FIRE RESPONSE OF REINFORCED CONCRETE BEAMS STRENGTHENED WITH
NEAR-SURFACE MOUNTED FRP REINFORCEMENT
By
Baolin Yu

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Civil Engineering – Doctor of Philosophy
2013

ABSTRACT
FIRE RESPONSE OF REINFORCED CONCRETE BEAMS
STRENGTHENED WITH NEAR-SURFACE MOUNTED FRP
REINFORCEMENT
By
Baolin Yu
In recent years, the use of near-surface mounted (NSM) fiber-reinforced polymer
(FRP) reinforcement has become a promising technology in strengthening of reinforced
concrete (RC) structures. When used in buildings, FRP strengthened RC members have
to satisfy fire resistance requirements specified in codes and standards. Due to sensitivity
of FRP to high temperatures, FRP strengthened RC members usually exhibit relatively
low fire resistance. However, NSM FRP strengthening is considered to possess higher
fire resistance than traditional externally bonded FRP strengthening. But there are no
specific studies on fire response of NSM FRP strengthened RC members. Therefore,
experimental and numerical studies were carried out for developing a fundamental
understanding on the behavior of NSM FRP strengthened RC beams under fire conditions.
To develop test data on fire response of NSM FRP strengthened members,
experimental studies were undertaken at both material level and structural level. As part
of material property characterization, extensive high temperature property tests were
carried out for evaluating strength, bond, and thermal expansion properties of NSM FRP
over a wide temperature range. As part of structural characterization, fire resistance tests
were conducted on four NSM FRP strengthened concrete T-beams. Results from these
fire tests show that with proper design and configuration, NSM FRP strengthened RC
beam can achieve more than three hours of fire resistance, even without fire insulation.

As part of numerical studies, a numerical model was developed for tracing the fire
response of NSM FRP strengthened RC beams. The model is based on a macroscopic
finite element approach and utilizes moment-curvature relationships to trace the response
of beam from pre-loading stage to failure under fire conditions. The model accounts for
high temperature properties of constituent materials, various strain components, and fire
induced bond degradation. The numerical model was validated using test data generated
on various NSM FRP strengthened RC beams at both ambient and fire conditions.
The validated model was further applied to conduct a set of parametric studies to
quantify the influence of critical factors on fire response of NSM FRP strengthened RC
beams. Results from the studies indicate that type of strengthening, reinforcement ratio of
FRP to steel, load level, axial restraint, fire scenario and fire insulation have significant
influence on fire resistance of NSM FRP strengthened RC beams. Other factors such as
location of NSM FRP and concrete strength have moderate influence on the fire response.
Results from fire experiments and parametric studies were utilized to develop a
rational methodology for evaluating the fire resistance of FRP strengthened RC beams.
As the first step of this methodology, a set of simplified equations were derived to predict
cross sectional temperatures in an FRP strengthened RC beam exposed to fire. Then
moment capacity of the strengthened beam is evaluated utilizing an approach similar to
that at room temperature but incorporated with temperature dependant strength properties
of concrete, steel and FRP. Finally the fire resistance of FRP strengthened RC beam can
be determined as the time when external load exceeds moment capacity. This approach
facilitates a quick and reliable access on fire resistance of FRP strengthened RC beams,
and thus it is attractive for incorporation in design codes and standards.

This dissertation is dedicated to my parents and my wife. Without their emotional support
and encouragement, I could not complete this work.

iv

ACKNOWLEDGMENTS

I would like to express my greatest gratitude to my advisor, Professor Venkatesh
Kodur, for his continued support, encouragement, and guidance during the course of my
studies. I would like to convey my sincere thanks for his ideas and perseverance which
made my graduate studies very rewarding.
Also, special thanks to the distinguished faculty members, Prof. Parviz
Soroushian, Prof. Lawrence Drzal, and Prof. Nizar Lajnef, who served on my committee
and provided me with their valuable advice and useful guidance during my Ph.D. studies.
I would like to thank my friends Anuj Shakya, Esam Aziz, Mohannad Naser, Yi
Sun, Nan Hu, Purushutham Pakala, Nikhil Raut, Wasim Khaliq, Aqeel Ahmad, Mahmud
Dwaikat, Dr. Xiaomeng Hou and Dr. Haiyan Zhang, for their support, particularly in the
experimental part of this study.
I would also like to thank Mr. Siavosh Ravanbakhsh and Mr. Charles Meddaugh
for their support and help during the experimental program in this research. Additionally,
I would like to thank all the faculty members and students at the Civil and Environmental
Engineering department at Michigan State University for their help and support during
my doctoral studies.

v

TABLE OF CONTENTS
LIST OF TABLES………………….………..…………………….……………………….xi
LIST OF FIGURES………………….…………..…..…………………...………………..xiv
CHAPTER 1
INTRODUCTION………...……..……………………………………..…………………….1
1.1 Background and Motivation ................................................................................. 1
1.2 Strengthening Strategies for Concrete Structures .............................................. 4
1.3 Behavior of FRP Strengthened RC Beams under Fire Conditions ................... 7
1.4 Objectives .............................................................................................................. 10
1.5 Scope ...................................................................................................................... 11
CHAPTER 2
STATE-OF-THE-ART REVIEW……………………………….…………...……………....14
2.1 General .................................................................................................................. 14
2.2 Configuration and Installation of NSM FRP Strengthening ........................... 15
2.2.1 NSM FRP reinforcement and groove filler .................................................. 15
2.2.2 Installation procedure................................................................................... 17
2.3 Behavior of NSM FRP Strengthened Members at Ambient Conditions ........ 21
2.3.1 Bond behavior of NSM FRP system ............................................................ 21
2.3.2 Behavior of NSM FRP strengthened RC members ..................................... 24
2.4 Material Properties at Elevated Temperatures ................................................. 25
2.4.1 Concrete ....................................................................................................... 26
2.4.1.1 Thermal properties........................................................................... 26
2.4.1.2 Mechanical properties ..................................................................... 29
2.4.1.3 Deformation properties .................................................................... 32
2.4.1.4 Fire induced spalling ....................................................................... 34
2.4.2 Reinforcing steel .......................................................................................... 36
2.4.2.1 Thermal properties........................................................................... 36
2.4.2.2 Mechanical properties ..................................................................... 37
2.4.2.3 Deformation properties .................................................................... 39
2.4.3 FRP reinforcement ....................................................................................... 40
2.4.3.1 General ............................................................................................ 40
2.4.3.2 Thermal properties........................................................................... 42
2.4.3.3 Mechanical properties ..................................................................... 44
vi

2.4.3.4 Deformation properties .................................................................... 46
2.4.3.5 Bond properties ................................................................................ 48
2.4.4 Fire insulation .............................................................................................. 52
2.5 Fire Response of Concrete Beams Incorperated with FRP Reinforcement ... 55
2.5.1 Concrete beams reinforced with interal FRP rebars .................................... 55
2.5.2 RC beams strengthened with external FRP laminates ................................. 60
2.5.3 RC beams strengthened with NSM FRP reinforcement .............................. 66
2.6 Codes and Standards for FRP Strengthened RC members ............................. 67
2.7 Summary ............................................................................................................... 69
CHAPTER 3
HIGH TEMPERATURE MATERIAL PROPERTY...………………………………..………..71
3.1 General .................................................................................................................. 71
3.2 Tensile Strength Tests .......................................................................................... 71
3.2.1 Preparation of test specimens....................................................................... 72
3.2.2 Test set-up .................................................................................................... 75
3.2.3 Results and discussion ................................................................................. 78
3.2.4 Relations for tensile strength and modulus with temperature ...................... 87
3.2.5 Summary of tension test results ................................................................... 91
3.3 Bond Strength Tests ............................................................................................. 91
3.3.1 Preparation of test specimens....................................................................... 92
3.3.2 Test set-up .................................................................................................... 95
3.3.3 Results and discussion ................................................................................. 97
3.3.3.1 Bond strength and modulus at room temperature ........................... 97
3.3.3.2 Bond strength and modulus at elevated temperature .................... 101
3.3.3.3 Bond stress-slip relations............................................................... 107
3.3.4 Relations for bond strength and modulus with temperature ...................... 110
3.3.5 Summary of bond test results ..................................................................... 114
3.4 Thermal Expansion Tests .................................................................................. 114
3.4.1 Preparation of test specimens..................................................................... 115
3.4.2 Test apparatus and test procedure .............................................................. 116
3.4.3 Results and discussion ............................................................................... 117
3.4.4 Summary of thermal expansion tests ......................................................... 121
3.5 Summary ............................................................................................................. 122
CHAPTER 4
FIRE RESISTANCE EXPERIMENTS…………………………………………………..….124
4.1 General ................................................................................................................ 124
vii

4.2 Preparation of Test Specimens ......................................................................... 124
4.2.1 Design and fabrication of RC T-beams ..................................................... 125
4.2.2 NSM FRP strengthening ............................................................................ 128
4.2.2.1 Design of flexural strengthening.................................................... 128
4.2.2.2 Installation of NSM FRP strips ...................................................... 129
4.2.3 Fire insulation on T-beams ........................................................................ 131
4.2.3.1 Fire insulation properties .............................................................. 131
4.2.3.2 Installation of fire insulation ......................................................... 132
4.2.4 Instrumentation .......................................................................................... 134
4.3 Test Apparatus ................................................................................................... 135
4.4 Test Conditions and Procedure......................................................................... 137
4.5 Material Tests ..................................................................................................... 138
4.6 Test Results and Discussion .............................................................................. 140
4.6.1 Test observations ....................................................................................... 140
4.6.2 Thermal response ....................................................................................... 144
4.6.2.1 Furnace temperatures .................................................................... 144
4.6.2.2 NSM FRP temperatures ................................................................. 145
4.6.2.3 Steel rebar temperatures ................................................................ 148
4.6.2.4 Concrete temperatures ................................................................... 151
4.6.3 Structural response ..................................................................................... 153
4.6.3.1 Deflections ..................................................................................... 153
4.6.3.2 Axial restraint force ....................................................................... 156
4.6.3.3 Strain in longitudinal reinforcement .............................................. 158
4.6.4 Fire resistance ............................................................................................ 158
4.7 Residual Strength Tests of NSM FRP Strengthened RC Beams ................... 160
4.7.1 Test procedure ............................................................................................ 161
4.7.2 Results and discussion ............................................................................... 161
4.8 Summary ............................................................................................................. 165
CHAPTER 5
NUMERICAL MODEL…………………………………………………………………....167
5.1 General ................................................................................................................ 167
5.2 Macroscopic Finite Element Model for Fire Resistance Analysis ................. 167
5.2.1 General approach ....................................................................................... 168
5.2.2 Fire temperatures ....................................................................................... 171
5.2.3 Thermal analysis ........................................................................................ 171
5.2.4 Structural analysis ...................................................................................... 175
5.2.4.1 General analysis procedure ........................................................... 175
viii

5.2.4.2 Evaluating temperature induced slip and axial restraint force ..... 177
5.2.4.3 Generation of moment-curvature (M-κ) relationships .................. 183
5.2.4.4 Beam analysis ................................................................................ 185
5.3 Computer Implementation ................................................................................ 188
5.3.1 Input data ................................................................................................... 188
5.3.2 Output results ............................................................................................. 190
5.3.3 Material properties ..................................................................................... 190
5.4 Validation of Numerical Model ........................................................................ 192
5.4.1 Response at ambient conditions ................................................................. 192
5.4.2 Response under fire conditions – Rectangular beams ............................... 196
5.4.3 Response under fire conditions – T-beams ................................................ 200
5.5 Summary ............................................................................................................. 209
CHAPTER 6
PARAMETRIC STUDIES.………………………………………………………………....211
6.1 General ................................................................................................................ 211
6.2 Critical Factors Influencing Fire Resistance ................................................... 211
6.3 Parametric Studies ............................................................................................. 212
6.3.1 Beam configuration and parameters in study............................................. 212
6.3.2 Material properties ..................................................................................... 215
6.3.3 Discretization and analysis details ............................................................. 218
6.3.4 Failure criteria ............................................................................................ 218
6.4 Results of Parametric Studies ........................................................................... 219
6.4.1 Effect of FRP strengthening....................................................................... 221
6.4.2 Effect of NSM FRP location ...................................................................... 226
6.4.3 Effect of reinforcement ratio of FRP and steel rebar ................................. 228
6.4.4 Effect of concrete compressive strength .................................................... 231
6.4.5 Effect of load level ..................................................................................... 233
6.4.6 Effect of axial restraint............................................................................... 234
6.4.7 Effect of fire scenario................................................................................. 238
6.4.8 Effect of insulation layout .......................................................................... 241
6.5 Summary ............................................................................................................. 245
CHAPTER 7
RATIONAL DESIGN METHODOLOGY……………………………………...…………....247
7.1 General ................................................................................................................ 247
7.2 Simplifed Approach for Predicting Temperatures in RC Members ............. 248
7.2.1 An approach for predicting temperature in an uninsulated RC member ... 248
ix

