, respectively. Both beams failed by rupture of the CFRP plates.

Dawood (2005) also used UHM-CFRP strips with elastic modulus of 460 GPa to

strengthen 3050 mm long concrete-steel composite beams. CFRP end wraps were also

used in this investigation to prevent debonding of the CFRP plates. Substantial increases

in both stiffness and strength of 46 and 66 percent, respectively, were achieved. Rupture

of CFRP plates was also the dominant failure mode.

2.4.2.4 Retrofit of I-girders in shear

Web damage of I-girders has been simulated and studied by Shully et al. (1994).

Specimens of 711 mm span were tested in three-point bending, where a 100 mm diameter

hole was drilled within the shear span at mid-height of the web, as shown in Figure

2.5(d). Different types of bonded FRP sheets were used to repair the web. All repaired

specimens failed in a similar fashion. As the load was increased, the FRP systems began

to buckle over the area of the hole, and then separated from the web. As such, all the

repaired specimens could not recover the strength of the undamaged specimen. The

specimens were able, however, to achieve up to 7 percent increase in strength. The fibre

orientations in the different FRP repair systems were not reported.

Chapter 2

32

Patnaik and Bauer (2004) designed a built-up I-section with wide and thick flanges to

promote elastic buckling of the 3.2 mm thick web under shear stresses. Two CFRP-

strengthened beams of 3350 mm span were tested in four-point bending and compared to

a third control beam. The two 1270 mm long shear spans of the strengthened beams were

identically strengthened from both sides with adhesively bonded 1.4 mm thick vertical

CFRP strips. An increase of 26 percent in shear strength of the beam was reported. The

beams failed by web buckling due to high shear stresses, associated with debonding of

the CFRP plates, as shown in Figure 2.10.

For shear strength applications, it is believed that the most effective fibre orientation of

the CFRP material bonded to the web would be in the directions of principal stresses (i.e.

45 degree). No studies have been reported in literature on this aspect.

2.4.2.5 Flexural strengthening of tubular sections

Tubular structures have become increasingly popular in both the steel and aluminium

construction industries, because of their aesthetical and economical values. Tubular

members can be used either as flexure members in floor beams and telecommunication

monopoles or as axially loaded members in truss structures and bridges. In tubular cross

sections, FRP sheets could be bonded in both the transverse and longitudinal directions.

The transverse wrapping could be used to minimize the debonding of the longitudinal

FRP sheets and also to provide bracing for the steel section itself against the outward

local buckling.

Chapter 2

33

Schnerch et al. (2004) tested twelve-sided tubular cantilevered monopoles of 6090 mm

length, used in telecommunication applications. The specimens were tapered with a base

diameter of 457 mm, a tip diameter of 330 mm, and a wall thickness of 4.7 mm. The

poles were strengthened using either HM-CFRP sheets (E = 229 GPa) or strips (E =338

GPa) in the longitudinal direction, from the base up to mid-height. A mechanical

anchorage system was used by bolting steel angles to the base plate on top of the CFRP

sheets. Additional transverse sheets were used to wrap the longitudinal sheets or strips to

prevent them from premature buckling. Figure 2.11 shows the load versus the cantilever

tip deflection of one specimen. Test results showed that both the elastic stiffness and

ultimate strength were increased by 25 and 17 percent, respectively. In all tests, the

longitudinal CFRP strips on the tension side, near the base, were ruptured and a drop in

the applied load was observed. Eventually, failure occurred by local buckling of the

monopole on the compression side, 150 mm away from the base. This was associated

with rupture of the transverse sheets, as shown in Figure 2.11. The study recommended

prestressing the HM-CFRP strips to further enhance the stiffness of the monopoles.

Seica et al. (2006) tested seven 168 x 4.8 mm circular HSS beams of 2200 mm long

spans in four-point bending. The study simulated repair of offshore pipelines, and

included one control specimen, two specimens wrapped with CFRP under standard

conditions “in air”, and four specimens wrapped with CFRP in artificial sea water. Two

layers of CFRP sheets with fibres oriented in the longitudinal direction were first bonded

to each tube and then wrapped with a third layer with fibres oriented in the transverse

direction. For the tubes wrapped and cured in air, both the stiffness and strength were

Chapter 2

34

increased by 18 and 27 percent, respectively. On the other hand, the tubes wrapped and

cured underwater were not able to attain the flexural capacity of those cured in air.

Failure typically occurred by buckling and debonding of the CFRP on the compression

side. Haeider et al. (2006) carried out a similar research on 85 mm diameter circular tubes

of 1.1 mm wall thickness and varied the number of layers in each direction. The study

showed that sheets with fibres oriented in the transverse direction have a considerable

effect on the plastic rotation capacity of the tube.

Vatovec et al. (2002) filled the middle half of 152 x 152 x 4.8 mm HSS beams with

concrete, in addition to using 50 mm x 1.2 mm SM-CFRP strips (E = 165 GPa) bonded to

the tension and compression flanges. No transverse wraps were used in this study. Test

results showed that the ultimate moment capacity was increased from 6 percent for the

tube strengthened with one strip attached to the compression flange only, to 26 percent

for the specimen with two strips attached to the tension flange and one strip attached to

the compression flange. The governing failure mode of all specimens was delamination

of the CFRP strips on the compression flange, followed by delamination of the strips on

the tension flange. The CFRP strips on the compression flange buckled upwards, split

longitudinally, and then fractured.

Photiou et al. (2006a) induced an artificial degradation to rectangular 120 x 80 x 5 mm

HSS beams of 1700 mm long span. The tension flange was machined to be reduced to

half of its original thickness in order to simulate material loss due to corrosion. The study

showed that bonding 60 mm x 1.20 mm SM-CFRP sheets of relatively high strength

Chapter 2

35

result in a higher increase in both strength and ductility than the 60 mm x 2.40 mm HM-

CFRP, which exhibits sudden rupture of fibres due to its low ultimate strain. Failure,

generally, occurred by debonding of the CFRP sheets. The study also investigated the

effect of adding ± 45 degree GFRP U-wraps, extended to the mid-height of the webs, to

the previous repair system. The test results showed that the GFRP U-wraps prevented the

debonding and rupture of CFRP sheets.

2.4.2.6 Other special cases of strengthening and repair studies

Tension tests have been done by Jiao and Zhao (2004) and Fawzia et al. (2007) on pairs

of very high strength (VHS) 38 mm diameter circular steel tubes of 1350 MPa yield

strength. The tubes were butt-welded together and strengthened with either HM-CFRP

(i.e. E = 240 GPa) or UHM-CFRP (i.e. E = 640 GPa) wraps with fibres oriented in the

longitudinal direction. The bonded length was varied among the specimens from 23 to

126 mm. Figure 2.12 shows the load versus the bond length for specimens strengthened

with HM-CFRP. The study showed that the higher the modulus of elasticity of CFRP

material, the shorter the development length required. All specimens strengthened with

HM-CFRP experienced bond failure, rather than tension failure. Nevertheless, they

achieved higher strengths than specimens strengthened with UHM-CFRP, which failed in

tension by rupture of CFRP. Both modes of failure are also shown in Figure 2.12.

Zhao et al. (2006) addressed the problem of web crippling at regions of bearing stresses,

in thin walled 100x50 mm rectangular HSS tubes with wall thicknesses of 2, 3, and 5

mm. The study investigated five different schemes of bonding SM-CFRP plates or HM-

Chapter 2

36

CFRP sheets to the rectangular HSS, as shown in Figure 2.13. The study was focused on

Type 3 and Type 5. Test results showed the Type 3 strengthening achieved 50 percent

increase in the web crippling capacity, due to the change of failure mode from web

crippling to web yielding. The study also indicated that thinner sections benefit more

from Type 5 strengthening.

Fam et al. (2006) introduced a new technique for repair of cracked welded joints of truss-

type aluminum highway overhead sign structures comprised of circular tubular members.

The repair system utilized narrow longitudinal FRP strips wrapped around the truss k-

joint and attached to the diagonal members in alternating v-shape patterns, as shown in

Figure 2.14. The longitudinal layers were then wrapped with additional layers in the

circumferential direction for anchorage. The study showed a complete restoration of the

joint capacity that had a 90 percent loss in the weld perimeter, when CFRP sheets were

used. When a similar number of GFRP layers was used, only 79 percent of the joint

strength was restored.

2.4.2.7 Fatigue and cyclic load behaviour of retrofitted members

Steel plates have conventionally been welded to steel girders for retrofit applications.

However, the welded detail of steel plates is sensitive to fatigue failure. Several

experimental studies involving fatigue testing of (a) tension coupons (Buyukozturk et al.,

2003 and Jones and Civjan, 2003), (b) notched beams (Tavakkolizadeh and Saadat-

manesh, 2003c), and (c) beams removed from old bridges (Gillespie et al., 1996a and

Bassetti et al., 1998) have been performed to investigate the effectiveness of bonded

Chapter 2

37

CFRP plates in improving fatigue life of steel structures. For the different stress ranges

considered in these studies, the CFRP retrofitting techniques have improved fatigue life

of specimens by a factor ranging from 1.2 to 5.7 times that of the unretrofitted specimens,

depending on the retrofit configuration and the applied stress range.

Dawood (2005) applied three million fatigue cycles to three steel-concrete composite

beams of a 3050 mm span. The beams consist of W200 x 19 steel section acting

compositely with 525 mm wide and 65 mm thick concrete slabs. At the end of the applied

fatigue cycles, the control unstrengthened beam exhibited a 30 percent increase in the

mean deflection, whereas the two strengthened beams (same amount of CFRP but

different thickness of the epoxy adhesive) exhibited only 10 percent increase of their

mean deflection. The degradation of the mean deflection of the beams, normalized to the

mean deflection of their first fatigue cycle, versus the number of cycles is plotted in

Figure 2.15.

Bassetti et al., (2000) reported that applying prestress forces to the CFRP plates has

significantly decreased the crack growth rate and increased the fatigue life by a factor as

high as twenty, depending on the prestressing level.

In general, the studies have demonstrated the effect of increasing both the width and

length of FRP laminates (i.e. bonded area) on increasing the fatigue lives of the steel

specimens.

Chapter 2

38

The load resistance of CFRP-strengthened steel frame connections was also studied under

cyclic loading (Mosallam et al., 1998). Two strengthening details were investigated,

namely, an adhesively bonded CFRP stiffener and a mechanically fastened CFRP

stiffener. The effectiveness of the two techniques was compared to that of a fully welded

control specimen. Test results indicated that using CFRP stiffeners has resulted in

increasing ductility. The CFRP bonded stiffener provided the highest ductility with an

increase of more than 1.25 times that of the fully welded control specimen.

2.5 Surface Preparation and Bond Issues

Surface preparation is the key for a strong and durable adhesive bond. Since

rehabilitation takes place on site, surface treatment must also be environmentally

friendly, and easily accomplished under field conditions.

Surface grinding or sandblasting is recommended to remove all rust, paint, and primer

from the steel surface. Additionally, the bare steel surface may be pre-treated using either

an adhesion promoter or a primer/conditioner, which leaves a thin layer attached to the

metal oxide surface (AASHTO, 2000). This type of treatment significantly improves the

long-term durability of the bond as it prevents water from penetrating through to the

surface. The bonded side of the FRP plates may be sanded to increase the surface

roughness, using medium grit sandpaper or a sandblaster, and then wiped clean with

acetone. However, excessive surface preparation of FRP plates may cause damage and

expose the carbon fibres, leading to a possible galvanic corrosion if it becomes in direct

contact with the steel surface. The adhesive is then applied to the pre-treated steel

Chapter 2

39

surface. The adhesive typically used is a two-component viscous epoxy. A less viscous

epoxy resin is typically used in the case of bonding flexible sheets. It is generally

recommended to leave the bonded FRP plates or sheets to cure for a sufficient time, not

less than 48 hours. Application of an accelerated curing method such as heating blankets

or induction heaters is preferred (Buyukozturk et al., 2003).

Generally, the adhesive must perform three functions. It must have adequate bond

strength so that the FRP plates or sheets can be optimally utilized. This requires the

failure mode of the system to be governed by the ultimate strength of the FRP and not by

a premature bond failure. The adhesive must also be sufficiently durable in the

environment of the structure to match the extended life expectancy of the structure.

Finally, the adhesive must also be easy to handle and apply under field conditions.

Analysis has also shown that bond failure of the FRP sheets or plates could occur due to

high peeling stresses normal to the surface. In order to prevent peel-off failure, different

techniques have been proposed. Vinson and Sierakowski (1987) stated that tapering the

thickness of the CFRP plates to a 45o angle at all terminations, as shown in Figure

2.16(a), could effectively limit the peeling stresses. Furthermore, Schnerch et al. (2007)

reported that reverse tapering [Figure 2.16(b)] could even enhance the performance of the

bonded joint more. Mechanical clamping [Figure 2.16(c)] can also be applied over the

ends of the laminates to withstand the peeling stresses (Sen et al., 2001). Bolts could be

used to augment the load transfer capacity of the epoxy adhesive, especially with thicker

laminates. Liu et al. (2001) suggested wrapping GFRP sheets around the tension flange

Chapter 2

40

and part of the web, perpendicular to the longitudinal CFRP laminates. These transverse

sheets would be applied along the length of the girder to avoid delamination of the CFRP

laminates. Schnerch (2005) has also indicated that spew fillets [Figure 2.16(b)], which

result from excess epoxy being squeezed out of the joint when pressed or clamped can

significantly reduce the shear stresses in the adhesive. An extensive review of surface

preparation and FRP bonding problems can also be found in Hollaway and Cadei (2002)

and Schnerch et al. (2007).

2.6 Analysis and Design

2.6.1 Analysis of bonded joints

One of the problems associated with adhesive bonding is the complexity of the stress

analysis. Albat and Romilly (1999) introduced a simplified unidirectional linear-elastic

model to investigate the adhesive shear and normal stresses along the bonded length of

two joint types. These types included the double-sided reinforcement joint and double-

sided splice joint, as shown in Figure 2.17. The model included a correction to account

for shear lag in the adhesive and was capable of analysing joints with tapered

reinforcement (or splice) ends. Figure 2.17 also shows the typical shear stresses of the

adhesive and normal stresses of the adherent plates for both joint types. The model was

experimentally verified by Miller et al. (2001), as shown in Figure 2.3, and also by

Colombi and Poggi (2006), and showed good correlation. Schnerch et al. (2006) also

verified the model when splicing two FRP plates using another FRP plates in long beams.

The model showed accurate predictions of the tensile stress distribution along the bonded

plates as well as the adhesive shear stresses.

Chapter 2

41

Finite element modeling (FEM) of bonded joints is very sensitive to the number of

elements used in the regions of the expected high shear and peel stresses. The need for

large number of elements is necessary to account for the very small thickness of adhesive

relative to the member’s size, while maintaining reasonable aspect ratios of the elements.

This makes the computational effort very tedious. Attempts to develop finite element

models were, however, made by few researchers. Photiou et al. (2006b) developed a two

dimensional linear elastic FEM to simulate a double lap joint with two different adhesive

thicknesses, namely, 0.1 mm and 0.5 mm. The study showed that the peak shear stress

value in the adhesive layer [Figure 2.17(b)] increases as the adhesive thickness decreases.

The study recommended performing extra experimental verification for the results.

Linear elastic analytical models for the interfacial shear and peel stresses arising when a

thin FRP plate is bonded to the soffit of a steel beam have also been developed by several

researchers, in lieu of the finite element methods. Figure 2.18 shows the typical shear and

peel stress distributions at the cut-off point of CFRP bonded plate. Taljsten (1997)

developed a simple model based on compatibility of the deformations among the

strengthened beam, adhesive, and FRP plate. The derivation was based on a single point

load acting on the beam. The model, however, does not account for bending of the FRP

plate and neglects the shear variation through the thickness of the adhesive. Due to the

previous assumptions, the solution does not satisfy the zero shear boundary condition at

the ends of the adhesive layer. This approximation is acceptable and the model gives

reasonable results, except at a very small zone near the ends of the adhesive layer, which

is equal to the adhesive thickness (Buyukozturk et al., 2004). Smith and Teng (2001)

Chapter 2

42

developed a model which covers all three common load cases, namely, single point load,

double point load, and uniformly distributed load. Additionally, the model accounts for

the bending deformation of the FRP plate when calculating the normal stresses. Deng et

al. (2004) presented a model that includes the thermal effects as well as tapered ends of

the FRP plates. A parametric study was carried out and showed that the maximum shear

and peel stresses decrease as: (a) the thickness of the adhesive increases, (b) the shear

modulus of the adhesive decreases, or (c) the thickness of the FRP plate decreases. The

tapers were also found to reduce both the maximum shear stresses and peel stresses by

about 30 and 50 percent, respectively, as shown in Figure 2.18. Al-Emrani and Kliger

(2006) developed a model to determine the shear and normal stresses when prestressed

FRP plates are used. The results suggest that using a mechanical anchorage device is

recommended to avoid premature failure of the adhesive, due to the high shear stresses at

the ends of the prestressed FRP plates.

2.6.2 Analysis of steel girders strengthened with FRP bonded material

In order to model the behaviour of FRP-strengthened girders, researchers have either

used basic principles of mechanics (i.e. equilibrium and strain compatibility) to develop

the moment-curvature response of the section and load-deflection curves (Tavakkoli-

zadeh and Saadatmanesh, 2003a, Al-Saidy et al., 2004, and Schnerch, 2005) or the finite

element method (El Damatty et al., 2003, and Deng et al., 2004).

In order to establish the moment-curvature response, the cross section is divided into

layers. The principles of strain compatibility and internal force equilibrium are then

Chapter 2

43

applied by varying the depth of the neutral axis and summing the forces acting on the

cross section until equilibrium is satisfied for a predefined strain value. In this process,

the FRP material is assumed to be fully bonded to the steel flange. The internal moment

is calculated by summing the moments of the internal forces. The curvature is determined

as the slope of the strain profile. The process is repeated for different strain values, until

the full response of the section is determined. The deflection can then be calculated by

integrating the curvature along the span. Failure is considered when FRP is ruptured in

tension or when the concrete slab is crushed in compression.

Three-dimensional finite element analysis has also been conducted to simulate the FRP-

strengthening technique, where the adhesive bond between steel and FRP plates was

modeled using a spring system with two constants (El Damatty et al., 2003). The first

constant is in-plane of the steel surface to simulate the shear resistance, while the second

constant is normal to the plane to simulate the peel resistance. It should be noted that the

two constants were experimentally obtained from shear lap tests (El Damatty and

Abushagur, 2003). Results obtained from the finite element analysis showed an excellent

agreement with experimental results in both the elastic and inelastic ranges, as shown in

Figure 2.19. The model was also able to predict the distribution of the peeling stresses of

FRP plate bonded to the tension flange of a beam subjected to four-point bending. The

model showed a symmetric behaviour about the mid-span with the critical sections of the

peel-off failure located at the free edges of the FRP plate.

Chapter 2

44

Modeling cracked steel sections and capturing their full behaviour, including the effect of

crack propagation is a complex fracture mechanics problem. The problem has not been

addressed analytically in the available literature to date. In this thesis, a simplified

approach is developed and introduced in Chapter 7.

2.6.3 Design of bonded joints

The strength of a bonded joint is generally dictated by the strength of the adhesive. In the

presence of combined shear and peel stresses, failure of the adhesive layer can be

characterised by the maximum principal stress σ1 (Cadei et al., 2004), as given below:

στσσσ ≤+⎟⎠⎞

⎜⎝⎛+= 2

2

1 22 (2.1)

where, σ and τ are the maximum normal and shear stresses of the joint. σ is the

characteristic strength of the adhesive and is determined from representative tests.

The design of reliable bonded joints, in general, requires limiting the stresses in the

adhesive material to its proportional limit of the elastic range (Hart-Smith, 1980). This

requirement suggests that any of the previously mentioned linear-elastic analytical

solutions may be reasonable for design of bonded joints. More detailed design guidelines

for adhesive joints can also be found in “A guide to the structural use of adhesives”

prepared by the Institution of Structural Engineers (1999).

Chapter 2

45

2.6.4 Flexural design of CFRP strengthening of steel structures

Cadei et al., (2004) have introduced design guidelines for strengthening of steel structures

using FRP materials. Section analysis was recommended to calculate the amount of FRP

material required to achieve the desired strength. It was noted, however, that sectional

analysis should take into account the initial stress in the structure at the time of

strengthening. Additional design methods for strengthening of brittle metallic structures,

such as historic structures constructed using cast iron, were proposed by Cadei et al.,

(2004). They also gave design guidelines for strengthening metallic structures acting

compositely with concrete slabs.

Schnerch et al. (2007) proposed another set of design guidelines for strengthening bridge

girders based on moment-curvature analysis and load-deflection curves, with emphasis

on the use of HM-CFRP, as summarized in Figure 2.20. The guidelines stated that the

allowable increase of live load for a steel–concrete composite beam strengthened with

HM-CFRP materials should be selected to satisfy the following four conditions:

1. The flexural yield load of the strengthened beam should be greater than the

flexural yield load of the unstrengthened beam.

2. The strengthened member should remain elastic under the effect of the increased

live load. This is achieved by insuring that the total service load of the

strengthened beam, including the dead load and the increased live load should not

exceed 60% of the calculated new yield capacity of the strengthened beam.

3. To satisfy the ultimate strength requirements, the total factored load based on the

appropriate dead load and live load factors should not exceed the ultimate

Chapter 2

46

capacity of the strengthened beam after applying an appropriate strength reduction

factor.

4. To ensure that the structure remains safe in the case of a possible loss of the

strengthening system, the total load, including the dead load and the increased live

load, should not exceed the capacity of the unstrengthened beam.

2.7 Durability of Steel Structures Retrofitted with FRP

Durability of FRP materials bonded to metallic structures, combined with fatigue loading,

has been carefully studied in the aircraft industry. Armstrong (1983) reported on the

condition of an FRP repair that was used for 20 months to patch cracks on the leading

edge of the aluminium wing of a Concord that was flown for 2134 hours and subjected to

576 supersonic flights. At the end, the repair was in such an excellent shape, that it had to

be chiselled off, in order to be removed. It was clear that this repair appeared to still be

very well bonded over the entire patched area.

One of the most important factors affecting durability is the environmental surroundings.

The FRP retrofitting system itself is non-corrosive, however, when carbon fibres become

in contact with steel, a galvanic corrosion process may be generated. Three requirements

are necessary for galvanic corrosion to occur between carbon and steel: (a) an electrolyte

(such as salt water) must bridge the two materials, (b) there must be an electrical

connection between the materials, and (c) there must also be a sustained cathodic reaction

on the carbon (Mays and Hutchinson, 1992). By eliminating any of these requirements,

the galvanic cell is disrupted. A good selection of adhesives with inherent durability and

Chapter 2

47

high degree of resistance to chlorides, moisture, and freeze-thaw cycles is also very

important. For example, for repairs of steel ships with CFRP patches, Allan et al. (1988)

reported that a moisture barrier comprised of an additional GFRP sheet could be used to

cover the CFRP patch, which is attached directly to the metal using an adhesive. In this

case, in addition to the electrical isolation of the carbon fibres from the metal surface by

the resin matrix, two of the three conditions required for galvanic corrosion to occur were

controlled.

In order to test the durability of the bond between composite materials and steel, the

wedge test method (ASTM, D3762-03) is used. This test has great sensitivity to

environmental attack on the bond and is considered more reliable than conventional lap

shear or peel tests (Scardino and Marceaue, 1976). Shulley et al. (1994) performed wedge

tests on five different types of carbon and glass fibres bonded to steel surfaces.

Specimens were placed in five different environmental conditions (hot water, freezing,

freeze/thaw, salt water, and room temperature water) for two weeks before initiation of

the wedge test. After the wedge was inserted into the bond line, the specimens were

returned to their respective environments. The recorded crack growth rate after seven

days showed no dominance of one environmental effect over the others. There was

evidence that the GFRP reinforced systems have a more durable bond with steel than

CFRP. Also, the most durable bond systems were those subjected to a sub-zero

environment.

Chapter 2

48

Brown (1974) studied the corrosion of CFRP bonded to metals in silane environments.

The metals investigated included aluminium, steel, stainless steel and titanium.

Specimens were fabricated by either bolting the CFRP laminate to the metal or by

bonding with epoxy resin. Accelerated testing was performed by placing the specimens in

a continuous fog of neutral sodium chloride solution at a temperature of 35o C for 42

days. It was found that for all the metals studied, there was no accelerated deterioration

due to galvanic coupling for the adhesively bonded specimens. However, considerable

deterioration occurred for the bolted specimens. Since most structural adhesives are

insulators, and provided that a continuous film of adhesive can be maintained over the

bonded region, galvanic corrosion should not occur. As indicated earlier, numerous

studies have been conducted on aluminium and steel structures retrofitted with CFRP for

aerospace and marine applications. The studies showed that coupling CFRP with

aluminium is rather a more critical test for durability against galvanic corrosion,

compared to steel, since the electrode potential between carbon and aluminium is even

greater than the potential between carbon and mild steel (Francis, 2000).

The effects of the thickness of epoxy coating and salt water on galvanic corrosion have

also been investigated (Tavakkolizadeh and Saadatmanesh, 2001a). Test results showed

that applying a thin film of epoxy coating (0.1 mm) decreased the corrosion rate in

seawater sevenfold, relative to the specimens with direct contact (i.e. no epoxy) between

steel and CFRP. Furthermore, by applying a thicker epoxy coating (0.25 mm) the

corrosion rate was decreased by twenty-one times.

Chapter 2

49

In summary, several techniques have been recommended for preventing galvanic

corrosion, including the use of a nonconductive layer of fabric between the carbon fibres

and steel, an isolating epoxy film on the steel surface, or a moisture barrier applied to the

bonded area. The use of a glass fabric layer between CFRP and steel during the bonding

process has been shown to be effective in preventing galvanic corrosion (Karbhari and

Shully, 1995 and West, 2001).

Other durability issues such as temperature, creep, ultraviolet, and fire also have

significant effects on the overall response and life-cycle durability of the FRP system. Up

to a certain temperature, thermal exposure may be advantageous, as it can result in post-

cure for the FRP composite and adhesive. However, beyond a certain level of elevated

temperature, resins and adhesives can soften, which causes an increase in the visco-

elastic response, a reduction in the mechanical performance, and a possible increase in

the susceptibility to moisture absorption.

The mechanical properties of polymers have characteristics of both elastic solids and

viscous fluids, and hence they are classified as visco-elastic materials. The ambient

operating temperatures of these materials are very close to their visco-elastic phase. Thus,

creep becomes a significant consideration in assessing their long-term carrying capacity.

A basic requirement to minimize creep is to ensure that the service temperatures do not

approach the glass transition temperature of the polymer. The creep characteristic of a

polymer composite is also dependent upon the direction of alignment, the type of fibres,

and the fibre volume fraction. Furthermore, it is also dependent upon the time-dependent

Chapter 2

50

nature of the micro-damage in the composite material under stress. Glass, carbon and

aramid fibres are considered to have small creep component. For composite plate bonded

structures, the resin at the interface between the composite plate and the structure

dominates the creep–stress relaxation properties. The ambient cured resin/fibre

composites will have glass transition temperature values about 20–30oC above the cure

temperature (i.e. 45–55oC for pre-impregnated materials cured at site temperatures and

150–160oC for pultruded cross sections cured at elevated temperatures).

The ultraviolet component of sunlight degrades the composite. Degradation is manifested

by a discoloration of the polymer and a breakdown of the surface of the composite. The

inclusion of ultraviolet stabilizers into epoxy resin formulations seems to have little effect

on discoloration, but there is no evidence that continuous exposure to sunlight affects the

mechanical properties of these polymers.

All structural materials undergo some degree of mechanical degradation when exposed to

a severe fire. For FRP-strengthened structures under fire, the resin can neither protect the

fibres nor transfer the load between them. In addition to degradation within the FRP

composite itself, the bond between the FRP and the substrate will eventually fail and

expose the member to the full fire effect. Supplementary insulation systems can,

however, significantly improve the FRP performance at high temperatures (Bisby, 2003).

Chapter 2

51

More details regarding the durability of FRP composite materials used in retrofitting steel

structures can also be found in Karbhari and Shully (1995) and Hollaway and Cadei

(2002).

2.8 Field Applications

Field installations to date demonstrate that retrofit of steel structures using FRP materials

can indeed be applied under actual field conditions. This section provides examples of

several field applications utilizing the use of FRP systems in upgrading steel structures.

The Christina Creek bridge (I-704), just outside of Newark (New Jersey State), was

selected by the Delaware Department of Transportation to assess the CFRP rehabilitation

process conducted by the University of Delaware (Miller et al., 2001). A 5.25 mm thick

SM-CFRP plate was bonded to the outer face of the tension flange of the W610x150 steel

girder, which has a span of 7500 mm. Six CFRP plates were placed side-by-side to cover

the entire flange width. The CFRP plates were installed over the full length by using four

overlapped 1500 mm long pieces, as shown in Figure 2.21. Consecutive CFRP plates

were tapered at a 45o angle to form a scarf joint instead of a typical butt joint. Load tests,

using a three-axle dump truck, were performed on the retrofitted girder, prior to and after

the rehabilitation. A comparison between the load test data indicated that adding a single

layer of CFRP plates resulted in 12 percent increase in the girder’s stiffness, and 10

percent decrease in strain.

Chapter 2

52

Several metallic bridges in the UK were also strengthened with CFRP plates. The Hythe

Bridge had eight inverted Tee sections (cast iron beams) of 7800 mm span (Luke, 2001).

Four prestressed HM-CFRP plates were bonded to each beam using epoxy adhesive, in

addition to the mechanical end anchorages. The prestressing level was designed to

remove all tensile stresses under service loads. The prestressing technique of FRP was

recommended for the cast iron beams because of their brittleness and limited tensile

strain capacity at failure.

In order to overcome fatigue problems in The Acton Bridge of the London Underground,

it was decided to reduce the live load stresses by 25 percent. Prefabricated UHM-CFRP

plates were epoxy bonded to the underside of the girders supporting the track. The post-

installation monitoring verified that the desired reduction in stresses was achieved (Moy

and Nikoukar, 2002).

The Tickford Bridge, Newport Pagnell, Buckinghamshire, UK, was built in 1810 and is

the oldest cast iron bridge in service. The bridge was strengthened by bonding wet lay-up

CFRP sheets instead of plates, in order to conform to the curved surfaces. The restoration

was successful to increase the bridge capacity and also in terms of visible effect on the

bridge appearance (Hollaway and Cadei 2002).

In the Slattocks Canal Bridge, Rochdale, UK, the steel girders were 510 mm deep and

191 mm wide, and supported a reinforced concrete deck. HM-CFRP plates, 8 mm thick,

were bonded to the bottom flanges of the 12 innermost girders. Repair of the bridge

Chapter 2

53

allowed for upgrading its load capacity from 17 to 40 tonnes. A feasibility study

indicated that it would have cost much more to install a set of special traffic lights for

traffic control, if traditional bridge repairs were used as compared to the cost of

strengthening using CFRP plates. Repair using CFRP allowed for traffic on the bridge

during the strengthening process.

On September 2003, an aluminium truss overhead sign structure with cracked welded

joints due to fatigue has been successfully repaired using FRP sheets (Fam et al., 2006).

The structure is located over Route 88 (westbound direction) in New York State, east of

exit 2. To date, no signs of unsatisfactory performance have been reported.

Other field applications, including King Street Railway Bridge, Bid Bridge, and Bow

Road Bridge involving retrofitting using FRP materials have also been reported by

Hollaway and Cadei (2002).

Chapter 2

54

Figure 2.1 Residual stresses in hot-rolled and cold-formed sections.

Figure 2.2 Typical stress-strain curves for CFRP, GFRP, and steel.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20 25 30 35

Stre

ss (M

Pa)

GFRP

Tyfo SHE-51A

Strain x 10-3 (mm/mm)

SM-C

FRP

Sika

Carb

oDur

M91

4

HM

-CFR

PSi

kaC

arbo

Dur

H51

4

UH

M-C

FRP

Mits

ubis

hi D

iale

adK6

3712

Steel

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20 25 30 35

Stre

ss (M

Pa)

GFRP

Tyfo SHE-51A


SM-C

FRP

Sika

Carb

oDur

M91

4

HM

-CFR

PSi

kaC

arbo

Dur

H51

4

UH

M-C

FRP

Mits

ubis

hi D

iale

adK6

3712

Steel

(a) Residual stresses in a hot-rolled I-section

+Frs

+Frs

+

-Frs

+Frs

-Frs

+--

(b) Perimeter (membrane) residual stresses in a

cold-formed HSS

+Frs

t/3 t/3 t/3

_ -Frs

t/3t/3

t/3t =

wal

l thi

ckne

ss

-Frp

+Frp

-Frp

+-

-

+

(a) Residual stresses in a hot-rolled I-section

+Frs

+Frs

+Frs

+Frs

+

-Frs

+Frs

-Frs

+--

(b) Perimeter (membrane) residual stresses in a

cold-formed HSS

+Frs

t/3 t/3 t/3

_ -Frs

t/3t/3

t/3t =

wal

l thi

ckne

ss

t/3t/3

t/3t =

wal

l thi

ckne

ss

-Frp

+Frp

-Frp

+-

-+

--

+

Chapter 2

55

Figure 2.3 Measured and predicted strain distributions along the bonded length of a double lap joint. [Miller et al., 2001]

Figure 2.4 Test setup for bonded FRP plates in flexure. [Nozaka et al., 2005a]

Adhesive 1Analytical Model

-250 -200 -150 -100 -50 0 50 100 150 200 250

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Stra

in x

10-

3(m

m/m

m)

100 mm

Distance (mm)

Adhesive 2

5.25 mm thick CFRP plates12.7 mm thick steel plate

Adhesive 3

Adhesive 1Analytical Model

-250 -200 -150 -100 -50 0 50 100 150 200 250

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Stra

in x

10-

3(m

m/m

m)

100 mm

Distance (mm)

Adhesive 2

5.25 mm thick CFRP plates12.7 mm thick steel plate

Adhesive 3

Bottom view x-x

Steel plateTh.= 13 mm


hole

Stiffeners

W360x101

x

Elevation

x

2032

4064

Bottom view x-x



Bottom view x-x



hole

Stiffeners

W360x101

x

Elevation

x

2032

4064

hole

Stiffeners

W360x101

x

Elevation

x

2032

4064

Chapter 2

56

Figure 2.5 Various techniques of introducing artificial damage to steel girders. [Edberg et al., 1996 and Gillespie et al., 1996a]

Figure 2.6 Load-deflection responses of artificially damaged non-composite girders. [Liu et al., 2001]

(d) Web cutting(a) Complete flange cutting

(b) Partial cutting of the flange width

Hole diameter

(c) Partial cutting of the flange thickness

(d) Web cutting(a) Complete flange cutting

(b) Partial cutting of the flange width

Hole diameter

(c) Partial cutting of the flange thickness

5.0

50

100

150

200

250

00.0 1.0 2.0 3.0 4.0

Deflection (mm)

Load

(kN

)

Specimen 1

Specimen 3

Specimen 4

Debonding

Specimen 2

100 mm long cut

Load

Deflection

L

L / 4 L / 4Lateral support

5.0

50

100

150

200

250

00.0 1.0 2.0 3.0 4.0

Deflection (mm)

Load

(kN

)

Specimen 1

Specimen 3

Specimen 4

Debonding

Specimen 2

100 mm long cut

Load

Deflection

L


Load

Deflection

L


Chapter 2

57

Figure 2.7 Failure modes of artificially damaged steel-concrete composite girders.

[Tavakkolizadeh and Saadatmanesh, 2003b]

(a) Specimen with 25% loss in tension flange

(b) Specimen with 100% loss in tension flange

(a) Specimen with 25% loss in tension flange

(b) Specimen with 100% loss in tension flange

Chapter 2

58

Figure 2.8 Different strengthening schemes of steel beams. [Edberg et al., 1996 and Gillespie et al., 1996a]

Figure 2.9 Load-deflection response of a composite girder strengthened with HM-CFRP plates. [Tavakkolizadeh and Saadatmanesh, 2003a]

100

200

300

400

600

0

0

Load

(kN

)

500

700

10 20 30 40 50 60 70

4780 mm

Deflection (mm)

CFRP(th.=6.4 mm)

500 mm

Concrete crushing

Control (calculated)

Strengthened (experiment)

Strengthened (calculated)

100

200

300

400

600

0

0

Load

(kN

)

500

700

10 20 30 40 50 60 70

4780 mm

Deflection (mm)

CFRP(th.=6.4 mm)

500 mm

Concrete crushing

Control (calculated)

Strengthened (experiment)

Strengthened (calculated)

(a) CFRP-plated (b) Sandwich CFRP- plated

(c) GFRP wrapped (d) PultrudedGFRP channel

CFRP

Aluminum Honeycomb Foam Core GFRP section

GFRP(±45 degree)

(a) CFRP-plated (b) Sandwich CFRP- plated

(c) GFRP wrapped (d) PultrudedGFRP channel

CFRP

Aluminum HoneycombAluminum

Honeycomb Foam Core GFRP sectionGFRP

(±45 degree)

Chapter 2

59

Figure 2.10 Failure mode of web-strengthened beams. [Patnaik and Bauer, 2004]

Figure 2.11 Load-deflection response and failure mode of a tubular pole. [Schnerch, 2005]

Web buckling and debonding of CFRP plates

Web buckling and debonding of CFRP plates

Tip displacement (mm)

Load

(kN

)

Debonding/rupture of strips on tension side near the base

Tip displacement (mm)

Load

(kN

)

Debonding/rupture of strips on tension side near the base

Chapter 2

60

Figure 2.12 Effective bond length for steel tube strengthened with HM-CFRP. [Jiao and Zhao, 2004 and Fawzia et al., 2007]

Figure 2.13 Different strengthening schemes of rectangular HSS against bearing stresses. [Zhao et al., 2006]

Effective bond length = 75 mm

Empirical model by Jiao and Zhao (2004)

Debondingof CFRP

Rupture of CFRP

CFRP bond length (mm)

Load

(kN

)

Test Data

0 50 100 150

160

140

120

100

80

60

40

20

0

Effective bond length = 75 mm

Empirical model by Jiao and Zhao (2004)

Debondingof CFRP

Rupture of CFRP

CFRP bond length (mm)

Load

(kN

)

Test Data

0 50 100 150

160

140

120

100

80

60

40

20

0

Type 1 Type 2 Type 3




Chapter 2

61

Figure 2.14 Installation of CFRP sheets on cracked aluminum truss k-joint. [Fam et al., 2006]

Figure 2.15 Degradation of mean deflection of beams under fatigue loading. [Dawood, 2005]

1.3

1.2

1.1

1.0

0.9

0.0 1.0 2.0 3.0 4.0

Number of cycles (millions)

Nor

mal

ized

def

lect

ion

CFRP-Strengthened beams

Control beam

1.3

1.2

1.1

1.0

0.9

0.0 1.0 2.0 3.0 4.0


Nor

mal

ized

def

lect

ion


Control beam

1.3

1.2

1.1

1.0

0.9

0.0 1.0 2.0 3.0 4.0


Nor

mal

ized

def

lect

ion


Control beam

Chapter 2

62

Figure 2.16 Different techniques used to reduce peeling stresses.

Figure 2.17 Stress distribution in adhesively bonded double-sided joints. [Albat and Romilly, 1999]

10

20

30

40

Tapered edgeUniform thickness



Adh

esiv

e sh

ear s

tress

Nor

mal

stre

ss in

re

info

rcin

g pl

ate

Nor

mal

stre

ss

in s

ubst

rate

PPPP

Adh

esiv

e sh

ear s

tress

Distance Distance

Distance Distance

Distance Distance




(a) Double-sided reinforcement (b) Double-sided splice

Nor

mal

stre

ss in

sp

lice

plat

eN

orm

al s

tress

in

sub

stra

te

10

20

30

40




Adh

esiv

e sh

ear s

tress

Nor

mal

stre

ss in

re

info

rcin

g pl

ate

Nor

mal

stre

ss

in s

ubst

rate

PPPP

Adh

esiv

e sh

ear s

tress

Distance Distance

Distance Distance

Distance Distance




(a) Double-sided reinforcement (b) Double-sided splice

Nor

mal

stre

ss in

sp

lice

plat

eN

orm

al s

tress

in

sub

stra

te

(a)Tapered thickness

[Schnerch et al., 2007]

(b) Reverse tapering and spew fillet


(c) Mechanical clamp

Spew filletCFRP plate

(a)Tapered thickness


(b) Reverse tapering and spew fillet


(c) Mechanical clamp

Spew filletCFRP plate

Chapter 2

63

Figure 2.18 Comparisons of shear and peel stresses for plates with and without taper under UDL. [Deng et al., 2004]

Figure 2.19 Finite element analysis versus experimental load-deflection responses. [El Damatty et al., 2003]

Analytical shear stressFE shear stressAnalytical peel stressFE peel stress


(a) Uinform thickness FRP plate (b) Tapered thickness FRP plate



(a) Uinform thickness FRP plate (b) Tapered thickness FRP plate

Delamination between GFRP layers in B2

GFRP tensile failure

Steel beam

GFRP plate

Load

(kN

)

Delamination between GFRP layers in B2

GFRP tensile failure

Steel beam

GFRP plate

Load

(kN

)

Chapter 2

64

Figure 2.20 Design guidelines for steel–concrete composite beams strengthened with HM-CFRP materials. [Schnerch et al., 2007]

Figure 2.21 Installation of CFRP plate on the Christina Creek bridge (I-704). [Miller et al., 2001]

CFRP plates before application

CFRP plates during application

CFRP plates after application

CFRP plates before application

CFRP plates during application

CFRP plates after application

Chapter 3

65

Chapter 3

Experimental Program

3.1 Introduction

An experimental research program was conducted to investigate the performance of steel

structures retrofitted using carbon-FRP (CFRP) sheets and plates, in flexure and under

axial compressive loads. The experimental program consisted of three phases. The first

phase, Phase I, was focused on the axial compression behaviour of 50 short and slender

Hollow Structural Section (HSS) steel columns strengthened using different types of

CFRP sheets and plates. The parameters considered were the effect of CFRP

reinforcement ratio, the effect of fibre orientation, namely, in the longitudinal and

transverse directions, and the slenderness ratio of the columns. The columns were

instrumented to examine their behaviour in terms of the following responses: load-axial

displacement, load-lateral displacement, and load-longitudinal strains.

The other two phases of the experimental program were essentially focused on the

flexural behaviour of steel W-sections acting compositely with concrete slabs and

retrofitted with different CFRP materials. In Phase II, three large-scale girders, scaled

Chapter 3

66

down from an actual bridge, were tested in four-point bending to investigate the

effectiveness of CFRP plates in strengthening intact girders. Phase III was focused on the

repair of artificially damaged beams using CFRP sheets. The tension flanges of 10

beams, out of 11 beams in total, were completely saw-cut at mid-span to simulate a

fatigue crack or a severe loss of the cross section due to corrosion. The beams were then

repaired with CFRP sheets of different configurations and tested in four-point bending.

The parameters considered were the type of CFRP sheets, force equivalence ratio,

number of CFRP-bonded sides of the tension flange (i.e. upper and lower sides), and the

length of CFRP repair patch. Test specimens in phases II and III were instrumented to

measure their flexural behaviour in terms of both the load-mid span deflection, and the

load-strains responses.

This chapter presents properties of the materials used to fabricate the specimens, details

of the fabrication processes, testing configurations, and instrumentation.

3.2 Materials

This section describes the properties of various materials used in the experimental

program, namely, steel, concrete, and FRP of different types. Cold-formed HSS sections

were used in Phase I, whereas hot-rolled W-sections were used in Phases II and III. Five

different types of CFRP sheets and plates as well as one type of glass-FRP (GFRP) sheets

were used. Three different concrete batches were prepared for composite girders of

phases II and III.

Chapter 3

67

3.2.1 Structural steel

In this section, a detailed description of the cold-formed HSS sections used in Phase I and

the hot-rolled W-sections used in phases II and III is given.

3.2.1.1 Cold-formed HSS

Phase I of the research program included two different cross sections of cold-formed

HSS, namely, HSS1 and HSS2. Both sections were manufactured according to CSA

Standard S136-94, class C (Cold-formed non-stress-relieved). The two sections HSS1

and HSS2 are 44 x 44 x 3.2 mm and 89 x 89 x 3.2 mm, respectively. A schematic of their

cross sections is shown in Figure 3.1(a).

