Post on 14-Apr-2022
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
Table of Contents
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
Table of Contents
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
3.4.4 Instrumentation ......................................................................................87
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
3.5.4 Instrumentation ......................................................................................93
Chapter 4 Experimental Results and Discussion of Phase I:
Axial Compression Members ......................................... 120
Table of Contents
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
Table of Contents
ix
5.3.1.2 Failure modes..........................................................................................165
5.3.2 Effect of type of CFRP .........................................................................166
5.3.2.1 Flexural behaviour...................................................................................166
5.3.2.2 Failure modes..........................................................................................168
5.3.3 Effect of number of repaired sides of flange.........................................169
5.3.3.1 Flexural behaviour...................................................................................169
5.3.3.2 Failure modes..........................................................................................170
5.3.4 Effect of CFRP force equivalence index ..............................................171
5.3.4.1 Flexural behaviour...................................................................................171
5.3.4.2 Failure modes..........................................................................................172
5.3.5 Effect of bonded length of CFRP .........................................................172
5.3.5.1 Flexural behaviour...................................................................................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
Table of Contents
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
Table of Contents
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
Table of Contents
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 4.2 Load-axial displacement responses of column sets 3 and 4 of group A. .....137
Figure 4.3 Load-axial displacement responses of column sets 5 and 6 of group A. .....138
Figure 4.4 Load-lateral displacement of column sets 1 and 2 of group A. ....................138
Figure 4.5 Load-lateral displacement of column sets 3 and 4 of group A. ....................139
Figure 4.6 Load-lateral displacement of column sets 5 and 6 of group A. ....................139
Figure 4.7 Load-axial strain responses based on strain gauge S1 of column sets 1 and 2
of group A. ..............................................................................................................140
Figure 4.8 Load-axial strain responses based on strain gauge S1 of column sets 3 and 4
of group A. ..............................................................................................................140
Figure 4.9 Load-axial strain responses based on strain gauge S1 of column sets 5 and 6
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
Figure 4.11 Load-axial strain responses based on strain gauge S2 of column sets 3 and
4 of group A. ...........................................................................................................142
Figure 4.12 Load-axial strain responses based on strain gauge S2 of column sets 5 and
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 4.20 Load-axial strain responses of specimen 8 of group B. .............................147
Figure 4.21 Load-axial strain responses of specimen 9 of group B. .............................147
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 5.16 Load-deflection responses of specimens B3 and B4 in Phase III. .............186
Figure 5.17 Load-deflection responses of specimens B5 and B6 in Phase III. .............186
Figure 5.18 Strain distributions along the CFRP sheets of specimen B3 in Phase III...187
Figure 5.19 Strain distributions along the CFRP sheets of specimen B4 in Phase III...187
Figure 5.20 Strain distributions along the CFRP sheets of specimen B5 in Phase III...188
Figure 5.21 Strain distributions along the CFRP sheets of specimen B6 in Phase III...188
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 5.25 Load-deflection responses of specimens B6 and B7 in Phase III. .............191
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 5.29 Load-deflection responses of specimens B7 and B8 in Phase III. .............194
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
Figure 5.34 Strain distributions along the lower CFRP sheets of specimen B8 in Phase
III.............................................................................................................................196
Figure 5.35 Strain distributions along the lower CFRP sheets of specimen B9 in Phase
III.............................................................................................................................197
Figure 5.36 Strain distributions along the lower CFRP sheets of specimen B10 in Phase
III.............................................................................................................................197
Figure 5.37 Strain distributions along the lower CFRP sheets of specimen B11 in Phase
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
Figure 5.42 Load-average shear stress responses along the lower CFRP sheets of
specimen B9 in Phase III. .......................................................................................200
Figure 5.43 Load-average shear stress responses along the lower CFRP sheets of
specimen B10 in Phase III. .....................................................................................201
Figure 5.44 Load-average shear stress responses along the lower CFRP sheets of
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 6.15 Measured and predicted load-lateral displacement responses of set 2. ....244
Figure 6.16 Measured and predicted load-lateral displacement responses of set 3. ....244
Figure 6.17 Measured and predicted load-lateral displacement responses of set 4. ....245
Figure 6.18 Measured and predicted load-lateral displacement responses of set 5. ....245
Figure 6.19 Measured and predicted load-lateral displacement responses of set 6. ....246
Figure 6.20 Measured and predicted load-lateral displacement responses of specimen 7.
................................................................................................................................246
Figure 6.21 Measured and predicted load-lateral displacement responses of specimen 8.
................................................................................................................................247
Figure 6.22 Measured and predicted load-lateral displacement responses of specimen 9.