7.2.1.1 General .......................................................................................... 248
7.2.1.2 Generation of temperature data for regression analysis ............... 250
7.2.1.3 Cross section division for 1-D and 2-D heat transfer area ........... 252
7.2.1.4 Nonlinear regression analysis ....................................................... 256
7.2.1.5 Regression analysis results ............................................................ 259
7.2.1.6 Verification of temperature equations using test results ............... 262
7.2.1.7 Verification of temperature equations using FEA results.............. 269
7.2.2 An approach for predicting temperatures in an insulated RC member ...... 275
7.2.2.1 Converting fire insulation layer to equivalent concrete layer ....... 275
7.2.2.2 Regression analysis........................................................................ 280
7.2.2.3 Verification of temperature equations uing test results ................. 284
7.2.2.4 Verification of temperature equations uing FEA results ............... 288
7.3 Evaluating Moment Capacity of FRP-Strengthened RC Beams ................... 293
7.3.1 Degradation of steel and FRP properties ................................................... 293
7.3.2 Effective concrete width under fire exposure ............................................ 294
7.3.3 Evaluating moment capacity at a given fire exposure time ....................... 296
7.4 Validaion of the Proposed Approach ............................................................... 300
7.5 Limitation of Applicability ................................................................................ 305
7.6 Summary ............................................................................................................. 305
CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS………………………………………..…….307
8.1 General ................................................................................................................ 307
8.2 Key Findings ....................................................................................................... 308
8.3 Recommendations for Future Research........................................................... 311
8.4 Research Impact ................................................................................................. 312
APPENDICES……………………………………………………………………...……..315
APPENDIX A Material Properties at Elevated Temperatures ........................... 316
APPENDIX B Design and Load Calculations ....................................................... 335
APPENDIX C Finite Element Formulation .......................................................... 341
APPENDIX D Design Exmaples ............................................................................. 343
REFERENCES……………………………………………………………………...…….355

x

LIST OF TABLES

Table 2.1 Thermal expansion of FRP reinforcement reported in previous studies .......... 49
Table 2.2 Comparison of thermal properties for different fire insulation......................... 55
Table 2.3 Experimental studies on fire response of concrete beams reinforced with
internal FRP rebars ............................................................................................ 59
Table 2.4 Numerical studies on fire response of concrete beams reinforced with internal
FRP rebars.......................................................................................................... 59
Table 2.5 Experimental studies on fire response of RC beams strengthened with external
FRP laminates .................................................................................................... 64
Table 2.6 Numerical studies on fire response of RC beams strengthened with external
FRP laminates .................................................................................................... 65
Table 2.7 Experimental studies on fire response of RC beams strengthened with NSM
FRP reinforcement ............................................................................................. 65
Table 3.1 Properties of NSM CFRP reinforcement as specified by manufacturer ........... 72
Table 3.2 Tensile strength and elastic modulus of CFRP strips at various temperatures . 81
Table 3.3 Tensile strength and elastic modulus of CFRP rods at various temperatures ... 82
Table 3.4 Bond test program on NSM FRP system .......................................................... 92
Table 3.5 Bond strength and modulus of Tyfo T300 epoxy for NSM CFRP strip at
various temperatures .......................................................................................... 99
Table 3.6 Bond strength and modulus of Tyfo T300 epoxy for NSM CFRP rod at various
temperatures ....................................................................................................... 99
Table 3.7 Bond strength and modulus of Tyfo S epoxy for NSM CFRP strip at various
temperatures ..................................................................................................... 100
Table 3.8 Bond strength and modulus of Tyfo S epoxy for NSM CFRP rod at various
temperatures ..................................................................................................... 100
Table 3.9 NSM FRP specimens used for thermal expansion test ................................... 115
xi

Table 3.10 Transverse and longitudinal CTEs for various NSM FRP reinforcement .... 122
Table 4.1 Batch proportion of concrete .......................................................................... 126
Table 4.2 Properties of Tyfo NSM CFRP strips ............................................................. 129
Table 4.3 Variables studied in fire tests on NSM FRP strengthened T-beams............... 138
Table 4.4 Compressive strength of concrete ................................................................... 139
Table 4.5 Visual observation for Beams I and II in the first fire resistance test ............. 142
Table 4.6 Visual observation for Beams III and IV in the second fire resistance test .... 143
Table 4.7 Configuration and test conditions of RC beams with various FRP strengthening
......................................................................................................................... 153
Table 4.8 Test variables and results in residual strength tests on fire exposed beams ... 161
Table 5.1 Strain components in concrete, steel, and FRP ............................................... 186
Table 5.2 Configuration and properties of RC beams used for validation ..................... 194
Table 6.1 Geometric and material properties of FRP strengthened RC beams used in
parametric study............................................................................................... 213
Table 6.2 Critical factors investigated in parametric study ............................................ 217
Table 6.3 Summary of fire resistance values for the beams in parametric studies ......... 220
Table 6.4 Configuration and moment contribution of NSM FRP and steel rebar in Beams
III 1-3 ............................................................................................................... 230
Table 6.5 Effect of insulation layout on fire response of NSM FRP strengthened beams
......................................................................................................................... 242
Table 7.1 Characteristics of RC members for regression analysis ................................. 252
Table 7.2 Sections of RC members used in validation of temperature equations .......... 264
Table 7.3 Characteristics of insulated RC beams used for the regression analysis ........ 281
Table 7.4 Factors for calculating effective concrete width for various RC beams exposed
to ASTM E119 standard fire............................................................................ 295
xii

Table 7.5 Comparison of fire resistance using proposed approach against fire tests and
FEA results ...................................................................................................... 302
Table A.1 Values for main parameters of the stress-strain relationships of NSC at
elevated temperature (Eurocode 2) .................................................................. 321
Table A.2 Values for main parameters of stress-strain relationships of reinforcing steel at
elevated temperatures (Eurocode 2) ................................................................ 324
Table A.3 Previous studies on thermal properties of epoxy ........................................... 329
Table D.1 Properties of Beams D1 and D2..................................................................... 344

xiii

LIST OF FIGURES
Figure 1.1 Application of NSM FRP on concrete members (For interpretation of the
references to color in this and all other figures, the reader is referred to the
electronic version of this dissertation) ................................................................. 3
Figure 1.2 Comparison between EBR and NSM strengthening systems under bending.... 6
Figure 1.3 Comparison of temperature in NSM FRP and external FRP under standard fire
............................................................................................................................ 10
Figure 2.1 Procedures of installing NSM FRP (Hughes Brothers 2011) .......................... 18
Figure 2.2 Requirement on dimensions of NSM groove (ACI 440.2R 2008) .................. 20
Figure 2.3 Typical failure modes of NSM FRP system .................................................... 22
Figure 2.4 Typical bond-slip curve of NSM FRP system ................................................. 23
Figure 2.5 Variation of thermal properties with temperature for various types of concrete
............................................................................................................................ 27
Figure 2.6 Variation of compressive strength with temperature for various types of
concrete (Kodur et al. 2008) .............................................................................. 30
Figure 2.7 Variation of elastic modulus with temperature for various types of concrete . 31
Figure 2.8 Variation of residual strength of concrete with temperature ........................... 32
Figure 2.9 Variation of thermal strain with temperature for various types of concrete.... 33
Figure 2.10 Variation of thermal properties with temperature for reinforcing steel ........ 37
Figure 2.11 Variation of yield strength and ultimate strength with temperature for
reinforcing steel ................................................................................................. 38
Figure 2.12 Variation of thermal expansion with temperature for reinforcing steel ........ 40
Figure 2.13 Variation of thermal properties with temperature for FRP ........................... 43
Figure 2.14 Variation of bond strength with temperature for externally bonded FRP ..... 51
Figure 2.15 Variation of thermal properties with temperature for VG insulation ............ 54
xiv

Figure 3.1 Fabrication of anchor system for FRP specimens ........................................... 74
Figure 3.2 Test apparatus and specimens for room temperature test ................................ 75
Figure 3.3 Test setup for FRP tension test at elevated temperatures ................................ 76
Figure 3.4 Temperature progression in FRP during high temperature tension tests ........ 77
Figure 3.5 Comparison of measured stresses using loading cell with strain gauges ........ 78
Figure 3.6 Variation of tensile strength and elastic modulus of CFRP strips with
temperature ........................................................................................................ 83
Figure 3.7 Variation of tensile strength and elastic modulus of CFRP rods with
temperature ........................................................................................................ 83
Figure 3.8 Stress-strain response of CFRP strips at various temperatures ....................... 85
Figure 3.9 Stress-strain response of CFRP rods at various temperatures ......................... 85
Figure 3.10 Failure modes of CFRP strips at various temperatures ................................. 86
Figure 3.11 Failure modes of CFRP rods at various temperatures ................................... 87
Figure 3.12 Comparison of tensile strength predicted by empirical formula with test data
............................................................................................................................ 90
Figure 3.13 Comparison of elastic modulus predicted by empirical formula with test data
............................................................................................................................ 90
Figure 3.14 Fabrication of NSM FRP bond test specimen ............................................... 92
Figure 3.15 Groove size for installation of NSM FRP specified in ACI 440.2 (2008) .... 94
Figure 3.16 Test set-up for evaluating bond strength of NSM systems at high
temperatures ....................................................................................................... 96
Figure 3.17 Variation of bond strength and elastic modulus of NSM CFRP strip and rod
with Tyfo T300 epoxy with temperature ......................................................... 102
Figure 3.18 Variation of bond strength and bond modulus of NSM CFRP strip and rod
with Tyfo S epoxy with temperature ............................................................... 103
Figure 3.19 Variation of temperature inside Tyfo T300 and Tyfo S epoxy as a function of
heating time ...................................................................................................... 104
xv

Figure 3.20 Failure modes of NSM CFRP specimens with Tyfo T300 epoxy ............... 106
Figure 3.21 Failure modes of NSM CFRP specimens with Tyfo S epoxy ..................... 107
Figure 3.22 Bond stress-slip relations for NSM CFRP specimens with Tyfo T300 epoxy
at various temperatures .................................................................................... 108
Figure 3.23 Bond stress-slip relations for NSM CFRP specimens with Tyfo S epoxy at
various temperatures ........................................................................................ 109
Figure 3.24 Comparison of predicted bond strength from proposed empirical relations
with measured data from tests.......................................................................... 113
Figure 3.25 Comparison of predicted bond modulus from proposed empirical relations
with measured data from tests.......................................................................... 113
Figure 3.26 TMA apparatus and setup for thermal expansion test ................................. 117
Figure 3.27 Thermal expansion of NSM FRP specimens in transverse directions ........ 118
Figure 3.28 Thermal expansion of NSM FRP specimens in longitudinal directions ..... 119
Figure 4.1 Elevation, cross-section, and instrumentation of FRP strengthened RC beams
.......................................................................................................................... 127
Figure 4.2 Steps in fabrication of RC beams .................................................................. 128
Figure 4.3 Location and dimensions of NSM grooves (Units: mm)............................... 131
Figure 4.4 Installation of NSM FRP strengthening on RC T-beams .............................. 131
Figure 4.5 Steps in application of fire insulation on NSM FRP strengthened RC beams
.......................................................................................................................... 133
Figure 4.6 Layout of fire insulation scheme on NSM FRP strengthened RC beams ..... 134
Figure 4.7 Structural fire test furnace at MSU Civil and Infrastructure Laboratory ...... 136
Figure 4.8 Installation of axial restriant on NSM FRP strengthened RC beam (Beam III)
.......................................................................................................................... 136
Figure 4.9 Stress-strain relations of steel rebars used for flexural reinforcement .......... 139
Figure 4.10 Measured and specified time-temperature curve during fire tests............... 144
xvi

Figure 4.11 Variation of NSM FRP temperatures with fire exposure time in Beams I-IV
.......................................................................................................................... 147
Figure 4.12 Variation of temperatures at insulation/concrete interface with fire exposure
time in Beams II-IV ......................................................................................... 148
Figure 4.13 Variation of steel rebar temperatures with fire exposure time in Beams I-IV
.......................................................................................................................... 150
Figure 4.14 Variation of concrete temperatures with fire exposure time at various
locations in Beams I-IV ................................................................................... 152
Figure 4.15 Comparison of mid-span deflections of NSM FRP strengthened RC beams
with unstrengthened RC beam and external FRP strengthened RC beam ....... 156
Figure 4.16 Variation of axial force and displacement with fire exposure time............. 157
Figure 4.17 Strain measured in tension and compression rebars in Beams I and II during
the test (starting from pre-loading stage) ......................................................... 159
Figure 4.18 Strain measured in tension and compression rebars in Beams III and IV
during the test (starting from pre-loading stage).............................................. 159
Figure 4.19 Load-deflection response of Beams I-IV in residual strength tests ............. 163
Figure 4.20 Failure patterns of Beams I-IV in residual strength tests ............................ 164
Figure 4.21 Response of NSM FRP strips after failure in residual strength tests .......... 165
Figure 5.1 Typical beam layout and discretization of beam into segments and elements
.......................................................................................................................... 169
Figure 5.2 Flowchart illustrating the steps associated in the numerical model .............. 170
Figure 5.3 Bond stress-slip relations of NSM FRP strip at various temperatures .......... 178
Figure 5.4 Force equilibrium at NSM FRP-concrete interface in the ith segment (vertical
view) ................................................................................................................ 179
Figure 5.5 Illustration of axial restraint force calculations ............................................. 182
Figure 5.6 Force equilibrium and strain compatibility in an RC beam strengthened with
NSM FRP ......................................................................................................... 184
Figure 5.7 Illustration of curvature controlled iterative procedure for beam analysis.... 188
xvii