Stub-column tests are typically used in lieu of coupon tests to provide the average

compressive stress-strain curves (Bjorhovde and Birkemoe, 1979). This type of test

demonstrates the overall column performance at very low slenderness ratio. The yield

strength criterion is normally used when there is a gradual yielding without a distinct

yield point, and is defined as the stress at a 0.2 percent strain offset. Short columns with

built-in residual stresses typically show a gradual transition from the linear elastic

behaviour to the fully plastic plateau, as a result of gradual yielding. The magnitude of

residual stresses (Frs) can be estimated as suggested by Salmon and Johnson (1980), as

the difference between the yield strength and the proportional limit stress (i.e. the stress at

the end of the linear part).

Chapter 3

68

Two HSS1 and one HSS2 stub-column specimens, 150 mm and 175 mm long,

respectively, were tested. The lengths of the stubs were measured using a measuring tape

with an accuracy of ±1.00 mm. The ends of the stubs were machined to ensure flat and

square faces. Electrical resistance strain gauges were used to measure the longitudinal

strains at mid-height, at the middle of the flat sides of the columns. The strain gauges

were installed on the four sides of HSS1 and on two adjacent sides of HSS2. The

specimens were tested under stroke control at a rate of 0.20 mm/min, using a Riehle

testing machine, as shown in Figure 3.2.

The stress-strain curve of the HSS1 and HSS2 sections based on the average of strain

gauges measurements is shown in Figure 3.3(a and b). The behaviour of HSS1 shows a

proportional limit stress (Fp) of 257 MPa and yield strength (Fy) of 504 MPa, which

indicates that the magnitude of the residual stress is approximately 49 percent of the yield

strength. On the other hand, the behaviour of HSS2 shows a proportional limit stress (Fp)

of 255 MPa and yield strength (Fy) of 382 MPa, which indicate that the magnitude of

residual stress is approximately 33 percent of the yield strength.

The design provisions of the Canadian Standards Association (CAN/CSA-S16-01)

specify the limit for the flat width-to-thickness ratio ( )tb of HSS subjected to

compressive stresses as ( )yF670 , in order to permit yielding of steel prior to local

buckling under axial compression, where Fy is the yield strength of the steel in MPa. For

the HSS1 and HSS2 types of steel, these limits are 29.8 and 34.3, respectively, whereas,

Chapter 3

69

the actual (b/t) ratios are 9.75 and 23.8, respectively. Therefore, both sections satisfy the

width-to-thickness ratio limit.

3.2.1.2 Hot-rolled W-sections

W250x25 hot-rolled sections of weldable steel (Type W) were used for the girders of

Phase II of the research program. A schematic of the cross section is shown in Figure

3.1(b). Tension tests were performed on coupons cut from the web and flange of the same

sections by Savides (1989). The reported average stress-strain diagram is shown in Figure

3.4.

W150x22 hot-rolled steel sections were used for the beams of Phase III. A schematic of

the cross sections is shown in Figure 3.1(b). Uniaxial tension tests were performed

according to ASTM E 8M-04 on six dog-bone coupons. Three coupons, F1 to F3 were

cut from the flanges (with a thickness of 6.5 mm), whereas the other three coupons, W1

to W3, were cut from the web (with a thickness of 5.8 mm). The dimensions were

measured using a digital calibre with an accuracy of ±0.01 mm. A typical coupon is

shown in Figure 3.5. The stress-strain plots for all the six steel coupons are shown in

Figure 3.6. The average yield strengths of the flange and the web were 386 and 406 MPa,

respectively. The average modulus of elasticity of both flange and web was 197 GPa.

Details of the tensile properties of both the flange and web coupons are also presented in

Table 3.1.

Chapter 3

70

3.2.2 Fibre Reinforced Polymer (FRP)

Both FRP flexible sheets and FRP rigid plates were used in the experimental program.

The following sections describe the material properties of each type.

3.2.2.1 FRP sheets

Three different types of unidirectional CFRP sheets, referred to as C1, C2, and C3, were

used. The commercial names of C1, C2, and C3 types are Tyfo SCH-35, Tyfo SCH-41

(Tyfo Co. LLC, San Diego, California) and Dialead F637400 (Mitsubishi Chemical,

Chesapeake, Virginia), respectively. One type of GFRP sheet referred to as G, and

commercially known as Tyfo SHE-51A, was used. A layer of this GFRP was typically

installed on the steel surface prior to the application of the CFRP sheets to prevent direct

contact between steel and CFRP. This practice has been recommended by many

researchers (Allan et al., 1988, Karbhari and Shully, 1995, and West, 2001) to prevent

galvanic corrosion. Although this was a short term study, and galvanic corrosion was

unlikely to occur, the study was intended to simulate the actual practice that is likely to

take place. The typical thicknesses of a lamina (a single layer of dry fabric, wetted with

resin and cured) is 0.89 mm, 1.11 mm, 0.54 mm, and 1.46 mm for the C1, C2, C3, and G

types, respectively, based on actual measurements.

3.2.2.2 FRP plates

Two types of 1.4 mm thick pultruded CFRP plates were used (Sika Canada Inc., Pointe-

Claire, QC). The first type, C4, is commercially known as Sika CarboDur M914, and the

plate is 90 mm wide. The second type, C5, is commercially known as Sika CarboDur

Chapter 3

71

H514, and the plate is 50 mm wide. Since the rigid CFRP plates are typically installed

using a relatively thick epoxy layer (3.2 mm), no GFRP layer was used between the

CFRP plate and the steel surface as in the case of CFRP sheets.

3.2.2.3 Epoxy resins

Two types of epoxy resins were used. Resin 1 is a two-component Tyfo S (Tyfo Co.

LLC, San Diego, California) epoxy matrix, and was used in the case of flexible sheets.

The resin was used to bond the dry fabric layers to each other and to the steel surface

through a wet-lay up process. The mixing ratio of the epoxy is (2.9:1) of component A

(resin) and component B (hardener), by weight. The Tyfo S epoxy is relatively ductile

and has an ultimate elongation of 5 percent before failure, at a temperature of 21oC, as

reported by the manufacturer.

Resin 2, commercially known as Sikadur-30 (Sika Canada Inc., Pointe-Claire, QC), was

used in the case of CFRP rigid plates and is essentially a thixotropic adhesive mortar,

based on a two-component solvent free epoxy resin. The mixing ratio is (3:1) of

component A (resin) and component B (hardener), by weight.

3.2.2.4 Coupon tests of FRP sheets and plates

Several coupons of each FRP type were prepared and tested according to ASTM

D3039/D 3039M, as shown in Figure 3.7(a). The coupons were 250 mm long, with end

tabs of 60 mm long each, in order to minimize the effect of gripping stresses. The tabs

were made of two layers of epoxy-impregnated unidirectional GFRP sheets bonded to

Chapter 3

72

each side of the coupons. Tension tests were performed using an Instron Model 1350

testing machine with wedge-type mechanical grips, as shown in Figure 3.7(b). The

mechanical properties of all coupons of the different types of FRP sheets and plates are

listed in Table 3.2. Figure 3.8 shows the average stress-strain response for each type of

FRP material. A typical tension failure mode of the tested coupons is shown in Figure

3.7(c).

3.2.3 Concrete

One concrete batch was prepared for Phase II (batch 1), while two batches were prepared

for Phase III (batches 2 and 3), as shown in Table 3.3. The first batch of Phase III (batch

2) was mixed at the laboratory of Queen’s University with a target compressive strength

of 46 MPa after 28 days. The other two concrete batches were ordered from a ready-mix

plant, with target strengths of 40 MPa and 45 MPa for batches 1 and 3, respectively. It

should be noted that batch 1 was ordered with high slump, not less than 150 mm, to

increase its workability while pouring in the special formwork constructed for Phase II,

as will be described later. Three 100 x 150 mm cylinders were prepared for each test

specimen at the time of casting, and were kept at room temperature to the date of testing

of the respective specimen. The cylinders were tested using a 1300 kN Reihle testing

machine, as shown in Figure 3.9. The concrete age at the time of testing of each specimen

and its cylinders was at least 2 months. At this age, the concrete strength has already

stabilized. Table 3.3 shows the concrete strength measured for each batch, based on

cylinders tests. Generally, the average measured compressive strengths for batches 1, 2,

and 3 are 38.9 MPa, 49.9 MPa, and 50.2 MPa, respectively.

Chapter 3

73

3.3 Experimental Phase I – Strengthening HSS Columns

As mentioned earlier, in Chapter 2, when short HSS members are subjected to

compressive stresses, two opposite sides would typically buckle outward and the other

two sides would buckle inwards. Therefore, it is hypothesized that externally bonded FRP

sheets, particularly wraps oriented in the transverse direction, could help brace the flat

sides of the column and control the outward buckling, as shown in Figure 3.10(a). On the

other hand, FRP sheets may not contribute much on the sides that buckle inwards and

may in fact debond from the steel surface. In long columns, where global buckling takes

place, it is hypothesized that FRP sheets or plates oriented in the longitudinal direction

could provide tension reinforcement on the outer surface, as shown in Figure 3.10(b).

The following sections describe Phase I of the experimental program, undertaken to

evaluate the effect of strengthening axially loaded square HSS members with CFRP

sheets or plates. The fabrication and FRP installation processes, instrumentation, and test

setups and procedures are also presented.

3.3.1 Test specimens

In total, 50 square HSS columns were tested in compression. The specimens were divided

into 20 sets, falling into three groups, A, B, and C, as shown in Table 3.4. Groups A and

B included slender columns, whereas group C included short columns. Table 3.4 provides

all details of the columns, namely, the set number, number of similar specimens per set,

steel cross section type, length, and slenderness ratios (kL/r). The table also provides

information on strengthening schemes, including FRP type, number of layers, width, and

Chapter 3

74

fibre orientation. Groups A and C include three identical specimens in each set, whereas

group B includes one relatively large size specimen in each set. The identification of each

specimen in further sections of this thesis will indicate the set number, followed by the

specimen number (for example, 6-1 refers to the first specimen of set number 6). As

shown in Table 3.4, group A columns were fabricated using the HSS1 section (44 x 44 x

3.2 mm), while groups B and C columns were fabricated using the HSS2 section (89 x 89

x 3.2 mm). In group A, sets 1, 3, and 5 served as control (unstrengthened) sets with

slenderness ratios of 46, 70, and 93 respectively, while sets 2, 4, and 6 were the

corresponding strengthened sets. In groups B and C, sets 7 and 12, respectively, served as

control (unstrengthened) sets with slenderness ratios of 68 and 4, while sets 8 to 11 and

13 to 20 were the corresponding strengthened sets, using different CFRP schemes and

number of layers. The type of CFRP used, number of layers, and the fibre orientation are

shown in Table 3.4 and Figure 3.11.

The objective of Phase I is to study the effect of the following parameters:

(a) For slender columns:

1. The effectiveness of CFRP longitudinal strips in strengthening columns of

different slenderness ratios, through sets 1 to 6 of group A. In this case, a fixed

CFRP reinforcement ratio consisting of two layers, 25 mm and 16 mm wide of

type C5, is applied on two opposite sides of columns with kL/r ranging from 46 to

93.

2. The effect of number of layers of CFRP longitudinal sheets (i.e. effect of

reinforcement ratio) on strengthening effectiveness of columns of the same

Chapter 3

75

slenderness ratio, through sets 7 to 11 of group B. In this case, one, three, and five

layers of CFRP type C3, 75 mm wide, were installed on two opposite sides of the

columns. Also, another column included three layers attached to the four sides.

All columns had kL/r of 68 and had one layer, 75 mm wide, of GFRP between the

steel surface and CFRP.

(b) For short columns:

1. Effect of number of CFRP layers (i.e. reinforcement ratio) in group C, by

comparing sets 13 and 14 relative to 12 for C1 type and sets 17 and 18 relative to

12 for C3 type.

2. Effect of fibre orientation of CFRP sheets (i.e. longitudinal, transverse, and

combined) in group C, by comparing sets 13 and 15 relative to 12 as well as 14

and 16 relative to 12 for CFRP type C1, and sets 17 and 19 relative to 12 as well

as sets 18 and 20 relative to 12 for CFRP type C3.

3. Effect of CFRP type (i.e. C1 and C3) in group C, by comparing sets (13 and 17)

and sets (14 and 18), relative to the control set 12.

3.3.2 Fabrication of column specimens

The columns were cut to the desired lengths as listed in Table 3.4. The (L/r) values of the

specimens were 46, 70, 93, 68, and 5 for sets (1 and 2), (3 and 4), (5 and 6), (7 to 11), and

(12 to 20), respectively. The effective length factors (k), required to determine the

slenderness ratios (kL/r), depend on the end conditions and will be discussed later in the

test setup description ( 3.3.3). The ends of the columns in groups A and C were machined

Chapter 3

76

flat and perpendicular to the longitudinal axis, using a milling machine, as shown Figure

3.12(a). Although this type of machining could not be performed on the columns in group

B, due to their larger size and the limitations of the milling machine, every effort was

made during the cutting process of those particular specimens to ensure a flat and

perpendicular cut.

The overall buckling direction and strength are generally influenced by the out-of-

straightness geometric imperfection of slender columns (Allen and Bulson, 1980). The

out-of-straightness profiles of column sets 1 to 6 (group A) were measured using an

ILD1400 laser optical displacement sensor, as shown in Figure 3.12(b). The sensor

operates with a semiconductor laser having a wavelength of 670 nm, which classifies the

sensor in Laser Class II. The out-of-straightness profiles of longitudinal lines at the mid-

width of two perpendicular sides of a sample specimen (specimen 6-3) are shown in

Figure 3.13. The figure shows a single curvature along side “a” of the cross section with a

maximum value of 0.54 mm, and a triple curvature along side “b” with a maximum value

of 0.29 mm. The complete out-of-straightness profiles for column sets 1 to 6 are

presented in Appendix A. It should be noted, however, that the measured values of out-

of-straightness of the bare steel columns are very small, as shown in Figure 3.13. In fact

the installation process of CFRP on two opposite sides, using the hand lay up technique,

is likely to provide a different pattern of out-of-straightness due to the very unlikely

perfect symmetry of the CFRP installation. As such, another method will be described in

chapter 4 to estimate the final imperfection values of the CFRP-strengthened columns,

based on strain measurements. Group B columns were relatively large in size and could

Chapter 3

77

not be fit on the moving bed of the laser sensor. Their out-of-straightness imperfections

were interpreted from the strain measurements. For group C columns, the out-of-

straightness measurements have not been conducted since the columns were very short

and were expected to have local buckling, rather than overall buckling.

Prior to bonding the CFRP sheets or plates, the outer surface of all HSS columns was

sandblasted as shown in Figure 3.12(c), to remove mill-scale, rust, and debris and also to

roughen the steel surface in order to improve the mechanical interlock between the steel

surface and the adhesive. The outer surface was then cleaned using pressurized air to

remove any impurities remaining on the surface from the sandblasting process. The steel

surface was also wiped with acetone to remove any chemical impurities on the surface.

Two CFRP plates (C5 type) of widths 25 and 16 mm were bonded on each of the two

opposite sides of all specimens in sets 2, 4, and 6 of group A, as shown schematically in

Figure 3.11. For sets 8 to 10 of group B, 70 mm wide CFRP sheets (C3 type) were also

applied to two opposite sides. The plates and sheets in all these specimens were applied

to the two opposite surfaces perpendicular to the plane in which global buckling was

allowed in the test setup. Set 11 was strengthened with three layers of 70 mm wide sheets

(C3 type), applied to all four sides of the column. In all slender column specimens of

groups A and B, the CFRP plates or sheets were installed with the fibres oriented in the

longitudinal direction, as shown in Figure 3.14.

Chapter 3

78

For the short column sets 13 to 20 of group C, CFRP sheets of different orientations and

patterns were applied using either C1 or C3 types, as shown schematically in Figure 3.11

and Table 3.4. In sets 16 and 20, the longitudinal layer of CFRP was installed prior to

installing the transverse layer.

A single layer of GFRP (G) was first installed on the steel surface with fibres oriented in

the longitudinal direction for sets 8 to 11 of group B, and oriented in the transverse

direction (complete wrap) for sets 13 to 20 of group C. The FRP plates and sheets were

cut 25 mm shorter than the slender steel columns, from both ends in groups A and B,

mainly to simulate an actual case where access to the column ends may not be feasible.

The second layer of CFRP plates (16 mm wide) applied in column sets 2, 4, and 6 was

cut 50 mm shorter than the steel column from both ends. Loading was thus applied to the

steel cross-section only, without any contact with the CFRP plates or sheets. The ends of

CFRP plates in sets 2, 4, and 6 were wrapped with 50 mm wide GFRP sheets (G), as

shown in Figure 3.14 to hold the CFRP plates at the ends. For short column sets 13 to 20

of group C, the longitudinal and transverse FRP layers were completely wrapped and

overlaps of 50 mm and 75 mm, respectively, were provided and positioned symmetrically

at the round corners, as shown in Figure 3.11. Also, the FRP jacket was 5 mm shorter

than the steel specimens from both ends, for the same reasons indicated earlier for slender

columns.

Chapter 3

79

3.3.3 Test setup

All column specimens were tested under concentric loading using three different test

setups. Test setup A was prepared for group A using a 1000 kN Riehle testing machine,

as shown in Figure 3.15(a and b). The load was applied using stroke control at a rate of

0.50 mm/min, except for specimen (1-1), where a 0.20 mm/min rate was used. Lubricated

cylindrical bearings were used at both ends of the specimen to allow for free end rotation,

in one plane only, as shown in Figure 3.15(b and c). The specimens were braced against

out-of-plane displacement, using two L-shaped frames, as shown in Figure 3.15(a, b, and

d), in order to promote in-plane buckling only. Each L-shaped frame consists of a heavy

square HSS column, attached to the base of the Riehle machine, and a horizontal

cantilevered arm. One end of the cantilevered arm is attached to the column using two

plates and threaded rods, while the other end is welded to a 25 x 25 x 3.2 mm HSS

section to guide the column’s buckling in one plane only, as shown in Figure 3.15(d).

The tests on group B columns were carried out in a specially constructed horizontal setup

B, as shown in Figure 3.16(a and b), since they were too large to be accommodated in the

testing machine. The specimens were placed between two rigid steel reaction columns

anchored to the floor. A 1500 kN hydraulic loading ram was used to apply the load.

Lubricated cylindrical bearings were used at both ends of the specimen to allow for free

end rotation, in the horizontal plane only, as shown in Figure 3.16(c). The specimens

were braced against out-of-plane displacement, using another set of free sliding rollers, as

shown in Figure 3.16(d), in order to promote buckling in the horizontal plane only. The

Chapter 3

80

in-plane effective length factor (k) for the columns tested in setups A and B is assumed

equal to 1.0 based on the permissible rotation of the end supports.

The short columns in group C were tested under concentric loading in test setup C, using

the same Riehle machine used in test setup A, as shown Figure 3.17. The load in this case

was applied using a semi-spherical head on the top end of the specimen whereas the

bottom end was supported by a fixed flat plate, as shown in Figure 3.17. This setup is

analogous to a fixed-hinged condition and therefore the effective length factor (k) can

then be assumed equal to 0.8 (CAN/CSA-S16-01), which provides a slenderness ratio

(kL/r) of 4. The load was applied using a stroke control at a rate of 0.20 mm/min.

3.3.4 Instrumentation

For group A, one horizontal Linear Potentiometer (LP), with a range of 100 ± 0.01 mm,

was mounted at mid-height of the columns to measure lateral displacements, as shown in

Figure 3.15(a and d). Vertical displacement was measured directly through the moving

cross head of the testing machine. The longitudinal strains at mid-height of the columns

were also measured using two electric resistance strain gauges, attached directly to the

two opposite sides of the specimens. The strain gauges were 5 mm long with a gauge

resistance of 119.8 ± 0.2 Ω. The gauges were attached to the outer surface of the CFRP

plate (or to the steel surface of the control columns). The load was measured using a load

cell built-in the Riehle machine.

Chapter 3

81

For group B columns, which were tested in a horizontal plane, six LPs were used to

record both axial and lateral displacements, as shown in Figure 3.16(a). Two LPs were

mounted at each end of the specimen, parallel to the longitudinal direction, to measure its

net axial displacement. The two LPs at each end were placed on the opposite sides of the

specimen in the plane of the buckling. Two transverse LPs were mounted at mid- and

quarter-points of the height of the specimen to measure lateral displacements and capture

the buckling shape. The longitudinal strains at mid-height were measured using two 5

mm electric resistance strain gauges, attached to the two opposite sides of the specimens.

Additional displacement-type, position-indicator strain gauge transducers, (PI gauges)

were also attached to the specimen at mid-height (PI1 and PI2), over a gauge length of

200 mm, as shown in Figure 3.16(e). The PI gauges have a displacement range of ± 5.0 ±

0.005 mm. The load was measured using a 2000 kN load cell positioned between the end

of the reaction frame and the hydraulic jack, as shown in Figure 3.16(a).

For group C columns, three LPs were mounted around the specimen, in a vertical

position, to provide a reliable average for the axial displacement of the short columns and

also to check if any unintended eccentricity existed early during the test and correct the

alignment accordingly. Additionally, control set 12 was instrumented with 5 mm electric

resistance strain gauges, installed in the longitudinal direction on two adjacent sides of

the specimen, 30 mm below the top surface, where local buckling was anticipated [see

Figure 3.10(a)]. The same load cell used for group B columns was also used for group C

columns to monitor the applied load, as shown in Figure 3.17

Chapter 3

82

The data measured throughout all the tests by the LPs, PI-gauges, load cells, and strain

gauges as well as the load and stroke of the Riehle machine were recorded using a Vishay

System 5000 Data Acquisition System (DAS). The DAS receives the load and stroke of

the testing machine as well as the LPs readings through a high-level input card with an

accuracy of ±10 mV. Both strain gauges and PI gauges readings are transmitted through a

strain gauge card with an accuracy of ± 5 mV. Test data were collected and stored using

Strain Smart™ computer software.

3.4 Experimental Phase II – Strengthening of Intact Composite

Girders

This section describes the second phase of the experimental program undertaken to

evaluate the effectiveness of CFRP plates in strengthening intact steel-concrete composite

girders. Test specimens used in this part of the study were scaled down (4:1) from an

actual bridge, in order to provide realistic proportions of section size, concrete slab size,

and the span. Description of test specimens, and fabrication processes, including CFRP

installation, instrumentation, as well as test setup and procedures are presented in the

following sections.


A total of three steel-concrete large-scale composite girders were fabricated and tested to

failure in four-point bending. Each girder consists of 6100 mm long W250 x 25 hot-

rolled steel section acting compositely with a 65 mm thick, 500 mm wide, concrete slab,

as shown in Figure 3.18(a). The girders include one intact control (unstrengthened)

Chapter 3

83

specimen (G1) and two CFRP-strengthened specimens (G2 and G3). The strengthening

scheme of G2 and G3 consisted of one 90 mm x 1.4 mm layer of CFRP type C4, 4000

mm long, which covers 67 percent of the span. A second layer of 50 mm x 1.4 mm and

1500 mm long was installed. This layer was of CFRP type C4 in the case of G2 and type

C5 in the case of G3. Table 3.5 provides all details of the girders, including their

identification number as well as type, width, and bonded length of CFRP plates.

The objectives of Phase II are to:

1. Investigate the strengthening effectiveness of intact composite girders of

reasonable dimensional proportions relative to real bridge using CFRP bonded

plates.

2. Examine the effectiveness of the CFRP bonded plates when they cover a length

shorter than the full span of the girder.

3. Compare CFRP plates of different moduli.

3.4.2 Fabrication of girders

The steel girders were previously fabricated as part of experimental research programs

conducted in the structural laboratory of Queen’s University on scaled models of a bridge

by Savides (1989) and He (1992). The purpose of those studies was to investigate

transversely prestressed concrete bridge decks. The girders were used to support the deck

slabs, and failure occurred in the slabs under relatively low load levels such that the steel

girders were still elastic. In this study, the same girders were used with new concrete

Chapter 3

84

slabs. In the following section, a brief summary of the history of the girders, in terms of

both the prototype and scaled bridges is presented.

The prototype bridge selected to be modeled by Savides (1989) and He (1992) is a two-

lane bridge under loads specified by Ontario Highway Bridge Design Code (OHBDC) for

class A highway. The bridge is 6.6 m wide, with a simply supported span of 24.0 m long

and is supported with three steel girders at 2.3 m spacing and a 1.0 m overhang on each

side. The prototype deck slab was 175 mm thick, which is thinner than the minimum

requirements (225 mm) specified by the OHBDC. A scale factor of 1:4 was chosen for

the model bridge, based on the available laboratory space, testing apparatus, and the need

to model all the bridge components and details. Therefore, the scale bridge model

consisted of a 43 mm thick concrete slab supported on three 6090 mm long W250x25

simply supported steel girders spaced at 569 mm with a 248 mm slab overhang on each

side. The model was tested under statically applied concentrated loads. Each girder has

four pairs of stiffener plates welded to the web. The stiffener plates are 240x40x10 mm

and located at the end supports and at third points of each girder. Shear studs of 8.8 mm

diameter and 35 mm long were welded in pairs at a longitudinal and transverse spacing of

85 mm and 42 mm, respectively, along the compression flange, as shown in Figure

3.18(b). All tested slabs failed in punching shear at a maximum load of 95 kN. This level

of load produced tensile strains of 0.11 percent in the tension flange of the steel section,

as calculated using the analytical model introduced in Chapter 7 of this thesis. By

comparing this strain to the stress-strain curve shown in Figure 3.4, it was concluded that

these girders remained fully elastic and hence could be reused in the current study. A

Chapter 3

85

detailed design of both the prototype and the model bridges can be found in Savides

(1989). Prior to reusing the girders in the current study, the old concrete slab was

completely removed and the studs were fully exposed.

In the current study, due to the large size of the girders and space limitations in the

laboratory, it was decided to complete the CFRP installation process before casting the

new concrete slabs. The underside of the tension flanges were sandblasted, as shown in

Figure 3.18(c). Also, parts of the upper side of the tension flange and the web were

sandblasted to accommodate 50 mm wide transverse GFRP anchor sheets used at the

termination points of the CFRP strips. The CFRP plates were cut to the desired

dimensions listed in Table 3.5, using a guillotine cutter. Prior to bonding the plates, dust

was removed from the steel surface by thoroughly blowing compressed air. The side of

the CFRP plate, which was to receive the adhesive, was rubbed with a fine sand paper to

remove all residual carbon dust. The same side was then thoroughly wiped with acetone

using a clean white cloth. Adhesive 2 (Sikadur 30) was applied to the steel surface as a

prime coat using a saw-tooth spatula, as shown in Figure 3.18(d). In order to apply the

adhesive to the CFRP plate, a wooden hopper was specially fabricated and used, as

shown in Figure 3.18(e). A roof shaped spatula with 3 mm height at the edges and 5 mm

height at the middle was placed at one end of the hopper. The CFRP plate was then

pulled through the spatula, under the adhesive, to produce a regular cross section of the

adhesive layer. The plate was then placed on the steel surface and pressed with a rubber

roller, as shown in Figure 3.18(f), using enough pressure to squeeze the adhesive out

from both sides. This particular procedure was to provide a maximum bond line of 3.2

Chapter 3

86

mm thick. All the required tools and recommended procedures were provided by Sika

Canada Inc. A 50 mm wide GFRP sheet was used at all termination points of the CFRP

plates as a transverse wrap around the tension flange and also extended 50 mm within the

web, as shown in Figure 3.18(g).

The concrete slabs were cast in an inverted position on a smooth flat floor for

convenience, as shown in Figure 3.19. Simple wooden forms were fabricated, and a

double layer of 150x150x5 mm welded wire mesh reinforcement was provided at mid-

thickness of the concrete slab. The steel girders were supported on the edges of the

formwork in an inverted position with the shear studs projecting downwards into the

forms. High slump concrete (batch 1) was then poured into the formwork, vibrated, and

then the surface was troweled. Immediately after finishing the concrete surface, the

specimens were covered using a plastic sheet. The concrete surface was kept wet for

seven days following casting. After seven days, the specimens were released from the

formwork and allowed to air cure.

3.4.3 Test setup

All three girders were tested in a simply supported configuration with a span of 5940 mm

between the centerlines of the supports. Tests were performed using four-point bending

with a distance of 1000 mm between the two applied loads. The loads were applied using

a stiff HSS steel spreader beam. The two point loads were applied over two transverse

rectangular HSS section, which covered the entire width of the concrete slab. Steel rollers

were placed between the spreader beam and each of the rectangular HSS sections, as

Chapter 3

87

shown in Figure 3.20 and 3.21. A quick setting plaster was placed under the transverse

HSS section to avoid any stress concentrations associated with the irregularity of the

concrete surface and to uniformly distribute the load. Due to the length of the specimens,

which is longer than the base of the available Riehle machine, a 6200 long and stiff

welded wide flange (WWF350 x 263) reaction beam was first placed on the testing

machine base. The test setup was then assembled on top of the WWF beam. The details

of the test setup are shown in Figure 3.20 and 3.21. The specimen was supported on a

roller support at one end and on a hinged support at the other end. Both supports were

elevated using heavy HSS square stubs to accommodate the expected large deflection at

mid-span. Two 25 x 25 x 3.2 mm HSS vertical posts were mounted under the concrete

slab, on each side of the web, at the two ends for bracing, as shown in Figure 3.20(c). The

girders were monotonically loaded under stroke control at a rate of 1.75 mm/min, using

the 1000 kN Riehle machine.


Two LPs were placed at both sides of the girders, at mid-span to measure vertical

deflection and monitor any torsional rotation due to any misalignment. Another two LPs

were also mounted under the tips of the WWF steel reaction beam, below the support

locations to measure any settlement of the supports. The longitudinal strains along the

steel girder and CFRP plates were measured using several 5 mm long electric resistance

strain gauges. Three strain gauges were attached directly to the steel surface at mid-span,

including two strain gauges attached to the web, 50 mm and 150 mm above the tension

flange, while the third one was attached to the underside of the compression flange, as

Chapter 3

88

shown schematically in Figure 3.21(a). Several strain gauges were attached to the CFRP

plates to measure the longitudinal strains, and are spaced as shown schematically in

Figure 3.21(b). Two PI gauges, installed over a gauge length of 100 mm, were also

attached to both the top and bottom sides of the concrete slab, as shown schematically in

Figure 3.21(a). The same data acquisition system used in Phase I was also used to

monitor and record all test data.

3.5 Experimental Phase III – Repair of Artificially–Damaged

Composite Beams

This section describes the third phase of the experimental program undertaken to evaluate

the effectiveness of CFRP sheets used to repair artificially damaged steel-concrete

composite beams with a simulated section loss in the tension flange. This may be the case

of a fatigue crack or a severe localized corrosion. Description of specimens, the

fabrication process, including cutting the tension flange, welding the studs, casting the

concrete slab, installing FRP sheets, instrumentation, and testing of the specimens are

also presented.


A total of 11 steel-concrete composite beams were tested in a four-point bending

configuration. The cross section of the beams consists of W150x22 hot rolled steel

sections acting compositely with a 75 mm thick and 465 mm wide concrete slabs, as

shown in Figure 3.22(a). It should be noted that the size of the concrete slabs in these

specimens was over designed, relative to the size of the W150 x 22 sections. This was

Chapter 3

89

intended to avoid concrete crushing failure and ensure that failure would occur at the

tension side, either by CFRP rupture or debonding. Table 3.6 provides all details of the

beams, including their identification number (B1 to B11), CFRP type, total cross

sectional area of CFRP, the force equivalence index, which is discussed later, and the

FRP sheet dimensions including their width and bonded length. The specimens include

one control intact (undamaged) beam (B1) and ten artificially damaged beams (B2 to

B11), where the steel tension flanges were completely cut at mid-span, throughout the

entire thickness and width, to simulate a severe section loss in bridge girders. Specimens

B1 and B2 were tested without FRP material to serve as control intact and damaged

specimens, respectively. The remaining nine damaged specimens were repaired by

bonding CFRP sheets of different types and configurations to the artificially damaged

flanges. The force equivalence index (ω) is introduced to quantify the amount of FRP

reinforcement on the basis of a relative axial strength of the flange, as given by:

[ ]

ysf

n

iifif

FA

FA∑== 1ω (3.1)

where Ffi and Fy are the strength of FRP layer i, and the yield strength of steel,

respectively. ifA and sfA are the cross sectional areas of FRP layer i and the steel

flange, respectively.

The objective of Phase III is to study the effect of the following parameters:

1. The effect of force equivalence index on strengthening effectiveness. This

includes beams B3 and B4, which were repaired by bonding CFRP type C3 sheets

of different cross sectional areas on the bottom side of the tension steel flange, as

Chapter 3

90

well as beams B7 and B8 with CFRP type C2 sheets bonded on both the bottom

and top sides of the tension flange.

2. The effect of number of bonded sides of the steel flange (i.e. the bonded surface

area for a given force equivalence index) on strengthening effectiveness. This

includes beam B6 with CFRP sheets bonded on one side only and beam B7

having a samilar CFRP force equivalence index but the CFRP sheets are bonded

on both sides of the steel flange.

3. The effect of the bonded length of CFRP sheets on strengthening effectiveness.

Beams B8 to B11 were repaired using the same CFRP type C2 and the same force

equivalence index, applied to both sides of the tension flange. The total bonded

lengths of B8 to B11 were 1900, 1000, 250, and 150 mm, respectively.

4. The effect of timing of application of CFRP after sandblasting was studied by

comparing B5 to B6, which had the CFRP installed immediately and 22 months

after sandblasting, respectively. The two specimens have comparable force

equivalence index and although two types (C1 and C2) were used, they had

comparable properties, as shown in Figure 3.8.

3.5.2 Fabrication of beam specimens

The W150x22 steel sections were first cut to 11 beams, each 2030 mm long. One beam

was left intact to serve as a control specimen (B1). The tension flanges of the remaining

10 beams were completely cut (i.e. through the entire width and thickness) at mid-span,

as shown in Figure 3.22(b). The cut was done using a band saw with a 1.4 mm thick

blade. Four pairs of 76 x 76 x 9.5 mm angles, 130 mm long each, were bolted to the web

Chapter 3

91

at both the loading and supporting points to prevent web buckling. Each pair of angles

was bolted to the web through two 12 mm diameter holes drilled through the web. These

stiffener angles were reused in all test beams. Conventional Nelson shear studs, 41 mm

long and 9.5 mm in diameter, as shown in Figure 3.22(c), were welded to the

compression flange using Nelson Stud Welding’s Series 4500 welder. One electrode of

the welder was grounded to the steel beam and a special welding gun was attached to the

other electrode. The head of the stud was placed into the end of the welding gun and a

small porcelain ferrule was placed on the tip of the stud to contain the weld. The stud was

pushed against the top surface of the flange and the trigger of the welding gun was pulled

to activate the welder, as shown in Figure 3.22(d). The studs were welded in pairs at

longitudinal and transverse spacings of 60 mm and 75 mm, respectively.

The concrete slabs of beams B1, B3, and B4 were cast using the same concrete batch

(batch 3), while the concrete slabs of the remaining nine beams were cast at a different

time using concrete batch 2. After assembling the formwork, a double layer of

150x150x5 mm welded wire mesh reinforcement was provided at the mid-thickness of

the concrete slab, as shown in Figure 3.22(e). Concrete was then poured, vibrated,

troweled, and cured in a similar procedure to that described in Phase II, except that

casting was done in a normal position in this phase (i.e. the slab is cast above the steel

section).

In order to prepare the surface of the beams for FRP sheet installation, beams B7 to B11

were sandblasted along both the underside and top side of the steel tension flange,

Chapter 3

92

whereas beams B3 to B6 were sandblasted along the underside of the steel tension flange

only. A local contractor performed the sandblasting, using conventional equipment, as

shown in Figure 3.23.

In the cases of test beams accommodating FRP sheets on both sides of the flange, one

side was usually covered with plastic sheets and taped along the edges with masking tape

for protection, as shown in Figure 3.24(a), prior to installing the FRP on the other

surface. The flanges were cleaned with air pressure and wiped with acetone just before

applying the FRP sheets. The dry fabric sheets were cut to the desired dimensions shown

in Table 3.6 and were laid down on a plastic sheet and completely wetted with epoxy

adhesive 1 on both sides, as shown in Figure 3.24(b). The sheets were then carefully

lifted and attached to the surface of the steel tension flange and pressed with a roller to

squeeze out the excess epoxy resin, as shown in Figure 3.24(c). Long flat aluminum

plates and heavy steel blocks were placed on top of the wet sheets to apply some pressure

and ensure a finished flat surface. For beams designed to have additional FRP sheets on

the other side of the flange, the FRP installed on the first side was left for one day to

ensure that the adhesive had set sufficiently, before the beam was flipped upside down to

bond the FRP sheets on the other side of the flange. It should be noted that the entire

installation process of FRP was always completed within the first 8 to 36 hours after

sandblasting in the cases of one side or double sides installation. Only one beam (B5) was

left after sandblasting without applying the FRP sheets for a period of 22 months. The

steel surface of that beam, however, was covered with a thin layer of oil to be protected

against possible corrosion. Before applying the FRP sheets, the flange was cleaned with

Chapter 3

93

acetone. This beam was intended to investigate the effect of delayed application of FRP

after sandblasting, on bond.

3.5.3 Test setup

All 11 beams were tested in four-point bending, using a simply supported configuration

with a span of 1960 mm between the centerlines of the supports and a 400 mm distance

between the two loads, as shown in Figure 3.25. The beams were monotonically loaded

under stroke control, at a rate of 1.75 mm/min, using the 1000 kN Riehle machine. The

loads were applied using a stiff HSS steel spreader beam. The two point loads were

applied over two transverse rectangular HSS sections, which covered the entire width of

the concrete slab. Steel rollers were placed between the spreader beam and each of the

rectangular HSS sections, as shown in Figure 3.25. A quick setting plaster was placed

under the transverse HSS section to avoid any stress concentrations associated with the

irregularity of the concrete surface and to uniformly distribute the load.


Figure 3.25 shows the test setup of beams tested in Phase III. Two LPs were placed at

both sides of the beams, at mid-span, to measure vertical deflection and monitor any

torsional rotation due to any misalignment. The longitudinal strains along the tension

flange were measured using several 5 mm long electric resistance strain gauges, spaced

as shown in Figure 3.25(b). Another two strain gauges were attached directly to the steel

surface at mid-span. One strain gauge was attached to the web, right above the cut to

monitor the stress concentration, while the other strain gauge was attached to the

Chapter 3

94

underside of the compression flange. A different arrangement of strain gauges was used

for the damaged control beam (B2), as shown in Figure 3.25(c). This arrangement was

used to monitor the stress concentration in the web at the vicinity of the flange cut. Two

PI gauges, installed over a gauge length of 100 mm, were also attached to the top of both

the concrete slab and steel tension flange for all the beams, as shown schematically in

Figure 3.25(b). The same data acquisition system used in Phases I and II was also used to

monitor and record test data in Phase III.

Chapter 3

95

Table 3.1 Material properties of the W150x22 steel section used in Phase III.

Source Coupon Width, w (mm)

Thickness, t (mm)

Elastic Modulus, E (GPa)

Yield Strength, Fy (MPa)

Ultimate Strength, Fult (MPa)

F1 12.52 6.48 199 382 500

F2 12.53 6.49 196 379 499

F3 12.52 6.47 196 379 494

Average 12.52 6.48 197 380 498

Flange

St. Dev. 0.006 0.010 1.7 1.7 3.2

W1 12.51 5.81 197 394 510

W2 12.52 5.81 195 405 497

W3 12.53 5.79 200 407 496

Average 12.52 5.80 197 402 501

Web

St. Dev. 0.01 0.012 2.5 7.0 7.8

Chapter 3

96

Table 3.2 FRP material properties based on coupon tests.

FRP type

Coupon number

Width, w (mm)

No. of layers

Thickness, t (mm)

Elastic Modulus, E (GPa)

Ultimate Strength, Fult (MPa)

Ultimate Strain, εult

x 10-3 (mm/mm)*

1 19.00 3.11 18.3 381 20.8 2 19.20 3.05 18.1 341 18.8 3 19.40 2.98 16.5 N/A N/A 4 19.50 2.95 N/A 268 N/A 5 19.25

2

2.90 17.4 352 20.2 average 19.27 3.00 17.6 336 20.0

GFRP (G)

St. Dev. 0.19 0.08 0.8 48 1.0 1 19.43 1.17 111.3 1235 11.1 2 19.20 1.20 102.8 1062 10.3 3 19.34 1.19 117.0 1201 10.3 4 19.20 1.19 N/A 1029 N/A 5 19.14

1

1.20 127.9 N/A N/A average 19.26 1.19 114.8 1132 10.6

CFRP1 (C1)

St. Dev. 0.12 0.01 10.5 101 0.5 1 25.10 2.21 90.7 1117 12.3 2 24.80 2.23 94.4 966 10.2 3 24.90

2 2.22 85.7 878 10.3

average 24.93 2.22 90.3 987 10.9

CFRP2 (C2)

St. Dev. 0.15 0.01 4.3 121 1.2 1 19.40 1.02 222.3 564 2.5 2 19.40 1.03 212.1 N/A N/A 3 19.43 1.15 202.3 509 2.5 4 19.36 1.11 298.5 492 1.7 5 19.40

2

1.09 218.0 473 2.2 average 19.40 1.08 230.6 510 2.2

CFRP3 (C3)

St. Dev. 0.02 0.05 38.6 39 0.4 1 24.92 1.40 154.2 1823 11.8 2 24.91 1.40 145.4 2203 15.2 3 24.85

1 1.40 157.3 1716 10.9

average 24.89 1.40 152.3 1914 12.6

CFRP4 (C4)

St. Dev. 0.04 0.00 6.2 256 2.2 1 16.51 2.98 325.9 1456 4.5 2 16.41 2.95 305.2 1397 4.6 3 16.37

2 3.09 308.2 1572 5.1

average 16.43 3.01 313.1 1475 4.7

CFRP5 (C5)

St. Dev. 0.07 0.07 11.2 89 0.3 * All listed strain values in this column must be multiplied by 10-3.

Chapter 3

97

Table 3.3 Concrete strengths of the three batches.

Phase Batch Concrete strength, fc’ (MPa) Average Standard

deviation

39.0 36.9 II 1 40.7

38.9 1.9

50.1 49.1

49.4

50.1

49.1

49.4 51.1

51.6

2

48.8

49.9 1.0

51.8 49.5

III

3 49.2

50.2 1.4

Chapter 3

98

Table 3.4 Test matrix of HSS column specimens tested in Phase I.

FRP Layers /side

GFRP base layer CFRP

Col

umns

Gro

up

Set n

o.

No.

of s

imila

r spe

cim

ens

HSS

Des

igna

tion

Leng

th, L

(mm

.)

kL /

r

No.

of s

tren

gthe

ned

Type

No.

of l

ayer

s

wid

th

orie

ntat

ion

type

No.

of l

ayer

s

wid

th

orie

ntat

ion

Rei

nfor

cem

ent r

atio

ρ

= A

f / A

s x 1

00

1 3 762 46 --

2 3 762 46 2 C5 2 25, 16# L 23

3 3 1150 70 --

4 3 1150 70 2 C5 2 25, 16 L 23

5 3 1528 93 --

A

6 3 HS

S1

(44x

44x3

.2)

1528 93 2 C5 2 25, 16 L 23

7 1 2380 68 --

8 1 2380 68 2 G 1 75 L C3 1 75 L 9

9 1 2380 68 2 G 1 75 L C3 3 75 L 25

10 1 2380 68 2 G 1 75 L C3 5 75 L 43

Slen

der

B

11 1

HS

S2

(89x

89x3

.2)

2380 68 4 G 1 75 L C3 3 75 L 54

12 3 175 4 --

13 3 175 4 4 G 1 cw T C1 1 cw T

14 3 175 4 4 G 1 cw T C1 2 cw T

15 3 175 4 4 G 1 cw T C1 1 cw L

16 3 175 4 4 G 1 cw T C1 2 cw L, T

17 3 175 4 4 G 1 cw T C3 1 cw T

18 3 175 4 4 G 1 cw T C3 2 cw T

19 3 175 4 4 G 1 cw T C3 1 cw L

Shor

t

C

20 3

HS

S2

(89x

89x3

.2)

175 4 4 G 1 cw T C3 2 cw L, T

L = longitudinal, T = transverse,

L, T = two layers, one longitudinal, followed by one transverse, cw = complete wrap,

# See Figure 3.11

Chapter 3

99

Table 3.5 Test matrix of composite girders tested in Phase II.