................................................................................................................................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 6.26 Measured and predicted load-axial displacement responses of set 2. ......249
Figure 6.27 Measured and predicted load-axial displacement responses of set 3. ......250
Figure 6.28 Measured and predicted load-axial displacement responses of set 4. ......250
Figure 6.29 Measured and predicted load-axial displacement responses of set 5. ......251
Figure 6.30 Measured and predicted load-axial displacement responses of set 6. ......251
Figure 6.31 Measured and predicted load-axial displacement responses of specimen 7.
................................................................................................................................252
List of Figures
xxi
Figure 6.32 Measured and predicted load-axial displacement responses of specimen 8.
................................................................................................................................252
Figure 6.33 Measured and predicted load-axial displacement responses of specimen 9.
................................................................................................................................253
Figure 6.34 Measured and predicted load-axial displacement responses of specimen 10.
................................................................................................................................253
Figure 6.35 Measured and predicted load-axial displacement responses of specimen 11.
................................................................................................................................254
Figure 6.36 Measured and predicted load-axial strain responses of set 1....................254
Figure 6.37 Measured and predicted load-axial strain responses of set 2....................255
Figure 6.38 Measured and predicted load-axial strain responses of set 3....................255
Figure 6.39 Measured and predicted load-axial strain responses of set 4....................256
Figure 6.40 Measured and predicted load-axial strain responses of set 5....................256
Figure 6.41 Measured and predicted load-axial strain responses of set 6....................257
Figure 6.42 Measured and predicted load-axial strain responses of specimen 7. ........257
Figure 6.43 Measured and predicted load-axial strain responses of specimen 8. ........258
Figure 6.44 Measured and predicted load-axial strain responses of specimen 9. ........258
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 6.49 Load-lateral displacement responses for specimens with e’=L/600...........261
Figure 6.50 Load-lateral displacement responses for specimens with e’=L/750...........262
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
Figure A.2 Out-of-straightness geometric imperfection profile of specimen 1-2. ..........327
Figure A.3 Out-of-straightness geometric imperfection profile of specimen 1-3. ..........328
Figure A.4 Out-of-straightness geometric imperfection profile of specimen 2-1. ..........328
Figure A.5 Out-of-straightness geometric imperfection profile of specimen 2-2. ..........329
Figure A.6 Out-of-straightness geometric imperfection profile of specimen 2-3. ..........329
List of Figures
xxiv
Figure A.7 Out-of-straightness geometric imperfection profile of specimen 3-1. ..........330
Figure A.8 Out-of-straightness geometric imperfection profile of specimen 3-2. ..........330
Figure A.9 Out-of-straightness geometric imperfection profile of specimen 3-3. ..........331
Figure A.10 Out-of-straightness geometric imperfection profile of specimen 4-1. ........331
Figure A.11 Out-of-straightness geometric imperfection profile of specimen 4-2. ........332
Figure A.12 Out-of-straightness geometric imperfection profile of specimen 4-3. ........332
Figure A.13 Out-of-straightness geometric imperfection profile of specimen 5-1. ........333
Figure A.14 Out-of-straightness geometric imperfection profile of specimen 5-2. ........333
Figure A.15 Out-of-straightness geometric imperfection profile of specimen 5-3. ........334
Figure A.16 Out-of-straightness geometric imperfection profile of specimen 6-1. ........334
Figure A.17 Out-of-straightness geometric imperfection profile of specimen 6-2. ........335
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
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]
??
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
(a) Strengthening (upgrading) of intact girders
CFRP
W-section
CFRP
Concrete slab
(a) Strengthening (upgrading) of intact girders
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)
Strengthening (gain)
?
?CFRP failure
Upgraded
Original (intact)
deflection
Load
Damaged (cracked)
Repair (recovery)
Strengthening (gain)
??
??