Figure 5.8 Configuration of tested beams for room temperature response validation (Units:
mm) .................................................................................................................. 193
Figure 5.9 Load-deflection response in RC beams under monotonic loading (ambient
condition) ......................................................................................................... 196
Figure 5.10 Configuration of tested beams for fire condition response validation (Units:
mm) .................................................................................................................. 197
Figure 5.11 Comparison of predicted and measured temperatures and mid-span
deflections for Beams V4 and V5 .................................................................... 200
Figure 5.12 Configuration of tested T-beams for fire condition response validation (Units:
mm) .................................................................................................................. 201
Figure 5.13 Comparison of predicted and measured temperatures in NSM FRP and steel
rebar for MSU beams ....................................................................................... 203
Figure 5.14 Comparison of predicted and measured temperatures in concrete for MSU
beams ............................................................................................................... 205
Figure 5.15 Comparison of predicted and measured mid-span deflections in T-beams . 208
Figure 5.16 Comparison of predicted and measured axial forces in T-beams................ 209
Figure 6.1 Configuration and elevation of NSM FRP strengthened RC beam (Beam A)
for parametric study (Units: mm) .................................................................... 214
Figure 6.2 Layout of NSM FRP strengthened RC beam and discretization along beam
length and cross section ................................................................................... 219
Figure 6.3 RC beams analyzed for studying the effect of FRP strengthening (Unit: mm)
.......................................................................................................................... 221
Figure 6.4 Effect of FRP strengthening type on temperature rise in steel rebar and FRP
.......................................................................................................................... 223
Figure 6.5 Effect of FRP strengthening type on the variation of moment capacity of RC
beams ............................................................................................................... 224
Figure 6.6 Effect of FRP strengthening type on the variation of mid-span deflection of
RC beams ......................................................................................................... 225
Figure 6.7 RC beams analyzed for studying the effect of NSM FRP location (Units: mm)
.......................................................................................................................... 226
xviii

Figure 6.8 Effect of FRP location on temperatures rise in FRP ..................................... 227
Figure 6.9 Effect of FRP location on the variation of moment capacity of NSM
strengthened RC beams.................................................................................... 228
Figure 6.10 Effect of reinforcement ratio of FRP and steel rebar on the variation of
moment capacity of NSM strengthened RC beams ......................................... 231
Figure 6.11 Effect of concrete compressive strength on the variation of moment capacity
of NSM strengthened RC beams...................................................................... 232
Figure 6.12 Effect of load level on the variation of mid-span deflections of NSM
strengthened RC beams.................................................................................... 234
Figure 6.13 Effect of axial restraint on the variation of mid-span deflections of NSM FRP
strengthened RC beams.................................................................................... 236
Figure 6.14 Illustration of axial restraint force under fire conditions ............................. 236
Figure 6.15 Variation of axial force in NSM FRP strengthened RC beams as a function of
fire exposure time ............................................................................................ 238
Figure 6.16 Standard and design fire temperature curves used in parametric study ...... 239
Figure 6.17 Effect of fire exposure on temperature rise in corner FRP strip.................. 240
Figure 6.18 Effect of fire exposure on the variation of mid-span deflections in NSM FRP
strengthened RC beams.................................................................................... 241
Figure 6.19 RC beams analyzed for studying the effect of fire insulation scheme ........ 243
Figure 6.20 Effect of insulation thickness on temperature rise in NSM FRP strips ....... 244
Figure 6.21 Effect of insulation depth on temperature rise in NSM FRP strips ............. 245
Figure 7.1 Variation of temperature with depth from the bottom of an RC beam at various
times (section 300×500mm) ............................................................................ 253
Figure 7.2 Variation of temperature with distance from the side surface of an RC beam at
various times (section 300×500mm)................................................................ 254
Figure 7.3 Cross section idealization for heat transfer analysis in concrete members
exposed to different fire conditions ................................................................. 256
Figure 7.4 Comparison of predicted temperatures from the proposed equations with those
from FEA ......................................................................................................... 260
xix

Figure 7.5 Validation of the proposed approach by comparing predicted and measured
temperatures for NSC-CA members ................................................................ 265
Figure 7.6 Validation of the proposed approach by comparing predicted and measured
temperatures for HSC-CA members ................................................................ 267
Figure 7.7 Validation of the proposed approach by comparing predicted and measured
temperatures for NSC-SA members ................................................................ 268
Figure 7.8 Validation of the proposed approach by comparing predicted and measured
temperatures for HSC-SA members ................................................................ 269
Figure 7.9 Validation of the proposed approach by comparing predicted temperatures
with FEA results for NSC-CA members ......................................................... 271
Figure 7.10 Validation of the proposed approach by comparing predicted temperatures
with FEA results for HSC-CA members ......................................................... 272
Figure 7.11 Validation of the proposed approach by comparing predicted temperatures
with FEA results for NSC-SA members .......................................................... 273
Figure 7.12 Validation of the proposed approach by comparing predicted temperatures
with FEA results for HSC-SA members .......................................................... 274
Figure 7.13 Illustration of the equivalent concrete depth method .................................. 277
Figure 7.14 FRP strengthened RC beams used in FEA for regression and validation
(Units: mm) ...................................................................................................... 281
Figure 7.15 Comparison of predicted temperatures from the proposed equations (Eqns.
7.18-7.22) with those from FEA (Beam 200×300mm) ................................... 283
Figure 7.16 Comparison of predicted temperatures from the proposed equations (Eqns.
7.18-7.22) with those from FEA (Beam 250×400mm) ................................... 283
Figure 7.17 Comparison of predicted temperatures from the proposed equations (Eqns.
7.18-7.22) with those from FEA (Beam 300×500mm) ................................... 284
Figure 7.18 Validation of the proposed approach by comparing predicted and measured
temperatures (Blontrock et al. 2000) ............................................................... 286
Figure 7.19 Validation of the proposed approach by comparing predicted and measured
temperatures (Williams et al. 2008) ................................................................. 286
xx

Figure 7.20 Validation of the proposed approach by comparing predicted and measured
temperatures (Palmieri et al. 2012) .................................................................. 287
Figure 7.21 Validation of the proposed approach by comparing predicted and measured
temperatures (MSU Beam II)........................................................................... 287
Figure 7.22 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 200×350mm with Aestver insulation)...................... 289
Figure 7.23 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 200×350mm with VG insulation) ............................ 290
Figure 7.24 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 350×500mm with Aestver insulation)...................... 291
Figure 7.25 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 350×500mm with VG insulation) ............................ 292
Figure 7.26 Force equilibrium and strain compatibility of NSM FRP strengthened RC
beam at a given fire exposure time .................................................................. 296
Figure 7.27 A flowchart illustrating rational design approach for evaluating fire resistance
of FRP strengthened beam ............................................................................... 300
Figure 7.28 Validation of the proposed approach by comparing predicted moment
capacity with FEA results (Beam 200×350mm with VG insulation) .............. 303
Figure 7.29 Validation of the proposed approach by comparing predicted moment
capacity with FEA results (Beam 350×500 mm with VG insulation) ............. 304
Figure B.1 Cross section, elevation and internal force diagram of RC T-beam ............. 337
Figure B.2 Configuration of NSM FRP strengthened RC T-beam ................................. 339
Figure C.1 Q4 element in transformed coordinates ........................................................ 342
Figure D.1 Layout and cross section of NSM FRP strengthened RC beam (Beam D1) 343
Figure D.2 Variation of temperatures in steel rebar and NSM FRP with fire exposure time
in Beam D1 ...................................................................................................... 346
Figure D.3 Variation of moment capacity of Beam D1 with fire exposure time............ 348
Figure D.4 Layout and cross section of external FRP strengthened RC beam (Beam D2)
.......................................................................................................................... 349
xxi

Figure D.5 Variation of temperatures in steel rebar and external FRP with fire exposure
time in Beam D2 .............................................................................................. 351
Figure D.6 Variation of moment capacity of Beam D2 with fire exposure time............ 354

xxii

CHAPTER 1

INTRODUCTION
1.1 Background and Motivation
Concrete is one of the widely used construction materials in civil construction.
Concrete structures experience deterioration over a long time, due to poor maintenance,
corrosion of steel reinforcement, as well as aging of concrete. Moreover, older concrete
structures are often needed to be strengthened to resist extreme loading events such as
blast, earthquake, etc. Therefore, in recent years, retrofitting deteriorated or damaged
concrete structures has become an increasingly urgent task for civil engineers and stake
holders. Based on a recent “Report Card for America’s infrastructure” released by
American Society of Civil Engineers (ASCE 2013), the United States has made no
significant progress for more than a decade in improving either the conditions of roads,
bridges, power plants, or other vital infrastructure. Estimated investment on repairing the
nation’s infrastructure has grown to a daunting $3.6 trillion over the next ten years.
Additional repair and retrofitting costs of seismically deficient structures, deteriorating
civil and military infrastructure may run into additional billions of dollars annually.
In order to retrofit concrete structures efficiently and economically, a number of
innovative techniques for repairing and rehabilitation of reinforced concrete
infrastructures have been developed and implemented, and the most notable one is
through the use of fiber reinforced polymer (FRP) laminate as external flexural or shear
strengthening. Initially developed for aerospace and automotive industries, FRP has
1

become a promising material for reinforcing and strengthening of concrete infrastructures.
This is attributed to numerous advantages of FRP over other traditional materials (steel or
concrete), such as high strength to weight ratio, excellent resistance to corrosion, low
conductivity, and high fatigue resistance. Therefore, FRP has been increasingly used in
civil infrastructures, over a wide range of configurations for external strengthening and
reinforcing of masonry walls, for seismic retrofitting of bridges, and as internal
reinforcement in power plant and offshore structures.
In the last decade, there have been some advances in FRP strengthening
techniques for civil infrastructures. In addition to external FRP strengthening and internal
FRP reinforcement, an innovative strengthening technique, near-surface mounted (NSM)
FRP strengthening, is gradually gaining popularity. In this technique, an FRP strip or rod
is inserted into a pre-cut groove on the concrete cover of an RC member, and then filling
the groove with an epoxy adhesive or cementitious grout, as shown in Figure 1.1. The
adhesive or grout in the groove ensures that FRP strip or rod is well-anchored inside to
concrete and acts as an effective tensile or shear reinforcement in resisting loading on the
concrete members. Compared to other strengthening techniques, such as externally
bonded reinforcing method (EBR), NSM strengthening can utilize more of the strength of
FRP because of better bond adherence (Barros et al. 2007, Oehlers et al. 2008, Rashid et
al. 2008). Thus, NSM FRP strengthening is becoming an attractive strengthening method
in retrofitting of structures.
Until now, the application of FRP strengthening is mainly limited to bridges and
exterior structures, where fire resistance of the structural members is not a primary
concern. It has been established that FRP materials are highly combustible when
2

subjected to heat flux. The released heat, smoke, and toxic gases during burning of FRP
can significantly increase severity of fire. Also, the strength and stiffness of FRP decrease
considerably at high temperatures, and the bond between FRP and concrete also degrades
quickly due to melting of epoxy resin. Thus fire response is always a concern for FRP
strengthened RC members.
When used in buildings, the provision of appropriate fire resistance to structural
members is a major design requirement. So far there are limited studies on the fire
response of NSM FRP strengthened RC structures, and a large number of knowledge
gaps need to be filled for NSM FRP strengthening to be widely adopted in building
applications. Therefore, the main objective of current research is to undertake
comprehensive studies for tracing the fire response of RC beams strengthened with NSM
FRP.