CFRP layer number 1 2

Specimen I.D. Type Width

(mm) Length (mm) Type Width

(mm) Length (mm)

G1 G2 C4 90 4000 C4 50 1500 G3 C4 90 4000 C5 50 1500

Chapter 3

100

Table 3.6 Test matrix of repair of artificially damaged composite beams tested in Phase III.

Configurations of FRP layers [ Σ (number of layers x width x length) ] Specimen

I.D.

Type of

CFRP

Area of

CFRP (mm2)

ωa

%age

Bonded sides of

the tension flange

GFRP base layer CFRP layers

B1 Intact (control 1) B2 Damaged (control 2)

B3 C3 648 87 Lower 1 x 150 x 1900 1 x 150 x 1900 + 2 x 150 x 1850 + 2 x 150 x 1800 + 2 x 150 x 1750 + 1 x 150 x 1700

B4 C3 1134 152 Lower 1 x 150 x 19001 x 150 x 1900 + 2 x 150 x 1850 + 2 x 150 x 1800 + 2 x 150 x 1750 + 2 x 150 x 1700 + 2 x 150 x 1650 + 2 x 150 x 1600 + 1 x 150 x 1550

B5b C1 668 198 Lower 1 x 150 x 1900 1 x 150 x 1900 + 2 x 150 x 1850 + 2 x 150 x 1800 B6 C2 744 193 Lower 1 x 134 x 1900 1 x 134 x 1900 + 2 x 134 x 1850 + 2 x 134 x 1800 B7 C2 716 185 Lower 1 x 128 x 1900 1 x 128 x 1900 + 1 x 104 x 1850 + 1 x 87 x 1850

Upper 2 x 64 x 1900 2 x 64 x 1900 + 2 x 46 x 1850 + 2 x 35 x 1850 B8 C2 813 210 Lower 1 x 128 x 1900 1 x 128 x 1900 + 1 x 128 x 1850 + 1 x 128 x 1850




Upper 2 x 64 x 150 2 x 64 x 150 + 2 x 64 x 145 + 2 x 46 x 145

a force equivalence index 100*yflange

ff

FA

FA=ω b Late application of FRP

Chapter 3

101

Figure 3.1 Different steel cross sections used in the experimental investigation.

Figure 3.2 Test setup of HSS stub-column.

Semi-spherical loading head

Strain gauges

Flat plate

Semi-spherical loading head

Strain gauges

Flat plate

b = 31.2

t = 3.2

B = 44

R = 6.4

b = 76.2

t = 3.2

B = 89 b = 152

d =

152

w = 5.8 t = 6.6

b = 102

d =

257

t = 8.4

w = 6.1

HSS 44x44x3.2 mm HSS 89x89x3.2 mm W 150x22W 250x25

(a) Phase I: HSS columns’cross sections

(b) Phases II and III: I-beams’cross sections

A = 1072 mm2

Ix = 1.31x106 mm4

A = 495 mm2

Ix = 0.13x106 mm4

A = 2840 mm2

Ix = 12.0x106 mm4

A = 3230 mm2

Ix = 34.2x106 mm4

R = 6.4xxxx

xx

xxb = 31.2

t = 3.2

B = 44

R = 6.4

b = 76.2

t = 3.2

B = 89 b = 152

d =

152

w = 5.8 t = 6.6

b = 102

d =

257

t = 8.4

w = 6.1

HSS 44x44x3.2 mm HSS 89x89x3.2 mm W 150x22W 250x25

(a) Phase I: HSS columns’cross sections

(b) Phases II and III: I-beams’cross sections

A = 1072 mm2

Ix = 1.31x106 mm4

A = 495 mm2

Ix = 0.13x106 mm4

A = 2840 mm2

Ix = 12.0x106 mm4

A = 3230 mm2

Ix = 34.2x106 mm4

R = 6.4xxxx

xx

xx

Chapter 3

102

Figure 3.3 Compressive stress-strain responses of HSS stub-columns.

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16

Stre

ss (M

Pa)

(b) HSS2 (89 x 89 x 3.2 mm)

Proportional limit

F rs=

33%

Fy

Yield strength Fy= 382 MPa

Fp= 255 MPa

Axial strain x 10-3 (mm/mm)

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16

Stre

ss (M

Pa)

(b) HSS2 (89 x 89 x 3.2 mm)

Proportional limit

F rs=

33%

Fy


Fp= 255 MPa


0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16


Stre

ss (M

Pa)

(a) HSS1 (44 x 44 x 3.2 mm)

F rs=

49%

Fy


Fp= 257 MPaProportional limit

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16


Stre

ss (M

Pa)

(a) HSS1 (44 x 44 x 3.2 mm)

F rs=

49%

Fy


Fp= 257 MPaProportional limit

Chapter 3

103

Figure 3.4 Tensile stress-strain response of a coupon cut from W250x25 [Savides, 1989]

Figure 3.5 Sample coupon cut from W150x22.

Stre

ss (M

Pa)


Stre

ss (M

Pa)


20

50 100 50

12.512.5

Dims. are in mm.

Strain gauge

20

50 100 50

12.512.5

Dims. are in mm.

Strain gauge

50 100 50

12.512.5

Dims. are in mm.

Strain gauge

Chapter 3

104

Figure 3.6 Tensile stress-strain responses of coupons cut from W150x22.

Figure 3.7 Tension coupons and test setup of FRP materials.

0

50

100

150

200

250

300

350

400

450

500

550

0 0.005 0.01 0.015 0.02 0.025 0.03


Stre

ss (M

Pa)

5 10 15 20 25 300

Flange Web

0

50

100

150

200

250

300

350

400

450

500

550

0 0.005 0.01 0.015 0.02 0.025 0.03


Stre

ss (M

Pa)

5 10 15 20 25 3000

50

100

150

200

250

300

350

400

450

500

550

0 0.005 0.01 0.015 0.02 0.025 0.03


Stre

ss (M

Pa)

5 10 15 20 25 300

Flange Web

(b) Test setup(a) Coupons before testing

(c) Typical failure of CFRP coupons

C3

G

Extensometer

Typical failure of CFRP sheets (Type C3) Typical failure of CFRP plates (Type C4)

(b) Test setup(a) Coupons before testing

(c) Typical failure of CFRP coupons

C3

G

Extensometer

Typical failure of CFRP sheets (Type C3) Typical failure of CFRP plates (Type C4)

Chapter 3

105

Figure 3.8 Tensile stress-strain responses of different FRP materials.

Figure 3.9 Test setup for concrete cylinders.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20 25

Stre

ss (M

Pa)

G

C2C1

C4

C5C3


CFRP

GFRP

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20 25

Stre

ss (M

Pa)

G

C2C1

C4

C5C3


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20 25

Stre

ss (M

Pa)

G

C2C1

C4

C5C3


CFRP

GFRP

Chapter 3

106

Figure 3.10 Effect of FRP on local and overall buckling of short and slender HSS columns.

Figure 3.11 Details of FRP strengthening configurations of HSS columns in Phase I.

T

T


T

C

C

(b) Long Column(a) Short Column

TT

TT



T

T


T

C

C

(b) Long Column(a) Short Column

TT

TT



TT TTT

TTTT



75

50

3 Layers of C3

Set 9

5 Layers of C3

Set 10

3 Layers of C3

3 Layers of C3Set 11

1 Layer of C3 1 Layer of G

Set 8

Sets 13 to 20

2 Layers of C5 (25x1.4 & 16x1.4)

Sets 2, 4 and 6

L L

LCWL L

TCW

L = Longitudinal, T = Transverse, and CW = Complete wrapping

Slender Short

Group CGroup BGroup A

75

505050

3 Layers of C3

Set 9

5 Layers of C3

Set 10

3 Layers of C3


3 Layers of C3


1 Layer of C3 1 Layer of G

Set 8

Sets 13 to 20

2 Layers of C5 (25x1.4 & 16x1.4)

Sets 2, 4 and 6

2 Layers of C5 (25x1.4 & 16x1.4)

Sets 2, 4 and 6

L L

LCWL L

TCW

L = Longitudinal, T = Transverse, and CW = Complete wrapping

Slender Short

Group CGroup BGroup A

Chapter 3

107

Figure 3.12 Various preparation measures of the HSS columns in Phase I.

Specimen

Coordinates of the laser point

Moving bed

Laser sensor

Distance traveled by the laser beamSpecimen

(a) Machining the column end (b) Measuring out-of-straightness using laser sensor

Before sandblasting

After sandblasting

(c) Sandblasting of steel surface

Specimen

Coordinates of the laser point

Moving bed

Laser sensor

Distance traveled by the laser beamSpecimen

(a) Machining the column end (b) Measuring out-of-straightness using laser sensor

Before sandblasting

After sandblasting

Before sandblasting

After sandblasting

(c) Sandblasting of steel surface

Chapter 3

108

Figure 3.13 A typical out-of-straightness geometric imperfection profile of slender columns (specimen 6-3).

Figure 3.14 FRP installation on the HSS columns in Phase I.

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 400 800 1200 1600

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

Side (a)

Side (b)

a

b

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 400 800 1200 1600

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

Side (a)

Side (b)

a

b

Set 6

C5 strips before installation on the

other side

Specimen 8

Specimen 9

Set 2

Set 4

50 mm wide GFRP end wraps

50 m

m

Set 6

C5 strips before installation on the

other side

Specimen 8

Specimen 9

Specimen 8

Specimen 9

Set 2

Set 4


50 m

m

Set 2

Set 4


50 m

m


50 m

m

Chapter 3

109

Figure 3.15 Test setup A of columns in group A of Phase I.

Cantilever arm LP

(d) Lateral support

10 mm deep

sleeve

(c) Hinged support

(a) Picture of test setup Elevation

Specimen

Strain gauge

(S1 or S2)

10 mm deep sleeve

Late

ral s

uppo

rt co

lum

n

Late

ral s

uppo

rt co

lum

n

Steel platesTwo

threaded rods

CFRP plates

(b) Schematic of test setup

roller

roller

Plate attached to the machine cross head

Specimen

Cross head

LP

Hinged end

CFRP plates

Hinged end

Side view

Specimen

Late

ral s

uppo

rt c

olum

n

2 plates

Two threaded

rods

LP

Hinged end

Hinged end

S1 S2

Cantilever arm LP

(d) Lateral support

Cantilever arm LP

(d) Lateral support

10 mm deep

sleeve

(c) Hinged support

10 mm deep

sleeve

(c) Hinged support

(a) Picture of test setup Elevation

Specimen

Strain gauge

(S1 or S2)

10 mm deep sleeve

Late

ral s

uppo

rt co

lum

n

Late

ral s

uppo

rt co

lum

n

Steel platesTwo

threaded rods

CFRP plates

(b) Schematic of test setup

roller

roller

Plate attached to the machine cross head

Specimen

Cross head

LP

Hinged end

CFRP plates

Hinged end

Side view

Specimen

Late

ral s

uppo

rt c

olum

n

2 plates

Two threaded

rods

LP

Hinged end

Hinged end

S1 S2

Chapter 3

110

Figure 3.16 Test setup B of columns in group B of Phase I.

Hinge

Hydraulic jack

Load cell

Steel tieLP2 LP4LP6 LP5

PI1

PI2

S1

S2

LP1 LP3Column cap

Fixed columnFixed column

Specimen

2380 mm

3 pins(Lateral support)Steel tie

(a) Schematic of test setup

(b) Picture of test setup

(c) Hinged support

(e) Instrumentations

(d) Lateral support @ mid-height

Hinge

Hydraulic jack

Load cell

Steel tieLP2 LP4LP6 LP5

PI1

PI2

S1

S2

LP1 LP3Column cap


Specimen

2380 mm


Hinge

Hydraulic jack

Load cell

Steel tieLP2LP2 LP4LP4LP6 LP5

PI1

PI2

S1

S2

LP1LP1 LP3LP3Column cap


SpecimenSpecimen

2380 mm


(a) Schematic of test setup

(b) Picture of test setup

(c) Hinged support

(e) Instrumentations

(d) Lateral support @ mid-height

Chapter 3

111

Figure 3.17 Test setup C of columns in group C of Phase I.

LP 2LP 3

LP 1

Plan view for the 3 LPs

Specimen

Load Cell

Semi spherical loading head

Steel plate

LPs

(a) Schematic of test setup (b) Picture of test setup

LP 2LP 3

LP 1


Specimen

Load Cell


Steel plate

LPs

LP 2LP 3

LP 1


Specimen

Load Cell


Steel plate

LPs

LP 2LP 3

LP 1


Specimen

Load Cell


Steel plate

LPs

(a) Schematic of test setup (b) Picture of test setup

Chapter 3

112

Figure 3.18 A schematic and fabrication process of girders tested in Phase II.

(a) Typical cross section of G1 to G3

(b) Shear studs

(d) Applying adhesive to steel

(c) Sandblasting

(e) Applying adhesive to CFRP

(f) Attaching CFRP to steel

(g) GFRP end wraps

FRP plate covered with

epoxy

Wooden hopper

Pulling direction

65

257

500

W250x25

102

6.18.4

Dims. are in mm.

studs

(a) Typical cross section of G1 to G3

(b) Shear studs

(d) Applying adhesive to steel

(c) Sandblasting

(e) Applying adhesive to CFRP

(f) Attaching CFRP to steel

(g) GFRP end wraps

FRP plate covered with

epoxy

Wooden hopper

Pulling direction

65

257

500

W250x25

102

6.18.4

Dims. are in mm.

studs

Chapter 3

113

Figure 3.19 Casting concrete slabs of the girders tested in Phase II.

Chapter 3

114

Figure 3.20 Test setup of girders tested in Phase II.

(c) Close up at the support

2 HSS 25x25x3.2

(a) Elevation of test setup

(b) Oblique angle of test setup

(c) Close up at the support

2 HSS 25x25x3.2

(a) Elevation of test setup

(b) Oblique angle of test setup

Chapter 3

115

Figure 3.21 Schematic of test setup and instrumentations of girders tested in Phase II.

Concrete slab 500 mm x 65 mm

150040005940

1000

W250x25

Spreader beam

Stiffener plate

PI gauges50 mm wide GFRP wraps

(a) Schematic for test setup

CFRP plates

6200

hinge roller

LPLP

Strain gauges

WWF350x362

500

1000675

15001750

(b) Schematic for strain gauges arrangement on CFRP plates

50 mm wide GFRP wraps

1925

5940

supportsupport

Concrete slab 500 mm x 65 mm

150040005940

1000

W250x25

Spreader beam

Stiffener plate

PI gauges50 mm wide GFRP wraps

(a) Schematic for test setup

CFRP plates

6200

hinge roller

LPLP

Strain gauges

WWF350x362

500

1000675

15001750

(b) Schematic for strain gauges arrangement on CFRP plates

50 mm wide GFRP wraps

1925

5940

supportsupport

Chapter 3

116

Figure 3.22 A schematic and fabrication process of artificially-damaged beams tested in Phase III.

(b) Flange cut

1.40 mm thick cut

Porcelain ferrule

(c) Shear stud and ferrule

Shear stud

(d) Stud welding (e) Concrete forms

75

152

465

W150x22

152

5.86.6

Dims. are in mm.

(a) Typical cross section of beams B1 to B11

studs

(b) Flange cut

1.40 mm thick cut

Porcelain ferrule

(c) Shear stud and ferrule

Shear stud

(d) Stud welding (e) Concrete forms

75

152

465

W150x22

152

5.86.6

Dims. are in mm.

(a) Typical cross section of beams B1 to B11

studs

Chapter 3

117

Figure 3.23 Sandblasting the tension steel flanges of beams tested in Phase III.

Before sandblasting

After sandblasting

Before sandblasting

After sandblasting

Chapter 3

118

Figure 3.24 Installation process of FRP sheets on beams tested in Phase III.

(b) FRP sheets preparation

(c) FRP sheets installation(a) Covering one side of the tension flange

FRP sheet

(b) FRP sheets preparation

(c) FRP sheets installation(a) Covering one side of the tension flange

FRP sheet

Chapter 3

119

Figure 3.25 Test setup and instrumentations of beams tested in Phase III.

Concrete slab 75 mm thick.

25125

325875

75225

625

1960

400

W150x22

Spreader beam

Strain gaugesStiffenerangle

Stiffenerangle

PI gauges

(b) Schematic for test setup and strain gauges distribution

(a) Picture for the test setup

Side viewClose up @ mid-span

(c) Strain gauge arrangement on the damaged control beam (B2)

P/2mid-span

20

50 50152

3030


25125

325875

75225

625

1960

400

W150x22

Spreader beam


Stiffenerangle

PI gauges



25125

325875

75225

625

1960

400

W150x22

Spreader beam


Stiffenerangle

PI gauges


(a) Picture for the test setup

Side viewClose up @ mid-span

(c) Strain gauge arrangement on the damaged control beam (B2)

P/2mid-span

20

50 50152

3030

P/2mid-span

20

50 50152

3030

Chapter 4

120

Chapter 4

Experimental Results and Discussion of Phase I: Axial Compression Members1 4.1 Introduction

This chapter presents the results of Phase I of the experimental program, including

discussion of the behaviour and failure modes. Phase I was focused on strengthening

short and slender HSS steel columns using CFRP sheets and plates. A total of 50 HSS

columns of class 2 square sections were tested under a concentric compression loading.

The slenderness ratios of the columns ranged from 4 to 93. The study was intended to

evaluate the effect of the CFRP strengthening system on the axial load capacity, stiffness,

and stability of the columns.

1 Most of content of this chapter has been published as follows: Shaat, A. and Fam, A. (2006) “Axial Loading Tests on Short and Long Hollow Structural Steel Columns Retrofitted using Carbon Fibre Reinforced Polymers.” Canadian Journal of Civil Engineering, 33(4):458-470.

Chapter 4

121

The tests carried out in Phase I are divided into three groups A, B, and C, as shown in

Table 4.1 to 4.3. Group A includes slender column sets 1 to 6, which are intended to

evaluate the effect of slenderness ratio of the columns on the effectiveness of the CFRP

strengthening system, for a given CFRP reinforcement ratio. Group B includes slender

column sets 7 to 11, which are intended to evaluate the effect of CFRP reinforcement

ratio on the effectiveness of the CFRP strengthening system, for columns of a given

slenderness ratio. Group C includes short column sets 12 to 20, which are intended to

investigate the effect of the CFRP strengthening system on axial strength and stiffness of

short columns. This includes the effect of CFRP fibre orientation (i.e. in both the

longitudinal and transverse directions), number of layers, and the CFRP type (i.e.

standard and high modulus). A summary of the research findings for groups B and C

specimens can be found in Shaat and Fam (2006).

4.2 Results of Group A (Slender Column Sets 1 to 6)

As shown in Table 4.1, this group of specimens consists of three pairs of sets, namely, (1,

2), (3, 4), and (5, 6) of slenderness ratios of 46, 70, and 93, respectively. The first set of

each pair of each set consists of three similar control specimens (i.e. unstrengthened),

while the second set consists of three similar specimens strengthened using CFRP. A

summary of test results, including the measured geometric imperfections (i.e. the

maximum value of out-of-straightness as well as the value at mid-height), maximum load

capacity and the elastic stiffness of the columns is presented in Table 4.1. Typically, the

axial strength of slender columns is inversely proportional to the magnitude of initial out-

of-straightness (Allen and Bulson, 1980). However, the results suggest that this is not the

Chapter 4

122

case in all the specimens. It is believed that several possible factors have resulted in final

imperfection values different from the initial ones. These factors are related to the

installation process of CFRP and include the accuracy of alignment of the CFRP plates,

slight variation in the adhesive thickness of the plates on the two opposite sides, and the

possibility of inevitable minor misalignment in the test setup. Nevertheless, the testing of

three specimens in each set can provide a reliable average of test results, as shown in

Table 4.1. The table also shows the standard deviation of each set, which suggests a good

level of repeatability of test results. Also given in Table 4.1, are the percentage increases

in both the maximum axial load and stiffness, for the CFRP−strengthened column sets 2,

4, and 6, as compared to their counterpart control column sets 1, 3, and 5, respectively.

Table 4.1 shows that the percentage increases in axial strength of these sets were 6, 35,

and 71, respectively. It is also shown in Table 4.1 that the axial stiffness has increased by

12, 16, and 17 percent, respectively. All the percentage increases are generally based on

the average values of the three similar specimens of each set.

The load versus net axial displacement responses of column sets 1 to 6 are shown in

Figure 4.1 to 4.3, respectively. In each figure, the responses of both the control and

strengthened sets, including the three similar specimens in each set, are plotted. The

figures generally show reasonable repeatable responses for similar specimens. The load

versus lateral displacement responses at mid-height of the columns are shown in Figure

4.4 to 4.6. The low values of lateral displacement up to the peak load are a result of very

small values of out-of-straightness and precision in the test setup alignment. The load

versus axial strain responses are shown in Figure 4.7 to 4.9 for gauge S1 and Figure 4.10

Chapter 4

123

to 4.12 for gauge S2 (see Figure 3.15). The figures show that both sides of the columns

are under compression up to a certain load level, at which excessive buckling occurs. At

this point, the strains on one side (S2) revert to tension. Figure 4.7 to 4.12 also show the

effect of CFRP plates on reducing the axial strain values on both sides of the

strengthened specimens, relative to their counterpart control specimens, at a given load

level.

4.2.1 Effect of slenderness ratio on effectiveness of CFRP

Figure 4.13 shows the variation of the axial strength of the columns with slenderness

ratio. The variation is given for both the control and the CFRP-strengthened columns. For

each case, the average strength of the repetitive specimens within one set is reported,

along with the error bars. The figure shows that the axial strength of the control

specimens reduces as the slenderness ratio increases, which is expected according to the

Euler’s equation (Equation 6.16). Also, the axial strength of the CFRP-strengthened

specimens reduced as the slenderness ratio increases but at a much lower rate than the

control specimens. It should be noted that failure mode changes in CFRP-strengthened

columns, as will be discussed later. This behaviour clearly suggests that the effectiveness

of the CFRP system increases for higher slenderness ratios. It is also noted that the axial

strength of a CFRP-strengthened column (point “a” in Figure 4.13 for example) is

equivalent to that of a control column of a much lower slenderness ratio (point “b” in

Figure 4.13). This effect becomes more pronounced as the slenderness ratio of the

strengthened column increases.

Chapter 4

124

To summarize the effect of slenderness ratio, Figure 4.14 shows the variation of the

percentage increases in both the axial strength and axial stiffness with the slenderness

ratio. All columns have the same CFRP reinforcement ratio (ρ = 23 %). Figure 4.14

clearly demonstrates the effectiveness of the CFRP system, reflected by the percentage

increase in strength, as the slenderness ratio increases. The figure shows strength

increases of 5.5, 34.9, and 70.7 percent for columns with slenderness ratios of 46, 70, and

93, respectively. On the other hand, the figure shows increases in axial stiffness of 10.3,

15.5, and 17.4 percent, for the same slenderness ratios, respectively. It is clear that the

percentage increase in axial strength is substantially increased as slenderness ratio is

increased, whereas the increase in axial stiffness seems to be only slightly affected by

slenderness ratio.

4.2.2 Failure modes

In all specimens (i.e. sets 1 to 6), failure was mainly due to excessive overall bucking of

the columns for both the shortest columns with kL/r = 46 (i.e. sets 1 and 2) and the

longest columns with slenderness ratio kL/r = 93 (i.e. sets 5 and 6), as shown in Figure

4.15(a and b). For the CFRP-strengthened columns, two different failure modes were also

associated with overall buckling. The first mode was observed in sets 2 and 4 of

slenderness ratios of 46 and 70, respectively, where the CFRP layers on the inner side of

the buckled column debonded from the steel surface, as shown in Figure 4.15(c). Also,

the GFRP wraps at the ends partially ruptured, as shown in Figure 4.15(d). In set 2,

debonding was associated with a load drop, followed by a load increase and a second

peak, and then descending due to overall buckling, as shown in Figure 4.1 and 4.4. This

Chapter 4

125

suggests that debonding at this slenderness ratio occurred prematurely at one side, before

reaching the peak load, which is associated with overall buckling. In set 4, debonding of

CFRP on one side occurred almost simultaneously when the peak load was reached and

overall buckling occurred. This is evident by a clear load drop near the peak with

insignificant rising of the curves after the drop, as shown in Figure 4.2 and 4.5. The

second mode of failure was observed in set 6 with slenderness ratio of 93, where the

CFRP layers on the inner side have crushed at mid-height, as shown in Figure 4.15(e).

Crushing of CFRP in set 6 occurred when the load was already descending, long after

reaching the peak load and overall buckling has occurred, as shown in Figure 4.3 and 4.6.

By carefully examining the strains measured on the inner sides by gauge S1 at failure

(Figure 4.7 to 4.9), an average strain values of 0.161 and 0.226 percent can be observed

in sets 2 and 4, respectively, when debonding occurred. On the other hand, the strain at

which the CFRP crushed was 0.274 percent. It should be noted that this compressive

strain is only 58 percent of the tensile rupture strain given in Table 3.2. This compressive

failure strain is limited to this particular CFRP, and may vary for different types of CFRP

or HSS sections with different width-to-thickness ratios. Figure 4.16 shows the variation

of the compressive strains of CFRP at ultimate with slenderness ratio. The figure shows

that higher strains (and hence higher effectiveness) are developed as slenderness ratio

increases. No signs of CFRP failure by rupture or debonding have been observed on the

tension side (i.e. outer side) in any of the strengthened columns.

Chapter 4

126

4.3 Results of Group B (Slender Column sets 7 to 11)

The objective of this set of specimens is to examine the effectiveness of CFRP

strengthening system of different reinforcement ratios (i.e. different number of layers) for

columns of the same slenderness ratio. Due to the relatively large size of these specimens

(2380 mm long) tests were conducted horizontally using a specially designed setup as as

previously discussed in chapter 3. Also, the out-of-straightness (imperfection) of the bare

steel specimens could not be measured as the specimens did not fit in the laser sensor

apparatus. Instead, they were estimated from strain measurements as will be discussed

later. The load versus net axial displacement and lateral displacement at mid-height of

column sets 7 to 11 are shown in Figure 4.17 and 4.18, respectively. The lateral

displacements in Figure 4.18 are offset by the values of the estimated out-of-straightness.

The figures show that the gain in axial strength of the CFRP-strengthened specimens

ranged from 13 to 23 percent, as also given in Table 4.2.

Figure 4.19 to 4.23 show the load versus axial strain at the two opposite sides of all the

five specimens, based on both electrical resistance strain gauges and the 200 mm PI

gauges. The strain values indicate that global buckling started at strain values very close

to the yielding strain of steel, which is 0.19 percent.

4.3.1 Effect of out-of-straightness imperfection on the effectiveness of

CFRP-strengthening

Table 4.2 shows that the gains in axial strength among the different specimens do not

correlate with the number of CFRP layers used. For example, specimen 10 (with 5 layers)

Chapter 4

127

shows only 13 percent increase in axial strength, compared to specimen 8 (with 1 layer),

which showed a 20 percent increase. This discrepancy is attributed to the variation of the

out-of-straightness imperfections among the specimens. By examining the strains in

Figure 4.19 to 4.23, at low load levels before buckling, it becomes clear that both sides of

the column are not equally strained, right from the beginning. Furthermore, the difference

in strain values on both sides varies from one specimen to the other. This suggests that

the columns varied in their geometric out-of-straightness values, which are essentially

eccentricities relative to straight lines connecting both ends. The strain gradient through

the cross section of the column has been used to estimate this imperfection, in terms of

the initial eccentricity (e’), which is assumed to represent a maximum amplitude at mid-

height (i.e. at the location of strain gauges), as reported in Table 4.2. The strain gradient

is established using the following load-strain relationship on both sides of the loaded

columns:

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−=

ttstorc I

yePA

PE

)'(1 δε m (4.1)

where, εc or t are the strains at the high compression side or the low compression (or

tension) side of the column, P is the applied load, e’ is the imperfection at mid-height, δ

is the lateral deflection at mid-height due to the applied load, and y is the distance

between the extreme CFRP surface and the centroid of the cross section, and At and It are

the transformed cross sectional area and moment of inertia, respectively, and are given

by:

∑= ⎥

⎥⎦

⎤

⎢⎢⎣

⎡+=

n

iif

s

ifst A

E

EAA

1

(4.2)

Chapter 4

128

∑= ⎥

⎥⎦

⎤

⎢⎢⎣

⎡+=

n

iif

s

ifst I

E

EII

1

(4.3)

where Is and if

I are the moments of inertia of the steel section and CFRP layer i,

respectively, and n is the total number of CFRP layers.

A value of the out-of-straightness imperfection e’ can be obtained by using the measured

strains (εc or t) and the corresponding lateral deflection in Equation (4.1), within the elastic

range. It is noted that the calculated e’ differs when calculated using εc or εt and also

varies with the applied load P. This is probably attributed to the assumptions made,

including those used in the calculations of section parameters involved in Equations 4.1

to 4.3. A relation between the imperfection e’, based on the average value obtained from

the strains on both sides, and the applied load P is established. Figure 4.24 shows the

variation of the average e’ with the applied load for the column sets 1 and 2, as a sample.

The initial imperfection is then estimated as the y-intercept (i.e. the value at P = 0). The

average imperfection plots versus the applied loads for the other column set 3 to 11 are

given in Appendix B. It is believed that this method is more reliable than measuring the

out-of-straightness of the columns before applying the CFRP material as the method

accounts for all possible sources of imperfection combined in the final situation,

including the initial out-of-straightness, the variability of adhesive thickness in the FRP

system, the possibility of minor misalignment of the fibres in CFRP sheets, unintended

misalignment within the test setup, or a combination of all. The method, however,

assumes that the imperfection is at mid-height.

Chapter 4

129

Figure 4.18 shows the load versus total lateral deflection responses of specimens 7 to 11,

including the estimated imperfection values (e’) at mid-height of the columns. The curves

are offset with the value of their respective imperfections (e’). The figure indicates that

for specimens of comparable imperfections (i.e. specimens 7 and 9), the behaviour of

CFRP-strengthened specimen shows higher strength and stiffness, compared to the

control specimen, which indicates that the CFRP has improved the stability of the column

against lateral deflections. Specimen 8 showed a higher peak load than specimen 9,

despite the lower number of CFRP layers, due to its smaller imperfection. Typically, the

larger the imperfection, the lower the peak load for a given slenderness ratio. It is

hypothesised that the effectiveness of CFRP would increase for columns with larger

imperfections. This will be addressed in detail through a parametric study in Chapter 6.

4.3.2 Failure modes

Specimens 7 to 11 failed mainly due to excessive overall bucking, as shown in Figure

4.25(a and b). Unlike the specimens in sets 1 to 6, the overall buckling in this case was

followed by a secondary local buckling failure at the inner side, at or near the mid-height

of the specimen, as shown in the close up picture of Figure 4.25(a). The local buckling

was attributed to the relatively thin walls of the columns in this case (b/t = 23.8), and was

in the form of an inward buckling of the compression flange and outward buckling of the

two side webs. This was clearly revealed after the test by cutting the specimen, as shown

in Figure 4.25(c). For the CFRP-strengthened specimens, the secondary local buckling of

the compression flange was associated with a combined local crushing and debonding

between the FRP sheets and the steel surface, as shown in Figure 4.25(b). By carefully

Chapter 4

130

examining the longitudinal strains on the failed compression face, in Figure 4.20 to 4.23,

it can be seen that strains at failure were very close (0.143, 0.125, 0.148, and 0.118

percent for specimens 8, 9, 10, and 11, respectively). Therefore, an average strain of

0.133 percent can be defined as the strain at which the CFRP sheets failed in

compression. No signs of FRP failure have been observed on the tension side. For

specimen 11, strengthened on four faces, the CFRP on the side faces have also fractured

due to the outward buckling, as shown in Figure 4.25(b).

4.4 Results of Group C (Short Column sets 12 to 20)

The objective of these sets is to examine the strengthening effectiveness of standard

modulus (SM-) and high modulus (HM-) CFRP sheets in short HSS columns. The effects

of fibre orientation and number of CFRP layers are also examined. The load−axial

displacement curves for all short column specimens, sets 12 to 20, are shown in

Figure 4.26. In each graph, three curves are presented for three similar specimens. A

summary of test results, including the ultimate load capacity, axial displacement at

maximum load and the elastic stiffness, is presented in Table 4.3. Also given in Table

4.3, are the percentage increases in the axial load and stiffness as well as the percentage

reduction in the displacement at maximum load for the FRP−strengthened specimens, as

compared to the control steel specimens, set 12.

4.4.1 Effect of CFRP strengthening on the short column specimens

In order to understand the behaviour of HSS short columns and to assess the contribution

that CFRP sheets might provide, the load-axial strain behaviour of the control specimen

Chapter 4

131

12-1 is examined. Figure 4.27 shows the load-axial strain behaviour on two adjacent

sides of this specimen. Both gauges S1 and S2 showed an increase in the compressive

strains, up to point “a”, where substantial local buckling took place. At this point, one

side buckled outwards, as indicated by the strains measured by S2, which reverse

direction sharply, as a result of the reduction of compressive strain, and the other side

buckles inwards, as indicated by S1, which showed strains increasing further in

compression. It is, therefore, believed that the CFRP could brace the two opposite sides

that buckle outwards. It is also noted that CFRP would unlikely have any significant

contribution to the sides that buckle inwards. In fact, it debonds from the steel surface as

will be discussed in the failure modes section.

The effect of CFRP wrapped sheets on the behaviour of HSS short columns is presented

in terms of the load-axial displacement responses, as shown in Figure 4.28 and 4.29 for

the SM-CFRP (types C1) and HM-CFRP (type C3), respectively. The curves in Figure

4.28 and 4.29 are each based on the average of the responses of the three similar

specimens in each set. The maximum load values of the three similar specimens, of each

set, show good repeatability, as listed in Table 4.3. However, the repeatability of the

elastic stiffness was not as good. Figure 4.28 and 4.29 show that the axial strength and

stiffness of short HSS columns is increased with different degrees, depending on the

number of layers, fibre orientation, and type of CFRP, as will be discussed in the

following sections. Figure 4.28 and 4.29 also show that, while the CFRP system increases

both the strength and stiffness, it does not have much effect on the post-peak softening

rate.

Chapter 4

132

4.4.2 Effect of fibre orientation

Test results in Figure 4.28 and 4.29 as well as Table 4.3, based on the average values;

suggest that CFRP layers with fibres oriented in the transverse direction are more

efficient than those with fibres oriented in the longitudinal direction. This is evident from

comparing column sets 13 and 15 for the SM-CFRP (types C1) and column sets 17 and

19 for the HM-CFRP (type C3). All column sets had one CFRP layer. Also, results of

column sets 14 and 16 as well as 18 and 20 suggest that two transverse CFRP layers are

more efficient in increasing the strength than one longitudinal and one transverse layer,

for both types of CFRP. Given the level of variability among repeated tests, it is difficult

to have a distinct conclusion with regard to the effect of this parameter.

4.4.3 Effect of CFRP type, thickness, and number of layers

The effect of CFRP type is examined by comparing specimens of the same number of

layers in Figure 4.30. Test results in Table 4.3 and Figure 4.30 indicate that the SM-

CFRP (sets 13 and 14) resulted in better strengthening than the HM-CFRP (sets 17 and

18). This is attributed to the fact that each SM-CFRP lamina has 10 percent higher

stiffness (Ef Af) than the HM-CFRP. It was also noted that because of the very stiff

characteristics of the HM-CFRP (see properties of C3 in Table 3.2), fibres have fractured

at the round corners near the ultimate loads, which have reduced their efficiency. The

results also indicate that set 14 with two transverse layers of SM-CFRP achieved the

highest gain in strength (18 percent), among the short columns. Figure 4.28 and 4.29

show that adding a second layer enhances the strength, particularly if both layers are in

Chapter 4

133

the transverse direction as evident by comparing sets 13 and 14 for the SM-CFRP and

sets 17 and 18 for the HM-CFRP.

4.4.4 Failure modes

The typical failure mode of all short column specimens was essentially yielding, followed

by symmetric local buckling, where two opposite faces would buckle inwards and the

other two faces would buckle outwards, as shown in Figure 4.31(a). In all specimens

strengthened with CFRP layers oriented in the longitudinal direction, debonding occurred

between CFRP and steel at one end, as shown in Figure 4.31(b), even in the specimens

with additional transverse CFRP outer layer. In specimens with all CFRP layers oriented

in the transverse direction, debonding occurred between CFRP and steel, only on the two

opposite faces that experienced inward local buckling. This was revealed after the test

was completed by cutting the specimen as shown in Figure 4.31(c). This failure mode, in

Figure 4.31(c), supports the hypothesis described in Figure 3.10(a). For specimens with

HM-CFRP layers oriented in the transverse direction, rupture of the fibres was observed

near the corners, as shown in Figure 4.31(d). This is likely attributed to the very stiff

nature of this high modulus CFRP. In general, none of the short column specimens failed

by opening at the CFRP overlapped joint.

Chapter 4

134

Table 4.1 Summary of test results of slender columns in group A of Phase I.

Set Specimen

Measured out-of-straightness,

e’max. – e’mid-height (mm) Maximum

load, Pmax (kN) Stiffness (kN/mm)

1-1 0.29-0.21 202.4* 54.6 1-2 0.21-0.14 179.4 50.8 1-3 0.25-0.18 183.8 52.9

Average 181.6 53.8 1

St. dev. 3.1 1.9 2-1 0.26-0.21 193.2 61.4 2-2 0.21-0.15 190.1 57.8 2-3 0.17-0.06 191.5 58.8

Average 191.6 59.3 St. dev. 1.5 1.8

2

% gain 5.5 10.3 3-1 0.31-0.27 149.4 42.7 3-2 0.36-0.35 136.8 42.7 3-3 0.27-0.24 158.2 43.5

Average 148.2 43.0 3

St. dev. 10.8 0.4 4-1 0.32-0.28 203.9 49.5 4-2 0.29-0.29 189.1 50.0 4-3 0.21-0.20 206.6 49.5

Average 199. 9 49.7 St. dev. 9.4 0.3

4

% gain 34.9 15.5 5-1 0.54-0.54 98.7 33. 7 5-2 0.53-0.53 102.8 33.9 5-3 0.96-0.96 106.6 34.4

Average 102.7 34.0 5

St. dev. 3.9 0.4 6-1 0.84-0.84 158.3 39.8 6-2 0.42-0.28 181.0 39.8 6-3 0.54-0.50 186.5 40.0

Average 175.3 39.9 St. dev. 14.9 0.1

6

% gain 70.7 17.4 * Strength of specimen 1-1 was not included in the average or standard deviation because the guides used for bracing against out-of-plane buckling were accidentally over clamped, which caused partial restraint for the in-plane buckling. This has resulted in a relatively higher load.

Chapter 4

135

Table 4.2 Summary of test results of slender columns in group B of Phase I.

Set Maximum

load, Pmax (kN) %age gain in strength

Estimated out-of-straightness, e’ (mm)

Total deflection (e’+δ) at Pmax (mm)

7 295 --- 6.60 20.82 8 355 20 0.92 8.09 9 335 14 7.04 21.61 10 332 13 -2.04 8.62 11 362 23 5.00 16.26

Chapter 4

136

Table 4.3 Summary of test results of short columns in group C of Phase I.

Set

Spec

imen

Max

imum

Lo

ad, P

max

(kN

)

Stiff

ness

(k

N/m

m)

Dis

plac

emen

t @

Pm

ax (m

m)

Set

Spec

imen

Max

imum

Lo

ad, P

max

(kN

)

Stiff

ness

(k

N/m

m)

Dis

plac

emen

t @

Pm

ax (m

m)

12-1 385 1272 0.62 17-1 455.5 1271 0.62 12-2 411 1161 0.59 17-2 408 1335 0.51 12 12-3 393 954 0.66

17 17-3 420 1027 0.62

Average 396 1129 0.62 Average 428 1211 0.59 St. dev. 13 161 0.04 St. dev. 25 163 0.06 % gain 8 7 -5

13-1 453 1405 0.47 18-1 474 971 0.67 13-2 454 1161 0.57 18-2 412 1271 0.57 13 13-3 458 954 0.55

18 18-3 434 1376 0.59

Average 455 1173 0.53 Average 440 1206 0.61 St. dev. 3 226 0.05 St. dev. 31 210 0.05 % gain 15 4 -15 % gain 11 7 -2

14-1 511 1571 0.65 19-1 441 1335 0.54 14-2 444 1214 0.6 19-2 438 1335 0.49 14 14-3 447 1068 0.63

19 19-3 421 971 0.58

Average 467 1284 0.63 Average 433 1214 0.53 St. dev. 38 259 0.03 St. dev. 11 210 0.05 % gain 18 14 2 % gain 9 8 -15

15-1 444 1571 0.49 20-1 444 1214 0.57 15-2 420 1068 0.59 20-2 440 1405 0.54 15 15-3 429 1214 0.5

20 20-3 440 1469 0.51

Average 431 1284 0.52 Average 441 1363 0.54 St. dev. 12 259 0.06 St. dev. 2 133 0.03 % gain 9 14 -16 % gain 11 21 -13

16-1 453 1907 0.47 16-2 454 1161 0.57 16 16-3 458 1271 0.56

Average 455 1446 0.54 St. dev. 3 403 0.06 % gain 15 28 -13

Chapter 4

137

Figure 4.1 Load-axial displacement responses of column sets 1 and 2 of group A.


0

20

40

60

80

100

120

140

160

180

200

220

0 3 6 9 12 15

Load

(kN

)

Axial displacement ∆ (mm)

Set 3(Control)

Set 4 (strengthened)

(Pavg. )strengthened= 200 kN

(Pavg. )control= 148 kN

P

∆

HSS 44 x 44 x 3.2 mmkL/r = 70

Debondingof CFRP on inner side

1.5 3.0 4.5 6.0 7.5

4-34-2

4-1

3-13-2

3-3

0

20

40

60

80

100

120

140

160

180

200

220

0 3 6 9 12 15

Load

(kN

)


Set 3(Control)



(Pavg. )control= 148 kN

P

∆

P

∆

HSS 44 x 44 x 3.2 mmkL/r = 70

Debondingof CFRP on inner side

1.5 3.0 4.5 6.0 7.51.5 3.0 4.5 6.0 7.5

4-34-2

4-1

3-13-2

3-3

0

20

40

60

80

100

120

140

160

180

200

220

0 3 6 9 12 15

P

∆Lo

ad (k

N)


Set 1(Control)

Debonding of CFRP on inner side

(Pavg. )strengthened= 192 kN(Pavg. )control= 182 kN

HSS 44 x 44 x 3.2 mmkL/r = 46


1.5 3.0 4.5 6.0 7.5

1-21-3

2-2

2-3

2-1

0

20

40

60

80

100

120

140

160

180

200

220

0 3 6 9 12 15

P

∆

P

∆Lo

ad (k

N)


Set 1(Control)

Debonding of CFRP on inner side

(Pavg. )strengthened= 192 kN(Pavg. )control= 182 kN

HSS 44 x 44 x 3.2 mmkL/r = 46


1.5 3.0 4.5 6.0 7.51.5 3.0 4.5 6.0 7.5

1-21-3

2-2

2-3

2-1

Chapter 4

138


Figure 4.4 Load-lateral displacement of column sets 1 and 2 of group A.