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
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
(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
Steel plateTh.= 13 mm
hole
Stiffeners
W360x101
x
Elevation
x
2032
4064
Bottom view x-x
Steel plateTh.= 13 mm
Steel plateTh.= 13 mm
Bottom view x-x
Steel plateTh.= 13 mm
Steel plateTh.= 13 mm
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
L / 4 L / 4Lateral support
Load
Deflection
L
L / 4 L / 4Lateral support
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
Type 4 Type 5 Type 6
Type 1 Type 2 Type 3
Type 4 Type 5 Type 6
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
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
Number of cycles (millions)
Nor
mal
ized
def
lect
ion
CFRP-Strengthened beams
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
Tapered edgeUniform thickness
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
Tapered edgeUniform thickness
Tapered edgeUniform thickness
Tapered edgeUniform thickness
(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
Tapered edgeUniform thickness
Tapered edgeUniform thickness
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
Tapered edgeUniform thickness
Tapered edgeUniform thickness
Tapered edgeUniform thickness
(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
[Schnerch et al., 2007]
(c) Mechanical clamp
Spew filletCFRP plate
(a)Tapered thickness
[Schnerch et al., 2007]
(b) Reverse tapering and spew fillet
[Schnerch et al., 2007]
(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
Analytical shear stressFE shear stressAnalytical peel stressFE peel stress
(a) Uinform thickness FRP plate (b) Tapered thickness FRP plate
Analytical shear stressFE shear stressAnalytical peel stressFE peel stress
Analytical shear stressFE shear stressAnalytical peel stressFE peel stress
(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
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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
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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.
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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.
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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
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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.
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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
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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.
3.4.1 Test specimens
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)
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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
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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
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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
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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
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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.
3.4.4 Instrumentation
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
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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.
3.5.1 Test specimens
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
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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
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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
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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,
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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
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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.
3.5.4 Instrumentation
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
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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.
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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 1900 2 x 64 x 1900 + 2 x 64 x 1850 + 2 x 46 x 1850 B9 C2 813 210 Lower 1 x 128 x 1000 1 x 128 x 1000 + 1 x 128 x 950 + 1 x 128 x 950
Upper 2 x 64 x 1000 2 x 64 x 1000 + 2 x 64 x 950 + 2 x 46 x 950 B10 C2 813 210 Lower 1 x 128 x 250 1 x 128 x 250 + 1 x 128 x 200 + 1 x 128 x 200
Upper 2 x 64 x 250 2 x 64 x 250 + 2 x 64 x 200 + 2 x 46 x 200 B11 C2 813 210 Lower 1 x 128 x 150 1 x 128 x 150 + 1 x 128 x 145 + 1 x 128 x 145
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
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
Axial strain x 10-3 (mm/mm)
Stre
ss (M
Pa)
(a) HSS1 (44 x 44 x 3.2 mm)
F rs=
49%
Fy
Yield strength Fy= 504 MPa
Fp= 257 MPaProportional limit
0
100
200
300
400
500
600
0 2 4 6 8 10 12 14 16
Axial strain x 10-3 (mm/mm)
Stre
ss (M
Pa)
(a) HSS1 (44 x 44 x 3.2 mm)
F rs=
49%
Fy
Yield strength Fy= 504 MPa
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)
Strain x 10-3 (mm/mm)
Stre
ss (M
Pa)
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Longitudinal FRP layers
T
C
C
(b) Long Column(a) Short Column
TT
TT
Longitudinal FRP layer
Transverse FRP layer
T
T
Longitudinal FRP layers
T
C
C
(b) Long Column(a) Short Column
TT
TT
Longitudinal FRP layer
Transverse FRP layer
TT TTT
TTTT
Longitudinal FRP layer
Transverse FRP layer
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 C3Set 11
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
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 mm wide GFRP end wraps
50 m
m
Set 2
Set 4
50 mm wide GFRP end wraps
50 m
m
50 mm wide GFRP end wraps
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
Fixed columnFixed column
Specimen
2380 mm
3 pins(Lateral support)Steel tie
Hinge
Hydraulic jack
Load cell
Steel tieLP2LP2 LP4LP4LP6 LP5
PI1
PI2
S1
S2
LP1LP1 LP3LP3Column cap
Fixed columnFixed column
SpecimenSpecimen
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
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
Plan view for the 3 LPs
Specimen
Load Cell
Semi spherical loading head
Steel plate
LPs
LP 2LP 3
LP 1
Plan view for the 3 LPs
Specimen
Load Cell
Semi spherical loading head
Steel plate
LPs
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
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
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
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
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.
Figure 4.2 Load-axial displacement responses of column sets 3 and 4 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
)
Axial displacement ∆ (mm)
Set 3(Control)
Set 4 (strengthened)
(Pavg. )strengthened= 200 kN
(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)
Axial displacement ∆ (mm)
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
Set 2 (strengthened)
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)
Axial displacement ∆ (mm)
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
Set 2 (strengthened)
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 4.3 Load-axial displacement responses of column sets 5 and 6 of group A.
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
)
Axial displacement ∆ (mm)
Set 5(Control)
Set 6 (strengthened)
(Pavg. )strengthened= 175 kN
(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
)
Axial displacement ∆ (mm)
Set 5(Control)
Set 6 (strengthened)
(Pavg. )strengthened= 175 kN
(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
)
Lateral displacement δ (mm)
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
Figure 4.5 Load-lateral displacement of column sets 3 and 4 of group A.