(a) Application of NSM FRP

(b) NSM FRP reinforcement

Figure 1.1 Application of NSM FRP on concrete members (For interpretation of the
references to color in this and all other figures, the reader is referred to the electronic
version of this dissertation)
3

1.2 Strengthening Strategies for Concrete Structures
In light of accelerating deterioration in civil infrastructure, a number of
strengthening strategies for concrete structures have been developed since 1980s. Swamy
et al. (1987) proposed a method of bonding steel plates on tension and side surfaces of
beams and slabs, and the studies showed this method can increase flexure and shear
strength of concrete structural members. Priestly et al. (1994) strengthened concrete
columns utilizing steel jackets, and this approach was proved capable of enhancing both
strength capacity (axial, flexural, and shear) and ductility of concrete columns. Some
other researchers also successfully applied external post-tensioning technique to
strengthen concrete beams with steel tendons (Bruggeling 1992). These techniques
mainly utilize steel reinforcement plates to enhance strength capacity of concrete
elements. However, the disadvantages of using steel element, including susceptibility to
corrosion, difficulty to anchor, made these techniques not feasible and viable in many
applications.
More recently, many of the above strengthening strategies have been tried using
fiber-reinforced polymer (FRP) in place of steel. FRP is a composite which is made of
high-strength fibers and a matrix for binding these fibers into structural shapes. This
composite has the characteristics of high strength-to-weight ratio, good resistance to
electrochemical corrosion, etc. Thus application of FRP could overcome many
shortcomings of the above strengthening techniques using steel. A most common
implementation of FRP strengthening is to apply FRP laminates to the surface of a
concrete element, which is designated as externally bonded reinforcing (EBR) technique.
In this technique, FRP sheets are saturated on site with resin, and then bonded to the
4

concrete with the appropriate adhesive. Some practitioners also applied pre-cured
systems, where FRP sheets are saturated and cured prior to site delivery and then applied
to concrete surface with adhesive. In both methods, externally bonded FRP can provide
effective flexural or shear strengthening for beams, or provide seismic confinement for
columns. However, research to date indicates that EBR system has a number of
limitations in practice. The main limitation relates to insufficient bond between concrete
and FRP sheets, which usually causes premature failure of FRP strengthening system, as
shown in Figure 1.2. Consequently, design guidelines for EBR system often recommend
strict strain limits for FRP reinforcement, and this leads to uneconomical use of FRP
material.
In response to sensitivity of EBR system to premature debonding, researchers
have proposed use of near-surface mounted (NSM) FRP reinforcement as an alternative
strengthening approach. The application of is technique on an RC beam is illustrated in
Figure 1.1. It can be seen that in NSM strengthening technique, the bond between FRP
and concrete substrate is established on the entire surface of FRP strip or rod, and this
ensures tensile or shear forces to be effectively transferred from concrete to NSM FRP
reinforcement. If strengthening requires several NSM strips or rods, more parallel
grooves can be cut in a specified distance and multiple FRP strips or rods can be added.
Compared to EBR technique, NSM FRP strengthening system has a number of
advantages: (a) the amount of site installation work may be reduced, as surface
preparation other than grooving is not required (e.g. removal of plaster and weak laitance
layer is not necessary; irregularities of concrete surface is easily accommodated); (b)
NSM FRP is less prone to debonding from concrete substrate, since FRP is bonded with
5

concrete on the entire faces of FRP strip or rod; (c) NSM FRP can be more easily
anchored into adjacent members, and this feature is particularly attractive in flexural
strengthening of beam-column frame, where the maximum moment typically occurs at
the ends of the member; (d) NSM FRP reinforcement can more easily be pre-stressed; (e)
NSM FRP reinforcement is protected by concrete cover and thus is less susceptible to
accidental impact and mechanical damage, fire, and vandalism; this aspect makes this
technique particularly suitable for strengthening of negative moment regions of
beams/slabs; (f) the aesthetic of the strengthened structure is virtually unchanged (De
Lorenzis and Teng 2007). Due to above advantages, NSM FRP strengthening technique
is superior to EBR technique in many cases or can be used in combination with it.

w

w

Adhesive

Adhesive
NSM FRP

External FRP
Cross section

Strengthened Beam

Cross section

w

Strengthened Beam

w

Adhesive

Adhesive

External FRP

NSM FRP

Strengthened beam under high loading

Strengthened beam under high loading

(a) EBR strengthening system

(b) NSM strengthening system

Figure 1.2 Comparison between EBR and NSM strengthening systems under bending

6

1.3 Behavior of FRP Strengthened RC Beams under Fire Conditions
The susceptibility of FRP to damage in fire is one of its major disadvantages. This
is mainly attributed to poor performance of polymer at elevated temperatures. At ambient
conditions, the molecular bonds of polymer are intact and this state is known as glassy
state. As the temperature increases (about 80-150°C), the molecular bonds are weakened
and a new state, leathery state, is reached. The range between glassy and leathery state is
known as glass transition zone, and the corresponding temperature at which this
transformation occurs is referred to as glass transition temperature (Tg) (Ashby and Jones
1999). When the temperature in FRP exceeds that of Tg, the strength and stiffness of FRP
start to decrease. As the temperature further increases to 300-400°C, the molecular bonds
are severely damaged and polymer matrix starts to decompose, with release of smoke,
soot and toxic volatiles. These released heat, smoke and gases, during the burning of
decomposition, can make fire extremely hazardous, and increase the possibility of serious
injury and death. From the point view of structural behavior, FRP material may
experience creep and distortion due to decomposition of polymer matrix, and this will
result in significant degradation of strength and stiffness in FRP reinforcement.
When FRP reinforcement is applied in strengthening concrete structures, weak
fire properties of FRP influences the fire resistance of strengthened concrete members.
Typically, a conventional RC beam possesses required fire resistance for building
applications, as long as appropriate concrete cover is provided to steel rebars. However,
when an RC beam is strengthened with FRP reinforcement, the fire resistance of
strengthened beam depends on both properties of original concrete beam and properties
7

of added FRP. Since FRP has much faster strength and stiffness degradation with fire
exposure time than those of steel rebar, the strength capacity of FRP strengthened beam
deceases faster as compared to conventional RC beam, and failure will occur when
moment due to applied loading exceeds the remaining moment capacity of beam.
Therefore, under the same level of loading, fire resistance of FRP strengthened RC beam
is lower than that of conventional RC beam. Therefore, poor performance of FRP under
fire conditions has become a key issue that hinders its use in civil infrastructures where
fire safety is a concern.
Another critical issue affecting the fire response of FRP strengthened beam is
bond degradation between FRP and concrete under fire conditions. In EBR strengthening
system, FRP laminates are usually bonded to the external surface of concrete members
through epoxy-based adhesives. These adhesives are capable of generating good adhesion
at ambient conditions. However, under fire conditions, due to direct exposure to fire,
epoxy-based adhesive easily gets softened and melted, and the bond strength between
FRP and concrete decreases significantly. When a certain temperature (e.g. Tg for epoxy)
is reached, the bond strength might be smaller than shear stress at FRP-concrete interface,
leading to debonding of FRP laminates. Once debonding occurs, FRP strengthening
hardly contributes to flexural or shear strength of concrete members. Based on recent
experimental research performed by Firmo et al. (2012), external FRP laminates
debonded with original RC beam at about 20 minutes into fire, even though the
anchorage zone of FRP laminates was thermally protected. Therefore, current provisions
in design standards (ACI 440.2R 2008, FIB Bulletin 14 2007) do not consider the
contribution of FRP strengthening under fire conditions.
8

In light of susceptibility of FRP and epoxy adhesive to fire damage, fire insulation
has to be applied to achieve sufficient fire resistance on FRP strengthened RC beams.
Previous studies show that an RC beam externally strengthened with FRP system can
achieve two to four hours of fire resistance, if fire insulation is provided (Blontrock et al.
2000, Williams et al. 2008, Ahmed and Kodur 2011). However, application of fire
insulation is usually expensive and time consuming, which may not be practical (due to
limited space available) and economical for wide range of applications.
So far most studies on fire response of FRP strengthened RC members mainly
focused on the behavior of EBR FRP strengthened concrete members. There is very
limited information on NSM FRP strengthened RC members. Unlike externally bonded
FRP, NSM FRP reinforcement is embedded into concrete substrate, and concrete cover
provides certain level of protection to NSM FRP in the event of fire. Therefore, in the
event of fire, NSM FRP experiences slower temperature rise than that of FRP in external
strengthening system, so the strength degradation of FRP is alleviated. Also, high
temperature resistance materials (such as cement-based material) can be applied as
adhesive so that the bond between FRP and concrete might remain effective for a longer
time in the event of fire. Based on recent numerical studies presented by Kodur and Yu
(2013), the temperature in NSM FRP is about 300°C lower than that in external FRP at
most fire exposure duration, as shown in Figure 1.3. This indicated NSM FRP retains
much higher strength and stiffness than those of externally bonded FRP. Therefore, NSM
FRP strengthened RC member might achieve satisfactory fire resistance for building
application. However, fire response of FRP strengthened member is a complicate

9

problem. A comprehensive study is required to evaluate thermal and structural response
of NSM FRP strengthened RC member under fire conditions.

254

1000
External FRP

700

457

NSM FRP

800
600
500

254

400

Critical temp. of CFRP

300

457

Temperature (ºC)

900

200
100
0

0

15

30
45
Time (min)

60

75

Figure 1.3 Comparison of temperature in NSM FRP and external FRP under standard fire
1.4 Objectives
From the above discussion, it is clear that there is a need for developing a
comprehensive understanding on the fire response of NSM FRP strengthened RC
members. To achieve this objective, both experimental and numerical studies are
proposed to examine relevant high temperature material properties of NSM FRP as well
as to evaluate thermal and structural behavior of NSM FRP strengthened RC beams
under fire conditions. The specific research objectives of proposed study are as follows:
•

Conduct a detailed state-of-the-art review on high temperature properties of FRP
and on the fire response of FRP strengthened RC beams.

10

•

Carry out high temperature property tests on NSM FRP strips and rods to evaluate
the influence of high temperatures to tensile strength, bond strength, and thermal
expansion properties.

•

Conduct fire resistance experiments to evaluate the behavior of NSM FRP
strengthened RC beams under different fire, loading, and restraint conditions.

•

Develop a sophisticated macroscopic finite element based model for predicting
the response of NSM FRP strengthened concrete beams under any given fire and
loading conditions. Such model will account for nonlinear high temperature
properties of constituent materials, various strain components, fire induced
restraint effects, as well as temperature induced bond degradation at FRP-concrete
interface.

•

Validate the above numerical model by comparing predicted parameter response
against data from fire resistance tests.

•

Carry out parametric studies to quantify the influence of various factors on the
fire resistance of FRP reinforced or strengthened concrete beams.

•

Utilizing results obtained from experimental and numerical study, develop
simplified rational design methodology for evaluating fire resistance of FRP
strengthened concrete beams.

1.5 Scope
The work presented in this dissertation involves experimental and numerical studies on
characterization of fire performance of NSM FRP at both material and structural levels.
As part of experimental research, extensive high temperature property tests on NSM FRP
strips and rods were undertaken for characterizing mechanical, bond, and deformation
11

properties of NSM FRP reinforcement at material level. At structural level, four full
scaled RC T-beams strengthened with NSM FRP were fabricated and tested under
standard and design fire conditions, to evaluate the fire response of NSM FRP
strengthened RC members. To develop further understanding on critical factors
influencing fire resistance of NSM FRP strengthened RC beam, a macroscopic finite
element model available in literature was extended to trace the response of NSM FRP
strengthened RC beam from pre-loading stage to collapse. Data from fire resistance tests
was utilized to validate the macroscopic finite element model. The validated numerical
model was then applied to carry out parametric studies to quantify influence of various
factors on fire response of NSM FRP strengthened RC beam. The dissertation is
organized into eight chapters as follows:
•

Chapter 1 provides background information on strengthening of beams through
NSM technique, and lays out objectives of the dissertation.

•

Chapter 2 provides a literature review on room temperature behavior of NSM
FRP strengthening, and also summarizes high temperature material properties of
concrete, steel and FRP. A review of recent experimental and analytical studies on
fire response of RC beams incorporated with FRP reinforcement is also provided.

•

Chapter 3 presents high temperature property tests on tensile strength and
modulus, bond strength, and thermal expansion of NSM FRP. Empirical
relationships for predicting high temperature properties of NSM FRP are
developed over a wide temperature range.

12

•

In Chapter 4, details on fire resistance experiments on NSM FRP strengthened Tbeams are presented. Results from the fire tests are utilized to discuss the
comparative response of NSM FRP strengthened RC beams under fire conditions.

•

Chapter 5 covers details on macroscopic finite element model and analysis for
predicting fire resistance of NSM FRP strengthened RC beams. Development of
subroutines based on high temperature properties of NSM FRP, as well as
validation of the extended numerical model, are also presented in this chapter.

•

Chapter 6 presents results from parametric studies to illustrate the influence of
critical factors on fire response of NSM FRP strengthened RC beams.

•

Chapter 7 provides a rational design methodology developed based on
experimental and numerical studies. Such methodology can be applied to predict
the fire response of FRP strengthened RC beams under different scenarios.

•

Chapter 8 summarizes the key findings, recommendations for future work and
research impact based on this study.

13

CHAPTER 2

STATE-OF-THE-ART REVIEW
2.1 General
The use of FRP composites in aerospace and automotive industry has started since
1950s, due to their superior properties such as high strength to weight ratio and excellent
resistance to corrosion. Starting from 1990s, with decreasing cost of FRP products, fiberreinforced polymer (FRP) has been increasingly used in civil engineering applications,
especially as strengthening and retrofitting for concrete structures. Multiple advantages of
FRP strengthening have been demonstrated in civil constructions, such as ease of
application, cost effectiveness, as well as efficient performance. Therefore, wide varieties
of structural elements are being strengthened using FRP including beams, slabs, columns,
and shear walls.
Through extensive studies and applications in last two decades, it is believed that
fire behavior is an important factor limiting the wider use of FRP in many areas (Mouritz
and Gibson 2006). This is mainly attributed to faster strength and stiffness degradation of
FRP under fire conditions. Therefore, there is a concern on application of FRP
strengthening in building or other places where the fire performance of structural
members is a major design requirement.
This section provides a state-of-the-art review on fire performance of FRP as
material and as structural system. The review starts with an introduction of NSM FRP
technique and its application in concrete structural members, followed by a review of
14

high temperature properties of constituent materials of FRP strengthened RC member
(concrete, reinforcing steel, FRP and insulation). Then the main findings from previous
experimental and numerical studies on fire response of concrete beams incorporated with
FRP reinforcement are discussed, including concrete beams reinforced with internal FRP
rebars, RC beams strengthened with external FRP laminates, and RC beams strengthened
with NSM FRP. Finally, design provisions in current codes and standards for FRP
strengthened structural members are reviewed.