0

20

40

60

80

100

120

140

160

180

200

220

0 3 6 9 12 15

Load

(kN

)


Set 5(Control)



(Pavg. )control=103 kN

Overall Buckling

HSS 44 x 44 x 3.2 mmkL/r = 93

1.5 3.0 4.5 6.0 7.5

P

∆

Crushing of CFRP on inner side

6-26-36-15-3

5-25-1

0

20

40

60

80

100

120

140

160

180

200

220

0 3 6 9 12 15

Load

(kN

)


Set 5(Control)



(Pavg. )control=103 kN

Overall Buckling

HSS 44 x 44 x 3.2 mmkL/r = 93

1.5 3.0 4.5 6.0 7.51.5 3.0 4.5 6.0 7.5

P

∆

P

∆

Crushing of CFRP on inner side

6-26-36-15-3

5-25-1

020

40

60

80

100

120

140

160

180

200

220

-5 0 5 10 15 20 25 30 35 40 45 50

Load

(kN

)

Lateral displacement δ (mm)

Set 1(Control)

Set 2(strengthened)

HSS 44 x 44 x 3.2 mmkL/r = 46

e’ δ

PDebonding of CFRP

on inner side2-3

1-31-2

2-1

2-2

020

40

60

80

100

120

140

160

180

200

220

-5 0 5 10 15 20 25 30 35 40 45 50

Load

(kN

)


Set 1(Control)

Set 2(strengthened)

HSS 44 x 44 x 3.2 mmkL/r = 46

e’ δ

P

e’ δ

PDebonding of CFRP

on inner side2-3

1-31-2

2-1

2-2

Chapter 4

139



0

20

40

60

80

100

120

140

160

180

200

220

-5 0 5 10 15 20 25 30 35 40 45 50

Set 3(Control)

Set 4(strengthened)


Load

(kN

)

e’ δ

P

HSS 44 x 44 x 3.2 mmkL/r = 70

CFRP debonding on inner side

3-23-13-3

4-34-14-2

0

20

40

60

80

100

120

140

160

180

200

220

-5 0 5 10 15 20 25 30 35 40 45 50

Set 3(Control)

Set 4(strengthened)


Load

(kN

)

e’ δ

P

e’ δ

P

HSS 44 x 44 x 3.2 mmkL/r = 70

CFRP debonding on inner side

3-23-13-3

4-34-14-2

0

20

40

60

80

100

120

140

160

180

200

220

-5 0 5 10 15 20 25 30 35 40 45 50

Set 5(Control)

Set 6(strengthened)


Load

(kN

)

HSS 44 x 44 x 3.2 mmkL/r = 93

e’ δ

P

CFRP crushing on inner side

5-1

5-35-2

6-36-2

6-1

0

20

40

60

80

100

120

140

160

180

200

220

-5 0 5 10 15 20 25 30 35 40 45 50

Set 5(Control)

Set 6(strengthened)


Load

(kN

)

HSS 44 x 44 x 3.2 mmkL/r = 93

e’ δ

P

e’ δ

P

CFRP crushing on inner side

5-1

5-35-2

6-36-2

6-1

Chapter 4

140

Figure 4.7 Load-axial strain responses based on strain gauge S1 of column sets 1 and 2 of group A.


0

20

40

60

80

100

120

140

160

180

200

220

-16 -14 -12 -10 -8 -6 -4 -2 0

Set 1(Control)

Set 2(strengthened)

Axial strain x 10-3(mm/mm)

Load

(kN

)

(εav

g.)st

reng

then

ed=

-1.6

1x10

-3

HSS 44 x 44 x 3.2 mmkL/r = 46

S1

1-21-3

2-12-32-2

0

20

40

60

80

100

120

140

160

180

200

220

-16 -14 -12 -10 -8 -6 -4 -2 0

Set 1(Control)

Set 2(strengthened)


Load

(kN

)

(εav

g.)st

reng

then

ed=

-1.6

1x10

-3

HSS 44 x 44 x 3.2 mmkL/r = 46

S1S1

1-21-3

2-12-32-2

0

20

40

60

80

100

120

140

160

180

200

220

-16 -14 -12 -10 -8 -6 -4 -2 0

Set 4(strengthened)

(εav

g.)st

reng

then

ed=

-2.2

6x10

-3


Load

(kN

)

Set 3(Control)

HSS 44 x 44 x 3.2 mmkL/r = 70

S1

3-13-3

3-2

4-34-14-2

0

20

40

60

80

100

120

140

160

180

200

220

-16 -14 -12 -10 -8 -6 -4 -2 0

Set 4(strengthened)

(εav

g.)st

reng

then

ed=

-2.2

6x10

-3


Load

(kN

)

Set 3(Control)

HSS 44 x 44 x 3.2 mmkL/r = 70

S1S1

3-13-3

3-2

4-34-14-2

Chapter 4

141



0

20

40

60

80

100

120

140

160

180

200

220

-16 -14 -12 -10 -8 -6 -4 -2 0

Set 6(strengthened)

(εav

g.)st

reng

then

ed=

-2.7

4x10

-3Load

(kN

)

Set 5(Control)


S1

HSS 44 x 44 x 3.2 mmkL/r = 93

5-1

5-35-2

6-36-26-1

0

20

40

60

80

100

120

140

160

180

200

220

-16 -14 -12 -10 -8 -6 -4 -2 0

Set 6(strengthened)

(εav

g.)st

reng

then

ed=

-2.7

4x10

-3Load

(kN

)

Set 5(Control)


S1S1

HSS 44 x 44 x 3.2 mmkL/r = 93

5-1

5-35-2

6-36-26-1

0

20

40

60

80

100

120

140

160

180

200

220

-3 -1.5 0 1.5 3 4.5 6 7.5 9

Set 2(strengthened)

Load

(kN

)

Set 1(Control)


S2

HSS 44 x 44 x 3.2 mmkL/r = 46

1-21-3

2-1 2-22-3

0

20

40

60

80

100

120

140

160

180

200

220

-3 -1.5 0 1.5 3 4.5 6 7.5 9

Set 2(strengthened)

Load

(kN

)

Set 1(Control)


S2S2

HSS 44 x 44 x 3.2 mmkL/r = 46

1-21-3

2-1 2-22-3

Chapter 4

142



0

20

40

60

80

100

120

140

160

180

200

220

-3 -1.5 0 1.5 3 4.5 6 7.5 9

Set 4(strengthened)

Load

(kN

)

Set 3(Control)


S2

HSS 44 x 44 x 3.2 mmkL/r = 70

3-13-3

3-2

4-14-34-2

0

20

40

60

80

100

120

140

160

180

200

220

-3 -1.5 0 1.5 3 4.5 6 7.5 9

Set 4(strengthened)

Load

(kN

)

Set 3(Control)


S2S2

HSS 44 x 44 x 3.2 mmkL/r = 70

3-13-3

3-2

4-14-34-2

0

20

40

60

80

100

120

140

160

180

200

220

-3 -1.5 0 1.5 3 4.5 6 7.5 9

Set 6(strengthened)

Load

(kN

)

Set 5(Control)


S2

HSS 44 x 44 x 3.2 mmkL/r = 93

6-2

6-16-3

5-35-25-1

0

20

40

60

80

100

120

140

160

180

200

220

-3 -1.5 0 1.5 3 4.5 6 7.5 9

Set 6(strengthened)

Load

(kN

)

Set 5(Control)


S2S2

HSS 44 x 44 x 3.2 mmkL/r = 93

6-2

6-16-3

5-35-25-1

Chapter 4

143

Figure 4.13 Variation of axial strength with slenderness ratio of group A columns.

Figure 4.14 Effect of slenderness ratio on the CFRP effectiveness in group A columns.

0

50

100

150

200

250

40 50 60 70 80 90 100

Axia

l stre

ngth

(kN

.)

Slenderness ratio (kL/r)

Bare steel

CFRP-strengthened

a

ρ = 23 %

2 Layers of CFRP type C5(25x1.4 mm & 16x1.4 mm)

HSS 44x44x3.2 mm

bEffect

of CFRP

0

50

100

150

200

250

40 50 60 70 80 90 100

Axia

l stre

ngth

(kN

.)


Bare steel

CFRP-strengthened

a

ρ = 23 %

2 Layers of CFRP type C5(25x1.4 mm & 16x1.4 mm)

HSS 44x44x3.2 mm

bEffect

of CFRP

%ag

e in

crea

se in

axi

al s

treng

th (o

r stif

fnes

s)

0

10

20

30

40

50

60

70

80

40 50 60 70 80 90 100Slenderness ratio (kL/r)

Axial st

rength

Axial stiffness10.3 %

34.9 %

70.7 %

15.5 % 17.4 %

5.5 %

ρ = 23 %

2 Layers of CFRP type C5 (25x1.4 mm & 16x1.4 mm)

HSS 44x44x3.2

%ag

e in

crea

se in

axi

al s

treng

th (o

r stif

fnes

s)

0

10

20

30

40

50

60

70

80

40 50 60 70 80 90 100Slenderness ratio (kL/r)

Axial st

rength

Axial stiffness10.3 %

34.9 %

70.7 %

15.5 % 17.4 %

5.5 %

ρ = 23 %

2 Layers of CFRP type C5 (25x1.4 mm & 16x1.4 mm)

HSS 44x44x3.2

Chapter 4

144

Figure 4.15 Failure modes of group A columns.

(c) Debonding of CFRP plates

(d) Rupture of GFRP end wraps

crack

DebondedCFRP plates

(e) Crushing of CFRP plates

(a) Buckling of set 1 (kL/r = 46)

(b) Buckling of set 6

(kL/r = 93)

(c) Debonding of CFRP plates

(d) Rupture of GFRP end wraps

crack

DebondedCFRP plates

(e) Crushing of CFRP plates

(a) Buckling of set 1 (kL/r = 46)

(b) Buckling of set 6

(kL/r = 93)

Chapter 4

145

Figure 4.16 Variation of the compressive strain of CFRP at ultimate with slenderness ratio.

Figure 4.17 Load-axial displacement responses of column sets 7 to 11 of group B.

0

50

100

150

200

250

300

350

400

0 1 2 5 6 7Axial displacement ∆ (mm)

Load

(kN

)

7

9

8

10

11

P

∆

Set7 Control8 1 layer/ 2 sides9 3 layers / 2 sides

10 5 layers / 2 sides11 3 layers / 4 sides

3 40

50

100

150

200

250

300

350

400

0 1 2 5 6 7Axial displacement ∆ (mm)

Load

(kN

)

7

9

8

10

11

P

∆

P

∆



3 4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 20 40 60 80 100 120


Max

imum

com

pres

sive

stra

in x

10-

3 ( m

m/m

m)

Debonding

CrushingDebonding

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 20 40 60 80 100 120


Max

imum

com

pres

sive

stra

in x

10-

3 ( m

m/m

m)

Debonding

CrushingDebonding

Chapter 4

146

Figure 4.18 Load-lateral displacement responses of column sets 7 to 11 of group B.

Figure 4.19 Load-axial strain responses of specimen 7 of group B.

0

50

100

150

200

250

300

350

400

-5 0 5 10 15 20 25 30 35 40 45

79

8

10

11

Total lateral deflection (e’+δ) (mm)

Load

(kN

)

HSS 89 x 89 x 3.2 mmkL/r = 68



e’ δ

P

0 5 10 30 40 4515 20-5 25 350

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

-5 0 5 10 15 20 25 30 35 40 45

79

8

10

11

Total lateral deflection (e’+δ) (mm)

Load

(kN

)

HSS 89 x 89 x 3.2 mmkL/r = 68



e’ δ

P

e’ δ

P

0 5 10 30 40 4515 20-5 25 350

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

-0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004

PI1

PI2S1

S2

-2-6 -4-8-10 0 2


Load

(kN

)

PI1 PI2

S2S1 ε y=

1.94

x 1

0-3

40

50

100

150

200

250

300

350

400

-0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004

PI1

PI2S1

S2

-2-6 -4-8-10 0 2


Load

(kN

)

PI1 PI2

S2S1

PI1 PI2

S2S1 ε y=

1.94

x 1

0-3

4

Chapter 4

147



40

50

100

150

200

250

300

350

400

-0.01 0

PI1 PI2

S1

S2

100

150

200

250

300

350

400

50

0-2-6 -4-8-10 0 2


Load

(kN

)

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.43

x 1

0-3

40

50

100

150

200

250

300

350

400

-0.01 0

PI1 PI2

S1

S2

100

150

200

250

300

350

400

50

0-2-6 -4-8-10 0 2


Load

(kN

)

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.43

x 1

0-3

0

50

100

150

200

250

300

350

400

-0.01 0

PI1 PI2

S1

S2

100

150

200

250

300

350

400

50

0-2-6 -4-8-10 0 2


Load

(kN

)

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.43

x 1

0-3

0

50

100

150

200

250

300

350

400

-0.01 0

PI1 PI2

S1

S2

100

150

200

250

300

350

400

50

0-2-6 -4-8-10 0 2


Load

(kN

)

PI1 PI2

S2S1

0

50

100

150

200

250

300

350

400

-0.01 0

PI1 PI2

S1

S2

100

150

200

250

300

350

400

50

0-2-6 -4-8-10 0 2


Load

(kN

)

PI1 PI2

S2S1

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.43

x 1

0-3

0

50

100

150

200

250

300

350

400

-0.01 0

PI1PI2

S1

S2

Load

(kN

)

-2-6 -4-8-10 0 2 4

100

150

200

250

300

350

400

50

0


PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.25

x 1

0-3

0

50

100

150

200

250

300

350

400

-0.01 0

PI1PI2

S1

S2

Load

(kN

)

-2-6 -4-8-10 0 2 4

100

150

200

250

300

350

400

50

0


PI1 PI2

S2S1

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.25

x 1

0-3

Chapter 4

148



100

150

200

250

300

350

400

50

0-10

Load

(kN

)


0

50

100

150

200

250

300

350

400

-0.01 0

PI1 PI2

S1 S2

-2-6 -4-8 0 2

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.4

8 x

10-3

100

150

200

250

300

350

400

50

0-10

Load

(kN

)


0

50

100

150

200

250

300

350

400

-0.01 0

PI1 PI2

S1 S2

-2-6 -4-8 0 2

PI1 PI2

S2S1

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.4

8 x

10-3

40

50

100

150

200

250

300

350

400

-0.01 0

PI1PI2S1

S2

-2-6 -4-8-10 0 2

100

150

200

250

300

350

400

50

0

Load

(kN

)


PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.1

8 x

10-3

40

50

100

150

200

250

300

350

400

-0.01 0

PI1PI2S1

S2

-2-6 -4-8-10 0 2

100

150

200

250

300

350

400

50

0

Load

(kN

)


PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.1

8 x

10-3

0

50

100

150

200

250

300

350

400

-0.01 0

PI1PI2S1

S2

-2-6 -4-8-10 0 2

100

150

200

250

300

350

400

50

0

Load

(kN

)


PI1 PI2

S2S1

PI1 PI2

S2S1

(εcr

ushi

ng) C

FRP=

1.1

8 x

10-3

Chapter 4

149

Figure 4.24 Mid-height imperfection of specimen 7 of group B versus the applied load.

Applied load, P (kN)

Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50

Specimen 1-2, eP=0= 0.79





Note: imperfection measurements of specimen 1-1 are not included because the bracing guides were overclamped, which caused partial restraints at mid-height. This has resulted in development of additional bending moments on the specimen


Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50






Note: imperfection measurements of specimen 1-1 are not included because the bracing guides were overclamped, which caused partial restraints at mid-height. This has resulted in development of additional bending moments on the specimen

Chapter 4

150

Figure 4.25 Failure modes of group B columns.

(a) Specimen 7 (Control)

Local buckling

(b) Specimen 11 (Strengthened)

Debonding and fracture of

sheets

CFRP sheets on

2 sides

CFRP sheets on

4 sides

Inward buckling Outward buckling

(c) Cross section

(a) Specimen 7 (Control)

Local buckling



sheets

CFRP sheets on

2 sides

CFRP sheets on

4 sides



sheets

CFRP sheets on

2 sides

CFRP sheets on

4 sides

Inward buckling Outward buckling

(c) Cross section

Chapter 4

151

Figure 4.26 Load-axial displacement responses of column sets 12 to 20 of group C.

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.50

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

1 5 0

3 00

4 5 0

6 00

0 0.5 1 1 .5

Displacement (mm)

Load

(kN

)

150

300

450

600

0.5 1.51.000 0

150

300

450

600

0 0.5 1 1.5

150

300

450

600

0.5 1.51.000 0

100

200

300

400

500

600

0 0.5 1 1.50.5 1.51.00

150

300

450

600

0

150

300

450

600

0.5 1.51.000

150

300

450

600

0.5 1.51.000

0.5 1.51.00

150

300

450

600

0

0.5 1.51.00

150

300

450

600

0

150

300

450

600

0.5 1.51.000

150

300

450

600

0.5 1.51.000

(a) Set 12 (b) Set 13 (c) Set 14

(d) Set 15 (e) Set 16 (f) Set 17

(g) Set 18 (h) Set 19 (i) Set 20

∆P

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.50

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

1 5 0

3 00

4 5 0

6 00

0 0.5 1 1 .5

Displacement (mm)

Load

(kN

)

150

300

450

600

0.5 1.51.000 0

150

300

450

600

0 0.5 1 1.5

150

300

450

600

0.5 1.51.000 0

100

200

300

400

500

600

0 0.5 1 1.50.5 1.51.00

150

300

450

600

0

150

300

450

600

0.5 1.51.000

150

300

450

600

0.5 1.51.000

0.5 1.51.00

150

300

450

600

0

0.5 1.51.00

150

300

450

600

0

150

300

450

600

0.5 1.51.000

150

300

450

600

0.5 1.51.000

(a) Set 12 (b) Set 13 (c) Set 14

(d) Set 15 (e) Set 16 (f) Set 17

(g) Set 18 (h) Set 19 (i) Set 20

∆P

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.50

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

150

300

450

600

0 0.5 1 1.5

0

1 5 0

3 00

4 5 0

6 00

0 0.5 1 1 .5

Displacement (mm)

Load

(kN

)

150

300

450

600

0.5 1.51.000

150

300

450

600

150

300

450

600

0.5 1.51.00 0.5 1.51.00.5 1.51.000 0

150

300

450

600

0 0.5 1 1.5

150

300

450

600

0.5 1.51.0000

150

300

450

600

0 0.5 1 1.5

150

300

450

600

0.5 1.51.000

150

300

450

600

150

300

450

600

0.5 1.51.00 0.5 1.51.00.5 1.51.000 0

100

200

300

400

500

600

0 0.5 1 1.50.5 1.51.00

150

300

450

600

00.5 1.51.00 0.5 1.51.00.5 1.51.00

150

300

450

600

0

150

300

450

600

150

300

450

600

0

150

300

450

600

0.5 1.51.000

150

300

450

600

150

300

450

600

0.5 1.51.00 0.5 1.51.00.5 1.51.000

150

300

450

600

0.5 1.51.000

150

300

450

600

150

300

450

600

0.5 1.51.00 0.5 1.51.00.5 1.51.000

0.5 1.51.00

150

300

450

600

00.5 1.51.00 0.5 1.51.00.5 1.51.00

150

300

450

600

0

150

300

450

600

150

300

450

600

0

0.5 1.51.00

150

300

450

600

00.5 1.51.00 0.5 1.51.00.5 1.51.00

150

300

450

600

0

150

300

450

600

150

300

450

600

0

150

300

450

600

0.5 1.51.000

150

300

450

600

150

300

450

600

0.5 1.51.00 0.5 1.51.00.5 1.51.000

150

300

450

600

0.5 1.51.000

150

300

450

600

150

300

450

600

0.5 1.51.00 0.5 1.51.00.5 1.51.000

(a) Set 12 (b) Set 13 (c) Set 14

(d) Set 15 (e) Set 16 (f) Set 17

(g) Set 18 (h) Set 19 (i) Set 20

∆P

∆P

Chapter 4

152

Figure 4.27 Load-axial strain response of control specimen 12-1 of group C.

Figure 4.28 Effect of using SM-CFRP on load-axial displacement responses in group C columns.

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6 7

Specimen 12-1 (S2)

S1 S2

Local buckling


Load

(kN

)

a Specimen 12-1 (S1)

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6 7

Specimen 12-1 (S2)

S1 S2

Local buckling


Load

(kN

)

aa Specimen 12-1 (S1)

Axial displacement (mm)

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Load

(kN

)

12 (control)

15

16 13

14


0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Load

(kN

)

12 (control)

15

16 13

14

Chapter 4

153

Figure 4.29 Effect of using HM-CFRP on load-axial displacement responses in group C columns.

Figure 4.30 Effect of using two types of CFRP on strengthening short specimens.


0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2 1.4

12 (control)

1718

19

20

Load

(kN

)


0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2 1.4

12 (control)

1718

19

20

Load

(kN

)

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Load

(kN

)


12 (control)

18 (HM-CFRP)

14 (SM-CFRP)

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Load

(kN

)


12 (control)

18 (HM-CFRP)

14 (SM-CFRP)

Chapter 4

154

Figure 4.31 Failure modes of group C columns.

Localbuckling

Rupture of CFRP

Localbuckling

Debonding of CFRP

(a) Set 12 (Control) (b) Set 19

(c) Set 14

(d) Set 18

Debonding of CFRP

Localbuckling

Rupture of CFRP

Localbuckling

Debonding of CFRP

(a) Set 12 (Control) (b) Set 19

(c) Set 14

(d) Set 18

Debonding of CFRP

Chapter 5

155

Chapter 5 Experimental Results and Discussion of Phases II

and III: Flexural Members

5.1 Introduction

This chapter presents the results of Phases II and III of the experimental program,

including discussion of the behaviour and failure modes. Phase II was focused on

strengthening intact steel-concrete composite girders. Three girders, scaled down (4:1)

from an actual bridge, were tested in four-point bending. Phase III was focused on repair

of artificially damaged steel-concrete composite beams with a simulated loss of the

tension flange at the mid-span section. Eleven beams were tested in four-point bending in

Phase III. The flexural behaviour in both phases is evaluated in terms of the flexural

stiffness and strength. The force transfer between steel and CFRP material is evaluated in

terms of strain distribution along the CFRP plates or sheets.

5.2 Results of Phase II – Strengthening of Intact Girders

Three large scale steel-concrete composite girders (G1 to G3) were tested in this phase.

Each girder consisted of 5940 mm long W250x25 hot rolled steel section acting

Chapter 5

156

compositely with a 65 mm thick and 500 mm wide concrete slab. The girders included

one intact control (unstrengthened) specimen (G1) and two CFRP-strengthened

specimens (G2 and G3). The strengthening scheme of specimens G2 and G3 consisted of

one 90 mm x 1.4 mm layer of CFRP type C4 and a second layer of 50 mm x 1.4 mm,

which was CFRP type C4 for G2 and CFRP type C5 for G3. The lengths of layers 1 and 2

were 4000 mm and 1500 mm, respectively, in both G2 and G3. The objectives of this

phase were to investigate the effectiveness of CFRP bonded plates in strengthening intact

composite girders, examine the effectiveness of the bond between the steel surface and

CFRP plates with lengths shorter than the full span of the girder, and also compare CFRP

plates of different moduli in strengthening applications.

5.2.1 Effectiveness of the CFRP strengthening system

A summary of test results, including the flexural stiffness, yield load, and maximum load

of these girders, and their percentage increases relative to the control specimen, is

presented in Table 5.1. The flexural stiffness is calculated based on the slope of the load-

deflection curve within the linear elastic part. The results show that CFRP has indeed

increased both the flexural strength and stiffness. The flexural strength has increased by

50 and 51 percent for girders G2 and G3, respectively, relative to G1, whereas, the

flexural stiffness has increased by 17 and 19 percent, respectively.

Figure 5.1 shows the load versus mid-span deflection of the three girders of Phase II. The

figure shows a yield load of 85 kN for the control specimen, which is essentially the load

at the end of the linear part of the load-deflection curve. Figure 5.2 shows the load versus

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strain measurements of two strain gauges attached to the underside of the lower steel

flange of the control specimen. The figure shows a slight difference in the two strain

gauge measurements. The yield strain of the steel girder, based on coupon tests (Figure

3.6), is about 0.17 percent. Figure 5.2 shows that at this strain the behaviour indeed

changes, suggesting that yielding has started. This occurs at the 85 kN load, which agrees

with the estimated yielding load at the end of the linear part in Figure 5.1. The small

difference in behaviour, based on gauge S1 relative to S2 may possibly be attributed to

the location within the flange, where the level of residual stress varies. It is also possible

that a slight relative slip between the concrete slab and the steel beam has contributed to

the rather unusual behaviour just before the yielding flat plateau in Figure 5.2. The yield

loads of specimens G2 and G3 have also been obtained from Figure 5.1 and are 97 kN

and 103 kN, respectively. Table 5.1 shows that CFRP plates have increased the yield load

by 14 and 21 percent in the cases of G2 and G3, respectively, which satisfies the design

guidelines proposed by Schnerch et al. (2007), and reported in Chapter 2. This is

particularly important from the design point of view as it clearly reflects some increase in

the service load margin.

The outer CFRP layers (1500 mm long) in both G2 and G3 girders were debonded early

from the inner CFRP layer (4000 mm long), at loads of 129 kN and 111 kN, respectively,

because of their short length. It is also noted that debonding in specimen G3 with two

different types of CFRP occurred earlier than in G2 of the same type of CFRP for the two

layers. The load drop after debonding of the second layer was very small due to the small

cross sectional area of the second CFRP layer, relative to the total area of CFRP. After

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debonding has occurred, both girders showed a similar trend, where they both behaved as

a girder strengthened with one layer of CFRP type C4, 4000 mm long. Both girders

achieved almost the same strength (216 kN and 217 kN for G2 and G3, respectively), as

shown in Figure 5.1. This level of strength represents 51 percent increase in ultimate

strength, as given in Table 5.1. The similarity in behaviour of both G2 and G3 after

debonding of the outer layer also reflects good repeatability. It is clear that the effect of

the CFRP type on the ultimate flexural strength could not be assessed in this phase of

study, due to the early debonding of the outer layer.

Figure 5.3 shows the load versus the longitudinal strains in the web, measured at a height

of 50 mm above the lower flange, for the three girders. The figure clearly shows that

strains in the steel cross section have stabilized and remained almost constant at about

0.24 percent up to failure, due to bonding CFRP plates to the lower flanges of G2 and G3.

5.2.2 Effect of CFRP elastic modulus

The second (outer) layer of CFRP was type C4 in the case of G2 and type C5 in the case

of G3. Although the value of elastic modulus of CFRP type C5 is almost double that of

type C4 (Ec4 = 152 GPa and Ec5 = 313 GPa) the difference in the calculated transformed

moment of inertia of girders G2 and G3 is in fact quite small, as shown in Table 5.1. The

calculations accounted for the concrete slab, steel section, and the CFRP. The table shows

12 and 16 percent increases in the transformed moment of inertia of G2 and G3,

respectively, relative to G1. The observed increases in flexural stiffness, within the elastic

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region, for girders G2 and G3 (17 and 19 percent, respectively) are almost proportional to

the corresponding increases in their respective moments of inertia.

Figure 5.4 and 5.5 show the load versus strain at different locations along the CFRP

plates of both strengthened girders G2 and G3, respectively. The strain gauges and curves

are marked by their distance from mid-span of the girder. It should be noted that in the

case of G2, the strain gauge at zero distance was attached to the inner CFRP layer, which

remained bonded to the steel substrate until failure, whereas in G3 it was attached to the

outer CFRP layer, which debonded early. Figure 5.4 shows a linear relationship to the

end, at the location where the steel cross sections have not yielded (a cross section at

1925 mm from the mid-span). On the other hand, bi-linear relationships are observed at

all other locations, where the steel cross sections were at various stages of yielding. The

change of the strain behaviour to the reverse direction of the gauge at 675 mm (Figure 5.4

and 5.5), which is bonded at the end of the outer CFRP layer, indicates the initiation of

debonding.

The difference in tensile forces between two locations on the CFRP plate must be

balanced by the shear force acting between the CFRP plate and steel substrate, as noted

by Garden et al. (1998). The average shear stress could then be determined between two

strain gauge locations as follows:

⎥⎦

⎤⎢⎣

⎡−−

=12

12

xxtE pfavg

εετ (5.1)

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where ( )12 εε − is the difference in longitudinal strains between two adjacent gauges,

( )12 xx − is the distance between the gauges, Ef and tp are Young’s modulus and

thickness of the plate.

Figure 5.6 and 5.7 show the load versus the average shear stresses, based on Equation

5.1, at discrete locations representing mid-distances between the strain gauges along the

CFRP plates of girders G2 and G3, respectively. Insignificant shear stresses are observed

at a distance of 250 mm, since it is within the constant moment region. On the other hand,

high shear stresses have developed near the end of the outer CFRP plate, at a distance

588 mm from mid-span, which indicate the initiation of debonding. The shear stresses at

this location were linear up to load levels of 96 kN and 83 kN for G2 and G3,

respectively. Beyond these load levels, the adhesive yielded and a nonlinear behaviour

was observed. It can be noticed that debonding of the outer CFRP layer of both G2 and

G3, which is only 1500 mm long, occurred at load levels of 129 kN and 111 kN,

respectively, after the interfacial shear stresses reached a maximum average value of 2.25

MPa. It is clear that the CFRP type C5, used in G3, debonded at a lower load level than

type C4, used in G2. As indicated earlier, this is probably attributed to the large

difference in the elastic modulus values between the CFRP types C4 and C5.

5.2.3 Effect of bonded length of CFRP plates

The inner layer of CFRP of specimens G2 and G3 was 4000 mm long, followed by a

second (outer) layer, 1500 mm long. The strain gauges attached to the short layers (at

zero, 500, and 675 mm) indicate that the bonded length of the second layer was

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insufficient to fully utilize the CFRP plates. The maximum recorded strains in the outer

layer at mid-span for CFRP type C4 (in G2) and CFRP type C5 (in G3) just prior to

debonding are 2.8 and 1.75 percent, respectively, as shown in Figure 5.4 and 5.5. These

values represent only 22 and 37 percent, respectively, of the ultimate strains of CFRP

types C4 and C5 reported in Table 3.2.

The inner layer for both G2 and G3 specimens, on the other hand, had a sufficient bonded

length, 4000 mm long, to keep the layer attached to the steel substrate until failure of the

girders. Figure 5.4 shows that the mid-span strain of the inner CFRP layer of girder G2

reached 13 percent, which is slightly higher than the average ultimate rupture strain (12.6

percent), based on the coupon tests (Table 3.2 and Figure 3.8). However, failure of the

girder occurred due to crushing of the concrete slab, which was associated with lateral

torsional buckling prior to CFRP rupture as discussed next.

5.2.4 Failure modes

The unstrengthened control girder G1 exhibited large deflection at mid-span (142 mm),

as shown in Figure 5.9(a). This large deflection was associated with excessive yielding of

the steel cross section. Based on the strain measurements of gauges PI2 and S1, and

assuming a linear strain distribution, it is estimated that 90 percent of the depth of the

steel cross section (d) was yielded before the girder failed. Failure occurred due to

crushing of the concrete slab, as shown in Figure 5.9(b), when its compressive strains,

based on PI1, reached the 0.35 percent, as shown in Figure 5.8.

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In both girders G2 and G3, the outer CFRP layer was prematurely debonded first. The

debonding was associated with fracture of the GFRP transverse end wraps, as shown in

Figure 5.9(c). This premature debonding occurred at 60 and 51 percent of the maximum

loads of G2 and G3, respectively. The debonding was also associated with insignificant

drops of 3 kN and 4 kN in the load in girders G2 and G3, respectively. Both girders

continued to sustain an increasing load up to failure. The two girders became vulnerable

to lateral torsional buckling at high load levels, particularly because of the unsupported

and relatively long span, as shown in Figure 5.9(d). These girders were braced against

torsional rotation at the supports only. The lateral buckling of the compression flange

produced additional lateral bending stresses on the concrete slab. For this reason, the

concrete slabs in G2 and G3 girders crushed on one side only in an unsymmetric manner,

as shown in Figure 5.9(d and e). Also, this transverse gradient of compressive stresses in

the concrete flange explains the relatively low strains measured by gauge PI1 at failure,

which were lower than the typical 0.35 percent (Figure 5.8). This is because PI1 was

positioned at the mid-width of the concrete slab, while maximum strains were at one

edge. It is very important to note, however, that this failure should not be considered

premature from an ultimate load point of view; because the tensile strains measured in the

CFRP at ultimate (Figure 5.4) suggests that tension failure of the CFRP was indeed quite

imminent.

5.3 Results of Phase III – Repair of Artificially Damaged Beams

A total of 11 steel-concrete composite beams (B1 to B11) were tested in this phase. Each

beam consisted of 1960 mm long W150x22 hot rolled steel section acting compositely

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with a 75 mm thick and 465 mm wide concrete slab. Table 5.2 shows a summary of the

test results of Phase III, in terms of the flexural stiffness and strength of the control intact,

control damaged, and CFRP-repaired specimens. Also given in Table 5.2, are the

percentage differences of both the stiffness and strength for the control damaged

specimen B2 and repaired specimens B3 to B11 with respect to the control intact

specimen B1. The following sections present test results, comparisons, and discussions,

including the effect of each parameter investigated, on the effectiveness of using

adhesively-bonded CFRP sheets for repair of damaged steel-concrete composite beams.

5.3.1 Effect of cutting the tension flange at mid-span

5.3.1.1 Flexural behaviour

Figure 5.10 shows the load versus mid-span deflection of the control intact beam B1 and

the control damaged (unrepaired) beam B2. The figure shows that both the strength and

stiffness of beam B2 have been severely degraded as a result of the complete cutting of

the lower steel flange at mid-span. Table 5.2 shows 60 percent reduction in flexural

strength and 54 percent reduction in stiffness.

Figure 5.11 shows the load versus longitudinal strains of the underside of the upper steel

flange for both beams B1 and B2. The figure shows small tensile strain values initially at

the upper flange of both beams, which indicate that the neutral axis is inside the concrete

slab. The figure also shows that the strain of beam B2 is greater than that of beam B1, at

the same load levels, within the linear elastic part. This indicates a substantial upward

shift of the neutral axis as a result of cutting the lower flange of beam B2. In both cases, a

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sudden increase in the tensile strain is observed upon yielding of the lower part of the

beam, indicating spread of yielding throughout the steel cross section. However, the top

flange of B2 only is yielded at ultimate. Figure 5.12 shows the load versus strains of the

underside of the lower steel flange of both beams B1 and B2. Two strain gauges (S50-5

and S100-5) were attached to beam B2 at distances of 50 and 100 mm from mid-span,

while the strain of B1 was measured at mid-span. The figure shows that the strain values

of B2 at a distance of 100 mm from mid-span are higher than those at 50 mm and are

close to those of B1 up to a load level of 69 kN. At higher loads, the pre-cut in the flange

develops into a crack propagating within the steel web. This results in further spreading

of the stress flow away from mid-span. As a result, the strains along the steel flange of

B2 at 50 mm and 100 mm reduce and reverse direction.

As discussed earlier, cutting the lower steel flange at mid-span creates regions of stress

concentration, which leads to crack propagation within the web as the load increases.

This is discussed further in detail, in this section. Figure 5.13 shows the load versus

strains at four different locations along the depth of a mid-span section of specimen B2.

The figure shows that the entire steel section is under tensile stresses. The behaviour also

suggests a highly nonlinear strain distribution along the web at mid-span, as also shown

in the small diagram within Figure 5.13. It is clear from this figure that the closest region

to the cut flange yields much earlier than farther regions along the web, due to stress

concentration. The strains of gauge (S0-4), just above the cut, increase rapidly and reach

the yield strain at a very low load level of about 10 kN. The figure also indicates that the

entire steel section at mid-span, including the upper flange, yields excessively before the

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beam attains its maximum load. After this excessive yielding, the parts above the cut

completely separate leading to propagation of the crack from the flange into the web.

Figure 5.14 shows the load versus strains in the web, at heights of 20 mm and 80 mm

above the underside of the lower steel flange, at three different locations in the transverse

direction. The figure shows that just above the cut (i.e. at 20 mm from the bottom) the

effect of the stress concentration is minimal at a distance of 50 mm from mid-span, as

evident by the readings of S50-4 and S100-4 strain gauges, which show significantly

lower strain (below yielding) than that measured by S0-4, just above the cut. The figure

also shows that at a height of 80 mm from the bottom, the stress concentration effect

becomes more pronounced at a load level of about 50 kN, which is indicated by the

departure of strain readings of S0-2 gauge from the trend of the other gauges S50-2 and

S100-2. This is quite different from the strains at the 20 mm height, where stress

concentration effect was evident from the onset of loading (S0-4).

5.3.1.2 Failure modes

The failure mode of the intact control beam B1 was yielding of the steel cross section,

followed by concrete crushing, as shown in Figure 5.15(a). For the damaged beam B2,

significant yielding associated with crack propagation from the cut flange into the web, as

shown in Figure 5.15(b), was observed. At the end of the test, the measured crack width

and height were 14 and 67 mm, respectively. Because of the crack propagation within

almost 44 percent of the depth of the steel section, the neutral axis was significantly

shifted upwards, inside the concrete slab. Therefore, the bottom of the concrete slab

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experienced high tensile stresses, which led to tension cracks, as shown in Figure 5.15(b).

The concrete slab was eventually crushed at the compression side.

5.3.2 Effect of type of CFRP


Beams B3 and B4 were repaired by bonding high modulus- (HM-) CFRP type C3 (Ec3 =

231 GPa) of different number of layers, whereas beams B5 and B6 were repaired by

bonding standard modulus- (SM-) CFRP type C1 (Ec1 = 115 GPa) and type C2 (Ec2 = 90

GPa), respectively. It should be noted that for all four beams the CFRP sheets were

bonded on the lower side of the tension steel flange, along the full span. Figure 5.16

shows the load-deflection responses of beams B3 and B4, compared to the reference

(control) beams B1 (intact) and B2 (damaged). The figure shows that both the HM-CFRP

repaired beams (B3 and B4) reached flexural stiffness values higher than the intact beam

B1, which is attributed to the high value of elastic modulus of CFRP type C3. Table 5.2

shows gains in stiffness of 13 and 26 percent for beams B3 and B4, respectively. Figure

5.17 also shows a comparison between the load-deflection responses of beams B5 and B6

and control beams B1 and B2. The figure shows that beam B6, which has a larger area of

CFRP (i.e. higher force equivalence index, ω), but lower CFRP elastic modulus, could

not achieve the full stiffness of the intact beam B1 and was 14 percent lower, as indicated

in Table 5.2. Figure 5.16 and 5.17 show that only beam B4 (repaired with HM-CFRP and

ω = 152 percent) was able to recover the original strength of B1 and even exceed it by 10

percent. Beam B6 had an ω = 193 percent, higher than that of B4, but only achieved a

strength 13 percent lower than that of the intact beam B1. This is attributed to the

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different failure modes as will be discussed in section 5.3.2.2. It is also noted that the

behaviour of beam B6 is more ductile than B4.

Beam B5, which is almost similar to B6, but the CFRP sheets were applied 22 months

after sandblasting, clearly shows a much lower strength than B6. Table 5.2 shows that the

strength of B5 is 50 percent lower than that of the intact beam B1. The lower bond

integrity between the steel surface and the CFRP sheets has promoted the premature and

progressive debonding along the interface, which affected the load-deflection response,

as shown in Figure 5.17.

Figure 5.18 and 5.19 show the strain distributions along part of the length of the CFRP

sheets of beams B3 and B4, respectively, at different load levels. The figures show that

the CFRP sheets type C3 of both beams reached their ultimate (rupture) strain (εult = 2.2 x

10-3, as reported in Table 3.2). It is also clear that at any load level the strains in B3 are

higher than B4, due to the smaller number of CFRP layers.

Figure 5.20 and 5.21 show similar strain distributions along the CFRP sheets of beams

B5 and B6, respectively, at different load levels. The figures show that both beams

reached their maximum loads before utilizing the full tensile strength of the CFRP sheets.

It is also clear that the maximum strain value in the CFRP sheets of B5, at failure, is

much smaller than that of B6, due to the bond deficiency and the early initiation of

debonding.

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168

Figure 5.22 compares the load versus strains of the CFRP at mid-span of beams B3, B4,

and B6, relative to the control beam B1. The figure clearly shows that the HM-CFRP

sheets bonded on both B3 and B4 have reached their rupture strain. On the other hand,

the SM-CFRP sheets bonded on B6 reached only 48 percent of their rupture strain. Figure

5.23 shows the load versus strains of the upper steel flange at mid-span of beams B3, B4,

and B6, relative to control beams B1 and B2. The figure shows initial compressive strains

at the upper flanges of B3, B4, and B6, which suggest that adding the CFRP sheets to the

damaged beams has shifted the neutral axis down (i.e. within the steel cross section),

particularly in B4 with HM-CFRP and ω = 152 percent. The figure also shows that after

rupture of the CFRP sheets in beams B3 and B4 the strains of the upper steel flanges

convert suddenly to tension, whereas in the case of B6 the strains of the upper steel

flange convert gradually to tension as the debonding of the CFRP sheets progresses.


The failure mode of beams B3 and B4 occurred by rupture of the CFRP sheets at mid-

span, as shown in Figure 5.24(a and b), after reaching the ultimate strain of CFRP type

C3. There were no signs of local debonding in the vicinity of mid-span. After rupture of

the CFRP sheets, the cut in the lower flange developed into a crack that propagated up

into the web, as shown in Figure 5.24(a). The load capacity of both beams dropped after

the rupture of CFRP sheets, as shown in Figure 5.16, and then increased again, slightly

until the concrete slabs crushed. After crushing of the slabs, the behaviour followed the

same curve as the damaged beam B2.

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The failure of beam B5 occurred by premature debonding along the interface between the

steel and the FRP layers at a very early stage, as shown in Figure 5.24(c). Failure of beam

B6 occurred in multiple steps. The first step was debonding of the CFRP sheets within

the shear span at one end of the beam, as shown in Figure 5.24(d and e). The debonding

of the CFRP sheets was associated with complete and sudden separation of the debonded

portions of the sheets, followed by a drop in the load from 298 kN to 265 kN, as shown in

Figure 5.17. After this drop, the specimen gained additional load and reached its

maximum capacity of 311 kN when the concrete crushed. Local debonding was observed

in the vicinity of the steel flange cut (i.e. mid-span) for both the GFRP sheets and the

remaining portion of the CFRP sheets, as indicated by the discoloration in Figure 5.24(e).

5.3.3 Effect of number of repaired sides of flange


In order to study the effect of the bonded surface area, a comparison was performed

between beams B6 and B7 with almost similar force equivalence indices of 193 and 185

percent, respectively. In beam B6, the CFRP sheets were bonded on the bottom side of

the steel flange, whereas in B7 the CFRP sheets were bonded on both the top and bottom

sides of the flange. Figure 5.25 shows the load-deflection responses of both beams. The

figure shows that increasing the bonded surface area in B7 enhanced the overall stiffness

of the beam, compared to B6. Table 5.2 shows that B7 achieved the same stiffness as the

control intact beam B1 (33.8 kN/mm), which is 14 percent higher than B6. Both beams

achieved very similar strength (311 and 307 kN, respectively). These strengths resemble

a recovery of 87 and 86 percent, respectively, of the strength of the intact beam.

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170

However, debonding in beam B7 started earlier than in B6 and affected the behaviour as

will be discussed next.

Figure 5.26 and 5.27 show the strain distributions along the lower and upper CFRP sheets

bonded on both sides of the flange of beam B7, at different load levels. The figures

generally show that beam B7 reached its maximum capacity before utilizing the full

strength of the CFRP sheets. The smaller strain gradient of the upper CFRP sheets, with

respect to that of the lower CFRP sheets; indicate that debonding along the upper side

started earlier than in the lower side. The earlier debonding on the upper side is attributed

to the development of peeling (normal) stresses, as depicted schematically in Figure 5.25.

Peeling stresses on the upper side were developed as a result of the beam’s curvature.


The maximum load capacities of beams B6 and B7 were controlled by crushing of the

concrete slabs, as indicated in Figure 5.25. The detailed failure description of B6 was

discussed earlier in section 5.3.2.2. For B7, a stationary camera was mounted near the

mid-span to record the progressive failure of the beam as the load increases. Figure

5.28(a) shows four images throughout the history of loading of B7. Image 1 shows the

beam before loading (P = 0), while image 2 captures the initiation of debonding of the

upper CFRP layers and the opening of the steel flange cut (P = 180 kN). In image 3,

crack propagation in the web and crushing of the concrete slab as well as complete

debonding of the upper CFRP layers are observed (P = 300 kN). The load capacity of B7

was then dropped from 307 kN to 238 kN, as shown in Figure 5.25. After excessive

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171

deflection of the beam (19.8 mm), the lower CFRP layers was completely debonded, as

shown in image 4 (P = 130 kN). An overall picture of beam B7 after failure is shown in

Figure 5.28(b).