Figure 4.6 Load-lateral displacement of column sets 5 and 6 of group A.
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)
Lateral displacement δ (mm)
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)
Lateral displacement δ (mm)
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)
Lateral displacement δ (mm)
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)
Lateral displacement δ (mm)
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.
Figure 4.8 Load-axial strain responses based on strain gauge S1 of column sets 3 and 4 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)
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
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
Axial strain x 10-3(mm/mm)
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
Axial strain x 10-3(mm/mm)
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
Figure 4.9 Load-axial strain responses based on strain gauge S1 of column sets 5 and 6 of group A.
Figure 4.10 Load-axial strain responses based on strain gauge S2 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 6(strengthened)
(εav
g.)st
reng
then
ed=
-2.7
4x10
-3Load
(kN
)
Set 5(Control)
Axial strain x 10-3(mm/mm)
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)
Axial strain x 10-3(mm/mm)
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)
Axial strain x 10-3(mm/mm)
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)
Axial strain x 10-3(mm/mm)
S2S2
HSS 44 x 44 x 3.2 mmkL/r = 46
1-21-3
2-1 2-22-3
Chapter 4
142
Figure 4.11 Load-axial strain responses based on strain gauge S2 of column sets 3 and 4 of group A.
Figure 4.12 Load-axial strain responses based on strain gauge S2 of column sets 5 and 6 of group A.
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)
Axial strain x 10-3(mm/mm)
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)
Axial strain x 10-3(mm/mm)
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)
Axial strain x 10-3(mm/mm)
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)
Axial strain x 10-3(mm/mm)
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
.)
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
%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
∆
Set7 Control8 1 layer/ 2 sides9 3 layers / 2 sides
10 5 layers / 2 sides11 3 layers / 4 sides
3 4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 20 40 60 80 100 120
Slenderness ratio (kL/r)
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
Slenderness ratio (kL/r)
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
Set7 Control8 1 layer/ 2 sides9 3 layers / 2 sides
10 5 layers / 2 sides11 3 layers / 4 sides
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
Set7 Control8 1 layer/ 2 sides9 3 layers / 2 sides
10 5 layers / 2 sides11 3 layers / 4 sides
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
Load
(kN
)
PI1 PI2
S2S1
PI1 PI2
S2S1 ε y=
1.94
x 1
0-3
4
Chapter 4
147
Figure 4.20 Load-axial strain responses of specimen 8 of group B.
Figure 4.21 Load-axial strain responses of specimen 9 of group B.
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
PI1 PI2
S2S1
PI1 PI2
S2S1
(εcr
ushi
ng) C
FRP=
1.25
x 1
0-3
Chapter 4
148
Figure 4.22 Load-axial strain responses of specimen 10 of group B.
Figure 4.23 Load-axial strain responses of specimen 11 of group B.
100
150
200
250
300
350
400
50
0-10
Load
(kN
)
Axial strain x 10-3 (mm/mm)
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
)
Axial strain x 10-3 (mm/mm)
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
)
Axial strain x 10-3 (mm/mm)
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
)
Axial strain x 10-3 (mm/mm)
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
)
Axial strain x 10-3 (mm/mm)
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
Specimen 2-3, eP=0= 0.78
Specimen 2-1, eP=0= 0.47
Specimen 2-2, eP=0= 0.22
Specimen 1-3, eP=0= 0.47
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
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
Specimen 2-3, eP=0= 0.78
Specimen 2-1, eP=0= 0.47
Specimen 2-2, eP=0= 0.22
Specimen 1-3, eP=0= 0.47
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
(b) Specimen 11 (Strengthened)
Debonding and fracture of
sheets
CFRP sheets on
2 sides
CFRP sheets on
4 sides
(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
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
Axial strain x 10-3 (mm/mm)
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
Axial strain x 10-3 (mm/mm)
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
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
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.
Axial displacement (mm)
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
)
Axial displacement (mm)
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
)
Axial displacement (mm)
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
)
Axial displacement (mm)
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
Chapter 5
157
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
Chapter 5
158
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
Chapter 5
159
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)
Chapter 5
160
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
Chapter 5
161
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.
Chapter 5
162
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
Chapter 5
163
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
Chapter 5
164
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
Chapter 5
165
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
Chapter 5
166
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
5.3.2.1 Flexural behaviour
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
Chapter 5
167
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.
Chapter 5
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.
5.3.2.2 Failure modes
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.
Chapter 5
169
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
5.3.3.1 Flexural behaviour
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.