2.2 Configuration and Installation of NSM FRP Strengthening
The application of NSM steel rebars in Europe for the strengthening of RC
structures dates back to the early 1950s (Asplund 1949). In 1948, an RC bridge in
Sweden experienced excessive settlement of the negative moment reinforcement during
construction, and thus the negative moment capacity needed to be increased. The
strengthening was accomplished by grooving the surface, filling the grooves with cement
mortar and embedding steel rebars in the grooves. The arrival of FRP as NSM
reinforcement has amplified the advantages of NSM technique. As comparing to steel,
FRP reinforcement possesses better resistance to corrosion, facilitates installation and
construction due to its lightweight, and reduces the size of the groove due to its higher
tensile strength. This section specifically presents the materials and installation of NSM
FRP strengthening.

2.2.1 NSM FRP reinforcement and groove filler

15

In current NSM FRP applications, carbon FRP (CFRP) reinforcement has been
mostly used to strengthen concrete structures. Glass FRP (GFRP) has been used in many
NSM applications in masonry and timber structures. The tensile strength and elastic
modulus of CFRP are much higher than those of GFRP. Thus, for the same tensile
capacity, CFRP reinforcement has a smaller cross-sectional area than that of GFRP
reinforcement, and a smaller groove is needed, which leads to easier installation, less risk
of interfering with the internal steel reinforcement, and also savings in the groove-filling
material. Round (rod) and rectangular (strip) FRP bars are popular shapes used in NSM
applications. The rods are of 6 or 10 mm in diameter manufactured as a deformed
reinforcement. While NSM strips have a rectangular cross section, with typical
dimensions of 2-5 mm in thickness and 16 mm in width (See Figure 1.1b). The rods are
usually delivered to the site and cut to the required length, while the NSM strips are
delivered in rolls no greater than 250 feet in length (Hughes Brothers 2011). Each crosssectional shape has its own advantages. For example, narrow strips maximize the surface
area-to-sectional area ratio for a given volume and thus minimize the risk of debonding,
while round bars are more readily available and can be more easily anchored in prestressing operations. In practical applications, the choice depends strongly on the depth of
the cover, and the availability and cost of a particular type of FRP bar (De Lorenzis and
Teng 2007).
Groove filler is the medium for transferring stresses between FRP bar and
concrete. In terms of structural behavior, the most relevant mechanical properties of
groove filler are tensile and shear strengths, since the bond capacity of NSM
reinforcement is controlled by cohesive shear failure of the groove filler. Based on
16

published test data (De Lorenzis et al. 2002, Al-Mahmoud et al. 2011, Burke et al. 2012,
De Lorenzis and Teng 2007), the most common and best performing groove filler is a
two-component epoxy. The two components, resin and hardener, need to be thoroughly
blended using a mixer before filling into the groove. Usually the epoxy is designed with a
high-viscosity material to avoid dripping or flowing-away, and to accelerate the
hardening of material. Well-hardened epoxy is characterized by having excellent
weathering resistance and good temperature resistance. The use of cement paste or mortar
as a groove filler is also explored in an attempt to lower material cost, reduce hazard to
workers, and achieve better resistance to high temperatures. However, cement mortar has
inferior mechanical properties and durability, with a tensile strength an order of
magnitude smaller than that of common epoxies (Taljsten et al. 2003, Burke et al. 2013).

2.2.2 Installation procedure
Compared to externally bonded FRP technique, installation of NSM FRP for
strengthening has a relatively simple procedure, and requires less skill during the
installation. Based on experience gained during the laboratory installation process, a
recommended field application procedure for NSM FRP has been developed as follows
(Hughes Brothers 2011).
•

Step 1: Grooves are cut after making the layout on the surface of concrete
member. Proper equipment such as diamond crack chasing blades, guide rails and
sufficiently sized power tools can make groove cutting easier. Rather than cut the
groove in a single pass, sometimes it is more efficient to cut parallel grooves and
remove the concrete between the saw cuts.
17

•

Step 2: Chisel any remaining concrete between cut paths.

•

Step 3: Clean the groove and eliminate any residual dust with compressed air or
vacuum.

•

Step 4: For a clean appearance, mask the concrete adjacent to the groove.

•

Step 5: Fill the groove approximately half way with adhesive.

•

Step 6: Center and insert FRP strip or rod in the groove. The strip or rod should be
inserted until approximately flush with the surface of the concrete and shall be
approximately centered in the groove before final seating.

•

Step 7: Fill the entire groove with epoxy. Hardened epoxy should not extend more
than ¼ inch form the edge of the groove.

•

Step 8: Cure epoxy until full recommended time limit before resuming traffic
flow. The recommended time limit should be based on conditions during
application.

(a) Cut grooves on concrete cover

(b) Chisel remaining concrete in groove

Figure 2.1 Procedures of installing NSM FRP (Hughes Brothers 2011)

18

Figure 2.1 (cont’d)

(c) Clean grooves eliminate residual dust

(d) Mask concrete close to groove

(e) Fill groove half way with adhesive

(f) Center and insert NSM FRP strip

There are a few recommendations which should be followed during the
installation of NSM FRP, to ease the application process and to achieve better bonding
effect. Firstly, the location and dimension of NSM groove should be appropriately
designed. Based on the recommendation from ACI 440.2R specifications (2008), the
minimum dimension of the grooves for NSM strengthening should be taken at least 1.5
times the diameter of FRP bar. When a rectangular bar with large aspect ratio is used,
19

however, the limit may lose significance due to constructability. In such a case, a
minimum groove size of 3.0ab × 1.5bb, as depicted in Figure 2.2, is suggested, where ab
is the smallest bar dimension. The minimum clear groove spacing for NSM FRP bars
should be greater than twice the depth of the NSM groove to avoid overlapping of the
tensile stresses around NSM bars. Furthermore, a clear edge distance of four times the
depth of NSM groove is recommended to minimize the edge effects that could accelerate
debonding failure (Hassan and Rizkalla 2003).
Secondly, proper equipment is important to maintain uniform depth and thickness
during cutting. Theoretically, any configuration of blades is allowable, as long as the
minimum required thickness and depth can be achieved. When choosing a saw for cutting
the grooves, three viable options exist: a track mounted saw, a hand saw, and a standard
joint-cutting saw. Equipment availability and cost efficiency will determine the best
method for cutting.

bb
ab

1.5db
1.5db

1.5bb
3.0ab

Figure 2.2 Requirement on dimensions of NSM groove (ACI 440.2R 2008)
Thirdly, during the consolidating of epoxy, any tools with a small profile, roughly
one-quarter the width of the groove, can be applied to eliminate air voids created during
the injection process. Likewise, a few spacers with any approximate thickness of 1/16

20

inch can be employed to center FRP strip or rod in the groove during the epoxy filling.
This also ensures a proper bond generated on all the faces of NSM FRP rebar.
In field application of NSM FRP strengthening, the sequence of the above
procedure may be slightly different, depending on timeline of availability of FRP rebar
and adhesive products, cutting tools, etc. However, as long as NSM FRP is inserted at
proper position of FRP and sufficient bond is generated between FRP and concrete
substrate, the installation of NSM FRP strengthening is considered to be successful.

2.3 Behavior of NSM FRP Strengthened Members at Ambient Conditions
In recent years, near-surface mounted (NSM) FRP technique has received a great
deal of attention in civil engineering community. Considerable research has been
conducted on the behavior of NSM FRP bond and NSM FRP strengthened structural
members at ambient conditions. This section provides an overall review of previous
studies on the behavior of NSM FRP strengthening at room temperatures.

2.3.1 Bond behavior of NSM FRP system
In NSM FRP strengthened concrete members, NSM FRP reinforcement and
concrete substrate are bonded together through epoxy or cementitious adhesives, the
assembles of NSM FRP, adhesive and concrete substrate can be referred to as NSM FRP
system. It is no doubt that bond properties of NSM FRP system play a critical role in
ensuring the effectiveness of FRP strengthening.
A review of literature shows that a number of studies have been carried out on
bond properties of NSM FRP system at ambient conditions. Results from these studies
21

indicate that bond strength and modulus of NSM FRP system at ambient conditions
depends on a number of parameters such as FRP type, cross-sectional shape adhesive
materials, concrete strength, etc. These parameters can be grouped under two primary
factors, namely, roughness of contact surfaces (FRP or concrete surface) and shear
strength of groove adhesive. These two factors influence the mode of failure at concreteepoxy-FRP interface, and thus can produce varying bond strengths.
For an FRP strip or rod with a smooth or lightly sand-blasted surface, bond failure
usually occurs at FRP-epoxy interface, either through pure interfacial failure or cohesive
shear failure in the groove filler (De Lorenzis et al. 2002, Teng et al. 2006, Al-Mahmoud
et al 2011). However, for an FRP strip or rod with large deformation or sand coating on
the surface, NSM epoxy develops strong adhesion with FRP rebars, and thus bond failure
mostly occurs at epoxy-concrete interface, through fracture at concrete edge or cracking
of epoxy (Sena Cruz and Barros 2004, De Lornezis and Nanni 2002, Bilotta et al. 2011).
Failure at epoxy-concrete interface usually produces higher bond strength than that at
FRP-epoxy interface. The illustration of these two failure modes is plotted in Figure 2.3.

(a) Failure at FRP-epoxy interface

(b) Failure at epoxy-concrete interface

Figure 2.3 Typical failure modes of NSM FRP system
Other than failure modes of debonding, local bond-slip behavior is another
important aspect for evaluating the bond behavior of NSM FRP systems. Typically the
22

local bond stress-slip response can be grouped under two distinct stages: pre-peak stage
and post-peak stage, as shown in Figure 2.4. In pre-peak stage, the bond stress increases
at a high rate and quickly reaches its peak value, and the slip between FRP and concrete
is quite small. In this stage, there is good adhesion between FRP and adhesive, and the
measured slip is roughly equivalent to elastic deformation of CFRP and adhesive. Past
the peak point (post-peak stage), the bond stress drops quickly, and this is mainly due to
damage or deterioration of adhesive. In this stage, NSM system might drop abruptly to a
very small value (close to zero), or decrease gradually until the FRP is pulled out,
depending on failure modes of NSM systems (De Lorenzis et al. 2004, Sena Cruz and
Barros 2004). In previous NSM bond test, the local bond-slip behavior of NSM strips
from two different tests are very close to each other and are comparable to that of spirally
wound bars (Sena Cruz and Barros 2002, Blaschko et al. 2003). Thus some mathematical
models were proposed to predict the local bond-slip behavior of NSM FRP (De Lorenzis
et al. 2004, Sena Cruz and Barros 2004). However, due to numerous variations in FRP
reinforcement and adhesive materials, a variety of factors can influence the failure of
NSM bond. Thus further studies are still needed to develop complete understanding on
debonding mechanism of NSM FRP system at room temperature.

Bond stress (MPa)

10
8
6
4
2
0

0

1

2

3
4
5
Slip (mm)
Figure 2.4 Typical bond-slip curve of NSM FRP system
23

6

7

2.3.2 Behavior of NSM FRP strengthened RC members
Results from existing studies on strengthened beams, slabs, and columns indicate
that provision of NSM FRP reinforcement enhances their flexural capacity, both at
yielding of steel reinforcement and ultimate conditions, and post-cracking stiffness. Some
test programs compared the performance of EBR with NSM systems, by strengthening
identical beams with equivalent amounts of FRP. In all cases, NSM FRP achieved a
higher strain during debonding or no debonding occurred (El-Hacha and Rizkalla 2004,
Alkhrdaji et al. 1999, Hassan and Rizkalla 2002). Thus NSM FRP reinforcement
performed more effectively as compared to externally bonded FRP. El-Hacha and
Rizkalla (2004) also compared equivalent amounts of NSM reinforcement provided with
round bars or strips. As expected, NSM strips performed better, and failed by tensile
rupture as compared to debonding of NSM rods. This mainly results from larger lateral
surface to cross-sectional area ratio of NSM strips and relatively higher local bond
strength.
Based on previous experimental studies, the failure modes of NSM FRP
strengthened RC beams can be categorized in two main types. One possibility is
composite action between the original beam and NSM FRP is well maintained until the
failure of beam. In these beams, the failure occurs through crushing of top concrete or
rupture of FRP, after the yielding of internal steel bars. Another failure mode is the
“premature” debonding failure of NSM FRP system, which involves the loss of
composite action at FRP-concrete interface (De Lorenzis and Teng 2007). The debonding
mode of NSM FRP on flexural members depends on several parameters, including
internal steel reinforcement ratio, FRP reinforcement ratio, cross-sectional shape and
24

surface configuration of NSM reinforcement, and tensile strength of epoxy and concrete.
So far there is still limited understanding of the mechanism of debonding in beams
strengthened with NSM FRP system. Descriptions of failure modes in the existing
literature are often not sufficiently detailed to understand the progression of failure
process. Thus the design guidelines (ACI 440.2R 2008) recommended a reduction factor
(0.7) in the ultimate strain of NSM FRP to account for the uncertain debonding failure.
Another important issue in the design of NSM FRP strengthened RC beam is the
prediction of flexural strength. If the failure of a strengthened beam does not occur
through debonding, then the ultimate load capacity at which failure occurs can be easily
predicted using equations developed for externally bonded FRP based on the plane
section assumption (Teng et al. 2002). While accurate prediction on failure loads at
debonding is much more challenging. Some researchers have proposed theoretical
models to evaluate the ultimate load capacity of NSM FRP strengthened beams (Teng et
al. 2003, Lu et al. 2007), but these models only have limited use for certain types of NSM
FRP system, or certain debonding failure modes. Further research is needed to acquire a
thorough understanding of mechanics of composite action between NSM FRP and
concrete substrate. Then a more sophisticated model can be developed for tracing the
response of flexural members strengthened with NSM FRP reinforcement.