5.3.4 Effect of CFRP force equivalence index


Figure 5.29 shows the load-deflection behaviour of beams B7 and B8, relative to control

specimens B1 and B2. Beams B7 and B8 were repaired by bonding SM-CFRP sheets on

both the lower and upper sides of the steel flange, and have force equivalence indices of

185 and 210 percent, respectively. Also, beams B3 and B4, repaired by bonding HM-

CFRP sheets on the lower side of the steel flange, had force equivalence indices of 87

and 152 percent, respectively, and their load-deflection responses are given in Figure

5.16. Table 5.2 shows that for both types of CFRP, beams with the smaller force

equivalence indices (i.e. B3 and B7) did not reach the ultimate strength of the intact beam

B1. The recorded strengths of B3 and B7 were only 166 and 306 kN, respectively. These

strengths, however, represent increases of 15 and 112 percent relative to the strength of

the damaged beam B2, for B3 and B7 respectively. On the other hand, beams with higher

force equivalence indices (i.e. B4 and B8) were able to reach the strength of the intact

beam B1, and even exceeded it by 10 and 16 percent, respectively. Figure 5.30 shows the

flexural strengths of the beams versus the force equivalence indices for the two types of

CFRP. The figure shows similar trends of strength increase by increasing the amount of

CFRP used (i.e. increasing the force equivalence index). It is also noted that as the elastic

modulus of the CFRP material increases, a smaller amount of material is needed to

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172

restore the strength. This is a result of the change in failure mode from debonding to

rupture. The figure also indicates that the optimum force equivalence indices that would

just recover the strength of the undamaged beam are 142 and 197 percent for the HM-

CFRP and SM-CFRP, respectively.


In both beams B3 and B4 with HM-CFRP, failure was due to rupture of CFRP as

discussed before. The failure mode of the beams repaired using SM-CFRP (i.e. B7 and

B8) was initiated by debonding of CFRP on the upper side of the flange. However, the

load continued to increase until crushing of concrete slabs occurred and the peak load

was reached. The load then dropped gradually until the CFRP on the lower side of the

flange debonded. The behaviour of beams B7 and B8 was significantly nonlinear, relative

to B3 and B4, which were quite linear elastic. Figure 5.31 shows a picture of beam B8

after failure.

5.3.5 Effect of bonded length of CFRP


The repair scheme used in beam B8 achieved the best results in terms of restoring both

the strength and stiffness, among the beams repaired using the SM-CFRP type C2.

Therefore, the same repair scheme of B8 was chosen to investigate the effect of varying

the bonded length of CFRP sheets. Beams B9, B10, and B11 were repaired with a similar

system of the same force equivalence index but of various lengths, 1000, 250, and 150

mm, respectively. It is clear that the bonded lengths of beams B10 and B11 fall inside the

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173

constant bending moment zone, which is 400 mm long. Figure 5.32 shows the load-

deflection responses of the beams. It clearly shows a consistent decrease in the flexural

capacity of the beams with shortening the bonded length of the CFRP sheets. As

discussed earlier, beam B8 with CFRP sheets bonded along almost the full span (1900

mm) achieved a 16 percent higher strength than the intact beam B1. Table 5.2 indicates

that beam B9, which is bonded with 1000 mm long CFRP sheets achieved a strength of

353 kN, which is almost equal to that of the intact beam B1. Beams B10 and B11 with

bonded lengths of 250 and 150 mm, respectively, failed at lower load levels before they

reach the strength of the intact beam B1. Table 5.2 shows that the flexural strengths of

B10 and B11 are 319 and 256 kN, respectively. The table also shows that the stiffness of

the intact beam B1 has been fully achieved in the case of B9, and very closely achieved

in B10 and B11, regardless of the short bond length. Figure 5.33 shows a summary of the

effect of bond length. The figure gives the variation of ultimate load achieved relative to

that of control beam B1 versus the bonded length of CFRP, normalized to the span

length. Figure 5.32 also shows the effect of the bonded length on the ductility of the

repaired beams. The deflection at ultimate and the length of the linear part of the curve

increase by increasing the bonded length of CFRP. The maximum loads attained by

beams B8 to B11 were achieved at mid-span deflections of 19, 16, 13, and 9 mm,

respectively.

Figure 5.34 to Figure 5.37 show the axial strain distributions at different locations along

the lower CFRP sheets of beams B8 to B11, respectively, at different load levels. The

figures show sudden changes in the trends at certain locations in beams B8 to B10, which

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174

indicate the initiation of CFRP debonding and the associated redistribution of stresses in

the CFRP sheets. The consistent pattern of strain distribution of beam B11 up to failure,

without signs of redistribution (Figure 5.37), indicates a complete and sudden debonding

of the CFRP sheets. The load versus the strain readings of gauge S0-5 for beams B8 to

B11 are plotted in Figure 5.38. The figure shows higher strain values in the CFRP sheets

of the repaired specimens, compared to the strain values of the steel flange of the control

intact beam B1. This is attributed to the lower elastic modulus of CFRP type C2 with

respect to the steel. The figure also shows that the maximum strain attained by the CFRP

sheets at mid-span, at debonding failure, varies among the beams of different bonded

lengths. A small jump in the strain values can be observed in the behaviour of the

repaired beams at a load level of about 50 kN. This jump is attributed to a minor slip

between the concrete slab and the steel beam. This slip was detected using a 25 mm

horizontal LP to measure the relative displacement between the concrete slab and the

steel beam in specimen B9, and was only about 0.15 mm at ultimate, as shown in Figure

5.39.

Figure 5.40 shows the variation of the maximum strain reached in the CFRP sheets with

the bonded length of CFRP. The figure clearly shows a bilinear behaviour. The first

linear part represents the effect of the CFRP bonded length within the constant moment

zone in absence of shear, whereas the second part represents the effect of the bonded

length within the shear span, in presence of both bending and shear. The first line can be

extended down to the origin (point “a”), which represents a hypothesized case without

CFRP sheets. If the line is also extended up, to the rupture strain of the CFRP sheets

Chapter 5

175

(point “b”), the optimum bonded length required for repair in a constant moment zone

can be estimated, which is 181 mm in this case. The second linear part of the curve

clearly has a shallower slope due to the presence of additional high shear stresses within

the shear span of the beam, which necessitate longer bonded length. By extending the

second line to point “c”, the sufficient bonded length required to achieve rupture of CFRP

can be obtained. Obviously it is longer than the span of the beams tested in this study.

Figure 5.41 to Figure 5.44 show the load versus the average shear stresses of beams B8 to

B11, respectively. The shear stresses were calculated based on Equation 5.1, at discrete

locations along the CFRP sheets on both sides of the mid-span. Unlike the strengthening

situation (Figure 5.6 and Figure 5.7), significantly higher shear stresses are developed

along the interface between the CFRP sheets and the steel substrate near the edge of the

terminated steel flange (i.e. mid-span), in the case of repair. Figure 5.41 to 5.44 show that

a typical shear stress curve reaches a peak value then reverses direction after the

maximum stress, which is about 25 MPa, is reached. It is believed that once this peak is

reached, local debonding occurs at this specific location. It is noted then that these peaks

(debonding) occur in a progressive manner, starting from mid-span and spreading

towards the ends. This behaviour agrees well with the bi-linear bond-slip model

developed by Xia and Teng (2005), and discussed earlier in Chapter 2. It is clear that

when enough bonded length is provided, debonding is usually initiated at mid-span

locations. For beam B11 with the shortest CFRP sheets (Lsheet = 150 mm), the shear

stresses near the ends of the sheets were higher than those near the mid-span, as shown in

Chapter 5

176

Figure 5.44. This behaviour indicates the inadequacy of the bonded length of the CFRP

sheets in B11.

5.3.5.2 Failure Modes

The failure mode of beams B9 and B10 was debonding of both the upper and lower

CFRP layers, which started at mid-span (i.e. from the edge of the cut steel flange). After

debonding of the CFRP sheets, a large drop in the load was clearly observed. Loading

was then continued until the concrete slab crushed, as indicated in Figure 5.32. In the

case of B11, debonding occurred in the lower CFRP layers as well as on one side of the

two upper CFRP layers. The lower CFRP layers were debonded from one end, while the

upper CFRP layers were completely separated. Also, the tests of beams B10 and B11

were immediately terminated after debonding occurred; therefore, concrete crushing of

those two particular specimens was not reached.

Chapter 5

177

Table 5.1 Summary of test results of Phase II.

Spec

imen

I.D

.

Tran

sfor

med

m

omen

t of i

nert

ia

x 10

6 (m

m4 )

%ag

e ga

in

Stiff

ness

(k

N./m

m.)

%ag

e ga

in

Yiel

d lo

ad

(kN

.)

%ag

e ga

in

Ulti

mat

e lo

ad

(kN

.)

%ag

e ga

in

G1a 8.55 -- 3.67 -- 85 -- 144 -- G2 9.59 12 4.29 17 97 14 216 50 G3 9.88 16 4.36 19 103 21 217 51

a Control (unstrengthened) girder

Table 5.2 Summary of test results of Phase III.

Spec

imen

I.D

.

Stiff

ness

(k

N/m

m)

%ag

e di

ffere

ncea

Max

imum

lo

ad (k

N)

%ag

e di

ffere

nce

B1 33.8 --- 357 ---B2 15.4 -54 144 -60B3 38.2 +13 166 -54B4 42.7 +26 394 +10B5 31.6 -7 179 -50B6 29.5 -14 311 -13B7 33.9 0 307 -14B8 33.3 -1 415 +16B9 34.5 +2 353 0B10 31.4 -7 319 -10B11 31.0 -8 256 -28

a %age difference is calculated with respect to beam

B1 (intact control beam).

Chapter 5

178

Figure 5.1 Load-deflection responses of specimens tested in Phase II.

Figure 5.2 Load-strain responses of the lower flange of the control specimen G1.

Strain x 10-3(mm/mm)

Load

(kN

)

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

S2

S1

Py = 85 kN.

S2 S150 mm


Load

(kN

)

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

S2

S1

Py = 85 kN.

S2 S150 mm

S2 S150 mm

Deflection (mm)

Load

(kN

)

0

25

50

75

100

125

150

175

200

225

0 20 40 60 80 100 120 140 160 180

G1 (Control)

failure

G2

G3

Concrete crushing

Debonding of outer layer

(1500 mm long)

P = 111 kN.

P = 129 kN.

P = 144 kN.

P = 217 kN. P = 216 kN.

Py = 85 kNLoad

δ5940 mm

Deflection (mm)

Load

(kN

)

0

25

50

75

100

125

150

175

200

225

0 20 40 60 80 100 120 140 160 180

G1 (Control)

failure

G2

G3

Concrete crushing


(1500 mm long)

P = 111 kN.

P = 129 kN.

P = 144 kN.

P = 217 kN. P = 216 kN.

Py = 85 kNLoad

δ5940 mm

Load

δ5940 mm

Chapter 5

179

Figure 5.3 Load-steel strain responses at the web of specimens tested in Phase II.

Figure 5.4 Load-strain responses along the CFRP plates of specimen G2 in Phase II.

0

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14 16


Load

(kN

)

G1 (Control)

G2

G3

50 m

m

Strain gauge

0

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14 160

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14 160

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14 16


Load

(kN

)

G1 (Control)

G2

G3

50 m

m

Strain gauge

50 m

m

Strain gauge

0

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14Strain x 10-3(mm/mm)

Load

(kN

)

0

100015001925

500675

(εc4

) ult

= 12

.6 x

10-

3

(cou

pons

) (εm

ax) ac

tual

= 13

x 1

0-3

Max

. stra

in re

ache

d in

the

oute

r CFR

P la

yer


P/2

1000

675

5000

1500

1925

mid-span

On

inne

r la

yer

On

oute

r la

yer

On

inne

r la

yer

0

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14Strain x 10-3(mm/mm)

Load

(kN

)

00

100010001500150019251925

500500675

675

(εc4

) ult

= 12

.6 x

10-

3

(cou

pons

) (εm

ax) ac

tual

= 13

x 1

0-3

Max

. stra

in re

ache

d in

the

oute

r CFR

P la

yer


P/2

1000

675

5000

1500

1925

mid-span

On

inne

r la

yer

On

oute

r la

yer

On

inne

r la

yer

P/2

1000

675

5000

1500

1925

mid-span

On

inne

r la

yer

On

oute

r la

yer

On

inne

r la

yer

Chapter 5

180

Figure 5.5 Load-strain responses along the CFRP plates of specimen G3 in Phase II.

Figure 5.6 Load-average shear stress responses along the CFRP plates of specimen G2 in Phase II.

0

25

50

75

100

125

150

175

200

225

0 2000 4000 6000 8000 10000 12000 14000Strain x 10-3(mm/mm)

0 2 4 6 8 10 12 14

Load

(kN

)

0

15001925

675

500and

P/2

1000

675

5000

1500

1925

mid-span

On

inne

r la

yer

On

oute

r la

yer


0

25

50

75

100

125

150

175

200

225

0 2000 4000 6000 8000 10000 12000 14000Strain x 10-3(mm/mm)

0 2 4 6 8 10 12 14

Load

(kN

)

0

15001925

675

500and

P/2

1000

675

5000

1500

1925

mid-span

On

inne

r la

yer

On

oute

r la

yer

0

25

50

75

100

125

150

175

200

225

0 2000 4000 6000 8000 10000 12000 14000Strain x 10-3(mm/mm)

0 2 4 6 8 10 12 14

Load

(kN

)

00

1500150019251925

675675

500500and

P/2

1000

675

5000

1500

1925

mid-span

On

inne

r la

yer

On

oute

r la

yer

P/2

1000

675

5000

1500

1925

mid-span

On

inne

r la

yer

On

oute

r la

yer


0

25

50

75

100

125

150

175

200

225

0 0.5 1 1.5 2 2.5

250

Ulti

mat

e sh

ear

stre

ngth

of a

dhes

ive

P/2

588

250

mid

-spa

n

588

Average shear stress (MPa)

Load

(kN

)

Debonding(P = 129 kN)

Adhesive yielding @( τ , P ) = ( 0.16 MPa , 96 kN)

0

25

50

75

100

125

150

175

200

225

0 0.5 1 1.5 2 2.5

250

250

Ulti

mat

e sh

ear

stre

ngth

of a

dhes

ive

P/2

588

250

mid

-spa

n P/2

588

250

mid

-spa

n

588


Load

(kN

)

Debonding(P = 129 kN)

Adhesive yielding @( τ , P ) = ( 0.16 MPa , 96 kN)

Chapter 5

181

Figure 5.7 Load-average shear stress responses along the CFRP plates of specimen G3 in Phase II.

Figure 5.8 Load-concrete strain responses of specimens tested in Phase II.

0

25

50

75

100

125

150

175

200

225

0 0.5 1 1.5 2 2.5

250 588


Load

(kN

) Debonding(P = 111 kN)

Adhesive yielding @( τ , P ) = ( 0.37 MPa, 83 kN)

Ulti

mat

e sh

ear

stre

ngth

of a

dhes

ive

P/2

588

250

mid

-spa

n

0

25

50

75

100

125

150

175

200

225

0 0.5 1 1.5 2 2.5

250250 588


Load

(kN

) Debonding(P = 111 kN)

Adhesive yielding @( τ , P ) = ( 0.37 MPa, 83 kN)

Ulti

mat

e sh

ear

stre

ngth

of a

dhes

ive

P/2

588

250

mid

-spa

n P/2

588

250

mid

-spa

n

0

25

50

75

100

125

150

175

200

225

-4 -3 -2 -1 0 1Strain x 10-3(mm/mm)

Load

(kN

)

G1 (PI 1)

G2 (PI 1)G3 (PI 1) G2(PI 2)

G3(PI 2)

G1 (PI 2)

PI1

PI2

0.90

d(y

ield

ed)

d

S1

Concrete crushing

0

25

50

75

100

125

150

175

200

225

-4 -3 -2 -1 0 1Strain x 10-3(mm/mm)

Load

(kN

)

G1 (PI 1)

G2 (PI 1)G3 (PI 1) G2(PI 2)

G3(PI 2)

G1 (PI 2)

PI1

PI2

PI1

PI2

0.90

d(y

ield

ed)

d

0.90

d(y

ield

ed)

d

S1

Concrete crushing

Chapter 5

182

Figure 5.9 Failure modes of girders in Phase II.

(a) Overall deflected profile of the control girder (G1) at failure

(b) Crushing of concrete slab of G1 (c) Typical debonding of the outer CFRP layer in G2 and G3

(d) Lateral torsional buckling of G2 and G3

(e) Unsymmetrical crushing of concrete slab of G2 and G3

Spreader beam

Mid-span

crossloading beam

Debonding

Rupture of GFRP end

wraps

Concrete crushing in

compressionConcrete crack in tension

Mid-span

Lateral deflection of the concrete slab

(a) Overall deflected profile of the control girder (G1) at failure

(b) Crushing of concrete slab of G1 (c) Typical debonding of the outer CFRP layer in G2 and G3

(d) Lateral torsional buckling of G2 and G3

(e) Unsymmetrical crushing of concrete slab of G2 and G3

Spreader beam

Mid-span

crossloading beam

Debonding

Rupture of GFRP end

wraps

Debonding

Rupture of GFRP end

wraps

Concrete crushing in

compressionConcrete crack in tension

Mid-span

Lateral deflection of the concrete slab

Chapter 5

183

Figure 5.10 Load-deflection responses of specimens B1 and B2 in Phase III.

Figure 5.11 Load-strain responses of the upper steel flanges of specimens B1 and B2 in Phase III.

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5 3 3.5Strain x 10-3 (mm/mm)

Load

(kN

)

B1

B2

S0-1

ε y=

1.9

x 10

-3

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5 3 3.5Strain x 10-3 (mm/mm)

Load

(kN

)

B1

B2

S0-1

ε y=

1.9

x 10

-3Deflection (mm)

Load

(kN

)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

B1 (intact)

B2 (damaged)

Concrete crushingP = 357 kN

Load

δ1960 mm

Py = 270 kN


Deflection (mm)

Load

(kN

)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

B1 (intact)

B2 (damaged)


Load

δ1960 mm

Load

δ1960 mm

Py = 270 kN


Chapter 5

184

Figure 5.12 Load-strain responses of the lower steel flanges of specimens B1 and B2 in Phase III.

Figure 5.13 Load-strain responses along the mid-span cross section of specimen B2 in Phase III.


Load

(kN

)

0

50

100

150

200

250

300

350

400

-2 0 2 4 6 8 10 12 14 16

B1 (mid-span)

B2

S 50-5 S 100-5

P/2

mid

-spa

n

S10

0-5

S 5

0-5

50 50

152

cut


Load

(kN

)

0

50

100

150

200

250

300

350

400

-2 0 2 4 6 8 10 12 14 16

B1 (mid-span)

B2

S 50-5 S 100-5

P/2

mid

-spa

n

S10

0-5

S 5

0-5

50 50

152

cutcut

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18 20


Load

(kN

)

S0-1

S0-2

S0-3

S0-4

ε y=

2x10

-3

S0-1

S0-2S0-3S0-4

303020

152

0

20

40

60

80

100

120

140

160

0 4 8 12

255075100

Load, kN

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18 20


Load

(kN

)

S0-1

S0-2

S0-3

S0-4

ε y=

2x10

-3

S0-1

S0-2S0-3S0-4

303020

152

0

20

40

60

80

100

120

140

160

0 4 8 12

255075100

Load, kN

Chapter 5

185

Figure 5.14 Load-strain responses at a distance of 20 mm and 80 mm above the underside of the lower flange of specimen B2.

Figure 5.15 Failure modes of specimens B1 and B2 in Phase III.

(a) Failure mode of B1 (b) Failure mode of B2

Concrete crushing

Mid-sp

an

Mid-span

concrete crack

width of opening

height of opening

= 67 mmConcrete crushing

Mid-sp

an

Mid-span

concrete crack

width of cut

Crack height = 67 mm

(a) Failure mode of B1 (b) Failure mode of B2

Concrete crushing

Mid-sp

an

Mid-span

concrete crack

width of opening

height of opening

= 67 mmConcrete crushing

Mid-sp

an

Mid-span

concrete crack

width of cut

Crack height = 67 mm

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18 20


Load

(kN

)

ε y=

2x10

-3S50-4

S100-4

S0-4

S0-2

S50-2

S100-2

mid

-spa

n

20S100-4S50-4S0-4

50 50

15260

S100-2S50-2S0-2

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18 20


Load

(kN

)

ε y=

2x10

-3S50-4

S100-4

S0-4

S0-2

S50-2

S100-2

mid

-spa

n

20S100-4S50-4S0-4

50 50

15260

S100-2S50-2S0-2

mid

-spa

n

20S100-4S50-4S0-4

50 50

15260

S100-2S50-2S0-2

Chapter 5

186



Deflection (mm)

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

B1

B2

B4(ω = 152%)

Load

δ1960 mm

Rupture of CFRP sheets


Concrete crushing Concrete

crushing

B3(ω = 87%)

Deflection (mm)

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

B1

B2

B4(ω = 152%)

Load

δ1960 mm

Load

δ1960 mm



Concrete crushing Concrete

crushing

B3(ω = 87%)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

Deflection (mm)

Load

(kN

)

B1

B2

B5 (ω = 198 %)(late application of CFRP)

B6(ω = 193 %)

Load

δ1960 mm

First debondingof CFRP sheets

Concrete crushing

complete debondingof CFRP sheets


progressive debonding

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

Deflection (mm)

Load

(kN

)

B1

B2

B5 (ω = 198 %)(late application of CFRP)

B6(ω = 193 %)

Load

δ1960 mm

Load

δ1960 mm

First debondingof CFRP sheets

Concrete crushing



progressive debonding

Chapter 5

187

Figure 5.18 Strain distributions along the CFRP sheets of specimen B3 in Phase III.


0

0.5

1

1.5

2

2.5

0 50 100 150 200 250

50

100

140

165

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

(εc3)ult = 2.21 x 10-3Load (kN)

Mid-span

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250

50

100

140

165

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

(εc3)ult = 2.21 x 10-3Load (kN)

Mid-span

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250

50 100 150

200 300 394

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

(εc3)ult = 2.27 x 10-3Load (kN)

Mid-span

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250

50 100 150

200 300 394

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

(εc3)ult = 2.27 x 10-3Load (kN)

Mid-span

Chapter 5

188



P/2mid

-spa

nG

0-5

0

1

2

3

4

5

6

7

8

9

10

11

0 50 100 150 200 250

50

100

150

179

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

(εc1)ult = 10.6 x 10-3

εmax = 3.6 x 10-3

Load (kN)

Mid-span

P/2mid

-spa

nG

0-5

P/2mid

-spa

nG

0-5

0

1

2

3

4

5

6

7

8

9

10

11

0 50 100 150 200 250

50

100

150

179

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

(εc1)ult = 10.6 x 10-3

εmax = 3.6 x 10-3

Load (kN)

Mid-span

0

1

2

3

4

5

6

7

8

9

10

11

0 50 100 150 200 250

50 100 150 200

250 300 311

Stra

in x

10-

3(m

m/m

m)

Distance (mm)

(εc2)ult = 10.9 x 10-3

Mid-span

Load (kN)

0

1

2

3

4

5

6

7

8

9

10

11

0 50 100 150 200 250

50 100 150 200

250 300 311

Stra

in x

10-

3(m

m/m

m)

Distance (mm)

(εc2)ult = 10.9 x 10-3

Mid-span

Load (kN)

Chapter 5

189

Figure 5.22 Load-strain responses of CFRP at mid-span of specimens B3, B4, and B6 in Phase III.

Figure 5.23 Load-strain responses of the upper steel flange at mid-span of specimens B3, B4, and B6 in Phase III.

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12 14 16

B1

B6

B3

B4


(εc3

) ult

= 2.

2 x

10-3

(εc2

) ult

= 10

.9 x

10-

3

εmax = 5.2 x 10-3

P/2mid

-spa

nS0

-5

Yield of steel flange

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12 14 16

B1

B6

B3

B4


(εc3

) ult

= 2.

2 x

10-3

(εc2

) ult

= 10

.9 x

10-

3

εmax = 5.2 x 10-3

P/2mid

-spa

nS0

-5

P/2mid

-spa

nS0

-5

Yield of steel flange

0

50

100

150

200

250

300

350

400

450

-0.5 0 0.5 1 1.5 2 2.5

Load

(kN

)

B1

B6

B3

B4


P/2mid

-spa

n

S0-1

B2

0

50

100

150

200

250

300

350

400

450

-0.5 0 0.5 1 1.5 2 2.5

Load

(kN

)

B1

B6

B3

B4


P/2mid

-spa

n

S0-1

P/2mid

-spa

n

S0-1

B2

Chapter 5

190

Figure 5.24 Failure modes of specimens B3 to B6 in Phase III.

(a) Typical failure mode of B3 and B4 (b) Downside view of CFRP rupture in B3

(e) Downside view of CFRP debonding in B6

(d) Failure mode of B6

wid

th o

f CFR

P s

heet

s

Lower flange

Concrete slab

Rupture of CFRP sheets @ mid-span


fracture of steel web

Width of the flange crack

Debonding within the shear span

Loading beams

CFRP sheetsGFRP sheet

Debonded area(discoloration)

(c) Failure mode of B5

Debondedsheets

(a) Typical failure mode of B3 and B4 (b) Downside view of CFRP rupture in B3

(e) Downside view of CFRP debonding in B6

(d) Failure mode of B6

wid

th o

f CFR

P s

heet

s

Lower flange

Concrete slab

Rupture of CFRP sheets @ mid-span


fracture of steel web

Width of the flange crack

Debonding within the shear span

Loading beams

CFRP sheetsGFRP sheet

Debonded area(discoloration)

(c) Failure mode of B5

Debondedsheets

Chapter 5

191


Figure 5.26 Strain distributions along the lower CFRP sheets of specimen B7 in Phase III.

Stra

in x

10-

3(m

m/m

m)

Distance (mm)

0

1

2

3

4

5

6

7

8

9

10

11

-150 -100 -50 0 50 100 150 200 250

50

100

150

200

250

307

(εc2)ult = 10.9 x 10-3

Mid-spanLoad (kN)

Stra

in x

10-

3(m

m/m

m)

Distance (mm)

0

1

2

3

4

5

6

7

8

9

10

11

-150 -100 -50 0 50 100 150 200 250

50

100

150

200

250

307

(εc2)ult = 10.9 x 10-3

Mid-spanLoad (kN)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35Deflection (mm)

Load

(kN

)B1

B2

B7 (ω = 185 %)(two sides)

B6 (ω = 193 %)(one side)

Load

δ1960 mm

Concrete crushing

Debonding of lower CFRP

Debondingof CFRP

Debonding of upper CFRP

CFRP

CFRPSteel

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35Deflection (mm)

Load

(kN

)B1

B2

B7 (ω = 185 %)(two sides)

B6 (ω = 193 %)(one side)

Load

δ1960 mm

Load

δ1960 mm

Concrete crushing


Debondingof CFRP


CFRP

CFRPSteelCFRP

CFRPSteel

Chapter 5

192

Figure 5.27 Strain distributions along the upper CFRP sheets of specimen B7 in Phase III.

Stra

in x

10-

3(m

m/m

m)

Distance (mm)

0

1

2

3

4

5

6

7

8

9

10

11

-150 -100 -50 0 50 100 150 200 250

50

100

150

200

250

307

(εc2)ult = 10.9 x 10-3

Mid-span

Load (kN)

Stra

in x

10-

3(m

m/m

m)

Distance (mm)

0

1

2

3

4

5

6

7

8

9

10

11

-150 -100 -50 0 50 100 150 200 250

50

100

150

200

250

307

(εc2)ult = 10.9 x 10-3

Mid-span

Load (kN)

Chapter 5

193

Figure 5.28 Failure mode of specimen B7 in Phase III.

Upper CFRP layers

Lower CFRP layers

(b) Overall picture of B7 after failure

Mid-span cut

Stiffener angle

Crack opening

(1) P = 0 (2) P = 180 kN

(3) P = 300 kN

propagation of crack in the web

complete debonding

Debonding of lower layers

(a) step-by-step failure of B7

concrete cracking

Initiation of debonding

Crack height

(4) P = 130 kN(descending)

Upper CFRP layers

Lower CFRP layers

(b) Overall picture of B7 after failure

Mid-span cut

Stiffener angle

Crack opening

(1) P = 0 (2) P = 180 kN

(3) P = 300 kN

propagation of crack in the web

complete debonding

Debonding of lower layers

(a) step-by-step failure of B7

concrete cracking

Initiation of debonding

Crack height

(4) P = 130 kN(descending)

Chapter 5

194


Figure 5.30 Effect of force equivalence index (ω) on the strength of the repaired beams.

Deflection (mm)

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

B1

B2

B7(ω = 185 %)

Load

δ1960 mm

Concrete crushing



B8(ω = 210 %)

Deflection (mm)

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

B1

B2

B7(ω = 185 %)

Load

δ1960 mm

Load

δ1960 mm

Concrete crushing



B8(ω = 210 %)

Force equivalence index, ω (%)

Ulti

mat

e lo

ad ra

tio re

lativ

e to

con

trol b

eam

B1

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

50 70 90 110 130 150 170 190 210 230

E c2=

90 G

Pa

E c3=

230 G

Pa

Damaged beam (B2)

Intact beam (B1)

B3

B4

B7

B8

ω=

142

%

ω=

197

%

ω = x 100Af x Ff

Aflange x Fy

Force equivalence index, ω (%)

Ulti

mat

e lo

ad ra

tio re

lativ

e to

con

trol b

eam

B1

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

50 70 90 110 130 150 170 190 210 230

E c2=

90 G

Pa

E c3=

230 G

Pa

Damaged beam (B2)

Intact beam (B1)

B3

B4

B7

B8

ω=

142

%

ω=

197

%

ω = x 100Af x Ff

Aflange x Fy

ω = x 100Af x Ff

Aflange x Fy

ω = x 100Af x Ff

Aflange x Fy

Chapter 5

195

Figure 5.31 Failure mode of specimen B8.

Figure 5.32 Load-deflection responses of specimens B8 to B11 in Phase III.

Debonding of the upper

CFRP layers support

Concrete slab

Debonding of the upper

CFRP layers support

Concrete slab

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

Deflection (mm)

B1

B2

B8 (Lsheets = 1900mm)

Concrete crushingB9 (Lsheets = 1000mm)


B11(Lsheets = 150mm)

P = 353 kN

P = 319 kN

P = 256 kN

P = 415 kN

Deb

ondi

ng

ω = 210 %

Load

δ1960 mm

Load

(kN

)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35

Deflection (mm)

B1

B2


Concrete crushingB9 (Lsheets = 1000mm)


B11(Lsheets = 150mm)

P = 353 kN

P = 319 kN

P = 256 kN

P = 415 kN

Deb

ondi

ng

ω = 210 %

Load

δ1960 mm

Load

δ1960 mm

Chapter 5

196

Figure 5.33 Effect of bonded length of CFRP on ultimate load.


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

B8

B9B10

B11

B1

B2

Lsheet / Span

Ulti

mat

e lo

ad ra

tio re

lativ

e to

B1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

B8

B9B10

B11

B1

B2

Lsheet / Span

Ulti

mat

e lo

ad ra

tio re

lativ

e to

B1

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50

100

150

200

250

300

350

415

10

9

8

7

6

5

4

3

2

1

0

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

Mid-span

Load (kN)

Load

1900 mm1960 mm

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50

100

150

200

250

300

350

415

10

9

8

7

6

5

4

3

2

1

0

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

Mid-span

Load (kN)

Load

1900 mm1960 mm

Load

1900 mm1960 mm

Chapter 5

197



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50100150200250300353

10

9

8

7

6

5

4

3

2

1

0

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

Mid-spanLoad

1000 mm1960 mm

Load (kN)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50100150200250300353

10

9

8

7

6

5

4

3

2

1

0

Distance (mm)

Stra

in x

10-

3(m

m/m

m)

Mid-spanLoad

1000 mm1960 mm

Load (kN)

Distance (mm)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50

100

150

200

250

320

10

9

8

7

6

5

4

3

2

1

0

Stra

in x

10-

3(m

m/m

m)

Mid-span

Load

250 mm1960 mm

Load (kN)

Distance (mm)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50

100

150

200

250

320

10

9

8

7

6

5

4

3

2

1

0

Stra

in x

10-

3(m

m/m

m)

Mid-span

Load

250 mm1960 mm

Load

250 mm1960 mm

Load (kN)

Chapter 5

198


Figure 5.38 Load-strain responses of CFRP at mid-span of specimens B8 to B11 in Phase III.

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12 14 16


Load

(kN

)

(εc2

) ult

= 10

.9 x

10-

3

B1

B8

B9B10

B11

P/2mid

-spa

nS

0-5

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12 14 16


Load

(kN

)

(εc2

) ult

= 10

.9 x

10-

3

B1

B8

B9B10

B11

P/2mid

-spa

nS

0-5

P/2mid

-spa

nS

0-5

Distance (mm)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50

100

200

256

10

9

8

7

6

5

4

3

2

1

0

Stra

in x

10-

3(m

m/m

m)

Mid-spanLoad

150 mm1960 mm

Load (kN)

Distance (mm)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

-350 -250 -150 -50 50 150 250 350

50

100

200

256

10

9

8

7

6

5

4

3

2

1

0

Stra

in x

10-

3(m

m/m

m)

Mid-spanLoad

150 mm1960 mm

Load

150 mm1960 mm

Load (kN)

Chapter 5

199

Figure 5.39 Load versus slip of concrete slab of specimen B9 in Phase III.

Figure 5.40 Maximum strains versus the bonded length of the CFRP sheets.

0

50

100

150

200

250

300

350

400

0 0.05 0.1 0.15 0.2 0.25

Slip (mm)

Load

(kN

)

LP

LP

50 kN

0

50

100

150

200

250

300

350

400

0 0.05 0.1 0.15 0.2 0.25

Slip (mm)

Load

(kN

)

LP

LP

50 kN

Max

imum

stra

in x

10-

3(m

m/m

m)

Distance from mid-span (mm)

0

2

4

6

8

10

12

0 200 400 600 800 1000 1200 1400

(εc2)ult = 10.9 x 10-3

Mid

-spa

n

181 mm

B11

B10 B9

B8

ω = 210 %

a

b

1175 mm

Combined moment and shear zone

Constant moment zone

Max

imum

stra

in x

10-

3(m

m/m

m)

Distance from mid-span (mm)

0

2

4

6

8

10

12

0 200 400 600 800 1000 1200 1400

(εc2)ult = 10.9 x 10-3

Mid

-spa

n

181 mm

B11

B10 B9

B8

ω = 210 %

a

b

1175 mm

Combined moment and shear zone

Constant moment zone

Chapter 5

200

Figure 5.41 Load-average shear stress responses along the lower CFRP sheets of specimen B8 in Phase III.



Load

(kN

)

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30

12.5

-50

-100

-175-275

50100

175

275 475

-12.5


Load

(kN

)

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30

12.512.5

-50-50

-100-100

-175-175-275-275

5050100100

175175

275275 475475

-12.5-12.5

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30


Load

(kN

)

12.550

175

100

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30


Load

(kN

)

12.512.55050

175175

100100

Chapter 5

201




Load

(kN

)

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30

-12.5

-50

-9595

50

12.5


Load

(kN

)

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30

-12.5

-50

-9595

50

12.5


Load

(kN

)

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30

-12.5-12.5

-50-50

-95-959595

5050

12.512.5

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30


Load

(kN

)

12.5

50

-12.5-50

0

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30


Load

(kN

)

12.512.5

5050

-12.5-12.5-50-50

Chapter 6

202

Chapter 6

Analytical and Numerical Modeling of CFRP-Strengthened HSS Slender Columns1 6.1 Introduction

This chapter presents analytical and numerical models developed to predict the behaviour

and strength of concentrically loaded HSS slender steel columns strengthened using

bonded CFRP reinforcement oriented in the longitudinal direction.

The first model is an analytical fibre model based on the concepts of strain compatibility

and force equilibrium (Shaat and Fam, 2007a). The second model is an alternative

numerical non-linear finite element model (FEM) (Shaat and Fam, 2007b). Both models

were verified using experimental results.

1 Most of contents of this chapter have been published as follows: i. Shaat, A. and Fam, A. (2007a) “Fiber-Element Model for Slender HSS Columns Retrofitted with

Bonded High Modulus Composites.” Journal of Structural Engineering, ASCE, 133(1):85-95. ii. Shaat, A. and Fam, A. (2007b) “Finite Element Analysis of Slender HSS Columns Strengthened with

High Modulus Composites.” Steel & Composite Structures, 7(1):19-34.

Chapter 6

203

As discussed in chapter 4, the variation of out-of-straightness imperfection among test

specimens 7 to 11, of different CFRP reinforcement ratios have resulted in gains in the

axial strength that do not correlate to the reinforcement ratios. This led to difficulties in

assessing the effect of CFRP reinforcement ratio experimentally. As such, the models

presented in this chapter are quite useful, and in fact essential, to uncouple the two

effects, namely, the out-of-straightness imperfection and the CFRP reinforcement ratio. A

parametric study is also performed to examine columns of different slenderness ratios,

different out-of-straightness imperfections, different CFRP reinforcement ratios, and

different levels of residual stresses.

6.2 Fibre Model (Model 1)

In order to predict the load versus axial and lateral displacement responses of CFRP-

strengthened slender HSS steel columns, a non-linear fibre model has been developed.

The model accounts for both material and geometric (second order effects) non-linearities

as well as residual stresses. An incremental approach is used, where the concepts of force

equilibrium and strain compatibility are satisfied at each loading step. The stress-strain

curve of steel is assumed to follow an elastic-perfectly plastic model. FRP materials are

assumed to behave linearly up to failure. The numerical procedure is executed using

spread sheet-type programming. Sections 6.2.1 to 6.2.6 provide a detailed description of

different components of the model, whereas section 6.2.7 provides the procedures of

using the model in an organized set of steps.

Chapter 6

204

6.2.1 Residual stresses in HSS sections

In the proposed fibre model, the through-thickness residual stress distribution is idealized

as shown previously in the schematic drawing in Figure 2.1, which is suggested by

Davison and Birkemoe (1983) and by Chan et al. (1991). The residual stress, Frs is

obtained from the compression tests conducted on the stub-columns, as discussed in

chapter 3 and shown in Figure 3.3. The values of Frs are equal to 0.49 Fy and 0.33 Fy for

HSS1 and HSS2 sections, respectively. The effect of varying the level of residual stresses

is investigated later in the parametric study.

In order to generate the full load-displacement responses, the residual stress pattern

across the wall thickness was first defined by dividing the steel wall into three equal

layers, as shown in Figure 6.1. A uniform compressive stress value of (-Frs) was assigned

to the inner layer, while a tensile value of (+Frs) was assigned to the outer layer. The

middle layer was divided into two equal halves. The inner half was assigned a uniform

value of (-0.5 Frs), while the outer half was assigned a uniform value of (+0.5 Frs). This

distribution was used to simulate the prescribed residual stress pattern shown in Figure

2.1. It should be noted that the second type of residual stresses, namely, the perimeter

(membrane) residual stresses was not considered in the analysis since it was deemed

insignificant, relative to the through-thickness type (Davison and Birkemoe, 1983).

6.2.2 Meshing system

An element-by-element approach is adopted to integrate stresses over the cross sectional

areas of steel and FRP. The cross section is divided into four areas (A1 to A4), as shown

Chapter 6

205

in Figure 6.1. The flat part of the flanges oriented normal to the plane of buckling (A1) is

divided into 12 strips through the thickness, where the strain is assumed constant across

the width and thickness of each strip. The flat part of the flanges parallel to the plane of

buckling (A2) is divided into 12 x 80 elements to capture the strain gradient across the

depth of the section and also to capture the residual stress distribution within the

thickness. The corner section (A3) is idealized as a square and is divided into 12 x 12

elements. Area A4 represents the FRP layers attached to area A1, and is divided into 1 x

n elements, where n is the total number of FRP layers. To model specimens with FRP

material bonded on four sides, an additional area of FRP (A5) attached to area A2, is also

considered. The centroid of each element is located at its mid thickness and the stress is

assumed constant within the element area. Linear strain distribution and strain

compatibility (i.e. full bond between steel and FRP) are also assumed in the analysis.

6.2.3 Force equilibrium and moments

Figure 6.2 shows a cross-section at mid-height of a slender column. Due to overall

buckling, the axial force P is offset relative to the effective centroid of the mid-height

section by eccentricity e. For a given strain gradient induced by the eccentric load P, and

based on a strain level ε at the extreme compression side, and a neutral axis depth c, the

strain εi in each steel or FRP element i, located at a distance yi from the effective centroid

of the cross section, can be determined as follows:

εε ⎥⎦

⎤⎢⎣

⎡−−=

cy

cy ci

i 1 (6.1)

where yc is the distance between the extreme fibre in compression and the effective

centroid of the cross section, as shown in Figure 6.2. It should be noted that before

Chapter 6

206

yielding of steel or crushing of FRP, yc = h/2, where h is the depth of the section. The

effective centroid only shifts when parts of the section yield in an unsymmetrical manner,

due to the strain gradient. The stress in steel elements Fsi is then calculated as Fsi = Es εi,

where Es is Young’s modulus of steel, and is added to the residual stress Frs to obtain the

total stress Fsi + rs for every steel element, as given by Equation 6.2. The total stress Fsi + rs

is used to check whether the element has yielded or not. The effect of yielded elements is

accounted for as will be discussed in section 6.2.4.1.

rssirssi FFF +=+ (6.2)

Possible stress distributions at various stages of loading are shown in Figure 6.2. The

total axial load P at a given stage of loading (i.e. for a given ε and c) can be obtained by

numerical integration of stresses over the cross section, for both the yielded and elastic

steel elements as well as for the FRP elements, based on a linear stress-strain response, as

follows:

( ) ( ) ( )∑+∑+∑=FRP iffi

steelplastic isysteelelastic issi AEAFAFP ε (6.3)

and the corresponding moment M is:

( ) ( ) ( )∑+∑+∑=FRP

iiffisteelplastic

iisysteelelastic

iissi yAEyAFyAFM ε (6.4)

where isA and ifA are the areas of steel and FRP elements, respectively, Ef is Young’s

modulus of the FRP element, and yi is the distance between the element i and effective

centroid.

Chapter 6

207

6.2.4 Lateral displacement

Figure 6.3(a) shows a prismatic elastic pin-ended slender column, which is slightly

curved initially due to an out-of-straightness of amplitude e’ at mid-height. At any height

z, measured from the bottom, the lateral displacement due to out-of-straightness, before

loading, is wo. As the column is loaded, it deflects further and the additional lateral

deflection at mid-height is δ, while the total lateral deflection at any height z is w. An

expression can then be derived for the net lateral deflection d at mid-height under axial

load P, following the procedure suggested by Allen and Bulson (1980). The bending

moment in the loaded column at any height z is M = Pw. The bending moment is also

proportional to the change in curvature:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

oRREIM 11 (6.5)

where R and Ro are the radii of curvature for the loaded and unloaded columns,

respectively, and are defined by the following equations,

2

2

2

2 1,1dz

wdRdz

wdR

o

o−=−= (6.6)

Eliminating M from Equation 6.5 results in the following differential equation:

2

22

2

2

dzwd

wdz

wd o=+ µ where EIP

=2µ (6.7)

For any imperfect shape of the unloaded column, the column’s profile can be represented

by a Fourier series as follows,

∑∞

=⎥⎦

⎤⎢⎣

⎡=

1

sini

io Lzi

awπ

(6.8)

Chapter 6

208

where L is the length of column. The amplitudes ia are known or can be measured.

Similarly, the displacements of the loaded column can be written as follows,

∑∞

=⎥⎦

⎤⎢⎣

⎡=

1

sini

iL

ziaw

π (6.9)

in which the amplitudes ia are to be found. Substitution for wo and w from Equations 6.8

and 6.9 in Equation 6.7 gives,

∑∑∑∞

=

∞

=

∞

= ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎥

⎦

⎤⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

12

22

1

2

12

22sinsinsin

ii

ii

ii

Lzi

Lia

Lzi

aL

ziL

iaπππ

µππ (6.10)

The ith term is obtained by omitting the summation signs:

Lzi

Lia

Lzi

aL

ziL

ia iiiπππ

µππ sinsinsin

2

222

2

22

⎟⎟⎠

⎞⎜⎜⎝

⎛−=+⎟⎟

⎠

⎞⎜⎜⎝

⎛− (6.11)

If the previous equation is satisfied for all values of i, then Equation 6.10 is automatically

satisfied. Equation 6.11 can also be reduced to,

( )22221 πµ iL

aa i

i−

= , or ( )i

ii PP

aa

−=

1 where

2

22

LEIiPi

π= (6.12)

The effect of the load P is to increase the amplitude of the ith term of the original Fourier

series by an amplification factor, ( )[ ]iPP−1/1 , which becomes infinitely large as P

approaches Pi. Provided that the shape of the unloaded column is known and can be

broken down into its Fourier components ( ia ), then the Fourier components for the

loaded column ( ia ) can be found from Equation 6.12 and the total deformation of the

loaded column can be found from Equation 6.9. Assuming that the load is increased

Chapter 6

209

steadily from zero, as it approaches the first critical load (P1 or Pcr), the amplitude of the

first mode becomes very large, larger than all the other amplitudes, which can be

neglected in consequence, as an acceptable approximation. This means that for loads

close to Euler buckling load, the lateral deflection at any point along the column’s axis

can be written as:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=L

zPP

aw

cr

πsin

11 (6.13)

Due to the approximation stated above, Equation 6.13 provides acceptable deflections up

to 10Lw ≤ , as reported by Allen and Bulson (1980).