Chapter 5
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.
5.3.3.2 Failure modes
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
Chapter 5
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
5.3.4.1 Flexural behaviour
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
Chapter 5
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.
5.3.4.2 Failure modes
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
5.3.5.1 Flexural behaviour
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
Chapter 5
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
Chapter 5
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
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
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
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
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
Strain x 10-3(mm/mm)
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
Strain x 10-3(mm/mm)
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
Debonding of outer layer
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
Debonding of outer layer
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
Debonding of outer layer
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
Debonding of outer layer
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
Average shear stress (MPa)
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
Average shear stress (MPa)
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
Average shear stress (MPa)
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
Concrete crushingP = 144 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)
Concrete crushingP = 357 kN
Load
δ1960 mm
Load
δ1960 mm
Py = 270 kN
Concrete crushingP = 144 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.
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Figure 5.16 Load-deflection responses of specimens B3 and B4 in Phase III.
Figure 5.17 Load-deflection responses of specimens B5 and B6 in Phase III.
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
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
Rupture of CFRP sheets
Rupture of CFRP sheets
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
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
complete debondingof CFRP sheets
complete debondingof CFRP sheets
progressive debonding
Chapter 5
187
Figure 5.18 Strain distributions along the CFRP sheets of specimen B3 in Phase III.
Figure 5.19 Strain distributions along the CFRP sheets of specimen B4 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
Figure 5.20 Strain distributions along the CFRP sheets of specimen B5 in Phase III.
Figure 5.21 Strain distributions along the CFRP sheets of specimen B6 in Phase III.
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
Strain x 10-3 (mm/mm)
(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
Strain x 10-3 (mm/mm)
(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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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
Rupture of CFRP sheets
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
Rupture of CFRP sheets
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 5.25 Load-deflection responses of specimens B6 and B7 in Phase III.
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
Debonding of lower CFRP
Debondingof CFRP
Debonding of upper 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 5.29 Load-deflection responses of specimens B7 and B8 in Phase III.
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
Debonding of lower CFRP
Debonding of upper CFRP
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
Debonding of lower CFRP
Debonding of upper CFRP
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)
B10 (Lsheets = 250mm)
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
B8 (Lsheets = 1900mm)
Concrete crushingB9 (Lsheets = 1000mm)
B10 (Lsheets = 250mm)
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.
Figure 5.34 Strain distributions along the lower CFRP sheets of specimen B8 in Phase III.
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
Figure 5.35 Strain distributions along the lower CFRP sheets of specimen B9 in Phase III.
Figure 5.36 Strain distributions along the lower CFRP sheets of specimen B10 in Phase III.
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 5.37 Strain distributions along the lower CFRP sheets of specimen B11 in Phase III.
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
Strain x 10-3 (mm/mm)
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
Strain x 10-3 (mm/mm)
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.
Figure 5.42 Load-average shear stress responses along the lower CFRP sheets of specimen B9 in Phase III.
Average shear stress (MPa)
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
Average shear stress (MPa)
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
Average shear stress (MPa)
Load
(kN
)
12.550
175
100
0
50
100
150
200
250
300
350
400
450
-30 -20 -10 0 10 20 30
Average shear stress (MPa)
Load
(kN
)
12.512.55050
175175
100100
Chapter 5
201
Figure 5.43 Load-average shear stress responses along the lower CFRP sheets of specimen B10 in Phase III.
Figure 5.44 Load-average shear stress responses along the lower CFRP sheets of specimen B11 in Phase III.
Average shear stress (MPa)
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
Average shear stress (MPa)
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
Average shear stress (MPa)
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
Average shear stress (MPa)
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
Average shear stress (MPa)
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
Lateral displacement δ (mm)
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
Lateral displacement δ (mm)
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)
Axial displacement (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)
Axial displacement (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
Slenderness ratio (kL/r)
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
Slenderness ratio (kL/r)
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
Lateral displacement δ (mm)
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
Lateral displacement δ (mm)
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
Strain x 10-3 (mm/mm)
Stre
ss (M
Pa)
0
300
600
900
0 15 30 45
CFRP (type C3) Steel (bi-linear)
GFRP
(b) Modeling of residual stress
Strain x 10-3 (mm/mm)
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
(a) Materials stress-strain curves
Strain x 10-3 (mm/mm)
Stre
ss (M
Pa)
0
300
600
900
0 15 30 45
CFRP (type C3) Steel (bi-linear)
GFRP
(a) Materials stress-strain curves
Strain x 10-3 (mm/mm)
Stre
ss (M
Pa)
0
300
600
900
0 15 30 45
CFRP (type C3) Steel (bi-linear)
GFRP
(b) Modeling of residual stress
Strain x 10-3 (mm/mm)
Stre
ss (M
Pa)
Used for the 2 inside layers
Fy
Frs
Used for the 2 outside layers
FrsStrain x 10-3 (mm/mm)
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
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)
Exp. (kL/r=68)Model 1
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
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
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)
Exp. (kL/r=66)Model 1
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)
Exp. (kL/r=66)Model 1
Model 2
Chapter 6
244
Figure 6.15 Measured and predicted load-lateral displacement responses of set 2.