2.4 Material Properties at Elevated Temperatures
The fire response of concrete members incorporated with FRP reinforcement is
influenced by high temperature properties of constituent materials. Specifically, these
properties include thermal, mechanical and deformation properties. The thermal
25

properties govern the extent of heat transfer within structural members, while mechanical
properties influence the load carrying capacity and deformation of structural member.
The deformation properties, mainly referring to thermal expansion and creep, determine
the extent of deformation of structural member under certain loading. This section
provides a review on properties of concrete, reinforcing steel, FRP reinforcement and
insulation materials which are typically used in building construction.

2.4.1 Concrete
Concrete has been used as construction material for hundreds of years. The
information on variation of thermal properties of concrete with temperatures is well
established, based on extensive experimental and theoretical studies. Since normal
strength concrete is usually used in FRP strengthened concrete members, the literature
review herein mainly focuses on the properties of this type of concrete.

2.4.1.1 Thermal properties
Thermal properties of concrete, which mainly refer to thermal conductivity,
specific heat and density, have dominant influence on thermal response of concrete
members under fire conditions. A great deal of research has been conducted on variation
of thermal properties of concrete at elevated temperatures, and there are also some
recommendations on temperature-properties relations in various codes and standards.
Three major types of concrete are commonly used in buildings, namely, siliceous
concrete, carbonate concrete, and lightweight concrete, which are categories based on the
type of aggregate. Figure 2.5 illustrates the variation of thermal properties of different
26

concrete as a function of temperature (Lie 1992, Kodur et al. 2008). In Figure 2.5(a), it
can be seen that the thermal conductivity of carbonate concrete tends to decrease with
increased temperature. Comparably, siliceous concrete has a relatively larger initial value
of thermal conductivity, but it decreased more rapidly with temperatures. Lightweight
concrete, on the other hand, shows nearly constant thermal conductivity over a wide
range of temperature. Thus, thermal properties of concrete vary significantly depending

Thermal conductivity (W/m°C)

on types of aggregate used in the batch mix.
1.6
1.4
1.2
1
0.8
0.6
0.4

Carbonate
Lightweight
Siliceous

0.2
0

0

200

400
600
Temperature (°C)

800

1000

(a) Variation of thermal conductivity for various types of concrete (Lie 1992)
Figure 2.5 Variation of thermal properties with temperature for various types of concrete

27

Figure 2.5 (cont’d)

Volumetric specific heat (KJ/mm3-°C)

20
18

Carbonate
Lightweight
Siliceous

16
14
12
10
8
6
4
2
0

0

200

400
600
Temperature (°C)

800

1000

(b) Variation of specific heat with temperature for various types of concrete (Lie 1992)
The specific heat of different concrete is presented in Figure 2.5(b) (Lie 1992).
Overall, the specific heat values of three types of concrete are close, except that of
carbonate concrete which has much higher values at around 700°C. The character of
cement paste and aggregate contributes to these distinct peaks. It can be found that
carbonate aggregate concrete possess a higher specific heat and lower thermal
conductivity, as compared to siliceous concrete. Thus carbonate concrete is usually
preferred over siliceous aggregate, when a superior high temperature behavior is required
in structural members (Kodur et al. 2008).
Some studies indicated thermal conductivity and specific heat of concrete also
depend on moisture content and concrete porosity (Naus 2006, Flynn 1999). Therefore, in
the structural fire design guidelines in Eurocode 2 (2004), the influence of moisture
content is incorporated in the variation of specific heat as a function of temperatures.
28

2.4.1.2 Mechanical properties
Two types of studies have been conducted on the variation of mechanical
properties of concrete with temperature. One is to measure the properties during exposure
to certain high temperatures, and this measurement can be used to simulate the behavior
of concrete members during heating phase of fire (Lie and Kodur 1996, Khoury 1996,
Cheng et a. 2005). Another type of study is to evaluate mechanical properties after
exposure to high temperatures, and these measured values are mainly used to simulate the
behavior of concrete members during cooling phase of fire or post-fire behaviors (Lau
and Anson 2006, Chang et al. 2006, Savva et al. 2005). In this section, a review of
mechanical properties of concrete at both heating and post-heating phases is provided,
mainly including the variation of compressive strength and elastic modulus with
temperature.
The variation of compressive strength of concrete at heating phase is plotted in
Figure 2.6 (Kodur et al. 2008). It can be seen for different types of concrete, the
compressive strength follows a similar degradation trend as a function of temperature. In
20-300°C temperature range, no strength degradation is observed for all types of concrete.
Beyond 400°C, concrete strength decreases quickly, due to changes developed in the
internal concrete structures. It can be noticed that there is a clear difference on the
strength degradation at elevated temperature in ASCE and Eurocode 2 models. A major
reason for this difference is the ASCE manual (Lie 1992) does not specifically account
for the effect of aggregate types on compressive strength of concrete at elevated
temperatures. It can be seen that ASCE model is roughly the upper bound of test data,
29

while Eurocode model is close to the lower bound. Based on the results of recent
numerical studies (Kodur et al. 2008), both ASCE manual and Eurocode give
conservative predictions on fire resistance of columns made of carbonate concrete.
However, ASCE constitutive model provides better predictions in the simulations as
compared to Eurocode constitutive model.
1.2

fc(T) / fc(20°C)

1
0.8
0.6

EC2-Calcareous
EC2-Silieous
ASCE
Test-carbonate
Test-siliceous

0.4
0.2
0

0

200

400
600
Temperature (°C)

800

1000

Figure 2.6 Variation of compressive strength with temperature for various types of
concrete (Kodur et al. 2008)
The variation of elastic modulus with temperature for different concrete aggregate
is shown in Figure 2.7 (Schneider 1988). It can be seen that the modulus of elasticity of
concrete decreases starting from room temperature, which is different from the
degradation trend of compressive strength of concrete. At 400°C, only 40-50% of the
original modulus of elasticity is retained for siliceous and carbonate concrete. Carbonate
concrete retains slightly higher modulus than that of siliceous concrete, and this can result
from better temperature resistance of carbonate aggregate. Lightweight concrete has

30

relatively slower degradation on modulus of elasticity, and this is probably attributed to
less aggregate and less voids inside of concrete.
1.2

Ec(T) / Ec(20°C)

1
0.8
0.6
0.4

Carbonate
Lightweight
Siliceous

0.2
0

0

200

400
600
Temperature (°C)

800

Figure 2.7 Variation of elastic modulus with temperature for various types of concrete
Mechanical properties of concrete at post-heating phase mainly refers to residual
strength of concrete after heating, which is an important parameter for modeling concrete
structural members exposed to design fire (the fire with cooling phase). However, both
Eurocode 2 (2004) and ASCE manual (1992), do not specify any relationships for
residual strength of concrete after fire exposure. Some published data on residual strength
of concrete is shown in Figure 2.8 (Kumar 2003). Compared to trends in Figure 2.6, it
can be seen that residual strength of concrete at a given temperature is less than that of
concrete during heating. This is because during cooling phase of design fire, the process
of hydration in cement components is an ongoing process. These hydrated products have
larger volume that introduces more cracking in concrete, and thus concrete continues to
lose strength and stiffness (Kodur and Dwaikat 2008). It can be seen that there is
relatively large difference on test data of residual strength, and this can be attributed to
31

different heating and cooling rate during each test. The best fit of test data that can be
used for evaluating the residual strength of concrete is shown in Figure 2.8 (Kumar 2003).

Normalized residual strength

1.2
1
0.8
0.6
0.4
Fitted curve
Test data - upper bound
Test data - lower bound

0.2
0

0

200

400
Temperature (°C)

600

800

Figure 2.8 Variation of residual strength of concrete with temperature
2.4.1.3 Deformation properties
Recent research results indicate that at extreme temperatures, deformation
properties, which mainly refer to thermal expansion, creep and transient strain, have
important effects on strength and deformation of concrete structural members (Kodur and
Dwaikat 2008). Figure 2.9 illustrates the variation of thermal strain at elevated
temperatures (Lie 1992, Eurocode 2004). It can be seen that thermal expansion highly
depends on the aggregate of concrete, and this is mainly attributed to the fact that coarse
aggregate, which determines the extent of thermal expansion, makes up to 70-80% of
total solid concrete volume. Typically, thermal expansion of concrete with siliceous
aggregate is more significant as compared to concrete with carbonate aggregate. However,
if concrete is subjected to stress levels larger than 35% of its ultimate strength, thermal

32

expansion is essentially eliminated, as it is counteracted by the applied stress (Williams
2007).
18

Test upper bound -carbonate
Test upper bound-siliceous
Test lower bound - carbonate
Test lower bound - siliceous
EC2-Carbonate
EC2-Silieous
ASCE

Thermal strain (mm/m)

16
14
12
10
8
6
4
2
0

0

200

400
600
Temperature (°C)

800

1000

Figure 2.9 Variation of thermal strain with temperature for various types of concrete
The creep behavior of concrete is a complex problem, especially at high
temperatures. At fire conditions, creep strain becomes significant since moisture
movement occurs more rapidly. Creep strain depends on many factors including
temperature, stress level, time, loading and mix design of concrete. Previous studies show
that creep strain is significant in low-modulus aggregates, and is more pronounced at
higher load level and elevated temperatures (Dwaikat 2009).
Transient strain is a phenomenon that is related to creep behavior, which develops
in addition to creep during the first heating under load and is independent of time
(Khoury 2000). The mismatch in thermal expansion between aggregate and cement paste
leads to development of internal stresses and micro-cracking, and this results in the
growth of transient strain in concrete (Schneider 1988).
33

There is very limited information in the literature on high temperature creep and
transient strains (Kodur and Harmathy 2008). Anderberg and Thelandersson (1976)
proposed an evaluation equation for creep strain of concrete at high temperature, which is
ε cr = β1

σ
ted (T − 293)
fc,T

where εcr = creep strain, β1 = 6.28×10

-6

s

-0.5

, d = 2.658×10

(2.1)
-3

-1

K , T = concrete

temperature (K) at time t (s), fc,T = concrete strength at temperature T, and σ = stress in
the concrete at time t (s).
Harmathy (1993) proposed a formula to predict the transient strain at elevated
temperature, as shown below
ε tr = k2

σ
fc,20

ε th

(2.2)

where εtr = transient strain, σ = stress in the concrete, k2 = a constant ranges between 1.8
and 2.35, εth = thermal strain, and fc,20 = concrete strength at room temperature.
Based on previous studies (Kodur and Dwaikat 2008, Kodur and Ahmed 2010),
these equations generally produce reasonable estimates for creep and transient strains in
concrete under fire conditions.
Relations for the variation of thermal, mechanical and deformation properties of
concrete are given in codes and standards (Lie 1992, Eurocode 2 2004), and these are
included in Appendix A.

2.4.1.4 Fire induced spalling
34

Fire induced spalling has received a great deal of attention in recent years. Many
studies (Phan 1996, Kodur and Dwaikat 2008, Raut and Kodur 2011) have indicated the
spalling can accelerate the deterioration of concrete members under fire condition, and
the influence of spalling needs to be accounted in fire performance evaluations. Spalling
occurs when pore pressure in concrete exceeds tensile strength of concrete, causing
concrete chunks to fall off from concrete member. This falling off can often be explosive
due to high pore pressure, generated from high thermal gradients.
The extent of spalling in concrete depends on many factors, and the primary
factors influencing fire induced spalling are moisture content, concrete permeability,
concrete strength, fire scenario, and stress level (Phan 1996, Phan et al. 2000, Kodur and
Phan 2007). Compared to normal strength concrete, high strength concrete is believed
more susceptible to have spalling under fire conditions. One reason might be the low
permeability and high density of high strength concrete, which prevent water vapor from
escaping and lead to high pore pressure that causes spalling. Also, high strength concrete
is normally subjected to higher stress levels than normal strength concrete and this may
increase the chances of occurrence of fire induced spalling.
Fire induced spalling could cause reduction of concrete cross-section and
accelerate strength loss, and further leads to decease in fire resistance of a concrete
member. However, FRP strengthening is mainly applied to concrete members with
normal strength concrete. Also, due to long term aging and deterioration, concrete in the
strengthened members is in relatively low strength. Therefore, few data has been reported
on the occurrence of spalling in FRP strengthened RC members, especially when beams

35

are protected with insulation. Thus fire-induced spalling is not a primary concern in this
study.