At mid-height (i.e. z = L/2) the total lateral deflection w takes the following form:

( )crPPew

−=

1' (6.14)

where e' is the imperfection at mid-height. The net lateral displacement at mid-height δ is

then defined as 'ew −=δ , as shown in Figure 6.3(a).

An expression that relates the net lateral displacement δ at mid-height of the column to

the applied load P can then be written as follows:

( ) ⎥⎦

⎤⎢⎣

⎡−

−= 1

11'

crPPeδ (6.15)

where Pcr is the Euler buckling load and is given by:

( )2

2

kLEIPcr

π= (6.16)

Chapter 6

210

where EI is the flexural rigidity of a prismatic member, function of Young’s modulus E

and moment of inertia I of the column’s cross section. It should be noted that the

effective length factor k in Equation 6.16, which accounts for the column’s boundary

conditions, is taken as unity for the case of pin-ended columns.

It is important to note that Equations 6.15 and 6.16 assume linear elastic behaviour of the

material and that the residual stresses and the bonded FRP are not accounted for in these

expressions. In the following sections, methods are proposed to account for residual

stresses, material non-linearity due to yielding, and the contribution of FRP.

6.2.4.1 Effective moment of inertia (Ieff)

6.2.4.1.1 Bare steel column

In order to account for gradual yielding of different parts of the cross section under the

applied loads, which are essentially the axial load and the associated bending moment

induced from the P-δ effect, the concept of “effective moment of inertia” is incorporated

in this analysis (Salmon and Johnson, 1980). The location of the effective centroid of the

section is first determined, using the first moment of areas after discounting the yielded

elements. The contribution of a steel element of area isA , at a distance yi from the

effective centroid of the cross section (Figure 6.2), to the flexural rigidity ( )isEI is the

product of the tangent modulus and the element’s moment of inertia, as follows:

( ) 2iistis yAEEI = (6.17)

where Et is the tangent modulus of steel. If the idealized elastic-plastic stress-strain curve

with Young’s modulus Es is used, then: for |Fsi + rs| < Fy, Et = Es and for |Fsi + rs| ≥ Fy , Et =

Chapter 6

211

0. This indicates that the flexural rigidity of the yielded parts becomes zero. Therefore,

the stress level in each steel element must be checked for yielding at each load level to

determine whether the area of the element will be included in the effective bending

stiffness or not. Consequently, the effective bending stiffness ( )effsEI of the entire steel

section takes the following form:

( ) ( )∑=steelelastic

iisseffs yAEEI 2. (6.18)

The effective moment of inertia effsI for the section can then be introduced in terms of

the elastic parts only, as follows:

( )∑=steelelastic

iiseffs yAI 2 (6.19)

First yielding will typically occur at the inner side of the buckled column, at mid-height.

As the axial load and corresponding lateral deflection increase, yielding spreads within

the cross-section and also in the longitudinal direction of the column, as shown in Figure

6.4(a). The spreading of yielding indicates that the effective moment of inertia effsI

varies from one section to the other within the yielded length and also varies with the

applied load. The length of the partially yielded part of the column in the middle zone

depends on many factors, including the slenderness ratio, out-of-straightness profile, and

level of residual stresses. In the current model, an average value of 0.40 L for the length

of the partially yielded portion of the column is assumed. This assumption is made based

on the results of an independent nonlinear finite element analysis (Model 2) for columns

of kL/r = 68, e’ = L/500 to L/2000, and Frs = 0.33 Fy.

Chapter 6

212

It has been established that the effective moment of inertia of the section varies along the

length as a result of yielding, in spite of the prismatic geometry of the section. Therefore,

a more general expression for the Euler buckling load is needed in lieu of the

conventional Equation 6.16, which assumes a column of a constant moment of inertia. In

order to account for the variable cross sectional inertia along the length of the column, the

finite-difference method is used (Ghali and Neville, 1989), where the column is divided

into a number of segments of equal length ∆L, as shown in Figure 6.4(a), and the

equivalent concentrated elastic loads at each of the m internal nodes can be obtained. The

variation of moment of inertia of the steel section within the middle partially yielded zone

(0.4L) is assumed to follow a parabolic curve with minimum and maximum values

ofeffsI and

gsI , respectively, wheregsI is the gross moment of inertia of the steel

section. A series of simultaneous equations representing the elastic load at each node of

the internal m nodes are then written in the following matrix form:

[ ] [ ] [ ] 11 12 xmmxmmxmcr

xmmxm CBLP

A δ∆

δ = (6.20)

where [ ] [ ] [ ]CBA ,, , and ∆L are defined as follows:

[ ]

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−−−

−−−

=

21121

.........121

12

1L

A∆

, [ ]

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

1011101

.........1101

110

B ,

[ ]

( )( )

( )⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

mEI

EIEI

C

1...

11

2

1

, and 1+

=m

LL∆ (6.21)

Chapter 6

213

Multiplying both sides of Equation 6.20 by [A]-1, we obtain

δγδ =][ H (6.22)

where [ ] [ ] [ ] [ ]CBAH 1−= (6.23)

and LPcr ∆

γ 12= (6.24)

The solution of Equation 6.22 is an eigenvalue problem. An iterative procedure can be

used to satisfy Equation 6.22, by assuming a reasonable eigenvector δ in the left-hand

side and comparing both sides until the equation is satisfied. As a starting point, the

eigenvector δ was assumed to follow a second degree parabola with its apex at the

column’s mid-height. The buckling load Pcr can then be calculated from the largest

eigenvalue γ, using Equation 6.24.

6.2.4.1.2 FRP-strengthened steel column

For HSS sections with FRP layers, the transformed effective moment of inertia

efftI should be used in lieu ofeffsI within the middle 0.4L zone and the transformed

gross moment of inertia gtI should be used in lieu of

gsI outside the 0.4L zone. efftI is

calculated using the following equation:

∑⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

FRPif

s

if

effsefft IE

EII (6.25)

Chapter 6

214

where ( )2iifif yAI = . Ifi, Efi and Afi are the moment of inertia, Young’s modulus, and

the area of intact FRP element i, respectively. gtI is calculated using the following

Equation:

∑ ⎥⎦

⎤⎢⎣

⎡+=

FRPf

s

fgst i

i

gI

EE

II (6.26)

The lateral displacement of the column can now be calculated at any point along the

length of the column, at any load level, using Equation 6.13.

In order to establish the appropriate number of segments for the finite difference method,

a convergence study was carried out using 1, 5, 10, 15, and 20 segments along the entire

length L of one of the experimentally tested columns, specimen 9, and the full load-lateral

displacement response was predicted for each case. Details of the full procedure of

prediction are given later. It should be noted that treating the column as one segment can

be considered as a lower bound solution, as it assumes a constant cross sectional moment

of inertia ( efftI ) along the entire length of the column. Figure 6.4(b) shows the predicted

full load-lateral displacement responses, based on different number of segments, versus

the experimental response. Figure 6.4(c) shows the variation of the peak load with

number of segments. The figures show that convergence occurred when using 15 or more

segments as a very similar behaviour was observed when using 15 and 20 segments,

which also showed good agreement with the experimental response. As such, it was

decided to use 15 segments in the rest of the study.

Chapter 6

215

6.2.5 Axial displacement

The axial displacement ∆ is the sum of two components, referred to as ∆a and ∆b, as

shown in Figure 6.3(b):

ba ∆∆∆ += (6.27)

where ∆a and ∆b are the displacements due to axial shortening and curvature from the P-δ

effect, respectively, and can be approximated as follows:

tsa AE

PL=∆ (6.28)

where At is the transformed cross sectional area and is calculated as follows:

∑ ⎥⎦

⎤⎢⎣

⎡+=

FRPf

s

fst i

i AEE

AA (6.29)

where, As is the cross sectional area of the HSS section, and

SL ab −−= ∆∆ (6.30)

where S is the chord length of the deformed column [Figure 6.3(b)]. ∆b is calculated

based on a sine curve of an arc length (L-∆a) and amplitude (δ +e’), using the following

equation:

∫ +=−S

a dzwL0

2'1∆ (6.31)

where w’ is the first derivative of the lateral displacement function w(z) given by

Equation 6.13. Since the integration limit S is unknown, Equation 6.31 was solved

numerically by trial and error to get the chord length S.

Chapter 6

216

In order to illustrate and verify this simplified approach, the load axial displacement

response of the control specimen is predicted based on the superposition of the

components ∆a and ∆b, as shown in Figure 6.5. The figure shows that the contribution of

the ‘curvature’ component ∆b is only significant near and after the peak load, when

overall buckling occurs, whereas the axial shortening component ∆a is dominant before

excessive buckling.

6.2.6 Failure criteria

In the proposed fibre model, the strain values in the steel cross section are incrementally

increased, until the section reaches its full plastic capacity in the case of bare steel

column, as shown in Figure 6.2. Elements with compressive residual stresses would

typically yield before elements with tensile residual stresses. Eventually, all elements

yield and the effective moment of inertia of the steel cross section becomes zero, based

on Equation 6.19. Consequently, a value for the lateral displacement δ can no longer be

obtained using Equation 6.15 and the analysis is terminated.

For steel columns with bonded FRP material, a complex failure criterion involving

localized debonding associated with local buckling and crushing after the occurrence of

overall buckling was observed experimentally. When an adequate bonded length of

CFRP is provided (i.e. in columns that are sufficiently long), crushing of CFRP becomes

the dominant failure mode. In the experimental phase of the current study, crushing of

CFRP without debonding was observed in the case of column sets 6 (CFRP plates of type

C5) at an average strain of 0.274 percent. Debonding without crushing occurred in

Chapter 6

217

relatively shorter column sets 2 and 4 (CFRP plates of type C5) at average strains of

0.161 and 0.226 percent, respectively. Debonding associated with crushing occurred in

column sets 8 to 11(CFRP sheets of type C3) at an average strain of 0.133 percent, which

was actually independent of the number of layers. It is noted that for CFRP plates the

scatter in failure strain values increases as slenderness ratio gets higher. This may be

attributed to the larger bending associated with the axial loads in larger slenderness ratios,

which introduces a larger strain gradient through the thickness of CFRP plates. The

ultimate tensile strains (εult), based on tension coupon tests, of the two CFRP types C3

and C5 are 2.22 and 4.72 percent, respectively. The compressive strains of CFRP at

failure (εf cu), in the cases of either crushing or debonding, have been normalized with

respect to their respective ultimate tensile strains, and plotted versus slenderness ratio in

Figure 6.6. A simplified bi-linear regression is established with a transition between

debonding and crushing of CFRP occurring at a slenderness ratio of 76. The following

expressions may be used to calculate the compressive strain of CFRP at failure (εf cu), as a

function of kL/r:

76590

761087 3

>=⎟⎟⎠

⎞⎜⎜⎝

⎛

≤=⎟⎟⎠

⎞

⎜⎜⎝

⎛ −

rkLfor.

rkLfor

rkLx.

tuf

cuf

tuf

cuf

ε

ε

ε

ε

(6.32)

It is noted that these limiting strain expressions based on Figure 6.6 have been established

based on relatively few data points and two different types of CFRP. Further research

may be needed to enhance the database in Figure 6.6 and to examine the applicability of

these expressions to other types of CFRP or when CFRP is bonded to HSS sections of

Chapter 6

218

different (b/t) ratios, where secondary local buckling may or may not occur after overall

buckling.

Once CFRP fails in compression, it is eliminated from the cross section at mid-height

(i.e. discontinuity is introduced in CFRP) at all the subsequent steps of analysis. A

sudden drop in the effective moment of inertia (efftI ) is consequently introduced at this

cross section. A gradual change in the values of the effective moment of inertia,

following a second degree polynomial, is then defined with a value of the reduced efftI at

mid-height and a value of gtI at both ends of the 0.4L middle zone. This is particularly

accurate in case of local crushing, whereas in case of debonding, the CFRP should have

been completely removed along the entire height of the column. This is ignored in this

model, since the presence of CFRP outside the middle zone is likely to provide

insignificant contribution.

After excessive overall buckling, FRP on the outer surface could be subjected to some

tensile strains, which are well below the ultimate tensile strain values.

6.2.7 Generation of full load-displacement responses

In order to obtain the full load-lateral displacement (P-δ) response, the procedure of using

the model can be summarized as follows:

1. Assume a value of the extreme compressive strain ε and a neutral axis depth c (Figure

6.2). The full strain gradient across the section at mid-height is then defined.

Chapter 6

219

2. For each steel element of the cross section at mid-height, calculate its strain εsi,

(Equation 6.1), its stress Fsi = Es εsi and add the residual stress Frs (Equation 6.2).

Compare the total stress to the yield stress Fy to check for yielding. If yrssi FF ≥+ ,

the stress is limited to Fy.

3. Calculate the strain εfi (Equation 6.1 also), and the corresponding stress Ffi = Ef εfi for

each FRP element. Compare the strain to the ultimate compressive value εfcu (Equation

6.32) to check for failure of FRP in compression due to crushing or debonding.

4. Calculate the axial load P and bending moment M for the entire section, for the

assumed strain gradient (Equations 6.3 and 6.4).

5. Calculate the eccentricity e = M/P induced by the non uniform stress distribution,

resulting from the strain gradient.

6. Calculate the transformed effective moment of inertiaefftI , excluding both the yielded

steel elements and failed FRP elements (Equation 6.25). This is used to calculate the

critical buckling load Pcr (Equations 6.20 to 6.24), which is then used to calculate the

lateral displacement δ at mid-height for a prescribed out-of-straightness e’ (Equation

6.15).

7. Compare the eccentricity e calculated in step 5 with (δ + e'). If the two values are

different, assume a new value of neutral axis depth c and repeat steps 2 to 6 until the

values are equal. The load P calculated in step 4 and displacement δ calculated in step

6 provide one point on the load-lateral displacement curve.

8. Use a larger value of strain ε in step 1 and repeat the process until the complete P-δ

response is established.

Chapter 6

220

In order to generate the full load-axial displacement P-∆ response, for a given axial load

P and corresponding lateral deflection δ (obtained earlier), the following procedure can

be followed:

1. The axial shortening term ∆a of the displacement is calculated (Equation 6.28).

2. For a given δ, establish a deformed sine curve of the column with mid-height

amplitude of (δ + e’) and an arc length of (L-∆a), and calculate the chord length S of

this sine curve (Equations 6.31).

3. Calculate the curvature component of axial displacement, ∆ b, (Equation 6.30).

4. The total axial displacement ∆ is calculated using Equation 6.27.

5. Repeat the previous steps for each P and δ, until the complete P-∆ response is

established.

6.2.8 Illustration of key features of the fibre model

The fibre model developed has several significant features, namely, accounting for the P-

δ effects (geometric non-linearity), plasticity (material non-linearity) of steel, the effect of

through-thickness residual stresses, the effect of initial out-of-straightness, and a failure

criterion of FRP in compression. In order to illustrate the significance of these individual

features, the load-lateral displacement response of one of the test specimens, specimen 9

of Phase I of the current study has been predicted based on the estimated initial out-of-

straightness at mid-height (e’ = 7.04 mm) and residual stresses (Frs = 0.33 Fy). The

predictions are executed for four different cases. In case 1, Equations 6.15 and 6.16 have

been used in their original elastic form (i.e. ignoring steel yielding and residual stresses).

In case 2, plasticity of steel is considered, however, residual stresses are ignored. In case

Chapter 6

221

3, both steel plasticity and residual stresses are accounted for but the failure criterion of

FRP in compression is not applied. In case 4, all the features of the model presented

earlier are applied. Figure 6.7 shows the experimental response and the analytical

responses for the four cases. The figure clearly shows that ignoring the plasticity of steel

(case 1) would grossly overestimate the axial strength as the ultimate load approaches the

Euler elastic buckling load. Ignoring residual stresses (case 2) would overestimate the

load at which the behaviour departs from the elastic range. Also, by assuming that FRP

remains intact in compression throughout the full response (case 3), the ultimate load is

somewhat overestimated. It is then clear that case 4 represents the most accurate

prediction out of the four cases, using the full capabilities of the model. Therefore, it is

used later for the predictions of the behaviour of all cases in section 6.4 and also in the

parametric study in section 6.5.

6.3 Finite-Element Model (FEM) (Model 2)

The finite element analysis program ANSYS (revision 10) was used to model the non-

linear behaviour of the pin-ended HSS slender steel columns strengthened by CFRP

material. The primary objectives of the FEM are to introduce an alternative tool that may

be used in analysis or design and also for verifying the fibre model (Model 1). Both

models will also be verified using experimental results in section 6.4 and will be

compared to each other in section 6.6.

The finite element simulation consisted of two stages. In the first stage, an eigenvalue

elastic buckling analysis was performed on a perfectly straight specimen, including

Chapter 6

222

modeling of the entire cross section (i.e. not utilizing the symmetry) of the HSS2 column

(89 x 89 x 3.2 mm), to establish the probable buckling modes of the column for different

lengths (i.e. slenderness ratios of 5, 30, and 60). The analysis showed that the columns

with slenderness ratios of 5 and 30 experienced local buckling, whereas the column with

slenderness ratio of 60 experienced overall buckling, as shown in Figure 6.8. This

behaviour was also experimentally demonstrated for slenderness ratios of 4 (set 12) and

68 (specimen 7). In the second stage, a non-linear analysis was performed on slender

columns modeled with out-of-straightness geometric imperfections to promote the

predicted buckling shape (geometric nonlinearity) established through the first stage of

analysis. In this stage, the columns were loaded to failure to predict their full responses

and ultimate loads. Also in this stage, the analysis incorporated the material non-linearity

(plasticity of steel) and residual stresses. The centerline dimensions of the cross-sections

and the base metal thickness were used in the geometric modeling, based on the

measured cross-sectional dimensions of the specimens. The following sections address

various aspects of the finite element model such as element type, mesh density, boundary

conditions, material properties, geometric imperfections, and residual stresses.

6.3.1 Material properties

As mentioned earlier, the first stage of the numerical simulation was essentially a linear

elastic analysis of the control column, in which the stiffness of the structure remained

unchanged. As such, only the values of Young’s modulus (200 GPa) and Poisson’s ratio

of steel (0.30) were defined. On the other hand, the second stage of the numerical

simulation comprised a non-linear analysis, in which the stiffness of the structure changes

Chapter 6

223

as it deforms. The steel non-linearity (plasticity) was accounted for in the FEM by

specifying a bi-linear isotropic hardening model, as shown in Figure 6.9. The tangent

modulus for the steel was assumed equal to 0.5 percent of its elastic modulus as

suggested by Bruneau et al. (1998). For the FRP materials, unidirectional elastic

properties were assigned, namely, Young’s moduli of 20 GPa and 230 GPa for GFRP

type (G) and CFRP type (C3), respectively, as the model was used to predict the

behaviour of specimens 7 to 11. The ultimate compressive strain value of the CFRP type

(C3) was limited to 60 percent of its ultimate tensile strain to account for crushing of

CFRP in compression as discussed earlier in section 6.2.6. As this limiting strain is

reached, the stress level in CFRP is locked, however, the model is incapable of

eliminating the FRP material from the global stiffness matrix beyond this point, which

may slightly affect the predicted post-peak behaviour.

6.3.2 Elements’ types and mesh density

An eight-node quadrilateral layered shell element (SHELL91) was used for the steel

section in this model. The element configurations as well as its coordinate system are

shown in Figure 6.10(a). Each node has six degrees of freedom, namely, three

translations (Ux, Uy, and Uz) and three rotations (Rx, Ry, and Rz). The multiple layers of

the element were utilized to account for the residual stress distribution through the steel

wall thickness, as will be discussed later. When FRP sheets were used, the FRP was

modeled using three-dimensional two-node uniaxial truss element (LINK8), as shown in

Figure 6.10(b). This is considered reasonable because of the small flexural rigidity of the

thin FRP layers. Each node has three degrees of freedom, namely, translations in the

Chapter 6

224

nodal x, y, and z directions (Ux, Uy, and Uz). Perfect bond between steel and FRP sheets

was assumed by defining one node for both the SHELL91 and the LINK8 elements

having the same coordinates. This assumption is quite reasonable when thin FRP sheets

were used as no signs of debonding were observed experimentally, except at the very

end, well beyond the peak load when local debonding and crushing occurred as a result of

a secondary local buckling.

One quarter of the specimen was modeled, as shown in Figure 6.11(a), by taking

advantage of the double symmetry of the column. This symmetry was simulated by

introducing two planes of symmetry, one vertical plane in the longitudinal direction along

the full length and another horizontal plane in the transverse direction at mid-height of

the column. The final mesh configuration of the model was established after a mesh

refining process has been conducted. Three preliminary numerical simulations of

different mesh densities, namely, mesh 1, mesh 2, and mesh 3, were first carried out on

the control steel specimen, as shown in Figure 6.11(b). Different sizes of the elements in

the HSS flanges and their curved corners are also shown in Figure 6.11(b). The number

of elements varied from 1050 elements in the first mesh to 4730 elements in the third

mesh. The predicted maximum axial load for each mesh configuration as well as their

mathematical average is plotted in Figure 6.11(b). The figure shows almost identical

results with minor changes in the axial load capacities when refining the model beyond

mesh 1. However, the computer run-time dramatically increases with refining the mesh

size. As such, mesh 1 was deemed sufficient and was used in all the analyses that

followed.

Chapter 6

225

6.3.3 Loading and boundary conditions

In order to model the hinged end condition of the columns, shown in Figure 3.16, a rigid

end plate was simulated with controlled degrees of freedom. The translational degrees of

freedom in the transverse direction (Ux, and Uz) along the middle line of the rigid plate

were restrained, whereas the translational degrees of freedom in the longitudinal direction

(Uy) along the same line were released. The rotational degrees of freedom of the entire

plate in all directions (Rx, Ry, and Rz) were released. Loading was modeled by two lines

of point loads, spaced by a distance equal to the width of the hinged end of the test setup

shown in Figure 3.16(a and c).

6.3.4 Geometric imperfections

The out-of-straightness imperfection values at mid-height, reported in Table 4.2, were

introduced in the FEM to initiate the overall buckling mode of failure, indicated by the

buckling analysis (first stage analysis). The imperfect profile of the unloaded column was

assumed to follow a sine curve with its apex at the mid-height of the column.

6.3.5 Residual stresses

In the finite element model, the through-thickness residual stress distribution is idealized

as previously shown in Figure 6.1. In order to model the residual stress pattern, four

layers were defined in the multi layer steel shell element (SHELL91). A simplified and

approximate approach was used, in which the residual stress was defined by shifting the

origin of the axes of the stress-strain curve of the steel material of each layer along the

linear part of the curve upwards or downwards, depending on whether the residual stress

Chapter 6

226

is compression or tension. The magnitude of the shift is equal to the residual stress rsF ,

as shown in Figure 6.9. This means that, the origin of the ‘pre-tensioned’ steel at the two

outer layers of the wall thickness are defined as (-εrs , -Frs) and (-0.5εrs , -0.5Frs),

respectively, whereas the origin of the ‘pre-compressed’ steel at the inner two layers of

the wall thickness are defined as (0.5εrs , 0.5Frs) and (εrs , Frs), respectively.

6.4 Verification of Models 1 and 2

Both models were verified using two independent experimental studies. First, the models

were verified using test results reported by Key and Hancock (1985) on 152 x 152 x 4.9

mm and 203 x 203 x 6.3 mm conventional HSS steel columns. The columns were not

strengthened with FRP materials. The pin-ended columns had kL/r ranging from 66 to 98

and imperfection values e’ ranging from 0.3 mm to 1.75 mm, as shown in Table 6.2. The

reported Fy and Frs by Key and and Hancock (1985) were 350 MPa and 200 MPa,

respectively. The average axial stresses, based on the applied load divided by the cross

sectional area of the column, versus the normalized lateral displacement (δ/L) responses

for both the experiments and the two models are plotted in Figure 6.12 and 6.13. The

figures show that both models provide reasonable agreement with the experimental

behaviour within a maximum difference of 5 and 15 percent for models 1 and 2,

respectively. The maximum loads are also listed in Table 6.2.

The models were then verified using the experimental results of the current study. Model

1 was verified using all columns’ sets (1 to 11); whereas Model 2 was verified using

columns’ sets 7 to 11. The initial imperfections used in the predictions for column sets (1

Chapter 6

227

to 6) were obtained using two methods, namely, the laser sensor (section 3.3.2), before

CFRP installation, and the measured strain gradient through the cross section, under

loading (section 4.3.1). For columns sets’ 7 to 11, laser profiling could not be used, as

indicated earlier. A comparative study was performed to investigate the effect of each

method on the predicted axial strength. Table 6.1 shows the predicted axial strengths of

column sets 1, 2, 5, and 6, using Model 1, for both the minimum and maximum

imperfection values obtained from each method (i.e. the values at mid height and

maximum amplitude, respectively, in laser profiling and the values based on the strains

from both sides, respectively, in the strain gradient method). Sets 1 and 2 represent

unstrengthened and strengthened columns with the minimum slenderness ratio, while sets

5 and 6 represent the same for the maximum slenderness ratio. The table shows that, for

each method, the minimum and maximum imperfections yielded very close results. Also,

both methods yielded similar values. A maximum standard deviation of 4.99 kN is

obtained in set 6, which represents a maximum difference of 2.8 percent between the four

predicted strengths. This suggests that estimating the imperfection using either method is

reasonable. Therefore, it was decided to use the maximum imperfection values obtained

from the laser sensor in the complete sets of predictions of sets 1 to 6.

The full responses of load versus: lateral displacements, axial displacements, and axial

strains on two opposite sides of the columns, have been predicted and compared with the

experimental results. Figure 6.14 to 6.24 show the predicted versus experimental load-

lateral displacements of column sets 1 to 11. Figure 6.25 to 6.35 show the predicted

versus experimental load-axial displacements and Figure 6.36 to 6.46 show the predicted

Chapter 6

228

versus experimental load-axial strains on both side, for the same specimens. A summary

of axial strength and stiffness is also given in Table 6.2. While the models appear to

somewhat overestimate the axial strength and stiffness at very low slenderness ratios

(kL/r = 46) for the small scale columns (sets 1 and 2), they generally showed very good

agreement with the experimental results for all other column sets within a maximum

difference of 18 percent. In specimen 10, the overall buckling observed experimentally

was in fact not symmetric, and the maximum lateral displacement and failure occurred

near the quarter length point and not at the middle. For this reason, the predicted

maximum axial load, which is based on symmetric buckling, is higher than the

experimental value by 23 percent.

The failure mode predicted by the FEM (Model 2), which is an overall buckling [Figure

6.47(a)] is quite similar to the buckling failure mode observed in the tests [Figure

6.47(b)]. A typical deformed cross section of the tested specimens 7 to 11 at mid-height

is shown in Figure 6.47(c). As discussed in Chapter 4, after overall buckling took place,

inward local buckling occurred in the compression flange, whereas outward local

buckling occurred in the two side webs for specimens 7 to 11 with a relatively large b/t

ratio. This deformed shape was revealed after the test by cutting the specimen at mid-

height. Figure 6.47(d, e and f) show that the same pattern of deformation has been

predicted by the FEM, in terms of the displacement contours in both x- and z-directions,

Ux and Uz (i.e. displacements within the cross sectional plane) as well as the nodal

rotations about the longitudinal axis, Ry. The resemblance of deformations in Figure

6.47(d, e and f) to 6.47(c) provides confidence in the model.

Chapter 6

229

6.5 Parametric Study on CFRP–Strengthened HSS Slender

Columns

One of the objectives of developing the models is to assess the effect of individual

parameters that control the behaviour of CFRP-strengthened slender HSS columns, each

independently. It was shown in Section 4.3.1 that specimens 7 to 11 had different levels

of the out-of-straightness imperfections. As such, it was difficult to assess the effect of

CFRP reinforcement ratio (i.e. number of layers) exclusively, which was the main

original goal of testing specimens 7 to 11.

In the following sections, Model 1 is used in a parametric study to evaluate the

independent effects of the following parameters:

a) CFRP reinforcement ratio ρ, which is defined as the ratio of total CFRP to steel

areas Af /As (based on one to five layers of CFRP type C3 bonded on two opposite

sides).

b) The value of out-of-straightness at mid-height (e’= L/500 to L/2000).

c) The level of residual stress (0.25 Fy and 0.5 Fy).

d) Slenderness ratios (68 and 160).

Also, Model 2 was used to predict the strength and stiffness for some of the cases being

analyzed, in order to provide a direct comparison with Model 1.

A total of 28 HSS columns with the same cross sectional dimensions and material

properties as those used in the tested specimens 7 to 11 of the experimental program are

analyzed. The following identification system was adopted to distinguish the various

Chapter 6

230

cases. As shown in Table 6.3, the first number represents the slenderness ratio of the

column (kL/r), while the second number specifies the geometric out-of-straightness

imperfection as a ratio of (L/e’). These two numbers are followed by the CFRP

reinforcement ratio to quantify the amount of CFRP layers bonded on two opposite sides

of the HSS. Another number describing the residual stress level as a percentage of the

yield stress is also added at the end. For the unstrengthened control columns, the CFRP

reinforcement ratio is replaced by the word “control”. For example, “68-500-43-25”

describes a strengthened column that has a slenderness ratio of 68, a geometric

imperfection of (Length/500), CFRP reinforcement ratio of 0.43 (i.e. five layers of CFRP

type C3), and has a residual stress level of 25 percent of its yield stress. Figure 6.48 to

6.54 show the predicted load-lateral responses for all cases. The effect of each parameter

is discussed in the following sections.

6.5.1 Effect of number of CFRP layers

Figure 6.48 to 6.54 clearly show that bonding longitudinal CFRP sheets to slender steel

columns can indeed increase both their strength and stiffness. For example, the

percentage increases in axial strength of specimens with one, three and five CFRP layers

are 11, 26, and 39 percent for specimens with e’=L/500 and are 5, 9, and 11 percent,

respectively, for specimens with e’=L/2000. These increases in strength are equivalent to

increasing the steel tube thickness by as much as 12 to 47 percent, respectively. On the

other hand, the percentage increases in axial stiffness are in the order of 13, 31, and 45

percent for specimens strengthened with one, three and five CFRP layers, respectively.

Figure 6.55(b) shows that increasing the reinforcement ratio (ρ = Af /As) decreases the

displacement at ultimate loads.

Chapter 6

231

6.5.2 Effect of initial out-of-straightness (e’)

It is clear that the reinforcement ratio and the value of out-of-straightness have a

combined effect. The results listed in Table 6.3 suggest that the CFRP system is more

effective for columns with higher levels of out-of-straightness, as also shown in Figure

6.55(a and c), particularly for higher reinforcement ratios. Figure 6.55(c) shows the

variation of percentage increase of axial strength with the out-of-straightness values, for

various numbers of CFRP layers. Depending on the number of layers, there is a certain

level of out-of-straightness (for example L/750 for one layer of CFRP), before which, the

percentage gain in axial strength is reduced as the out-of-straightness decreases. Within

this range, both sides of the column are under compression and the CFRP fails at both

sides, consecutively. At higher levels of out-of-straightness, the percentage increase in

axial strength is constant and seems to be independent of the level of out-of-straightness,

and the CFRP crushes only at the inner curved side. Table 6.3 summarizes the axial load

capacities and stiffness of columns with different number of CFRP layers, for various

out-of-straightness values. The table shows that the out-of-straightness has a negligible

effect on the percentage increase of the columns’ axial stiffness. As such, the percentage

increases in axial stiffness appear to be constant for all values of out-of-straightness.

6.5.3 Effect of residual stresses

As shown in Table 6.3 and Figure 6.55(d), the through-thickness residual stress has a

little effect on the gain in axial strength of CFRP-strengthened HSS columns, and that the

lower the residual stress, the higher the gain in columns’ strength. The values listed in

Table 6.3 indicate that if the value of residual stress increased from 25 to 50 percent of

Chapter 6

232

the yield stress, the maximum load of the control specimen reduces from 297 kN to 290

kN, which represents only a 2.4 percent reduction. This reduction reaches 5.6 percent for

the specimen strengthened with 5 layers of CFRP sheets.

6.5.4 Effect of slenderness ratio

Figure 6.55(d) shows that the slenderness ratio perhaps had the most pronounced effect

on the effectiveness of CFRP-strengthening system. For the same CFRP reinforcement

ratio, the strength gain increases substantially as the slenderness ratio is increased,

particularly for higher CFRP reinforcement ratios. Table 6.3 indicates that the percentage

increase in axial stiffness due to increasing the number of CFRP layers is slightly affected

by slenderness ratio.

6.6 Comparison between models 1 and 2

As the two developed models were completely independent, it was not expected that they

will both yield identical results. The difference in the solution approach between both

models as well as the inherent differences in the assumptions in each model explain the

small differences in the results. In order to further assess the difference in results, the first

four cases in Table 6.3, “68-500-control-25”, “68-500-9-25”, “68-500-25-25”, and “68-

500-43-25” have also been analysed using Model 2. Figure 6.56 and 6.57 show a

comparison between the predicted axial strength and stiffness using both models,

respectively. Also, the predictions for the experimental specimens 7 to 11 are compared

in Figure 6.56 and 6.57. The figures show comparable results for both models with

Model 1 giving slightly higher axial strengths than Model 2 for most of the cases. The

Chapter 6

233

maximum difference in strength was seven percent for specimens with CFRP-

reinforcement ratios of 9, 25, and 43 percent. On the other hand, Model 2 gave slightly

higher axial stiffness than Model 1 for most of the cases. The maximum difference in

stiffness was 11 percent for specimen with CFRP-reinforcement ratio of 9 percent.

Chapter 6

234

Table 6.1 Comparison between both methods of estimating imperfection

Method 1: Laser Method 2: Strain gauge Set emin

(mm)

Ppred

(kN)

emax

(mm)

Ppred

(kN)

emin

(mm)

Ppred

(kN)

emax

(mm)

Ppre1

(kN)

(Ppr

ed) a

vg

(kN

) Standard deviation

(kN)

Set 1 0.14 247 0.25 246 0.46 247 0.78 245 246 0.96

Set 2 0.06 261 0.26 254 0.22 253 0.85 253 255 3.86

Set 5 0.53 107 0.96 106 0.37 108 0.57 107 107 0.82

Set 6 0.28 185 0.84 181 0.17 186 1.22 175 182 4.99

Chapter 6

235

Table 6.2 Comparison between experimental and predicted results using Models 1 and 2.

Axial strength, P Axial stiffness, k Model 1 Model 2 Model 1 Model 2

Sour

ce

Specimen cross section

Spec

imen

id

entif

icat

ion

kL/re’

(mm) Expe

rimen

t

P pre

d1 (k

N)

(Ppr

ed1 /

P e

xp)

P pre

d2 (k

N)

(Ppr

ed2 /

P e

xp)

Expe

rimen

t

k pre

d1

(kN

/mm

)

(kpr

ed1 /

k e

xp)

k pre

d2

(kN

/mm

)

(kpr

ed2 /

k e

xp)

i 68 0.30 898 831 0.93 933 1.04 N/A N/A N/A 152 x 152 x 4.9 ii 98 0.60 560 517 0.92 593 1.06 N/A N/A N/A

iii 66 0.50 1477 1454 0.98 1261 0.85 N/A N/A N/A

Key

and

H

anco

ck

(198

5)

203 x 203 x 6.3 iv 96 1.75 846 889 1.05 769 0.91 N/A N/A N/A Set 1 46 0.25 182 246 1.36 N/A N/A 108 135 1.25 N/A Set 2 46 0.26 192 254 1.32 N/A N/A 118 184 1.56 N/A Set 3 70 0.36 148 175 1.18 N/A N/A 86 88 1.02 N/A Set 4 70 0.32 200 236 1.18 N/A N/A 100 121 1.21 N/A Set 5 93 0.96 103 106 1.03 N/A N/A 68 65 0.96 N/A

44 x 44 x 3.2

Set 6 93 0.84 175 181 1.03 N/A N/A 80 88 1.10 N/A Set 7 68 6.60 295 268 0.91 267 0.91 90 88 0.98 85 0.94Set 8 68 0.92 355 360 1.01 359 1.01 89 102 1.15 98 1.10Set 9 68 7.04 335 343 1.02 326 0.97 88 109 1.24 109 1.24

Set 10 68 2.04 332 407 1.23 412 1.24 120 130 1.08 126 1.05Cur

rent

exp

erim

enta

l stu

dy

89 x 89 x 3.2

Set 11 68 5.00 362 378 1.04 383 1.06 110 135 1.23 135 1.23Average 1.08 1.01 1.16 1.11

Standard deviation 0.14 0.12 0.17 0.13

Chapter 6

236

Table 6.3 Summary of the parametric study on slender CFRP-strengthened HSS columns

Specimen I.D. Pu

(kN)* %age Gain

k (kN/mm)*

%age Gain δ (mm)*

%age Reduction

68-500-control-25 297 --- 80 --- 17.0 --- 68-500-9-25 330 11 91 13 16.0 6

68-500-25-25 374 26 105 31 14.9 12 68-500-43-25 413 39 117 46 13.5 21

68-600-control-25 306 --- 83 --- 16.5 --- 68-600-9-25 340 11 94 13 14.9 10

68-600-25-25 385 26 109 31 13.3 22 68-600-43-25 388 27 121 45 6.3 63

68-750-control-25 316 --- 86 --- 15.5 --- 68-750-9-25 352 11 97 13 13.6 12

68-750-25-25 365 16 112 31 5.7 63 68-750-43-25 373 18 124 45 4.4 72

68-1000-control-25 330 --- 88 0 14.3 --- 68-1000-9-25 355 8 99 13 13.9 3 68-1000-25-25 370 12 114 31 13.2 8 68-1000-43-25 375 14 127 45 13.1 9

68-2000-control-25 349 --- 89 0 14.0 --- 68-2000-9-25 366 5 101 13 14.0 0 68-2000-25-25 381 9 117 31 12.4 11 68-2000-43-25 387 11 130 45 11.4 19

68-500-control-50 290 --- 80 --- 19.2 --- 68-500-9-50 322 8 91 13 19.0 1

68-500-25-50 357 20 105 31 17.5 9 68-500-43-50 390 31 117 46 14.9 22

160-500-control-25 73 --- 42 --- 73 --- 160-500-9-25 86 17 48 14 67.1 8 160-500-25-25 107 46 57 35 63.6 13 160-500-43-25 129 76 65 55 60.5 17

*

Pu

k1

Axial displacement

Axial load

Pu

Lateral displacement

Axial load

δ

Chapter 6

237

Figure 6.1 Meshing system for stress integration.

Figure 6.2 Stress and strain distributions within the cross section of slender column at mid-height.

A2 (12 x 80)A1 (1 x 12)

A3 (12x12)

A4 (1 x n)

-Frs

+Frs

-0.5

F rs

+0.5

F rs

- 0.5 Frs Residual stresses- Frs

+ 0.5 Frs + Frs

t/3

t/3

t/3

t/3t/3t/3

A5 (n x 1)

A2 (12 x 80)A1 (1 x 12)

A3 (12x12)

A4 (1 x n)

-Frs

+Frs

-0.5

F rs

+0.5

F rs

- 0.5 Frs Residual stresses- Frs

+ 0.5 Frs + Frs

t/3

t/3

t/3

t/3t/3t/3

A5 (n x 1)

element i

x

x

yi

e

c

ε

εi

P

N.A.

+ = or or

Fully plastic

Partiallyyielded

Firstyielding

Residualstress

hyc

Effective centroid (c)

Strain distribution

Fy Fy Fy

Fy

Fully plasticPartially yieldedFirst yielding

Stress distribution

element i

x

x

yi

e

c

ε

εi

P

N.A.

+ = or or

Fully plastic

Partiallyyielded

Firstyielding

Residualstress

hyc

Effective centroid (c)

Strain distribution

Fy Fy Fy

Fy

Fully plasticPartially yieldedFirst yielding

Stress distribution

Chapter 6

238

Figure 6.3 Lateral and axial displacements of slender columns.

Figure 6.4 Summary of the finite difference model and convergence study.

(a) Lateral displacement and initial imperfection

Axial displacement due to shortening

P

∆a

L

∆b

S L - ∆aδ+e’

P

Axial displacement due to curvature

(b) Axial displacement components

Loaded column

P

LUnloaded column

z

e’ δ

wo

w

L/2

z

+

(a) Lateral displacement and initial imperfection

Axial displacement due to shortening

P

∆a

L

∆b

S L - ∆aδ+e’

P

Axial displacement due to curvature

(b) Axial displacement components

Loaded column

P

LUnloaded column

z

e’ δ

wo

w

L/2

z

Loaded column

P

LUnloaded column

z

e’ δ

wo

w

L/2

z

+

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35 40 45

(b) Effect of number of segments on load-lateral displacement response


Load

(kN

)

Experiment

1 Segment

5 Segments

10 Segments

15 Segments

20 Segments

e’ = 7.04 mmFrs = 0.33 Fy

Specimen 9

280290300310320330340350

0 5 10 15 20 25

(c) Variation of peak load with number of segmentsNumber of segments

Pea

k lo

ad (k

N)

(a) Variation of inertia along column’s height

using 15 segments

Ela

stic

Ela

stic

Par

tially

yie

lded

Iteff

Itg

0.3

L0.

3 L

0.4

L

∆L=

L/15

convergence

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35 40 45

(b) Effect of number of segments on load-lateral displacement response


Load

(kN

)

Experiment

1 Segment

5 Segments

10 Segments

15 Segments

20 Segments

Experiment

1 Segment

5 Segments

10 Segments

15 Segments

20 Segments

e’ = 7.04 mmFrs = 0.33 Fy

Specimen 9

e’ = 7.04 mmFrs = 0.33 Fy

Specimen 9

280290300310320330340350

0 5 10 15 20 25

(c) Variation of peak load with number of segmentsNumber of segments

Pea

k lo

ad (k

N)

(a) Variation of inertia along column’s height

using 15 segments

Ela

stic

Ela

stic

Par

tially

yie

lded

Iteff

Itg

0.3

L0.

3 L

0.4

L

∆L=

L/15

convergence

Chapter 6

239

Figure 6.5 Illustration of the superposition concept in predicting load-axial displacement response.

Figure 6.6 Variation of ultimate compressive-to-tensile strain ratio of CFRP at failure with slenderness ratio.

0

50

100

150

200

250

300

0 1 2 3 4 5 6

∆b Total (∆a + ∆b)

Control Specimen 7

(e’ = 6.60 mm)


Load

(kN

)Experiment

∆a

0

50

100

150

200

250

300

0 1 2 3 4 5 6

∆b Total (∆a + ∆b)

Control Specimen 7

(e’ = 6.60 mm)


Load

(kN

)Experiment

∆a

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120


ultim

ate

com

pres

sive

stra

in to

tens

ile s

train CFRP plates

CFRP sheets

Debonding

Crushing

kL/r

= 75

.6

Best fit to average values

Average

Set

6

Set

4S

ets

7 to

11

Set

2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120


ultim

ate

com

pres

sive

stra

in to

tens

ile s

train CFRP plates

CFRP sheets

Debonding

Crushing

kL/r

= 75

.6

Best fit to average values

Average

Set

6

Set

4S

ets

7 to

11

Set

2

Chapter 6

240

Figure 6.7 Illustration of significance of various features of the fibre model.

Figure 6.8 Eigenvalue elastic buckling analysis.