Figure 6.16 Measured and predicted load-lateral displacement responses of set 3.
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Figure 6.17 Measured and predicted load-lateral displacement responses of set 4.
Figure 6.18 Measured and predicted load-lateral displacement responses of set 5.
0
20
40
60
80
100
120
0 10 20 30 40 50 60
e’
P
δ
Experiment
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Figure 6.19 Measured and predicted load-lateral displacement responses of set 6.
Figure 6.20 Measured and predicted load-lateral displacement responses of specimen 7.
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25 30 35 40
Experiment
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
Load
(kN
)
Model 1
Crushing of CFRP on the inner compression flange
e’
P
δe’
P
δ
kL/r = 93
e’ = 0.84 mm
Frs = 0.49 Fy
Chapter 6
247
Figure 6.21 Measured and predicted load-lateral displacement responses of specimen 8.
Figure 6.22 Measured and predicted load-lateral displacement responses of specimen 9.
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25 30 35 40
Experiment
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
Load
(kN
)Model 2
Model 1
e’
P
δe’
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
Lateral Displacement δ (mm)
Load
(kN
)
Model 2Model 1
e’
P
δ
Crushing of CFRP on the compression flange
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
Lateral Displacement δ (mm)
Load
(kN
)
Model 2Model 1
e’
P
δe’
P
δ
Crushing of CFRP on the compression flange
kL/r = 68
e’ = 7.04 mm
Frs = 0.33 Fy
Chapter 6
248
Figure 6.23 Measured and predicted load-lateral displacement responses of specimen 10.
Figure 6.24 Measured and predicted load-lateral displacement responses of specimen 11.
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25 30 35 40
Experiment
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
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
Lateral Displacement δ (mm)
Load
(kN
)
Model 2
Model 1
e’
P
δ
Crushing of CFRP on the side walls
Crushing of CFRP on the compression flange
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
Lateral Displacement δ (mm)
Load
(kN
)
Model 2
Model 1
e’
P
δe’
P
δ
Crushing of CFRP on the side walls
Crushing of CFRP on the compression flange
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.
Figure 6.26 Measured and predicted load-axial displacement responses of set 2.
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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Figure 6.27 Measured and predicted load-axial displacement responses of set 3.
Figure 6.28 Measured and predicted load-axial displacement responses of set 4.
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 = 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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Figure 6.29 Measured and predicted load-axial displacement responses of set 5.
Figure 6.30 Measured and predicted load-axial displacement responses of set 6.
0
20
40
60
80
100
120
0 1 2 3 4 5 6 7
Experiment
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
Load
(kN
)
Model 1
P
∆
kL/r = 93
e’ = 0.96 mm
Frs = 0.49 Fy
Experiment
Axial Displacement ∆ (mm)
Load
(kN
)
Model 1
P
∆
P
∆
kL/r = 93
e’ = 0.96 mm
Frs = 0.49 Fy
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Figure 6.31 Measured and predicted load-axial displacement responses of specimen 7.
Figure 6.32 Measured and predicted load-axial displacement responses of specimen 8.
0
50
100
150
200
250
300
350
400
450
0 1 2 3 4 5 6
Experiment
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
Load
(kN
) Model 2Model 1
P
∆
P
∆
kL/r = 68
e’ = 0.92 mm
Frs = 0.33 Fy
Chapter 6
253
Figure 6.33 Measured and predicted load-axial displacement responses of specimen 9.
Figure 6.34 Measured and predicted load-axial displacement responses of specimen 10.
0
50
100
150
200
250
300
350
400
450
0 1 2 3 4 5 6
Experiment
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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 6.35 Measured and predicted load-axial displacement responses of specimen 11.
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
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
350
400
450
0 1 2 3 4 5 6
Experiment
Axial Displacement ∆ (mm)
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
Axial Displacement ∆ (mm)
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
Figure 6.37 Measured and predicted load-axial strain responses of set 2.
Figure 6.38 Measured and predicted load-axial strain responses of set 3.