2.4.2 Reinforcing steel
Although steel reinforcement forms only a small portion of cross sectional area in
concrete members, high temperature properties of steel reinforcement, especially
mechanical properties, has significant influence on the fire response of reinforced
concrete members. This section reviews some notable studies on the behavior of
reinforcing steel at elevated temperatures.

2.4.2.1 Thermal properties
Thermal properties of reinforcing steel mainly depend on the type of steel and
temperatures in steel reinforcement. These properties include thermal conductivity and
thermal capacity. It is well known that steel is a good heat conductor and its thermal
conductivity is quite high as compared to other construction materials. Figure 2.10
presents the idealized values of thermal conductivity of steel reinforcement at elevated
temperatures (Lie 1992). It can be seen that thermal conductivity of steel decreases
linearly with increasing temperature until reaching 900°C, and then remain almost
constant at higher temperatures.

36

60

10

50

8

40

6

30

4

20
Specific heat

2
0

10

Thermal conductivity
0

200

400
600
Temperature (°C)

800

Thermal conductivity (W/m-oC)

Volumetric specific heat(kJ/mm3-oC)

12

0
1000

Figure 2.10 Variation of thermal properties with temperature for reinforcing steel
Specific heat, is defined as the amount of heat required to raise a unit degree of
temperature in a unit volume. The variation of specific heat as a function of temperature
is shown in Figure 2.10. The specific heat of reinforcing steel increases slightly at
o

elevated temperatures, and the peak value at around 700 C can be attributed to phase
transformation of steel material. As mentioned earlier, the area of steel reinforcement is
much smaller as compared to the care of overall concrete, and thus thermal properties of
reinforcing steel has negligible influence on temperature distribution within concrete
cross section (Lie and Irwin 1993).

2.4.2.2 Mechanical properties
Since steel reinforcement primarily contributes to tensile force in an RC beam, the
degradation on mechanical properties of steel reinforcement has critical influence on fire
response of RC beams. Overall high temperature degradation of mechanical properties of
37

steel can be very different depending on the composition and strength of steel
reinforcement. Figure 2.11 plots a variation of strength properties of reinforcing steel as a
function of temperatures, based on the specifications as per ASCE (Lie 1992) and
Eurocode 2 (2004). For yield strength, Eurocode 2 assumes that reinforcing steel retains
o

its original strength up to 400 C, while in ASCE manual (Lie 1992) the yield strength
gradually decreases starting from the initial increase in temperature. Also, Eurocode 2
does not consider strain hardening effect in steel rebar, and specifies ultimate strength is
the same with yield strength. ASCE manual accounts for strain hardening after steel
yields, and it specifies that degradation of ultimate strength is always slightly smaller
than that of yielding strength, as plotted in Figure 2.11.
1.2
1
fs (T)/fs (20°C)

0.8
0.6
0.4

Yielding strength - ASCE
Ultimate strength - ASCE
Yielding strength - Eurocode 2

0.2
0

0

200

400
600
Temperature (°C)

800

1000

Figure 2.11 Variation of yield strength and ultimate strength with temperature for
reinforcing steel
Another mechanical property of steel rebar is that original yield strength of heated
steel rebar can be recovered after the cooling. Previous study shows that the yield
strength of steel after cooling is almost same with the room temperature yield strength, as
38

long as heating temperature does not exceed 500°C. When temperature in steel attains
above 500°C, the strength after cooling starts to decrease gradually with the highest
temperature steel ever reached (Neves et al. 1996). In addition, at this temperature level,
stress-strain relation of steel rebar also changes due to phase transition.
Relations for high-temperature mechanical properties of reinforcing steel, as
given in Eurocode 2 and ASCE manual (Lie 1992) are presented in the Appendix A.

2.4.2.3 Deformation properties
In comparison to concrete, reinforcing steel experiences higher thermal expansion
at elevated temperatures. The thermal expansion of steel at elevated temperatures can be
evaluated using the coefficient of thermal expansion (CTE), which is defined as
dimensional variation in unit length of reinforcing steel due to unit change in temperature.
The variation of thermal strain as a function of temperature suggested by ASCE Manual
(Lie 1992) is shown in Figure 2.12. Overall, CTE of reinforcing steel increases with the
rise in temperature. However, in the range of 650-815°C, CTE decreases at elevated
temperatures, and this is mainly attributed to molecular transformation in steel.

39

Thermal expansion
(% of original strength)

1.2
1
0.8
0.6
0.4

Transformation
to Austenite

0.2
0

0

200

400
600
Temperature (°C)

800

1000

Figure 2.12 Variation of thermal expansion with temperature for reinforcing steel
Creep is anther important variation to be considered for reinforcing steel at high
temperatures. At room temperature, the creep of steel highly depends on its stress level,
o

and creep strain increases at very low pace. However, at high temperature (above 450 C),
creep strain can be significant within a short time, due to the variation on crystal
structures of steel. So far there is limited information found in the literature about the
variation of creep strain with temperature for steel reinforcement. The available creep
models, such as the one proposed by Harmathy (Harmathy 1967), are based on Dorn’s
theory, which relates creep strain to the temperature, stress, and time. More information
on Harmathy’s creep model is provided in Chapter 4.

2.4.3 FRP reinforcement
2.4.3.1 General
FRP materials are highly combustible and burn when exposed to fire. A large
amount of combustible gases, ignite, release heat and propagate flame are generated
40

during burning of FRP. The emitted smoke, which affects visibility, hinders ability of the
occupants to escape and poses difficulties for fire fighters to conduct evacuation
operations and suppress the fire. Flammability, which is one of the indicators of fire
hazard generally, refers to the tendency of a substance to ignite easily and burn rapidly
with a flame. The flame spread and generation of toxic smoke, which are the two major
concerns with FRP material, largely depend on the type of FRP formulation
(composition). When used in buildings, structural members have to satisfy flame spread,
smoke generation and fire resistance ratings prescribed in the building codes (Ahmed
2010).
For evaluating flame spread and smoke generation, ASTM recommends three
different standard tests. ASTM E84 (2013) specify procedures for relative burning
behavior of a building material by measuring flame spread index (FSI) and smoke density
index (SDI). ASTM E662 (2013) specifies optical density test to measure characteristics
of smoke concentration, while ASTM E162 (2013) describes test procedures for
measuring and comparing surface flammability of different building materials when
exposed to radiant heat energy. Generally, FRP manufacturers list their products for
smoke generation and flame spread classifications in directories after getting specified
tests from the specialized. Thus, in this research, it is assumed that FRP’s have met the
relevant flame spread and smoke generation rating specified in building codes and
standards.
From the point view of structural fire engineering, the variations of thermal,
mechanical, and deformation properties of FRP are more concerned, since they
significantly influence the load resistance capacity of FRP strengthened RC members.
41

Currently, a wide range of FRP products are available in the market and any small
changes in the composition of FRP (matrix or fiber) can influence their high temperature
properties. Thus it is difficult to quantify the variation of each FRP product at elevated
temperatures. This section reviews thermal, mechanical, and deformation properties of
some primary FRP products in civil engineering applications, and these properties are
critical to simulate thermal and structural behavior of concrete members incorporated
with FRP under fire conditions.

2.4.3.2 Thermal properties
The influence of thermal properties of FRP to fire response of structural members
depends on the type and amount of FRP reinforcement in use. For concrete members
wrapped with external FRP laminates, FRP laminates might cover much of the surface of
concrete members. When exposed to fire, FRP laminates essentially transforms to a char
layer. Thus the charring from FRP laminates can provide certain level of thermal
protection for original concrete members. In this case, thermal properties of FRP can
significantly affect heat propagation within the concrete member. However, when FRP is
used as internal reinforcement or as NSM strengthening, the influence of thermal
properties of FRP is usually negligible, due to its small cross-sectional area as compared
to concrete section. In these two case, FRP reinforcement can be handled in the same way
as reinforcing steel in concrete members.
Thermal properties of FRP, which mainly refer to thermal conductivity, specific
heat and density, vary significantly at elevated temperatures. There is very limited
information on the variation of thermal properties of FRP at elevated temperatures,
42

especially for the temperatures above 400°C. Griffis et al. (1984) expressed the
temperature dependence of thermal conductivity of carbon/epoxy composites as starting
at an initial value of approximately 1.4 W/m-K, decreasing to about 0.2 W/m-K by 500°C,
as shown in Figure 2.13. After this point, thermal conductivity of FRP remained almost
constant with increased temperatures.
7

Specific heat (kJ/kg-K)
Thermal conductivity (W/m-K)

6
5
4
3
2
1
0

0

200

400
600
Temperature (°C)

800

1000

Figure 2.13 Variation of thermal properties with temperature for FRP
Specific heat is another critical parameter that influences heat transfer.
Kalagiannakis and Van Hemdrijck (2003) reported specific heat of 0.8 kJ/kg-K for both
glass and carbon/epoxy FRPs at room temperature. Specific heat for both types of FRP
increased with temperature, and reached 1.45 kJ/kg-K for carbon and 1.3 kJ/kg-K for
glass at 170°C. Evseeva et al. (2003) reported a specific heat of 1.0 kJ/kg-K at 0°C,
increasing to 1.5 kJ/kg-K at 100°C for phosphorous carbon/epoxy FRP material. Griffis
et al. (1984) reported specific heat data for carbon/epoxy FRP used in aerospace
applications which varied over a much wider range. The suggested property-temperature
relation on thermal conductivity and specific heat of FRP, as a function of temperature, is
compiled in Figure 2.13.
43

2.4.3.3 Mechanical properties
FRP is highly susceptible to temperature effects. It is known that most fibers are
capable of maintaining strength at relatively high temperature, while it is polymer matrix
component in FRP composites are vulnerable even at moderate temperatures. Thus, when
polymer matrix experiences phrase change (glass to rubber state, or rubber to leathery
state), the mechanical properties of FRP degrade significantly.
There have been a few studies on mechanical properties of FRP at elevated
temperatures. Kumahara et al. (1993) studied tensile strength and elastic modulus of FRP
rebars at elevated temperature and residual strength after cooling. The test results
indicated that at 400°C, the strength of aramid rebars dropped to 20% of their original
values, and glass fiber bars with a vinyl ester binder retained relatively higher portion of
original strength (40%). While carbon/epoxy bars did not lose strength until 250°C. For
the residual strength after cooling, aramid bars was able to recover most of the original
strength if AFRP temperature was within 150°C, while glass and carbon bars regained
most of their strength even when they were heated to 250°C.
Fujisaki et al. (1993) tested carbon/vinyl ester FRP grids in tension under both
stationary and non-stationary thermal regimes. Tensile strength of CFRP declined at
around 100°C. When reaching 250°C, CFRP maintained 60% of its original strength. In
the residual strength tests, negligible loss was observed for temperature up to 250°C. This
study shows that FRP might retain most of its strength at moderately high temperatures,
and FRP may possess high resilient strength.
Bisby et al. (2005) compiled temperature dependant strength and stiffness of FRP
from a number of studies and proposed empirical equations to describe the
44

strength/stiffness degradation. These equations were assumed to fit a sigmoid function,
and they reflected the variation of strength and stiffness with temperature. The proposed
relations for strength and modulus of FRP (ff,T and Ef,T) at a given temperature T were
given as follows.
= f 20°C (
f f ,T

1 − aσ
1 + aσ
) tanh(−bσ (T − cσ ) +
)
2
2

(2.3)

1 − aE
1 + aE
= E20°C (
E f ,T
) tanh(−bE (T − cE ) +
)
2
2

(2.4)

where, f20°C and E20°C are the original stress and elastic modulus of FRP at room
temperature respectively. aσ, bσ, cσ, aE, bE, and cE are the coefficients obtained from
curve-fitting.
Wang et al. (2007) carried out an experimental study on high temperature strength
degradation on FRP bars used as internal reinforcement. Totally 57 tension tests at
various temperatures were conducted. The test results indicated that carbon and glass
FRP lose 50% of their original strength at 325°C and 250°C, respectively. Modulus of
elasticity of FRP showed negligible loss up to about 400°C, and then started to decrease
rapidly beyond 400°C.
The above review indicates that previous studies on mechanical properties of FRP
mainly focused on those of FRP laminates or internal rebars. There are no specific studies
on high temperature properties of NSM FRP. Due to wide variety in shape (strip and rod)
and composition (fiber volume, epoxy type), FRP reinforcement used for NSM
strengthening might be significantly different from the above properties. Therefore,
additional information on high temperature strength and stiffness properties of NSM FRP
45

is required to obtain reliable assessment on fire performance of NSM FRP strengthened
beams.