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 5 10 15 20 25 30 35 40 45


Euler Load = 695 kN

Case 1

Case 2

Case 3

Experiment

Load

(kN

)

Failure of FRP in compression

Case 1 Linear elastic HSS section (No yielding + No residual stress + No CFRP failure)Case 2 Elasto-plastic HSS section (No residual stress + No CFRP failure)Case 3 Same as case 2 + residual stresses (No CFRP failure)Case 4 Same as case 3 + CFRP fails in compression

Specimen 9 (e’ = 7.04 mm)

Case 4

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0 5 10 15 20 25 30 35 40 45


Euler Load = 695 kN

Case 1

Case 2

Case 3

Experiment

Load

(kN

)

Failure of FRP in compression

Case 1 Linear elastic HSS section (No yielding + No residual stress + No CFRP failure)Case 2 Elasto-plastic HSS section (No residual stress + No CFRP failure)Case 3 Same as case 2 + residual stresses (No CFRP failure)Case 4 Same as case 3 + CFRP fails in compression

Specimen 9 (e’ = 7.04 mm)

Case 4

Local Buckling

kL/r = 30

Local Buckling Overall Buckling

kL/r = 60

kL/r = 5

HSS2 (89 x 89 x 3.2 mm)

Local Buckling

kL/r = 30

Local Buckling Overall Buckling

kL/r = 60

kL/r = 5

HSS2 (89 x 89 x 3.2 mm)

Chapter 6

241

Figure 6.9 Stress-strain curves used in the FEM.

Figure 6.10 Elements used in the FEM.

z y

i

x

k

(b) 2-node truss element for FRP

Layer 1

Layer n

Layer 2

Top

Bottom

(a) 8-node layered shell element for steel

i j x

y

kl

mn

o

p

z

z y

i

x

k

(b) 2-node truss element for FRP

Layer 1

Layer n

Layer 2

Top

BottomLayer 1

Layer n

Layer 2

Top

Bottom

(a) 8-node layered shell element for steel

i j x

y

kl

mn

o

p

z

i j x

y

kl

mn

o

p

z

(a) Materials stress-strain curves


Stre

ss (M

Pa)

0

300

600

900

0 15 30 45

CFRP (type C3) Steel (bi-linear)

GFRP

(b) Modeling of residual stress


Stre

ss (M

Pa)

Used for the 2 inside layers

Fy

Frs

Used for the 2 outside layers

Frs

-0.5

F rs

+ Frs

- Frs

+ 0.5Frs

- 0.5Frs

Thickness (t)

+ F r

s

-Frs

+ 0.

5Frs

t/3

t/3

t/6t/6



Stre

ss (M

Pa)

0

300

600

900

0 15 30 45


GFRP



Stre

ss (M

Pa)

0

300

600

900

0 15 30 45


GFRP

(b) Modeling of residual stress


Stre

ss (M

Pa)


Fy

Frs


FrsStrain x 10-3 (mm/mm)

Stre

ss (M

Pa)


Fy

Frs


Frs

-0.5

F rs

+ Frs

- Frs

+ 0.5Frs

- 0.5Frs

Thickness (t)

+ F r

s

-Frs

+ 0.

5Frs

t/3

t/3

t/6t/6

Chapter 6

242

Figure 6.11 Mesh refinement and results.

Figure 6.12 Verification of models 1 and 2 using test results on HSS 203 x 203 x 6.3 mm.

[Key and Hancock, 1985]

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600

δ /L (x 10-5)

Ave

rage

stre

ss (M

Pa)

Model 1

Model 2Exp. (kL/r=98)

Exp. (kL/r=68)Model 1

Model 2

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600

δ /L (x 10-5)

Ave

rage

stre

ss (M

Pa)

Model 1

Model 2Exp. (kL/r=98)


Model 2

4620 elements3590 elements1050 elements

(b) Mesh configurations

Mesh 2 Mesh 3

(a) One quarter of the specimen

Hei

ght /

2

Mesh 1

290.8

290.9

291

291.1

291.2

291.3

291.4

291.5

291.6

291.7

mesh 1 mesh 2 mesh 3

Axi

al lo

ad c

apac

ity (k

N)

Average load = 291.28 kN

0.03%0.07%

0.10%

89 x 89 x 3.2 mmL = 2380 mm, e’=L/500

Fy = 380 MPa, Frs = 0.33 Fy

4620 elements3590 elements1050 elements

(b) Mesh configurations

Mesh 2 Mesh 3

(a) One quarter of the specimen

Hei

ght /

2

Mesh 1

290.8

290.9

291

291.1

291.2

291.3

291.4

291.5

291.6

291.7

mesh 1 mesh 2 mesh 3

Axi

al lo

ad c

apac

ity (k

N)

Average load = 291.28 kN

0.03%0.07%

0.10%

89 x 89 x 3.2 mmL = 2380 mm, e’=L/500

Fy = 380 MPa, Frs = 0.33 Fy

Chapter 6

243

Figure 6.13 Verification of models 1 and 2 using test results on HSS 152 x 152 x 4.9 mm.

[Key and Hancock, 1985]

Figure 6.14 Measured and predicted load-lateral displacement responses of set 1.

0

50

100

150

200

250

0 5 10 15 20 25

e’

P

δ

Experiment

Lateral Displacement δ (mm)

Load

(kN

)

Model 1

kL/r = 46

e’ = 0.25 mm

Frs = 0.49 Fy

0

50

100

150

200

250

0 5 10 15 20 25

e’

P

δe’

P

δ

Experiment


Load

(kN

)

Model 1

kL/r = 46

e’ = 0.25 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600δ /L (x 10-5)

Ave

rage

stre

ss (M

Pa)

Model 1

Model 2

Exp. (kL/r=96)


Model 2

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600δ /L (x 10-5)

Ave

rage

stre

ss (M

Pa)

Model 1

Model 2

Exp. (kL/r=96)


Model 2

Chapter 6

244



0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35 40 45 50

e’

P

δ

Experiment


Load

(kN

)

Model 1

kL/r = 70

e’ = 0.36 mm

Frs = 0.49 Fy

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35 40 45 50

e’

P

δe’

P

δ

Experiment


Load

(kN

)

Model 1

kL/r = 70

e’ = 0.36 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

-1 4 9 14 19 24

Experiment


Load

(kN

)

Model 1Debonding of CFRP

e’

P

δ

kL/r = 46

e’ = 0.26 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

-1 4 9 14 19 24

Experiment


Load

(kN

)

Model 1Debonding of CFRP

e’

P

δe’

P

δ

kL/r = 46

e’ = 0.26 mm

Frs = 0.49 Fy

Chapter 6

245



0

20

40

60

80

100

120

0 10 20 30 40 50 60

e’

P

δ

Experiment


Load

(kN

)

Model 1

kL/r = 93

e’ = 0.96 mm

Frs = 0.49 Fy

0

20

40

60

80

100

120

0 10 20 30 40 50 60

e’

P

δe’

P

δ

Experiment


Load

(kN

)

Model 1

kL/r = 93

e’ = 0.96 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

-1 4 9 14 19 24 29 34

Experiment


Load

(kN

)Model 1

Debonding of CFRP

e’

P

δ

kL/r = 70

e’ = 0.32 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

-1 4 9 14 19 24 29 34

Experiment


Load

(kN

)Model 1

Debonding of CFRP

e’

P

δe’

P

δ

kL/r = 70

e’ = 0.32 mm

Frs = 0.49 Fy

Chapter 6

246



0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2Model 1

e’

P

δ

kL/r = 68

e’ = 6.6 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2Model 1

e’

P

δe’

P

δ

kL/r = 68

e’ = 6.6 mm

Frs = 0.33 Fy

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60

Experiment


Load

(kN

)

Model 1

Crushing of CFRP on the inner compression flange

e’

P

δ

kL/r = 93

e’ = 0.84 mm

Frs = 0.49 Fy

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60

Experiment


Load

(kN

)

Model 1


e’

P

δ

kL/r = 93

e’ = 0.84 mm

Frs = 0.49 Fy

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60

Experiment


Load

(kN

)

Model 1


e’

P

δe’

P

δ

kL/r = 93

e’ = 0.84 mm

Frs = 0.49 Fy

Chapter 6

247



0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)Model 2

Model 1

e’

P

δ

Crushing of CFRP on the compression flange

kL/r = 68

e’ = 0.92 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)Model 2

Model 1

e’

P

δe’

P

δ


kL/r = 68

e’ = 0.92 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2Model 1

e’

P

δ


kL/r = 68

e’ = 7.04 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2Model 1

e’

P

δe’

P

δ


kL/r = 68

e’ = 7.04 mm

Frs = 0.33 Fy

Chapter 6

248



0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2

Model 1

e’

P

δ

Successive crushing of CFRP layers on the compression flange

kL/r = 68

e’ = 2.04 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2

Model 1

e’

P

δe’

P

δ

Successive crushing of CFRP layers on the compression flange

kL/r = 68

e’ = 2.04 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2

Model 1

e’

P

δ

Crushing of CFRP on the side walls


kL/r = 68

e’ = 5.00 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Experiment


Load

(kN

)

Model 2

Model 1

e’

P

δe’

P

δ

Crushing of CFRP on the side walls


kL/r = 68

e’ = 5.00 mm

Frs = 0.33 Fy

Chapter 6

249

Figure 6.25 Measured and predicted load-axial displacement responses of set 1.


0

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment

Axial Displacement ∆ (mm)

Load

(kN

)Model 1

P

∆

kL/r = 46

e’ = 0.25 mm

Frs = 0.49 Fy

1 2 3 4 5 6 70

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment


Load

(kN

)Model 1

P

∆

P

∆

kL/r = 46

e’ = 0.25 mm

Frs = 0.49 Fy

1 2 3 4 5 6 71 2 3 4 5 6 7

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment


Load

(kN

)

Model 1

P

∆

1 2 3 4 5 6 7

kL/r = 46

e’ = 0.26 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment


Load

(kN

)

Model 1

P

∆

P

∆

1 2 3 4 5 6 71 2 3 4 5 6 7

kL/r = 46

e’ = 0.26 mm

Frs = 0.49 Fy

Chapter 6

250



0

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment


Load

(kN

)

Model 1

P

∆

kL/r = 70

e’ = 0.36 mm

Frs = 0.49 Fy

1 2 3 4 5 6 70

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment


Load

(kN

)

Model 1

P

∆

P

∆

kL/r = 70

e’ = 0.36 mm

Frs = 0.49 Fy

1 2 3 4 5 6 71 2 3 4 5 6 7

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment


Load

(kN

)

Model 1

P

∆

kL/r = 70

e’ = 0.32 mm

Frs = 0.49 Fy

1 2 3 4 5 6 70

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Experiment


Load

(kN

)

Model 1

P

∆

P

∆

kL/r = 70

e’ = 0.32 mm

Frs = 0.49 Fy

1 2 3 4 5 6 71 2 3 4 5 6 7

Chapter 6

251



0

20

40

60

80

100

120

0 1 2 3 4 5 6 7

Experiment


Load

(kN

)

Model 1

P

∆

kL/r = 93

e’ = 0.96 mm

Frs = 0.49 Fy0

20

40

60

80

100

120

0 1 2 3 4 5 6 7

Experiment


Load

(kN

)

Model 1

P

∆

kL/r = 93

e’ = 0.96 mm

Frs = 0.49 Fy

Experiment


Load

(kN

)

Model 1

P

∆

P

∆

kL/r = 93

e’ = 0.96 mm

Frs = 0.49 Fy


Load

(kN

)

0

20

40

60

80

100

120

140

160

180

200

0 2 4 6 8 10

Experiment

Model 1

P

∆

kL/r = 93

e’ = 0.84 mm

Frs = 0.49 Fy


Load

(kN

)

0

20

40

60

80

100

120

140

160

180

200

0 2 4 6 8 10

Experiment

Model 1

P

∆

P

∆

kL/r = 93

e’ = 0.84 mm

Frs = 0.49 Fy

Chapter 6

252



0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 1

Model 2

P

∆

kL/r = 68

e’ = 6.6 mm

Frs = 0.33 Fy0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 1

Model 2

P

∆

P

∆

kL/r = 68

e’ = 6.6 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

) Model 2Model 1

P

∆

kL/r = 68

e’ = 0.92 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

) Model 2Model 1

P

∆

P

∆

kL/r = 68

e’ = 0.92 mm

Frs = 0.33 Fy

Chapter 6

253



0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 2

Model 1

P

∆

kL/r = 68

e’ = 7.04 mm

Frs = 0.33 Fy0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 2

Model 1

P

∆

P

∆

kL/r = 68

e’ = 7.04 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 1

Model 2P

∆

Crushing of CFRP on the concave side

kL/r = 68

e’ = 2.04 mm

Frs = 0.33 Fy0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 1

Model 2P

∆

P

∆

Crushing of CFRP on the concave side

kL/r = 68

e’ = 2.04 mm

Frs = 0.33 Fy

Chapter 6

254


Figure 6.36 Measured and predicted load-axial strain responses of set 1.

Axial strain (x 10-3)

0

50

100

150

200

250

300

-8 -6 -4 -2 0 2

Load

(kN

)

kL/r = 46

e’ = 0.25 mm

Frs = 0.49 Fy

Experiment

Model 1Model 1

Experiment

S2S1


0

50

100

150

200

250

300

-8 -6 -4 -2 0 2

Load

(kN

)

kL/r = 46

e’ = 0.25 mm

Frs = 0.49 Fy

Experiment

Model 1Model 1

Experiment

S2S1

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 2

Model 1

P

∆Crushing of CFRP on

the concave side

kL/r = 68

e’ = 5.00 mm

Frs = 0.33 Fy0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6

Experiment


Load

(kN

)

Model 2

Model 1

P

∆

P

∆Crushing of CFRP on

the concave side

kL/r = 68

e’ = 5.00 mm

Frs = 0.33 Fy

Chapter 6

255



0

50

100

150

200

250

300

-8 -6 -4 -2 0 2


Load

(kN

)

kL/r = 70

e’ = 0.36 mm

Frs = 0.49 Fy

Experiment

Model 1Model 1

Experiment

S2S1

0

50

100

150

200

250

300

-8 -6 -4 -2 0 2


Load

(kN

)

kL/r = 70

e’ = 0.36 mm

Frs = 0.49 Fy

Experiment

Model 1Model 1

Experiment

S2S1 S2S1

0

50

100

150

200

250

300

-8 -6 -4 -2 0 2


Load

(kN

)Model 1

Experiment

S2S1

kL/r = 46

e’ = 0.26 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

-8 -6 -4 -2 0 2


Load

(kN

)Model 1

Experiment

S2S1 S2S1

kL/r = 46

e’ = 0.26 mm

Frs = 0.49 Fy

Chapter 6

256



0

20

40

60

80

100

120

-4 -3 -2 -1 0 1 2


Load

(kN

)

kL/r = 93

e’ = 0.96 mm

Frs = 0.49 Fy

Experiment

Model 1Model 1

Experiment

S2S1

0

20

40

60

80

100

120

-4 -3 -2 -1 0 1 2


Load

(kN

)

kL/r = 93

e’ = 0.96 mm

Frs = 0.49 Fy

Experiment

Model 1Model 1

Experiment

S2S1 S2S1

0

50

100

150

200

250

300

-8 -6 -4 -2 0 2


Load

(kN

)

Model 1

Experiment

S2S1

kL/r = 70

e’ = 0.32 mm

Frs = 0.49 Fy

0

50

100

150

200

250

300

-8 -6 -4 -2 0 2


Load

(kN

)

Model 1

Experiment

S2S1 S2S1

kL/r = 70

e’ = 0.32 mm

Frs = 0.49 Fy

Chapter 6

257


Figure 6.42 Measured and predicted load-axial strain responses of specimen 7.


Load

(kN

)

0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

Experiment

Model 2Model 1

Model 1Model 2

Experiment

S2S1kL/r = 68

e’ = 6.60 mm

Frs = 0.33 Fy


Load

(kN

)

0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

Experiment

Model 2Model 1

Model 1Model 2

Experiment

S2S1 S2S1kL/r = 68

e’ = 6.60 mm

Frs = 0.33 Fy

0

20

40

60

80

100

120

140

160

180

200

-4 -3 -2 -1 0 1 2


Load

(kN

)

kL/r = 93

e’ = 0.84 mm

Frs = 0.49 Fy

Experiment

Model 1

Model 1Experiment

S2S1

0

20

40

60

80

100

120

140

160

180

200

-4 -3 -2 -1 0 1 2


Load

(kN

)

kL/r = 93

e’ = 0.84 mm

Frs = 0.49 Fy

Experiment

Model 1

Model 1Experiment

S2S1 S2S1

Chapter 6

258



0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1


Load

(kN

)

Experiment

Model 2Model 1

Model 1

Experiment

S2S1kL/r = 68

e’ = 0.92 mm

Frs = 0.33 Fy

Model 2

0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1


Load

(kN

)

Experiment

Model 2Model 1

Model 1

Experiment

S2S1 S2S1kL/r = 68

e’ = 0.92 mm

Frs = 0.33 Fy

Model 2


0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

Load

(kN

)

Experiment

Model 2

Model 1Model 1

Model 2

Experiment

S2S1kL/r = 68

e’ = 6.60 mm

Frs = 0.33 Fy


0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

Load

(kN

)

Experiment

Model 2

Model 1Model 1

Model 2

Experiment

S2S1 S2S1kL/r = 68

e’ = 6.60 mm

Frs = 0.33 Fy

Chapter 6

259



0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1


Load

(kN

)

Experiment

Model 2

Model 1

Model 1

Model 2

Experiment

S2S1kL/r = 68

e’ = 2.04 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1


Load

(kN

)

Experiment

Model 2

Model 1

Model 1

Model 2

Experiment

S2S1 S2S1kL/r = 68

e’ = 2.04 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1


Load

(kN

)

Experiment

Model 2

Model 1

Model 1

Model 2

Experiment

S2S1

kL/r = 68

e’ = 5.00 mm

Frs = 0.33 Fy

0

50

100

150

200

250

300

350

400

450

-2.5 -2 -1.5 -1 -0.5 0 0.5 1


Load

(kN

)

Experiment

Model 2

Model 1

Model 1

Model 2

Experiment

S2S1 S2S1

kL/r = 68

e’ = 5.00 mm

Frs = 0.33 Fy

Chapter 6

260

Figure 6.47 Comparison between the deformed shapes in experiments and FEM (Model 2).

Undeformed

shape

(a) Overall buckling based on Model 2

(b) Overall buckling of test specimen

Spe

cim

en

(c) Deformed cross section of slender column

(d) Displacement in x-direction (Ux)

(e) Displacement in z-direction (Uz)

(f) Rotation about y-axis (Ry)

xy

z

Min. Ux

Max. Uz

Min. Ry

xy

z

xy

z

Max. Ry

Values are in mm

Values are in rad.

Values are in mm

xyz

Undeformed

shape

(a) Overall buckling based on Model 2

(b) Overall buckling of test specimen

Spe

cim

en

(c) Deformed cross section of slender column

(d) Displacement in x-direction (Ux)

(e) Displacement in z-direction (Uz)

(f) Rotation about y-axis (Ry)

xy

z

xy

z

Min. Ux

Max. Uz

Min. Ry

xy

z

xy

z

xy

z

xy

z

Max. Ry

Values are in mm

Values are in rad.

Values are in mm

xyz

xyz

Chapter 6

261

Figure 6.48 Load-lateral displacement responses for specimens with e’=L/500.


0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRP

kL/r = 68 e’ = L/500 Frs = 0.25 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRPCFRP

kL/r = 68 e’ = L/500 Frs = 0.25 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRP

kL/r = 68 e’ = L/600 Frs = 0.25 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

CFRP crushing in the convex

side

CFRP crushing in the concave

side

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRPCFRP

kL/r = 68 e’ = L/600 Frs = 0.25 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

CFRP crushing in the convex

side

CFRP crushing in the concave

side

Chapter 6

262



0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)ρ = 9 % (1 layer)

CFRP

kL/r = 68 e’ = L/750 Frs = 0.25 Fy

ρ = 25 % (3 layers) ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)ρ = 9 % (1 layer)

CFRPCFRP

kL/r = 68 e’ = L/750 Frs = 0.25 Fy

ρ = 25 % (3 layers) ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRP

kL/r = 68 e’ = L/1000 Frs = 0.25 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRPCFRP

kL/r = 68 e’ = L/1000 Frs = 0.25 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

Chapter 6

263


Figure 6.53 Load-lateral displacement responses for specimens with Frs = 0.50 Fy.

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRP

kL/r = 68 e’ = L/500 Frs = 0.50 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50

Load

(kN

)


Control (no CFRP)

ρ = 9 % (1 layer)

CFRPCFRP

kL/r = 68 e’ = L/500 Frs = 0.50 Fy

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40 45 50

Load

(kN

)


CFRP

kL/r = 68 e’ = L/2000 Frs = 0.25 Fy

Control (no CFRP)

ρ = 9 % (1 layer)

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40 45 50

Load

(kN

)


CFRPCFRP

kL/r = 68 e’ = L/2000 Frs = 0.25 Fy

Control (no CFRP)

ρ = 9 % (1 layer)

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

Chapter 6

264

Figure 6.54 Load-lateral displacement responses for specimens with kL/r =160.

0

25

50

75

100

125

150

0 50 100 150 200 250 300

Load

(kN

)


CFRP

kL/r = 160 e’ = L/500 Frs = 0.25 Fy

Control (no CFRP)

ρ = 9 % (1 layer)

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

0

25

50

75

100

125

150

0 50 100 150 200 250 300

Load

(kN

)


CFRPCFRP

kL/r = 160 e’ = L/500 Frs = 0.25 Fy

Control (no CFRP)

ρ = 9 % (1 layer)

ρ = 25 % (3 layers)

ρ = 43 % (5 layers)

Chapter 6

265

Figure 6.55 Summary of results of parametric study.

FRP reinforcement ratio ρf = Af /As x 100

(b) Effect of CFRP layers on displacement

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45

L/500

L/60

0

L/750

L/1000L/2000

5 La

yers

3 La

yers

1 La

yer

% a

ge R

educ

tion

in la

tera

l di

spla

cem

ent @

max

imum

load

(a) Effect of number of CFRP layers on strength

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40 45

% a

ge In

crea

se in

axi

al s

treng

th

3 La

yers

1 La

yer

5 La

yers

L/500

L/600

L/750

L/1000

L/2000

0

5

10

15

20

25

30

35

40

0.0005 0.001 0.0015 0.002

% a

ge In

crea

se in

axi

al s

treng

th

ρ = 43% (5 Layers)

L/10

00 L/75

0

L/60

0

L/50

0

L/20

00

Out-of-straightness multiplier x L

(c) Effect of out-of-straightness on strength

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45

5 La

yers3

Laye

rs

1 La

yer

kL/r = 68, res. Stress = 50%

FRP reinforcement ratio ρ = Af /As x 100

(d) Effect of residual stress and slenderness ratio on strength

% a

ge In

crea

se in

axi

al s

treng

th

kL/r =

160

, res

. Stre

ss =

25%

e’ = L/500

Frs = 0.25 FykL/r = 68

Frs = 0.25 FykL/r = 68

Frs = 0.25 FykL/r = 68

ρ = 25% (3 Layers)

ρ = 9% (1 Layer)

kL/r = 68, res. S

tress = 25%



0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45

L/500

L/60

0

L/750

L/1000L/2000

5 La

yers

3 La

yers

1 La

yer

% a

ge R

educ

tion

in la

tera

l di

spla

cem

ent @

max

imum

load


0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40 45

% a

ge In

crea

se in

axi

al s

treng

th

3 La

yers

1 La

yer

5 La

yers

L/500

L/600

L/750

L/1000

L/2000

0

5

10

15

20

25

30

35

40

0.0005 0.001 0.0015 0.002

% a

ge In

crea

se in

axi

al s

treng

th

ρ = 43% (5 Layers)

L/10

00 L/75

0

L/60

0

L/50

0

L/20

00



0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45

5 La

yers3

Laye

rs

1 La

yer




% a

ge In

crea

se in

axi

al s

treng

th

kL/r =

160

, res

. Stre

ss =

25%

e’ = L/500

Frs = 0.25 FykL/r = 68

Frs = 0.25 FykL/r = 68

Frs = 0.25 FykL/r = 68

ρ = 25% (3 Layers)

ρ = 9% (1 Layer)

kL/r = 68, res. S

tress = 25%



0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45

L/500

L/60

0

L/750

L/1000L/2000

5 La

yers

3 La

yers

1 La

yer

% a

ge R

educ

tion

in la

tera

l di

spla

cem

ent @

max

imum

load


0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40 45

% a

ge In

crea

se in

axi

al s

treng

th

3 La

yers

1 La

yer

5 La

yers

L/500

L/600

L/750

L/1000

L/2000

0

5

10

15

20

25

30

35

40

0.0005 0.001 0.0015 0.002

% a

ge In

crea

se in

axi

al s

treng

th

ρ = 43% (5 Layers)

L/10

00 L/75

0

L/60

0

L/50

0

L/20

00



0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45

5 La

yers3

Laye

rs

1 La

yer




% a

ge In

crea

se in

axi

al s

treng

th

kL/r =

160

, res

. Stre

ss =

25%

e’ = L/500

Frs = 0.25 FykL/r = 68

Frs = 0.25 FykL/r = 68

Frs = 0.25 FykL/r = 68

ρ = 25% (3 Layers)

ρ = 9% (1 Layer)

kL/r = 68, res. S

tress = 25%

Chapter 6

266

Figure 6.56 Strength comparison between Models 1 and 2.

Figure 6.57 Stiffness comparison between Models 1 and 2.

268

360

343

407

378

297 33

0

374

413

267

359

326

412

383

289 30

7

346 38

3

0

50

100

150

200

250

300

350

400

450

500

Spe

cim

en 7

Spe

cim

en 8

Spe

cim

en 9

Spe

cim

en 1

0

Spe

cim

en 1

1

68-5

00-

cont

rol-2

5

68-5

00-9

-25

68-5

00-2

5-25

68-5

00-4

3-25

Model 1Model 2

Axia

l stre

ngth

(kN

)

Specimen identification

268

360

343

407

378

297 33

0

374

413

267

359

326

412

383

289 30

7

346 38

3

0

50

100

150

200

250

300

350

400

450

500

Spe

cim

en 7

Spe

cim

en 8

Spe

cim

en 9

Spe

cim

en 1

0

Spe

cim

en 1

1

68-5

00-

cont

rol-2

5

68-5

00-9

-25

68-5

00-2

5-25

68-5

00-4

3-25

Model 1Model 2

Axia

l stre

ngth

(kN

)


Axia

l stif

fnes

s (k

N/m

m)


88

102 10

9

130 13

5

80

91

105

117

85

98

109

126 13

5

89

96

111

125

0

20

40

60

80

100

120

140

160

Spe

cim

en 7

Spe

cim

en 8

Spe

cim

en 9

Spe

cim

en 1

0

Spe

cim

en 1

1

68-5

00-

cont

rol-2

5

68-5

00-9

-25

68-5

00-2

5-25

68-5

00-4

3-25

Model 1Model 2

Axia

l stif

fnes

s (k

N/m

m)


88

102 10

9

130 13

5

80

91

105

117

85

98

109

126 13

5

89

96

111

125

0

20

40

60

80

100

120

140

160

Spe

cim

en 7

Spe

cim

en 8

Spe

cim

en 9

Spe

cim

en 1

0

Spe

cim

en 1

1

68-5

00-

cont

rol-2

5

68-5

00-9

-25

68-5

00-2

5-25

68-5

00-4

3-25

Model 1Model 2

Chapter 7

267

Chapter 7 Analytical Modeling of CFRP-Retrofitted

Steel-Concrete Composite Girders

7.1 Introduction

This chapter discusses the analytical models developed to predict the flexural strength

and behaviour of steel-concrete girders repaired or strengthened using FRP materials. In

the case of strengthening of intact girders, the model is based on establishing the

moment-curvature relationship of the cross section, which is then integrated along the

span to develop the entire load-deflection behaviour of the girder, up to failure. A

parametric study is also performed to examine the effects of elastic modulus and rupture

strain of CFRP, as well as the CFRP reinforcement ratio on the behaviour of the

strengthened steel-concrete girders. In the case of repair of steel-concrete composite

girders having a cut in the steel flange, a simplified analytical approach is proposed to

predict their ultimate moment capacity, and deflection at service load.

Chapter 7

268

7.2 Intact Steel-Concrete Composite Girders Strengthened

using CFRP Materials

Figure 7.1(a) illustrates the strain and stress distributions over a typical cross section. An

incremental approach, similar to the one used for the fibre-element model of HSS

columns and described in chapter 6, is used. The concepts of equilibrium and strain

compatibility are satisfied at each loading step. The analytical procedure is executed

using a spread sheet-type programming. The following assumptions are considered in this

flexural model:

1. Plane sections remain plane after deformation.

2. The following constitutive models are assumed to represent the behaviour of the

materials, as shown in Figure 7.1(b): (a) the stress-strain curve of steel is assumed

to follow an elastic-perfectly plastic model, (b) concrete is assumed to follow a

second degree parabola in compression (Collins and Mitchell, 1997), and (c) FRP

materials are assumed to behave linearly up to rupture. The curves shown in

Figure 7.1(b) are based on the material properties used in test specimens G1 to

G3.

3. Residual stresses of the steel section are neglected.

4. Perfect bond exists between the FRP bonded plates and steel.

5. Two different limit states may occur in the model, namely, concrete crushing or

rupture of FRP material.

Chapter 7

269

7.2.1 Moment-curvature relationship

In order to establish the moment-curvature curve of a given cross section, the strain at the

top level of the concrete compression flange (εtop) is first assumed. The cross section of

the strengthened girder is divided into horizontal layers (elements), as shown in Figure

7.1(a), and the strain (εi) of each element i located at a distance di from the extreme top

fibres of the cross section can then be determined using the concept of similar triangles as

follows:

topi

i cd

εε ⎥⎦

⎤⎢⎣

⎡−= 1 (7.1)

where (c) is the neutral axis depth.

The stress in each element can then be determined from strain using the corresponding

material stress-strain relationship, as given by Equations 7.2 to 7.4 for concrete, steel

cross section (or reinforcing bars), and FRP materials, respectively.

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−=

2

''' 2

c

ci

c

cicci fF

ε

ε

ε

ε (7.2)

ysiyis

ysissis

whenFF

whenEF

εε

εεε

>=

≤= (7.3)

ufififfif whenEF εεε ≤= (7.4)

where 'cf = concrete compressive strength obtained from cylinder tests.

ciF = concrete compressive stress at any element i before failure.

'cε = strain corresponding to '

cf and is assumed to be 0.25 percent.

Chapter 7

270

siF = steel stress at any element i.

yF = yield strength of steel.

fiF = FRP stress at any element i before rupture.

ufε = rupture strain of FRP.

For a given value of the neutral axis depth (c), the strain distribution over the entire cross

section can be determined and the internal force of each element can then be calculated.

Using Simpson’s Rule, the stress integration (i.e. internal forces) of the cross section can

be determined using the following equation:

( ) ( ) ( ) ( )∑∑∑∑ +++=FRP

ififsteel

sisibars

rbrbconcrete

cici AFAFAFAFR (7.5)

where ifsirbci AandAAA ,,, are the areas of the concrete, reinforcing bar, steel, and

FRP elements, respectively, and rbF is the stress at the reinforcing bars.

An iterative approach is followed by varying the values of (c) until force equilibrium is

satisfied (i.e. R = 0). The moment capacity of the cross section can then be determined by

summing the bending moments of the element forces about the extreme top fibres of the

cross section as follows:

( ) ( ) ( ) ( )∑∑∑∑ +++=FRP

iiffisteel

isisibars

irbrbconcrete

icici dAFdAFdAFdAFM (7.6)

Based on the assumption of strain compatibility and plane deformed sections, the

curvature (ψ) may be determined as,

ctopε

ψ = (7.7)

Chapter 7

271

A point (ψ, M) on the moment-curvature response has now been determined for the

concrete strain εtop. The procedure can be repeated for the next level of concrete

compressive strain (εtop). The process is continued until one of two limit states is reached,

either crushing of concrete, or rupture of the FRP material. Since both limit states are

strain-controlled, and the process is based on increasing the strains incrementally, the

ultimate strength and mode of failure are easily determined.

7.2.2 Load-deflection behaviour

Once the moment-curvature of the section is obtained, the load-deflection response of the

girder can be estimated for a given loading scheme. The deflection (y) is calculated by

integrating the curvatures (ψ) along the span using the moment-area method, as shown in

Figure 7.2, and given by the following equations:

2

2

dxyd

=ψ (7.8)

∫∫= dxdxxy )(ψ (7.9)

The deflection at any point is essentially the moment of the curvature diagram, which is

considered as elastic load acting on the conjugate beam (Ghali and Neville, 1989).

7.2.3 Verification of the model

The model was verified using the test results of experimental Phase III, including a

control and two strengthened girders. Figure 7.3 to 7.5 show comparisons between the

experimental and predicted moment-curvature responses of girders G1 to G3. The

experimental curvature was calculated based on the longitudinal strain measurements on

Chapter 7

272

the top side of the concrete slab, and the bottom side of the tension steel flange (or the

CFRP plates for the strengthened girders). For girder G2, the strain gauge was attached to

the first layer of CFRP, which remained bonded to the steel flange throughout the test,

unlike the second CFRP short layer, which debonded at a tensile strain of 0.29 percent.

For girder G3, there was only one strain gauge attached to the outer CFRP plate, and was

lost after debonding of the outer CFRP plate at a tensile strain of 0.18 percent. Therefore,

the experimental moment-curvature response in Figure 7.5 is incomplete. In Figure 7.4

and 7.5, the predictions are made for two cases. In one case, the two CFRP layers are

assumed fully bonded to the end and in the second case, only the first (inner) CFRP layer

is present from the onset of steel yielding. Figure 7.6 to 7.8 show comparisons between

the experimental and predicted responses of moment-strain of the tension flange, while

Figure 7.9 to 7.11 show the load-deflection responses of all the three girders. In the

predictions of all three girders, failure occurred at ultimate by crushing of concrete slab

before rupture of CFRP. Generally, the model shows good agreement with the

experimental results in all responses of control and CFRP-strengthened girders.

7.3 Parametric Study on Girder Strengthening

In this section, a parametric study is performed using the proposed model to study the

effects of the elastic modulus and the rupture strain (i.e. tensile strength) of CFRP

material, as well as the reinforcement ratio (i.e. amount of CFRP) on the flexural

behaviour of the strengthened girders. The same cross section of the girders tested in

experimental Phase III was selected for the analysis. Three commercially available CFRP

products with a wide range of elastic moduli are used in the analysis. CFRP types C4 and

Chapter 7

273

C5, which were previously used in the experimental program (EC4 = 152 GPa and EC5 =

313 GPa), as well as a third type, referred to here as C6 (EC6 = 457 GPa) are used in the

parametric study. CFRP type C6 is produced by Epsilon Composite and commercially

known as THM-450 (Schnerch, 2005). These types of CFRP are chosen to represent

Standard Modulus- (SM-), High Modulus- (HM-), and Ultra High Modulus- (UHM-)

CFRP. Three CFRP reinforcement ratios (ρ) of 1.3, 2.6, and 3.9 percent are considered

by having a constant plate thickness of 1.4 mm, and various plate widths of 30, 60, and

90 mm, respectively. Failure modes considered are either CFRP rupture or concrete

crushing. Table 7.1 summarizes the results of the parametric study. Figure 7.12 to 7.14

show the moment-curvature responses for all cases. The effect of each parameter is

discussed in the following sections.

7.3.1 Effect of CFRP elastic modulus

Table 7.1 and Figure 7.12 to 7.14 clearly show the increase in flexural strength as a result

of increasing the reinforcement ratio for each type of CFRP. It is noted, however, that a

small reduction in strength and a large reduction in ductility are associated with the

increase in the elastic modulus of CFRP. Table 7.1 also indicates that for the same

reinforcement ratio (ρ = 3.9 percent), the stiffness of the strengthened girders is increased

by 6, 12, and 17 percent for CFRP elastic moduli of 152, 313, and 457 GPa, respectively.

It is also noted that the CFRP contribution and the effect of the elastic modulus on

flexural stiffness are more pronounced after yielding of steel, compared to those in elastic

range. Figure 7.15 shows the percentage increase in the elastic stiffness of the

strengthened girders versus the ratio of the CFRP-to-steel elastic moduli, for different

Chapter 7

274

reinforcement ratios. The figure shows linear relationships with a slope depending on the

reinforcement ratio.

Table 7.1 and Figure 7.16 show the relationships between the percentage increase in the

yielding moment of the strengthened girders and the ratio of the steel-to-CFRP elastic

moduli for different reinforcement ratios. The relationships are also linear with a slope

depending on the reinforcement ratio.

Figure 7.17 shows the effect of elastic modulus of CFRP on the percentage reduction

inductility. The figure shows that the rate of reduction is higher between SM-CFRP and

HM-CFRP. Also, the reduction in ductility is independent of the reinforcement ratio.

Table 7.1 suggests that using UHM-CFRP with a small reinforcement ratio may not be as

effective as using a SM-CFRP with a large reinforcement ratio in increasing the flexural

strength. In other words, using two different types of CFRP having the same (Ef Af)

product (i.e. product of modulus and area) will not provide the same increase in flexural

strength. This is attributed to the different tensile strengths of the different types of

CFRP.

7.3.2 Effect of CFRP reinforcement ratio

Table 7.1 and Figure 7.15 and 7.16 show that, within the elastic range, the same gain in

either the stiffness or the yielding moment could be achieved by increasing either the

CFRP elastic modulus Ef or the reinforcement ratio ρ. It should be noted that, these

Chapter 7

275

results are based on increasing the CFRP reinforcement ratio by increasing the width of

the plate (i.e. a corresponding increase in contact surface area is also achieved, and hence

the bond strength is maintained). However, had the thickness of the CFRP material been

increased instead of the width, a debonding type of failure, rather than rupture could

occur, which may lead to a reduction in the yielding moment. Moreover, increasing the

thickness of the CFRP material could magnify the shear lag effect, which may affect the

stiffness of the girder.

7.3.3 Effect of rupture strain of CFRP

In general, increasing the CFRP elastic modulus is usually associated with reduction of

its ultimate tensile strength (Figure 3.8). Therefore, it was decided to compare three

actual CFRP products in the parametric study. Table 7.1 lists the ultimate strain at rupture

for each type of CFRP. Figure 7.18 clearly shows that the strength of the CFRP

reinforced girders is directly proportional to the rupture strain of the CFRP.

7.4 Damaged Steel-Concrete Composite Girders Repaired using

CFRP Materials

This section presents a simplified model used to predict the ultimate moment and

deflection at service load of damaged and the repaired steel-concrete composite girders

using FRP materials. The damage is assumed to be a complete loss of the tension flange

at one cross section. The following sections provide a detailed description of the model.

Chapter 7

276

7.4.1 Ultimate moment capacity

A similar approach to the one described previously in Section 7.2 is used to predict the

ultimate moment. However, a few additional assumptions are made to account for the

stress concentration in the vicinity of the damaged flange as well as the crack propagation

from the cut flange into the web, in a simplified manner. The model covers the following

cases:

1. Intact cross section.

2. Damaged cross section (but not repaired).

3. Repaired cross sections, including two conditions:

i. Repair using HM-CFRP (governed by CFRP rupture).

ii. Repair using SM-CFRP (governed by CFRP debonding).

Additionally, a calibration for the assumptions made in the model is introduced. The

model is verified using the experimental results of Phase III.

7.4.1.1 Intact cross section

The intact cross section resembles an undamaged conventional steel-concrete composite

control girder. The calculations of flexural strength are based on first principles of strain

compatibility and force equilibrium, exactly as discussed in section 7.2 7.2.1. The cross

sectional moment capacity M will be calculated using Equation (7.6), at one point only

when the uppermost concrete fibres reach the crushing strain (εc top = εcr = 0.35 percent),

as shown in Figure 7.19(a).

Chapter 7

277

7.4.1.2 Damaged cross section (but not repaired)

The introduced cut in the steel tension flange creates a zone of stress concentration,

which eventually leads to crack propagation through the steel web, as observed

experimentally. In calculating the ultimate moment capacity at the damaged cross

section, a simplified approach is proposed to account for this phenomenon. This approach

ignores the lower flange as well as a part of the web of a height (ηd), as shown in Figure

7.19(b), where d is the total depth of the section. The value of (η) is assumed and then

calibrated. It should be noted that linear strain distribution is assumed within the

remaining part of the steel section and the concrete slab for simplicity, which may not be

quite the case in reality. The cross sectional moment capacity M is calculated using

Equation (7.6), when concret crushes (εc top = εcr = 0.35 percent).

7.4.1.3 Damaged and repaired cross sections

The value of the elastic modulus of the CFRP used in the repair of damaged girders plays

an important role in determining the failure mode of the repaired girder. Based on the

results of Phase III of the experimental program, it was shown that CFRP rupture occurs

when using HM-CFRP, due to the very high modulus and consequently the small strain at

rupture of CFRP. This rupture strain is usually close to or slightly higher than the yield

strain of steel. On the other hand, debonding typically occurs when using SM-CFRP

since the ultimate (rupture) strain of CFRP is very high, relative to the yielding strain of

steel. It was also observed experimentally that debonding happens at different strain

levels, depending on the bonded surface area (i.e. length and width of the CFRP). In the

Chapter 7

278

following sections, the procedure used to account for the type of CFRP and the associated

failure mode is discussed.

7.4.1.3.1 Cross section repaired using HM-CFRP

In the case of HM-CFRP, failure may be due to rupture of the CFRP material. Since this

type of tension failure occurs at a very small tensile strain, crushing of the concrete slab

is highly unlikely to occur. Also, most of the intact part of the steel section would still be

elastic at failure. Therefore, the flexural strength calculations would be very similar to

that described in section 7.2.1, except that the ultimate moment capacity M is calculated

when the CFRP strain reaches the rupture strain (εf = εr), instead of assuming a

compressive crushing strain in the extreme fibre of the concrete slab. The concrete strain

can then be checked at ultimate to ensure that it has not reached the crushing strain.

7.4.1.3.2 Cross section repaired using SM-CFRP

In the case of SM-CFRP, failure may either be due to debonding of CFRP or crushing of

the concrete slab. The flexural strength can also be calculated using the same procedure

described in section 7.2.1. The main difference would be the governing strain of CFRP at

debonding. It has been shown in Figure 5.40 that the axial strain in CFRP at debonding

depends on the bonded length. Also, the effect of bond length on strain at ultimate varies

in the shear span from the constant moment region. Therefore, the following two

equations are proposed to obtain the strain εmax in CFRP at debonding of SM-CFRP,

based on fitting the experimental results in Figure 5.40:

Chapter 7

279

CFRPult

L0055.0max =ε

ε (No shear) (7.10)

6324.00003.0max += CFRPult

Lε

ε (Bending and shear) (7.11)

where εult is the reported rupture strain of CFRP and LCFRP is the bonded length of CFRP

on one side of mid-span, in mm.

Debonding may be assumed first by using εmax and then check that the top concrete strain

is below crushing strain. If it is not, the analysis should be revised assuming concrete

crushing prior to CFRP debonding.

7.4.1.4 Calibration of parameter η for the neglected part of the steel web

A calibration study is carried out to assess the length of the lower part of the web (ηd),

which is considered inefficient due to crack propagation, and can then be neglected in

section analysis. Three values of η (0.25, 0.33, and 0.50) were assumed in this study. The

moment capacities of the beams tested in Phase III, except for B5, were calculated using

the different values of η. Table 7.2 shows the maximum strain of CFRP at ultimate, based

on Equations 7.10 and 7.11, the measured and predicted ultimate moment capacities for

each beam and η value as well as their ratio. Also given in Table 7.2, is the average and

standard deviation values of the (predicted moment / measured moment) ratios for each

value of η. The same results are plotted in Figure 7.20 for beams B3 to B11 (except B5)

as well as for B2. Generally, Table 7.2 and Figure 7.20 show that η has a relatively small

yet significant effect on the predicted moment. It is noted that the model tends to

Chapter 7

280

underestimate the moment capacity of the damaged and unrepaired specimen (B2) for all

the three values of η. On the other hand, the model tends to overestimate the moment

capacity of the damaged and repaired specimens (B3, B4, and B6 to B11) for all values of

η. It is also noted that the value of η has less effect on the repaired specimens. This is

attributed to the fact that the unrepaired section is reduced to a T-section, where its

moment of inertia becomes much more sensitive to the intact height of the web. CFRP

repair, on the other hand, provides a supplementary lower flange, resulting in an I-

section, for which the moment of inertia is not greatly affected by the intact height of the

web. Figure 7.20 suggests that the optimum values of η, which result in an average

moment ratio of 1.00, are 0.57 and 0.23 for the repaired and unrepaired beams,

respectively. It should be noted that this study investigated the effect of η on specimens

with several variables, namely, different types of CFRP, different force equivalence

indices (ω), and different bonded lengths and areas. The approach adopted in this model

to deal with the cut in the flange, the crack propagation, and the associated stress

concentration is certainly a simplification of a problem that is otherwise quite complex.