0
50
100
150
200
250
300
-8 -6 -4 -2 0 2
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
Load
(kN
)Model 1
Experiment
S2S1 S2S1
kL/r = 46
e’ = 0.26 mm
Frs = 0.49 Fy
Chapter 6
256
Figure 6.39 Measured and predicted load-axial strain responses of set 4.
Figure 6.40 Measured and predicted load-axial strain responses of set 5.
0
20
40
60
80
100
120
-4 -3 -2 -1 0 1 2
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
Load
(kN
)
Model 1
Experiment
S2S1 S2S1
kL/r = 70
e’ = 0.32 mm
Frs = 0.49 Fy
Chapter 6
257
Figure 6.41 Measured and predicted load-axial strain responses of set 6.
Figure 6.42 Measured and predicted load-axial strain responses of specimen 7.
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
Load
(kN
)
kL/r = 93
e’ = 0.84 mm
Frs = 0.49 Fy
Experiment
Model 1
Model 1Experiment
S2S1 S2S1
Chapter 6
258
Figure 6.43 Measured and predicted load-axial strain responses of specimen 8.
Figure 6.44 Measured and predicted load-axial strain responses of specimen 9.
0
50
100
150
200
250
300
350
400
450
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
Axial strain (x 10-3)
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
Axial strain (x 10-3)
Load
(kN
)
Experiment
Model 2Model 1
Model 1
Experiment
S2S1 S2S1kL/r = 68
e’ = 0.92 mm
Frs = 0.33 Fy
Model 2
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Figure 6.45 Measured and predicted load-axial strain responses of specimen 10.
Figure 6.46 Measured and predicted load-axial strain responses of specimen 11.
0
50
100
150
200
250
300
350
400
450
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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
Axial strain (x 10-3)
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.
Figure 6.49 Load-lateral displacement responses for specimens with e’=L/600.
0
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50
Load
(kN
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
Figure 6.50 Load-lateral displacement responses for specimens with e’=L/750.
Figure 6.51 Load-lateral displacement responses for specimens with e’=L/1000.
0
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50
Load
(kN
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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 6.52 Load-lateral displacement responses for specimens with e’=L/2000.
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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
)
Lateral displacement δ (mm)
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%
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%
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%
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
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378
297 33
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374
413
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359
326
412
383
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346 38
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Axia
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(kN
)
Specimen identification
268
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297 33
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Model 1Model 2
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(kN
)
Specimen identification
Axia
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fnes
s (k
N/m
m)
Specimen identification
88
102 10
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130 13
5
80
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Model 1Model 2
Axia
l stif
fnes
s (k
N/m
m)
Specimen identification
88
102 10
9
130 13
5
80
91
105
117
85
98
109
126 13
5
89
96
111
125
0
20
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100
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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
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
Curvature (1/m) x 10-3
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
Curvature (1/m) x 10-3
Mom
ent (
kN.m
)
Experiment
Model(Two CFRP layers)
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
Strain in tension flange x 10-3
0
25
50
75
100
125
150
175
200
225
250
275
0 10 20 30 40 50 60 70 80
Curvature (1/m) x 10-3
Mom
ent (
kN.m
) Experiment
Model
Debonding of outer layer
Model(Two CFRP layers)
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
Curvature (1/m) x 10-3
Mom
ent (
kN.m
) Experiment
Model
Debonding of outer layer
Model(Two CFRP layers)
Model(One CFRP layer)
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
Strain in tension flange x 10-3
Mom
ent (
kN.m
)
Experiment
Model(Two CFRP layers)
Debonding of outer layer
Model(One CFRP layer)
0
25
50
75
100
125
150
175
200
225
250
275
0 5 10 15 20
Strain in tension flange x 10-3
Mom
ent (
kN.m
)
Experiment
Model(Two CFRP layers)
Debonding of outer layer
Model(One CFRP layer)
0
25
50
75
100
125
150
175
200
225
250
275
0 5 10 15 20
Mom
ent (
kN.m
)
Experiment
Debonding of outer layer
Strain in tension flange x 10-3
CFRP ruptureModel(Two CFRP layers)
Model(One CFRP layer)
CFRP rupture
0
25
50
75
100
125
150
175
200
225
250
275
0 5 10 15 20
Mom
ent (
kN.m
)
Experiment
Debonding of outer layer
Strain in tension flange x 10-3
CFRP ruptureModel(Two CFRP layers)
Model(One CFRP layer)
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
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
Mid-span deflection (mm)
Load
(kN
)
Model
0
20
40
60
80
100
120
140
160
180
200
220
0 25 50 75 100 125 150 175
Experiment
Debonding of outer layer
Model(One CFRP layer)
Model(Two CFRP layers)
CFRP rupture
Mid-span deflection (mm)
Load
(kN
)
Model
0
20
40
60
80
100
120
140
160
180
200
220
0 25 50 75 100 125 150 175
Experiment
Debonding of outer layer
Model(One CFRP layer)
Model(Two CFRP layers)
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
Curvature (1/m) x 10-3
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
Curvature (1/m) x 10-3
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 %
Mid-span deflection (mm)
0
20
40
60
80
100
120
140
160
180
200
220
0 25 50 75 100 125 150 175
Load
(kN
)
Experiment
Model(One CFRP layer)
Model(Two CFRP layers)
CFRP ruptureCFRP rupture
Mid-span deflection (mm)
0
20
40
60
80
100
120
140
160
180
200
220
0 25 50 75 100 125 150 175
Load
(kN
)
Experiment
Model(One CFRP layer)
Model(Two CFRP layers)
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.