This is suited for engineers and designers. A more rigorous approach could possibly

employ the concepts of fracture mechanics.

7.4.2 Deflection at service load

This section provides a simplified procedure for calculating the mid-span deflection at

service load. The service load is defined as the unfactored dead plus live loads. In order

to estimate the equivalent service load of the test beams at which deflection will be

predicted, the following classic load combination equation is used:

Chapter 7

281

LLDDf MMM αα += (7.12)

where fLD MandMM ,, are the dead and live service moments, and the total factored

moment, respectively. LD and αα are the dead and live load factors, and are taken as

1.25 and 1.5, respectively, (NBCC, 2005). Equation (7.12) is then rearranged to isolate

ML as follows:

L

DDfL

MMM

αα−

= (7.13)

By setting αL ML equal to the experimental measured maximum moment of the beam and

MD equal to the self weight of the beam, the moment at service load (Mservice = MD + ML)

can be obtained.

The deflection at service load can be calculated using various methods, including the

virtual work method (Ghali and Neville, 1989). The general virtual work equation used to

calculate the vertical deflection at any point along the beam span (L) can be formulated as

follows:

∫∫ +=L

ws

serviceL

ts

service dxAG

vVdx

IEmM

00

δ (7.14)

where m and v are the internal virtual bending moment and shear force, respectively, due

to a virtual unit load at the deflection point of interest along the beam. M and V are the

actual bending moment and shear force, respectively, acting on the beam due to service

loads. Gs is the elastic shear modulus of steel, and is taken as 77 GPa (Kulak and

Grondin, 2002). It is the transformed moment of inertia, and Aw is the area of the steel

web. It should be noted that for girders with relatively large shear span-to-depth ratio, the

Chapter 7

282

second term of Equation (7.14) becomes insignificant and can be neglected. This,

however, is not the case for the beams tested in Phase III of this study, since the spans

were relatively short.

The transformed moment of inertia (It) is calculated after transforming the concrete slab

breadth (bc) and the FRP breadth (bf) to equivalent steel breadths beqc and beqf, according

to the following relationships, as shown in Figure 7.19.

cs

ctceq b

EE

b = (7.15)

fs

f

feq bE

Eb = (7.16)

where Ect is the initial tangent modulus of concrete. For the assumed parabolic stress-

strain relationship of concrete, Ect is given by:

'

'

2c

cct

fE

ε= (7.17)

Alternatively, the product (Es It) of the cross section can easily be calculated using the

moment-curvature relationship within the elastic range, as follows:

ψservice

tsM

IE = (7.18)

For concrete-steel composite girders with shear connectors, the effective moment of

inertia (Ieff) is used in Equation (7.14) in lieu of It to account for the increase in deflection

that may result from the interfacial slip between the concrete slab and the steel girder. Ieff

can be obtained using the following formula (CAN/CSA-16-01):

( )stseff IIII −+= 25.0)(85.0 ρ (7.19)

Chapter 7

283

where Is is moment of inertia of the steel cross section alone (i.e. without the concrete

slab) and ρ is a fraction of full shear connection and is calculated by:

nn '

=ρ (7.20)

where n’ is the actual number of shear connectors used in the girder, and n is the number

of shear connectors required for full composite action. For the beams tested in Phase III,

n’ equals to 33 studs and n is calculated using the following Equation (CAN/CSA-S16-

01) and was 51 studs:

( ) ( )[ ]( ) ( )[ ]uscctcsc

cccys

FAorEfA

ftborFAn

'5.0min

'85.0min= (7.21)

where Asc is the cross sectional area of one shear stud, As is the area of the steel cross

section, Fy is the yield stress of steel, and Fu is the ultimate stress of the shear stud.

The following sections provide a proposed methodology to account for the effects of

section loss and the resulting stress distribution in the vicinity of the crack as well as the

effect of the bonded length of the CFRP sheets in deflection calculations.

7.4.2.1 Effect of stress flow in the vicinity of the crack

It has been established in section 7.4.1.4, that the lower flange and 57 percent of the web

are ignored at the mid-span section, to account for the crack propagation at ultimate. For

simplicity and as a conservative approach, the same same level of section loss is assumed

at service. The upward propagation of the crack within the web affects the stress flow in

the region around the crack. The stress flow within the web and flange is idealized, as

shown in Figure 7.21(a). The inclined line starts from point “a” at 0.57d of the web and

Chapter 7

284

follows a slope of (z:1) until it reaches the flange at point “b”. The line then spreads

within the flange in the transverse direction with a slope (1:z), until it reaches the edges

of the flange at line “c-c”. The slope value (z) is determined through a calibration study.

For the damaged unrepaired girders [Figure 7.19(b)], the moment of inertia of the intact

section (Ieff1) [Figure 7.19(a)] beyond line “c-c” can be assumed and is calculated using

Equation 7.19. Equation 7.19 is also used to calculate (Ieff2) at mid-span accounting for

section loss. Between the mid-span section and line “c-c”, the moment of inertia is

assumed to vary linearly from Ieff1 to Ieff2.

For the CFRP-repaired girders, the moment of inertia at mid-span is referred to as Ieff4,

based on the cross section shown in Figure 7.19(c or d). For sections beyond line “c-c”,

and if CFRP extends beyond line “c-c”, the moment of inertia is referred to as Ieff3, which

is based on intact cross section strengthened with CFRP. The moment of inertia is

assumed to vary linearly between Ieff3 to Ieff4 as shown in Figure 7.21(b, left side). Both

Ieff3 and Ieff4 are also calculated using Equation 7.19, where Is in this case is the moment of

inertia of the cross section at mid-span without the concrete slab (i.e. Is = IT-section + ICFRP).

The contribution of FRP is also considered in the calculation of It [Equation (7.18)].

Based on the conclusions drawn by Miller (2000), Colombi and Poggi (2006), and the

experimental observations of Phase III of this study, the development length of CFRP

sheets can reasonably be assumed 100 mm from the free edge of the sheets. As shown in

Figure 7.21(b, left side), a linear transition is assumed between from Ieff1 and Ieff3 within

this length.

Chapter 7

285

If the CFRP is terminated before line “c-c” [Figure 7.21(b, right side)], then Ieff4 is

assumed at mid-span. A fictitious Ieff3 value is assumed at line “c-c” and linearly

connected to Ieff4 at mid-span. The diagram is then corrected with a 100 mm transfer

length measured from the termination point of CFRP.

7.4.2.2 Calibration of the slope (z:1)

Three slopes (1:1, 1.5:1, and 2:1) were examined in this study. The deflections were

calculated using Equation 7.14 and compared with the experimental results of the beams

tested in Phase III. Table 7.3 shows the service load and moment at which the deflection

is calculated, the measured deflection at service load, the predicted deflection at service

load, and the ratio of the two values for each beam. The values are calculated for each of

the three assumed slopes. Also given in Table 7.3, are the average and standard deviation

values of the (predicted deflection / measured deflection) ratios for each slope. The same

results are plotted in Figure 7.22 for beams B3 to B11 (except B5) as well as for B2. The

figure suggests that deflections are highly sensitive to the z value. Also, extending the

average lines of the repaired and unrepaired beams to intercept the unity ratio leads to a

values of z equal to 0.48 and 2.85, respectively. It is noted from Figure 7.22 that this

approach has resulted in overestimating the deflections for the repaired beams and

underestimating the deflection for the unrepaired beam.

Chapter 7

286

Table 7.1 Summary of parametric study on strengthening steel-concrete composite girders.

CFRP

Elas

tic m

odul

us,

E (G

Pa)

Rup

ture

str

ain

(εr)

x 10

-3

ρ

Flex

ural

stif

fnes

s (k

N/m

m)

%ag

e ga

in

Yiel

ding

mom

ent

(kN

.m)

%ag

e ga

in

Mom

ent c

apac

ity

(kN

.m)

%ag

e ga

in

Cur

vatu

re @

m

axim

um lo

ad, ψ

(1

/m x

10-3

)

%ag

e re

duct

ion

control 17.6 132 180 63.1 152 12.57 1.3 18.0 2 135 2 201 12 47.3 25

2.6 18.3 4 138 5 223 24 47.7 24 3.9 18.7 6 141 7 244 36 48.0 24

313 4.71 1.3 18.3 4 138 5 182 1 18.7 70 2.6 19.0 8 144 9 199 11 19.0 70 3.9 19.7 12 151 14 216 20 19.1 70

457 3.35 1.3 18.7 6 141 7 180 0 13.8 78 2.6 19.7 12 150 13 192 7 14.0 78 3.9 20.7 17 160 21 210 17 14.3 77

Table 7.2 Calibration of the neglected part of the steel web in repair applications.

η 0.25 0.33 0.5

Spec

imen

I.D

.

Mexp εmax Mpred Mpred. Mexp.

Mpred Mpred. Mexp.

(Mn)pred Mpred. Mexp.

B1 139 N/A 138 0.99 138 0.99 138 0.99 B2 56 N/A 55 0.98 51 0.91 43 0.77 B3 65 0.22 86 1.32 82 1.27 77 1.19 B4 154 0.22 130 0.85 126 0.82 122 0.80 B6 121 0.63 127 1.05 123 1.01 117 0.96 B7 120 0.80 145 1.21 140 1.17 135 1.13 B8 162 0.96 172 1.06 170 1.05 167 1.03 B9 138 0.84 166 1.20 163 1.18 157 1.14

B10 125 0.64 137 1.10 134 1.07 127 1.02 B11 100 0.45 103 1.03 99 0.99 92 0.92

Average 1.08 1.05 0.99 Standard deviation 0.14 0.13 0.14

Chapter 7

287

Table 7.3 Calibration of the slope (z:1).

Slope (z:1) 1:1 1.5:1 2:1

Spec

imen

I.D

.

Service load, P

(kN)

Service moment

M, (k.Nm)

δexp. (mm)

δpred. (mm)

δpred.

δexp. δpred. (mm)

δpred.

δexp. δpred. (mm)

δpred.

δexp. B1 212 83 6.33 5.91 0.93 5.91 0.93 5.91 0.93 B2 85 33 5.92 4.45 0.75 4.63 0.78 4.84 0.82 B3 97 38 2.55 2.66 1.05 2.70 1.06 2.74 1.08 B4 235 92 5.49 5.47 1.00 5.51 1.00 5.37 0.98 B6 185 72 6.40 7.71 1.21 7.98 1.25 8.31 1.30 B7 182 71 5.65 5.99 1.06 6.10 1.08 6.26 1.11 B8 247 96 7.58 7.83 1.03 7.97 1.05 8.15 1.08 B9 210 82 6.24 6.75 1.08 6.88 1.10 6.99 1.12

B10 190 74 6.06 6.67 1.10 6.82 1.13 7.07 1.17 B11 152 59 4.87 5.69 1.17 5.85 1.20 6.14 1.26

Average 1.04 1.06 1.08 Standard deviation 0.13 0.13 0.15

P

1960

400

The effect of shear deformation is considered in the predicted deflection calculations. Gs = 77 GPa

Dims are in mm.

Chapter 7

288

Figure 7.1 Steel-concrete composite girder strengthened with FRP and subjected to pure bending.

Figure 7.2 Constructing the load-deflection diagram.

bc

cdi

element i

εtop

εi

ψ

Bending moment

“M”

εf

εbottom

tc/2εrb

Reinforcing bars

FRP

Rs2

Fc

Ff

Rf

N.A.

Rc

Rs1

Rs3

(Strains) (Stresses)

(a) Cross section analysis

(b) Constitutive models

Fy = 345 MPa

Fs

ε s=

0.00

17

εs

Steel

f’c = 40 MPa

Fc

ε c’=

0.0

025

εc

Concreteε c

r’=

0.00

35

1534 MPa

εf

CFRP

Ff

1475 MPa

1914 MPaC6

C5

C4

Ec5 = 313 GPa

Ec6 = 457 GPa

Ec4 = 152 GPa

bc

cdi

element i

εtop

εi

ψ

Bending moment

“M”

εf

εbottom

tc/2εrb

Reinforcing bars

FRP

Rs2

Fc

Ff

Rf

N.A.

Rc

Rs1

Rs3

(Strains) (Stresses)

(a) Cross section analysis

(b) Constitutive models

Fy = 345 MPa

Fs

ε s=

0.00

17

εs

Steel

f’c = 40 MPa

Fc

ε c’=

0.0

025

εc

Concreteε c

r’=

0.00

35

1534 MPa

εf

CFRP

Ff

1475 MPa

1914 MPaC6

C5

C4

Ec5 = 313 GPa

Ec6 = 457 GPa

Ec4 = 152 GPa

M(x)

ψ (x) Curvature

Mom

ent

P

y(x) Deflection

Load

P/2 P/2

y(x)(y-diagram)

x

M(x)(M-diagram)

ψ(x)(ψ-diagram)

Get y(x) as the moment of the area under the ψ - diagram

∫∫= dxdxxy )(ψM(x)

ψ (x) Curvature

Mom

ent

P

y(x) Deflection

Load

P/2 P/2

y(x)(y-diagram)

x

M(x)(M-diagram)

ψ(x)(ψ-diagram)

Get y(x) as the moment of the area under the ψ - diagram

∫∫= dxdxxy )(ψ

Chapter 7

289

Figure 7.3 Predicted versus experimental moment-curvature behaviour of control girder G1 in Phase II.

Figure 7.4 Predicted versus experimental moment-curvature behaviour of girder G2 in Phase II.

Curvature (1/m) x 10-3

0

25

50

75

100

125

150

175

200

225

250

275

0 10 20 30 40 50 60 70 80

Mom

ent (

kN.m

)

Experiment

Model

Concrete crushing


0

25

50

75

100

125

150

175

200

225

250

275

0 10 20 30 40 50 60 70 80

Mom

ent (

kN.m

)

Experiment

Model

Concrete crushing

0

25

50

75

100

125

150

175

200

225

250

275

0 10 20 30 40 50 60 70 80


Mom

ent (

kN.m

)

Experiment

Model(Two CFRP layers)

Debonding of outer layer Model

(One CFRP layer)

CFRP rupture

0

25

50

75

100

125

150

175

200

225

250

275

0 10 20 30 40 50 60 70 80


Mom

ent (

kN.m

)

Experiment


Debonding of outer layer Model

(One CFRP layer)

CFRP rupture

Chapter 7

290

Figure 7.5 Predicted versus experimental moment-curvature behaviour of girder G3 in Phase II.

Figure 7.6 Predicted versus experimental moment-strain behaviour of control girder G1 in Phase II.

Mom

ent (

kN.m

)

0

25

50

75

100

125

150

175

200

225

250

275

0 5 10 15 20

Experiment

Model

Strain in tension flange x 10-3

Mom

ent (

kN.m

)

0

25

50

75

100

125

150

175

200

225

250

275

0 5 10 15 20

Experiment

Model


0

25

50

75

100

125

150

175

200

225

250

275

0 10 20 30 40 50 60 70 80


Mom

ent (

kN.m

) Experiment

Model



Model(One CFRP layer)

CFRP rupture

0

25

50

75

100

125

150

175

200

225

250

275

0 10 20 30 40 50 60 70 80


Mom

ent (

kN.m

) Experiment

Model




CFRP rupture

Chapter 7

291

Figure 7.7 Predicted versus experimental moment-strain behaviour of girder G2 in Phase II.

Figure 7.8 Predicted versus experimental moment-strain behaviour of girder G3 in Phase II.

0

25

50

75

100

125

150

175

200

225

250

275

0 5 10 15 20


Mom

ent (

kN.m

)

Experiment




0

25

50

75

100

125

150

175

200

225

250

275

0 5 10 15 20


Mom

ent (

kN.m

)

Experiment




0

25

50

75

100

125

150

175

200

225

250

275

0 5 10 15 20

Mom

ent (

kN.m

)

Experiment



CFRP ruptureModel(Two CFRP layers)


CFRP rupture

0

25

50

75

100

125

150

175

200

225

250

275

0 5 10 15 20

Mom

ent (

kN.m

)

Experiment



CFRP ruptureModel(Two CFRP layers)


CFRP rupture

Chapter 7

292

Figure 7.9 Predicted versus experimental load-deflection behaviour of control girder G1 in Phase II.

Figure 7.10 Predicted versus experimental load-deflection behaviour of girder G2 in Phase II.

Mid-span deflection (mm)

Load

(kN

)

0

20

40

60

80

100

120

140

160

180

200

220

0 25 50 75 100 125 150 175

Experiment

ModelConcrete crushing


Load

(kN

)

0

20

40

60

80

100

120

140

160

180

200

220

0 25 50 75 100 125 150 175

Experiment

ModelConcrete crushing


Load

(kN

)

Model

0

20

40

60

80

100

120

140

160

180

200

220

0 25 50 75 100 125 150 175

Experiment




CFRP rupture


Load

(kN

)

Model

0

20

40

60

80

100

120

140

160

180

200

220

0 25 50 75 100 125 150 175

Experiment




CFRP rupture

Chapter 7

293

Figure 7.11 Predicted versus experimental load-deflection behaviour of girder G3 in Phase II.

Figure 7.12 Moment-curvature responses of composite sections strengthened using SM-CFRP.

0

25

50

75

100

125

150

175

200

225

250

0 10 20 30 40 50 60 70 80


Mom

ent (

kN.m

)

(E)FRP = 152 GPa

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

control

ρ = 3.9 %ρ = 2.6 %

ρ = 1.3 %

0

25

50

75

100

125

150

175

200

225

250

0 10 20 30 40 50 60 70 80


Mom

ent (

kN.m

)

(E)FRP = 152 GPa

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

control

ρ = 3.9 %ρ = 2.6 %

ρ = 1.3 %


0

20

40

60

80

100

120

140

160

180

200

220

0 25 50 75 100 125 150 175

Load

(kN

)

Experiment



CFRP ruptureCFRP rupture


0

20

40

60

80

100

120

140

160

180

200

220

0 25 50 75 100 125 150 175

Load

(kN

)

Experiment



CFRP ruptureCFRP rupture

Chapter 7

294

Figure 7.13 Moment-curvature responses of composite sections strengthened using HM-CFRP.

Figure 7.14 Moment-curvature responses of composite sections strengthened using UHM-CFRP.


Mom

ent (

kN.m

)

0

25

50

75

100

125

150

175

200

225

250

0 10 20 30 40 50 60 70 80

(E)FRP = 313 GPa

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

control

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %


Mom

ent (

kN.m

)

0

25

50

75

100

125

150

175

200

225

250

0 10 20 30 40 50 60 70 80

(E)FRP = 313 GPa

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

control

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %


Mom

ent (

kN.m

)

0

25

50

75

100

125

150

175

200

225

250

0 10 20 30 40 50 60 70 80

(E)FRP = 457 GPa

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

control

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %


Mom

ent (

kN.m

)

0

25

50

75

100

125

150

175

200

225

250

0 10 20 30 40 50 60 70 80

(E)FRP = 457 GPa

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

control

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %

Chapter 7

295

Figure 7.15 Effect of the modulus of CFRP on percentage increase in stiffness for different reinforcement ratios.

Figure 7.16 Effect of the modulus of CFRP on percentage increase in yielding moment for different reinforcement ratios.

0

2

4

6

8

10

12

14

16

18

0.5 1 1.5 2 2.5

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

Ef / Es

% in

crea

se in

stif

fnes

s

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %

1.96 ρ

1

1.98 ρ

1

2.00 ρ1

0

2

4

6

8

10

12

14

16

18

0.5 1 1.5 2 2.5

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

Ef / Es

% in

crea

se in

stif

fnes

s

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %

1.96 ρ

1

1.98 ρ

1

2.00 ρ1

0

5

10

15

20

25

0.5 1 1.5 2 2.5

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

Ef / Es

% in

crea

se in

Myi

eld

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %

2.34 ρ

1

2.25 ρ

1

2.26 ρ1

0

5

10

15

20

25

0.5 1 1.5 2 2.5

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

Ef / Es

% in

crea

se in

Myi

eld

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %

2.34 ρ

1

2.25 ρ

1

2.26 ρ1

Chapter 7

296

Figure 7.17 Effect of the modulus of CFRP on percentage reduction in ductility.

Figure 7.18 Effect of CFRP rupture strain on percentage increase in strength for different reinforcement ratios.

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

Rupture strain of CFRP x 10-3

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

% in

crea

se in

stre

ngth

E =

457

GP

a

E =

313

GP

a

E =

152

GP

a

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

Rupture strain of CFRP x 10-3

ρ = 3.9 %

ρ = 2.6 %

ρ = 1.3 %

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

% in

crea

se in

stre

ngth

E =

457

GP

a

E =

313

GP

a

E =

152

GP

a

0

10

20

30

40

50

60

70

80

90

0.5 1 1.5 2 2.5

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

% re

duct

ion

in d

uctil

ity

Ef / Es

E =

457

GP

a

E =

313

GP

a

E =

152

GP

a

ρ = 1.3, 2.6, and 3.9 %

0

10

20

30

40

50

60

70

80

90

0.5 1 1.5 2 2.5

(Fy)steel = 345 MPa

fc’ = 40 MPa

tc = 65 mm

% re

duct

ion

in d

uctil

ity

Ef / Es

E =

457

GP

a

E =

313

GP

a

E =

152

GP

a

ρ = 1.3, 2.6, and 3.9 %

Chapter 7

297

Figure 7.19 Effective cross sections and corresponding stress and strain distributions in intact, damaged, and repaired girders.

tc

tc

tc

tc

(a) Intact cross section

b

d

bc

N.A.

εs botFy

Fc

(b) Damaged cross section

b

ηd

bc

N.A.

εc top

Fy

Fc

d

(c) Cross section repaired using HM-CFRPb

bc

Fs bot

Rs

Fc

d

εf = εmaxFf = Fr

Rs

Rs

Rf

(d) Cross section repaired using SM-CFRPb

bc

Fs bot

Rs

Fc

d

εfFf

Rf

b

d

bc x (Ect/Es)

tc

b

bc x (Ect/Es)

tc

bc x (Ect/Es)

tc

bf x (Ef /Es)

tc

Ieff1

Ieff2

Ieff4

Y

CRc

CRc

N.A. CRc

N.A. CRc

εs top

εi

yi

fi

εs top

εs bot

εs bot

(1-η

)d

ηd

ηd

εc top

εc top

εc top

bc x (Ect/Es)

bf x (Ef /Es)

= εcr

= εcr

= εcr

= εcr

>> εy

εs bot >> εy

(1-η

)d(1

-η)d

For strength calculationsFor deflection calculations

bf

bf

tc

tc

tc

tc

(a) Intact cross section

b

d

bc

N.A.

εs botFy

Fc

(b) Damaged cross section

b

ηd

bc

N.A.

εc top

Fy

Fc

d

(c) Cross section repaired using HM-CFRPb

bc

Fs bot

Rs

Fc

d

εf = εmaxFf = Fr

Rs

Rs

Rf

(d) Cross section repaired using SM-CFRPb

bc

Fs bot

Rs

Fc

d

εfFf

Rf

b

d

bc x (Ect/Es)

tc

b

bc x (Ect/Es)

tc

bc x (Ect/Es)

tc

bf x (Ef /Es)

tc

Ieff1

Ieff2

Ieff4

Y

CRc

CRc

N.A. CRc

N.A. CRc

εs top

εi

yi

fi

εs top

εs bot

εs bot

(1-η

)d

ηd

ηd

εc top

εc top

εc top

bc x (Ect/Es)

bf x (Ef /Es)

= εcr

= εcr

= εcr

= εcr

>> εy

εs bot >> εy

(1-η

)d(1

-η)d

For strength calculationsFor deflection calculations

bf

bf

Chapter 7

298

Figure 7.20 Effect of parameter η on the predicted-to-measured ultimate moment ratio.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

η

Mpr

ed/ M

exp

Repaired beams (B3, B4, B6-B11)

Damaged and unrepaired beam (B2)

η=

0.57

η=

0.23

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

η

Mpr

ed/ M

exp

Repaired beams (B3, B4, B6-B11)

Damaged and unrepaired beam (B2)

η=

0.57

η=

0.23

Chapter 7

299

Figure 7.21 Schematic to illustrate the effect of damage and CFRP-repair on variation of moment of inertia of girders.

b

Ieff1

L

(a) Unrepaired beam

(b) CFRP-repaired beam

L

Slope z:1

Ieff2Ieff1

da

b

c

c

c

c

b

ηd

2zηd

(L-(0.5d+4z))/2 (L-(0.5d+4z))/2

Ieff1

L

Ieff4

100 mm

Ieff1Ieff1 Ieff4

LCFRP/2

(L-LCFRP)/2100 mm

Ieff3

Slope 1:zSlope 1:z

Ieff3Ieff1

Ieff2Ieff1

Ieff3

2zηd + bz

Ieff4

Ieff4Ieff2

2zηd + bz

zηd + bz/2 zηd + bz/2

LCFRP/2

Ieff1

LCFRP/2 LCFRP/2

b

Ieff1

L

(a) Unrepaired beam

(b) CFRP-repaired beam

L

Slope z:1

Ieff2Ieff1

da

b

c

c

c

c

b

ηd

2zηd

(L-(0.5d+4z))/2 (L-(0.5d+4z))/2

Ieff1

L

Ieff4

100 mm

Ieff1Ieff1 Ieff4

LCFRP/2

(L-LCFRP)/2100 mm

Ieff3

Slope 1:zSlope 1:z

Ieff3Ieff3Ieff1Ieff1

Ieff2Ieff1Ieff1

Ieff3

2zηd + bz

Ieff4Ieff4

Ieff4Ieff2

2zηd + bz

zηd + bz/2 zηd + bz/2

LCFRP/2

Ieff1Ieff1

LCFRP/2 LCFRP/2

Chapter 7

300

Figure 7.22 Effect of slope z on the predicted-to-measured deflection ratio.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0 0.5 1 1.5 2 2.5 3

z

δ pre

d/ δ

exp

Repaired beams

(B3, B4, B6-B11)

Damaged and

unrepaired beam (B2)

z=

0.48

z=

2.85

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0 0.5 1 1.5 2 2.5 3

z

δ pre

d/ δ

exp

Repaired beams

(B3, B4, B6-B11)

Damaged and

unrepaired beam (B2)

z=

0.48

z=

2.85

Chapter 8

301

Chapter 8

Summary and Conclusions 8.1 Summary

The main objective of this study was to evaluate the use of CFRP composite materials in

retrofitting columns and steel-concrete girders. This included strengthening intact

members to increase their load carrying capacity and stiffness as well as repair of

damaged members to restore their original capacities. Both experimental and theoretical

investigations were carried out. In principle, the study demonstrated the great success of

this retrofitting technique. Also, the findings of this research program will enable

engineers to make more informative decisions regarding retrofit of steel structures using

adhesively bonded composites and can assist in developing reliable design guides.

The experimental investigation comprised three-phases. Phase I included 50 HSS steel

columns with slenderness ratios ranging from 4 to 93. The columns were strengthened

using different configurations of CFRP composites and were tested under axial

compression. The study considered the effects of number of CFRP layers, type of CFRP,

fibre orientation, and slenderness ratio of the columns, on their axial behaviour. Phases II

Chapter 8

302

and III of the experimental program were focused on strengthening and repair,

respectively, of steel W-sections acting compositely with concrete slabs, using different

CFRP materials. In Phase II, three large-scale intact girders were strengthened using

CFRP plates. In Phase III, 11 girders, most of which were artificially damaged, have been

repaired using CFRP sheets. All girders were tested in four-point bending. The

parameters considered were the effect of CFRP type, number of layers, number of

retrofitted sides of the tension flange, and the length of CFRP repair patch.

Four analytical and numerical models have been developed for the columns and girders.

The first and second models are an analytical fibre-element model and a non-linear

numerical finite element model, developed for FRP-strengthened HSS slender columns.

The third model is a fibre-element analytical model, developed for FRP-strengthened

intact steel-concrete composite girders. The fourth model is also a fibre-element

analytical model, developed for FRP-repaired steel-concrete composite girders with a

complete cut in their tension flanges. The models were verified using experimental

results and used in parametric studies to examine a wider range of parameters.

8.2 Conclusions

8.2.1 Axially loaded members

8.2.1.1 Slender columns

1. Both the axial strength and stiffness of HSS slender columns are increased using

CFRP-bonded sheets or plates oriented in the longitudinal direction. The stability of

Chapter 8

303

the columns against lateral deflection is improved, and hence, overall buckling occurs

at higher loads.

2. The effectiveness of the CFRP system in increasing the axial strength of slender

columns increases greatly as the slenderness ratios become higher. Its effectiveness in

increasing axial stiffness, on the other hand, is not much affected by slenderness ratio.

The strength of columns with slenderness ratios ranging from 46 to 93 was increased

by 6 to 71 percent, respectively, while their stiffness was increased by 10 to 17

percent.

3. The axial strength of a column reduces as slenderness ratio increases. However, the

rate of reduction in CFRP-strengthened columns is lower than that of their

counterpart bare steel columns.

4. The effectiveness of the CFRP system increases in columns with larger out-of-

straightness imperfections. However, for a given CFRP reinforcement ratio, there

could be a certain level of out-of-straightness, beyond which, the gain in strength

becomes constant. The gain in stiffness, on the other hand, is not affected much by

the level of out-of-straightness.

5. A fibre-element model (Model 1) and a nonlinear finite element model (Model 2)

were successfully developed and predicted reasonably well the complete behaviour of

CFRP-strengthened HSS slender columns. Generally, Model 1 produces a slightly

higher axial strength and a slightly lower axial stiffness than Model 2, and its

accuracy is better for higher slenderness ratios.

Chapter 8

304

6. Ignoring steel plasticity, residual stresses, or debonding (or crushing) of CFRP in

modeling CFRP-strengthened slender columns could overestimate their axial strength

significantly.

7. The level of through-thickness residual stress in cold-formed HSS slender columns

has little effect on the gain in axial strength when using CFRP. In general, the lower

the residual stress, the higher the gain in strength.

8. Slender columns fail by excessive overall buckling. In thin-walled sections, this may

be followed by a secondary local buckling at mid-height. For low slenderness ratios

up to kL/r = 76, the CFRP plate on the extreme compression face completely debonds

from the steel surface. For higher slenderness ratio (kL/r = 93), the CFRP plate

crushes at mid-height. For columns strengthened using CFRP sheets, the secondary

local buckling is associated with local debonding and crushing of CFRP. The CFRP

on the outer (tension) side remains intact.

9. Based on the experimental study, simple empirical equations are proposed to establish

the maximum strain that CFRP material can reach at ultimate as a function of

slenderness ratio, when debonding (or crushing) occurs.

8.2.1.2 Short columns

1. CFRP wraps with fibres oriented in the transverse direction appear to be more

efficient in increasing axial strength of HSS short columns than those with fibres in

the longitudinal direction. This is evident by achieving the highest gain among all

configurations considered in this study. However, the maximum gain in axial stiffness

was achieved using a longitudinal layer, followed by a transverse layer.

Chapter 8

305

2. The effectiveness of transverse wraps in strengthening HSS short columns depends

on the stiffness of the CFRP jacket (Ef Af). In this study, the SM-CFRP resulted in

better strengthening than the high modulus- (HM-) CFRP because it has 10 percent

higher stiffness. Also, the stiff nature of fibres in the HM-CFRP wraps resulted in

fracture of the fibres at the round corners, near ultimate.

3. In this study, HSS short columns failed by yielding, immediately followed by

symmetric local buckling, where two opposite sides buckled inwards and the other

two sides buckled outwards. Transverse CFRP wraps are effective in bracing the

outwards buckling but they tend to debond from the sides that buckle inwards.

4. In all short columns strengthened with longitudinal CFRP layers, debonding occurred

between CFRP and steel at one end, even in the columns with additional outer CFRP

transverse wrap.

8.2.2 Flexural members

8.2.2.1 Strengthening of intact girders

1. The SM-CFRP plates have indeed increased the flexural strength and stiffness of

intact steel-concrete composite girders by 51 and 19 percent, respectively, in this

experimental study.

2. The control girder failed by crushing of the concrete slab after excessive yielding of

the steel section. In the strengthened girders, the CFRP plate bonded to steel over a

length equals to 67 percent of the span remained fully bonded to the section till

ultimate. Failure occurred by concrete crushing associated with lateral torsional

buckling. At this stage, tensile rupture of the CFRP plate was quite imminent. The

Chapter 8

306

second CFRP plate, which was significantly shorter (25 percent of the span), was

debonded at almost 60 percent of the ultimate load.

3. Increasing the elastic modulus of CFRP leads to a reduction in flexural strength gain,

as a result of the reduced tensile strength of CFRP. It also leads to a reduction in the

ductility of girders, as a result of the reduced ultimate strain. However, it results in

increasing flexural stiffness of the girders.

4. Similar gains in the elastic flexural stiffness and yielding moment are achieved by

either increasing the elastic modulus or the cross sectional area of CFRP. The effect

of elastic modulus of CFRP on flexural stiffness is more pronounced after yielding of

steel than in the elastic range.

5. The percentage increases in both the elastic stiffness and yielding moment of the

girders are linearly proportional to the ratio of CFRP-to-steel elastic moduli. The rate

of increase, however, is higher for larger CFRP reinforcement ratios.

6. In strengthening applications, the shear stresses developed along the interface

between the CFRP plate and the steel substrate increase rapidly near the end of the

CFRP plates.

8.2.2.2 Repair of damaged girders

1. The flexural strength and stiffness of steel-concrete composite girders tested in this

study have been severely reduced by 60 and 54 percent, respectively, as a result of

complete loss of the tension flange at mid-span.

2. The girders repaired using HM-CFRP sheets of a 152 percent force equivalence index

(ω) recovered the original flexural strength and stiffness and even exceeded them by

Chapter 8

307

10 and 26 percent, respectively. On the other hand, the girder repaired using SM-

CFRP sheets required a higher ω of 210 percent to just recover the original stiffness

but exceeded the original strength by 16 percent. ω is the cross sectional area ratio of

CFRP and steel flange, normalized to the ratio of CFRP tensile strength and steel

yield strength.

3. In this study, girders repaired using SM-CFRP failed consistently by debonding of

CFRP sheets, before developing their full tensile strength. On the other hand, girders

repaired using HM-CFRP sheets failed by rupture of the sheets, without any sign of

debonding. This is attributed to the higher modulus and smaller rupture strain of the

HM-CFRP.

4. The bonded length of the SM-CFRP sheets has an insignificant effect on the elastic

stiffness of the repaired beams. However, a consistent reduction in flexural strength is

observed with shortening the bonded length.

5. The longer the bonded length of SM-CFRP sheets, the higher the maximum strain

reached in the sheets at failure. This strain is also affected by the state of stress in the

girder (i.e. pure bending or combined bending and shear). Although no SM-CFRP

rupture was observed in this study, it has been estimated that bonded lengths of at

least 180 and 1175 mm, from each side of the crack, are required to achieve rupture

and avoid debonding, in the cases of pure bending and combined bending and shear,

respectively. Empirical equations are proposed to obtain the maximum strain, as a

function of bond length.

6. Bonding SM-CFRP sheets to both sides of the steel flange, instead of the bottom

surface only, enhances flexural stiffness of the repaired girders, but has no effect on

Chapter 8

308

flexural strength. Curvature of the girders could induce peeling stresses and triggers

early debonding of the sheets at the top surface of the flange.

7. Increasing the force equivalence index (ω) increases the percentage recovery of

strength in CFRP-repaired girders. This rate of increase follows similar trends for

both SM- and HM-CFRP materials.

8. Shear stresses at the interface between the CFRP sheets and the steel substrate, in the

vicinity of the flange cut, increase rapidly with loading until they reach the

characteristic strength of the adhesive, and then drop to zero as debonding progresses.

Unlike CFRP-strengthened intact girders, significantly higher shear stresses develop

near the cut at mid-span, than at the ends. Although not investigated in this study, it is

believed that providing an anchorage system such as transverse wraps near the flange

cut would improve the bond strength.

9. An analytical approach has been developed to calculate flexural strength and service

load deflection of CFRP-repaired girders with a complete flange cut. It deals with the

stress concentrations and the associated crack propagation in a simplified manner, in

lieu of complex fracture mechanics approaches. Hence, it is suited for design

purposes. The approach is essentially based on ignoring a triangular segment of the

steel girder of a height of 0.57d and base length of (0.27 d + 0.24 b), at both sides of

the cut, where b and d are the flange breadth and steel section depth, respectively.

10. Late application of CFRP sheets (i.e. several months after sandblasting the surface)

resulted in significant deterioration of bond integrity at the interface, and hence

substantially lower flexural strength was achieved. This occurred despite the fact that

Chapter 8

309

steel surface was protected by a coating of oil, which was completely removed and

then the surface was thoroughly wiped with acetone, just prior to FRP installation.

8.3 Recommendations for Future Work

The research work carried out in this study on retrofit of steel structures using CFRP

materials covered a wide range of applications and parameters, and indeed demonstrated

an excellent promise of this method. A number of major achievements have been

accomplished in terms of thorough understanding of behaviour, failure modes, and

modeling. Future research in related areas, however, still needs to be carried out on the

following topics:

1. Optimizing the length of CFRP plates in steel columns with high slenderness ratios,

in which plating the full length may not be necessary.

2. A study focused on the effect of CFRP wraps on delaying local buckling of short HSS

columns (or box sections) with very thin walls, which are vulnerable to local buckling

prior to yielding. This may also be extended to include very thin webs in girders

subjected to shear.

3. Developing analytical and numerical models to predict the behaviour and axial

strength of HSS short columns strengthened using CFRP.

4. Examining the behaviour CFRP-strengthened beam-columns under combined axial

load and bending moment as well as slender columns with different end conditions.

5. Fatigue testing of large scale steel-concrete composite girders strengthened or

repaired using CFRP. The effect of CFRP on arresting fatigue cracks would be of

great interest.

Chapter 8

310

6. Studying the effect of using prestressed CFRP plates on the behaviour of fatigue-

damaged bridge girders.

7. Repair of steel-concrete composite girders with different levels of section loss,

primarily induced by actual corrosion in the tension flange.

8. Examining the behaviour of CFRP-retrofitted girders under combined service loads

and environmental conditions, including moisture and severe temperature gradient

exposures.

9. Developing techniques to use the FRP material in strengthening (or repair) of bolted

and welded connections.

10. Establishing comprehensive design guidelines for steel girders and columns

retrofitted using CFRP material.

References

1. ACI (2002). ACI 440. 2R-02: Guide for the design and construction of externally

bonded FRP systems for strengthening concrete structures, American Concrete

Institute, Farmington Hills, Michigan, 113 pp.

2. Albat, A. M., and Romilly, D. P. (1999) “A Direct Linear-Elastic Analysis of

Double Symmetric Bonded Joints and Reinforcements.” Composite Scince and

Technology 59(7):1127-1137.

3. Al-Emrani, M., and Kliger, R. (2006) “Analysis of Interfacial Shear Stresses in

Beams Strengthened with Bonded Prestressed Laminates.” Journal of Composites

Part B: Engineering, 37(4-5): 265-272.

4. Al-Emrani, M., Linghoff, D., and Kliger, R. (2005) “Bonding Strength and

Fracture Mechanisms in Composite Steel-CFRP Elements.” Proceedings of the

International Symposium on Bond Behaviour of FRP in Structures (BBFS 2005).

Hong Kong, China, December 7-9: 433-441.

5. Allan, R. C., J. Bird, and J. D. Clarke (1988) “Use of Adhesives in Repair of

Cracks in Ship Structures” Materials Science and Technology. 4(10):853-859.

6. Allen, H. G. and Bulson, P. S. (1980). Background to buckling. McGraw-Hill,

UK. 582 pp.

7. Al-Saidy, A. H., Klaiber, F. W., and Wipf, T. J. (2004) “Repair of Steel

Composite Beams with Carbon Fiber-Reinforced Polymer Plates.” Journal of

Composites for Construction, ASCE, 8(2):163-172.

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8. Al-Saidy, A. H., Klaiber, F. W., and Wipf, T. J. (2007) “Strengthening of Steel-

Concrete Composite Girders using Carbon Fiber Reinforced Polymer Plates.”

Construction and Building Materials, 21(2): 295-302.

9. American Association of State Highway and Transportation Officials (AASHTO)

(2000). “Standard Specifications for Highway Bridges” 16th Ed., Washington,

D.C.

10. American Society for Testing and Materials (ASTM), (2000), “Designation D

3762 –Standard Test Method for Adhesive-Bonded Surface Durability of

Aluminum (Wedge Test)” Annual Book of ASTM Standards, ASTM

International.

11. American Society for Testing and Materials (ASTM), (2000), “Designation D

3039/D 3039M –Standard test method for tensile properties of polymer matrix

composite materials” Annual Book of ASTM Standards, ASTM International.

12. American Society for Testing and Materials (ASTM), (2000), “Designation

D5868-01, Standard test method for lap shear adhesion for Fiber Reinforced

Plastic (FRP) Bonding” Annual Book of ASTM Standards, ASTM International.

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Appendix A

Measurements of Out-of-Straightness Profiles for

Column Sets 1 to 6

A.1 General

This appendix provides complete illustrations of the measured out-of-straightness

geometric imperfection profiles of HSS column sets 1 to 6, tested in Phase I of the

experimental program. The out-of-straightness profiles were measured along two

perpendicular sides (a and b) using an ILD1400 laser optical displacement sensor. Figure

A.1 to A.17 show the out-of-straightness profiles of all specimens in column sets 1 to 6,

except those of specimen 6-3, which are previously shown in Figure 3.13. It should be

noted that all specimens were oriented in the test setup such that the side of the highest

imperfection value [side (a)] is in the direction of permissible buckling.

Appendix A

327

Figure A.1 Out-of-straightness geometric imperfection profile of specimen 1-1.


Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Length (mm)

Side (a)

Side (b)

a

bO

ut-o

f-Stra

ight

ness

(mm

)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Length (mm)

Side (a)

Side (b)

a

b

a

b

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

Side (a)

Side (b)

a

b

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Length (mm)

Out

-of-S

traig

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ss (m

m)

Side (a)

Side (b)

a

b

Appendix A

328



Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Length (mm)

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-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Length (mm)

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-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Appendix A

329



Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800

Side (a)

Side (b)

a

b

Appendix A

330



Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Appendix A

331



Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Appendix A

332



Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Side (a)

Side (b)

a

b

Appendix A

333



Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Appendix A

334



Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Appendix A

335


Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Length (mm)

Out

-of-S

traig

htne

ss (m

m)

-0.2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400 1600

Side (a)

Side (b)

a

b

Appendix B

336

Appendix B

Estimated Out-of-Straightness Imperfections at

Mid-Height for Column Sets 1 to 11

B.1 General

This appendix provides the plots of the estimated out-of-straightness imperfections at

mid-height (e’) for column sets 3 to 11 (plots of column sets 1 and 2 were shown earlier

in Figure 4.24). The imperfection values at mid-height are calculated based on Equation

4.1 and plotted versus the applied load in Figure B.1 to Figure B.3. It is noted that e’

varies with the applied load P and also differs slightly when calculated from both sides of

the columns. The initial imperfection is then estimated as the y-intercept (i.e. the value at

P = 0) and is based on the average value from both sides.

Appendix B

337

Figure B.1 Mid-height imperfections of column sets 3 and 4 versus the applied load. Figure B.2 Mid-height imperfections of column sets 5 and 6 versus the applied load.


Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)

e’ = -0.0072 P + 2.15430

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50








Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)

e’ = -0.0072 P + 2.15430

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50







Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50







Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50







Appendix B

338

Figure B.3 Mid-height imperfections of specimens 7 to 11 versus the applied load.


Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)

-3

-2

-1

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70

Specimen 7, eP=0= 6.60






Mid

-hei

ght I

mpe

rfect

ion,

e’(

mm

)

-3

-2

-1

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70






STRUCTURAL BEHAVIOUR OF STEEL COLUMNS AND STEEL-CONCRETE …

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