Curvature (1/m) x 10-3
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 %
Curvature (1/m) x 10-3
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 %
Curvature (1/m) x 10-3
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 %
Curvature (1/m) x 10-3
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.
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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.
Figure A.2 Out-of-straightness geometric imperfection profile of specimen 1-2.
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
htne
ss (m
m)
Side (a)
Side (b)
a
b
Appendix A
328
Figure A.3 Out-of-straightness geometric imperfection profile of specimen 1-3.
Figure A.4 Out-of-straightness geometric imperfection profile of specimen 2-1.
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
329
Figure A.5 Out-of-straightness geometric imperfection profile of specimen 2-2.
Figure A.6 Out-of-straightness geometric imperfection profile of specimen 2-3.
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
Figure A.7 Out-of-straightness geometric imperfection profile of specimen 3-1.
Figure A.8 Out-of-straightness geometric imperfection profile of specimen 3-2.
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
Figure A.9 Out-of-straightness geometric imperfection profile of specimen 3-3.
Figure A.10 Out-of-straightness geometric imperfection profile of specimen 4-1.
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
Figure A.11 Out-of-straightness geometric imperfection profile of specimen 4-2.
Figure A.12 Out-of-straightness geometric imperfection profile of specimen 4-3.
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
Figure A.13 Out-of-straightness geometric imperfection profile of specimen 5-1.
Figure A.14 Out-of-straightness geometric imperfection profile of specimen 5-2.
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
Figure A.15 Out-of-straightness geometric imperfection profile of specimen 5-3.
Figure A.16 Out-of-straightness geometric imperfection profile of specimen 6-1.
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
Figure A.17 Out-of-straightness geometric imperfection profile of specimen 6-2.
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.
Applied load, P (kN)
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
Specimen 4-1, eP=0= 1.63
Specimen 4-2, eP=0= 0.77
Specimen 3-2, eP=0= 0.71
Specimen 3-3, eP=0= 0.27
Specimen 4-3, eP=0= 0.13
Specimen 3-1, eP=0= 0.17
Applied load, P (kN)
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
Specimen 4-1, eP=0= 1.63
Specimen 4-2, eP=0= 0.77
Specimen 3-2, eP=0= 0.71
Specimen 3-3, eP=0= 0.27
Specimen 4-3, eP=0= 0.13
Specimen 3-1, eP=0= 0.17
Mid
-hei
ght I
mpe
rfect
ion,
e’(
mm
)
Applied load, P (kN)
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 6-1, eP=0= 1.22
Specimen 6-2, eP=0= 0.74
Specimen 5-1, eP=0= 0.57
Specimen 5-3, eP=0= 0.37
Specimen 5-2, eP=0= 0.41
Specimen 6-3, eP=0= 0.17
Mid
-hei
ght I
mpe
rfect
ion,
e’(
mm
)
Applied load, P (kN)
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 6-1, eP=0= 1.22
Specimen 6-2, eP=0= 0.74
Specimen 5-1, eP=0= 0.57
Specimen 5-3, eP=0= 0.37
Specimen 5-2, eP=0= 0.41
Specimen 6-3, eP=0= 0.17
Appendix B
338
Figure B.3 Mid-height imperfections of specimens 7 to 11 versus the applied load.
Applied load, P (kN)
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
Specimen 8, eP=0= 0.92
Specimen 9, eP=0= 7.04
Specimen 10, eP=0= 2.04
Specimen 11, eP=0= 5.00
Applied load, P (kN)
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
Specimen 8, eP=0= 0.92
Specimen 9, eP=0= 7.04
Specimen 10, eP=0= 2.04
Specimen 11, eP=0= 5.00