2.4.3.4 Deformation properties
Under fire conditions, temperature induced thermal expansion in FRP
reinforcement can also influence the behavior of concrete members incorporated with
FRP reinforcement. Typically the coefficient of thermal expansion (CTE) of FRP varies
in longitudinal and transverse directions. The longitudinal coefficient of thermal
expansion is dominated by the properties of fibers, while the transverse coefficient is
dominated by the properties of resin (Bank 1993). The values of CTE are also
significantly different for various types of fiber, resin, and volume fraction of fiber. At
ambient conditions, ACI 440.1 Guide (2006) provides some CTE values in longitudinal
and transverse directions for different types of FRP rebars. However, at elevated
temperatures, there is limited information on the variation of CTE. Some notable studies
on high temperature thermal expansion of FRP are summarized in Table 2.1.
Since thermal expansion in longitudinal direction is a main factor that affects the
effective stress in FRP, the discussion herein focuses on thermal strain in longitudinal
direction. From Table 2.1, it can be seen in 20-200ºC temperature range, the CTE of
CFRP is quite small and fluctuates around zero, while CTE of GFRP reaches around
-6

15×10 /K. This is because glass fibers experience much higher expansion than that in
carbon fibers. In 200-800ºC range, there is lack of test data on thermal expansion of FRP,
this is attributed the fact that polymer matrix starts melting beyond 200°C and it is
difficult to measure CTE of FRP as a whole piece. Based on the results of theoretical
46

studies (Schaery 1968, Nomura and Ball 1993), CTE values for CFRP and GFRP
-6

reinforcement, in the temperature range of 20-1000ºC, can be assumed to be 5x10 /K
-6

and 15x10 /K respectively to account for temperature induced thermal strain.
Except thermal expansion, creep can also have critical influence on structural
behavior of FRP when exposed to fire, since high temperature significantly accelerates
creep strain and leads to relatively large deformation in FRP (Williams 2007). Generally,
creep behavior of FRP is mainly dependent on the behavior of matrix materials. A crosslinked thermoset matrix exhibits less creep than thermoplastics. Fiber orientation might
be another factor influencing the magnitude of creep in FRP. When fibers are in the
loading direction, creep in fibers highly affects deformation of the entire composite.
Since FRP experience softening and melting at high temperatures, it is extremely
difficult to evaluate creep strain of FRP at high temperatures. Rahman et al. (1993)
conducted tensile creep tests on uniaxial carbon/glass hybrid FRP with 40% ultimate
stress level at room temperatures. Data from the tests indicates that creep in the fiber
direction is only 1.8% of the initial strain. However, at elevated temperatures, the creep
strain can get enhanced. Raghavan and Meshii (1997) conducted experimental studies on
creep behavior of carbon fiber-reinforced polymer at various stress levels and in
temperature range of 20-150°C. The study shows that at the same stress levels, CFRP
composite experienced twice the creep effect at 150°C as that at room temperature. The
combination of high stress and high temperature makes creep strain very significantly.
Based on the experimental study results, Raghavan and Meshii (1997) proposed the
following to predict creep of FRP composites at elevated temperatures.
47

t

σ

0

kT

ε crf = ∫ Bσ 0.01e− H / kT sinh(
B =×10−4 T 1.55 ⋅ t 0.25
2.03

where,

)dt

(2.5)
(2.6)

εcrf is creep strain of FRP, T is FRP temperature (K), σ is the stress in FRP (MPa), t is the
fire exposure time (s), and k is Boltzmann’s constant. H is the activation energy whose
value follows the reported experimental data.

2.4.3.5 Bond properties
Bond plays a vital role in transfer of loads (forces) from concrete to FRP
reinforcement. Depending on type of FRP reinforcement in use (internal rebar, external
laminates, NSM strip), bond mechanism between FRP and concrete can be significantly
different. In concrete members strengthened with external or NSM FRP reinforcement,
the bond is generated through another intermediate adhesive layer applied between FRP
and concrete, and the bond strength is essentially the ultimate shear strength developed in
the adhesive materials (epoxy or cement mortar). While for concrete members reinforced
with internal FRP bars, the bond mainly rely on the interlock action between deformed
rebar and concrete. In light of these differences on bond mechanism, this section provides
a review of high temperature bond properties between FRP and concrete for each
individual case.

48

Table 2.1 Thermal expansion of FRP reinforcement reported in previous studies
Reference

Type of
study

Material

Smooth glass/vinylester composite rod
Gentry and Hudak
Experimental Glass/vinylester rebar with helical overwrap
(1996)
Composite rebar with molded reinforcing lugs
T300/5208 (graphite-epoxy)
T300/934 (graphite-epoxy)
Nomura and Ball
Analytical
(1993)
T100/2024 (graphite-epoxy)
Metal matrix composites
T300/5208 (graphite-epoxy)
Analytical
T300/934 (graphite-epoxy)
Bowles and
Tompkins (1988)
T100/2024 (graphite-epoxy)
Experimental T300/5208 (graphite-epoxy)
Anagnostopoulos
Analytical
LTM217 epoxy /Kevlar aramid fiber composite
(2008)
Gorji and
Analytical
Boron-epoxy composite
Mirzadeh (1989)
Foye (1975)
Experimental Carbon-epoxy
Ishikawa (1979)
Experimental Carbon-epoxy
Pirgon (1973)
Experimental CFRP
AFRP rebar
ACI 440.1 (2006) Experimental GFRP rebar
CFRP rebar

49

Temp.
(ºC)
20
20
20
25
25
25
25-815
25
25
25
-183-149

Longitudinal
-6
(10 / ºC)
4.8
8.2
7.5
-0.019
0.239
1.64
3.5-4.6
-0.113
-0.002
1.44
-2-16

Transverse
-6
(10 / ºC)
38
32
44
22.48
27.86
27.59
-25.23
29.03
26.12
--

25-100

0.2-0.7

--

20

5.29

30.38

20
20-150
0-130
20
20
20

5.42
-4-0
-10-5
-6 to -2
6-10
-9-0

30.7
--60-80
21-23
74-104

Katz et al. (1999) studied bond properties of concrete members reinforced with
internal FRP rebars using a number of commercially available FRP rebars, in temperature
range of 20-250°C. Test results show a reduction of 80-90% in bond strength when the
temperature increased from 20 to 250°C, while the conventional deformed steel rebars
only showed a reduction of 38% of original bond strength in the same temperature range.
A reduction in bond stiffness, which was determined from the slope of the ascending
branch of pullout load-slip curve, was also observed with increase in temperature. The
authors pointed out that bond properties between FRP rebar and concrete are highly
sensitive to high temperatures, and the degradation of bond strength at elevated
temperature relies mainly on polymer treatment at the surface of FRP rebar. Based on
these experimental results, Katz and Berman (2000) proposed the following empirical
relation to predict the degradation of bond properties at elevated temperatures.

 0.02 
k1

τ = 0.5(1 − τ r ) tanh −
T − k1 (Tg + 0.02 Cr )   + 0.5(1 + τ r )

 Cr 

1,


k1 =1 − 0.025(Tg − 80)

0






80 < Tg < 120, 

Tg ≥ 120 


(2.7)

Tg ≤ 80,

(2.8)

where, τ is the normalized bond strength, T is the temperature, τr is the residual bond
strength, Cr is the degree of cross-linking, Tg is the glass transition temperature of
polymer.
As to RC members strengthened with external FRP laminates, there are a few
studies on thermal effect to bond properties between FRP laminates and concrete
(Blontrock et al. 2002, Di Tommaso et al. 2001, Klamer et al. 2005b, Leone et al. 2009,
50

Wu et al. 2004). Ahmed (2010) complied the available test data on bond degradation in
externally bonded FRP, and they are plotted in Figure 2.14. These data was mainly
obtained from previous double-lap shear tests conducted on CFRP laminates bonded to
concrete with adhesive. It can be noticed that these test data is pretty scattered, and this is
because of the variation of FRP and adhesive materials used in different tests. Results
from these tests indicate that bond strength degradation is negligible at low temperatures
(around 40°C). However, significant reduction in bond strength was observed at
temperatures beyond Tg. An empirical relation on variation of bond strength with
temperature was also proposed as follows.

fT = f 20 (T ≤ 40°C)

(2.9)

fT
 1 
=  (T − 40) (40°C≤ T ≤ 120°C)
1− 
f 20
 80 

(2.10)

where, f20 and fT are the bond strength at room and higher temperatures respectively, T is

fb(T) / fb (20°C)

the temperature at the interface of FRP and concrete.
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

Fitted curve
Bond test data

0

20

40
60
80
Temperature (°C)

100

120

Figure 2.14 Variation of bond strength with temperature for externally bonded FRP
51

For concrete members strengthened with NSM FRP, Palmieri et al. (2011)
conducted high temperature bond tests on NSM FRP systems. A series of 18 pull-out
bond tests were performed on NSM FRP strengthened concrete blocks. Three types of
FRP reinforcement were used for NSM strengthening (CFRP rod, CFRP strip, and GFRP
rod), and the temperatures in the test was in a range of 20-100°C. Based on the test
results, bond strength of NSM strengthening system barely decrease until the temperature
in adhesive exceeds its glass transition temperature. When temperature increased beyond
Tg, the failure mode of NSM bond changed from splitting of resin (50°C) to pulling out
of FRP reinforcement (100°C). Also, strains along the bonded length became more
uniformly distributed and the transfer length increases.
In summary, it can be seen there is limited research on bond properties between
FRP and concrete, especially for NSM FRP system. Due to critical influence of bond
properties on the behavior of the strengthened member, extensive research is still needed
to identify the main factors that influence the bond behavior, and to develop a reliable
relation to predict the deterioration of bond properties at high temperatures.

2.4.4 Fire insulation
Fire insulation is often applied to steel and wood structural members in buildings
to enhance fire resistance. Concrete structures are not usually required to be protected
with insulation due to its excellent inherent temperature resistance properties. However,
based on results from previous study (Blontrock et al. 2000, Kodur et al. 2006, Williams
et al. 2007, Ahmed and Kodur 2010), fire insulation is necessary for FRP strengthened
RC members to maintain the strength and integrity of FRP reinforcement, due to
52

susceptibility of FRP to fire exposure. This section provides a brief review of
commercially available insulation materials used for fire protection.
Literature studies indicate there are two main categories of fire insulation
materials, insulation board (or mats) and sprayed insulation. Insulation board usually
consists of calcium silicate, gypsum and vermiculite. This type of insulation is typically
used to protect structural steel and aluminum, and it can provide thermal protection
through its low thermal conductivity (0.12-0.16 W/m-K) and also through the water
vapor which was trapped within the board during heating (BNZ Materials, 1998). For
example, gypsum board is a fire insulation product that has been widely used in building
applications. One reason is that gypsum board has low thermal conductivity of 0.16
W/m-k, which can significantly reduce conductive heat transfer in the insulation layer.
Moreover, moisture content within gypsum board absorbs large amount of heat during
evaporation process, and this also reduces heat energy passing through the board.
Spray-applied fire proofing is another commonly used insulation type. This type
of proof usually comprise of some low thermal conductivity material (e.g. vermiculite)
and a Portland cement or gypsum binder (Williams 2004). These materials are mixed
with water and then sprayed to the surface of structural members. Depending on its
specific composition, the sprayed fire proofing can achieve a low thermal conductivity of
0.043-0.078 W/m-K (Isolatek 2004). However, due to their light weight characteristics,
thermal capacity of sprayed materials is usually small.
Due to relatively large porosity (especially for sprayed insulation), thermal
properties of fire insulation often vary significantly with temperatures rise. For simulation
purpose, the variation of thermal capacity and thermal conductivity at elevated
53

temperatures needs to be known. However, there is limited information on high
temperature properties of insulation and the procedures for undertaking high temperature
property tests. Bisby (2003) performed thermogravimetric analysis on VG insulation and
proposed temperature-property relations in the range of 20-800°C, as shown in Figure
2.15. It can be seen that thermal conductivity of VG insulation initially decreases with
o

o

increase in temperature (up to 200 C), and then remains almost constant till 500 C.
Thereafter the thermal conductivity slightly increases with temperature. While the
thermal capacity of VG insulation of insulation mostly remains in a stable level in the
o

entire temperature range. The only exception is the peak at about 100 C, and this is due
to evaporation of trapped water which consumes most of heat energy.
There are a great number of fire insulation materials available in the market. The
thermal properties of some commonly used fire insulation materials are summarized in
Table 2.2. However, there is lack of data on the variation of thermal properties of fire

1.8E-04

4.5E-03

1.6E-04

4.0E-03

Thermal conductivity
Thermal capacity

1.4E-04

3.5E-03

Thermal capacity (J/mm3-k)

Thermal conductivity (W/mm-k)

insulation with temperature.

1.2E-04

3.0E-03

1.0E-04

2.5E-03

8.0E-05

2.0E-03

6.0E-05

1.5E-03

4.0E-05

1.0E-03

2.0E-05

5.0E-04

0.0E+00

0

200

400
600
Temperature (°C)

800

0.0E+00

Figure 2.15 Variation of thermal properties with temperature for VG insulation
54

Table 2.2 Comparison of thermal properties for different fire insulation

Insulation type
Tyfo Vermiculite-Gypsum
(VG) (Bisby, 2003)
Vermiculite
(www.vermiculite.org)
CAFCO 300 insulation
(www.cafco.com)
Gypsum board
(Manzello 2008)

Thermal
conductivity
(W/m-K)

Density
CTE
Specific heat
-6
3
(kJ/kg-K)
(10 /K) (kg/m )

0.1158

1.1763

--

351

0.064

0.84 to 1.08

--

80-96

0.078

--

--

240

0.25-0.32

0.9-1.0

7.22

711805

2.5 Fire response of Concrete Beams Incorporated with FRP Reinforcement
FRP reinforcement can be used in concrete structural members in a number of
ways. FRP rebar can be used as primary internal reinforcement in concrete beams or
slabs; FRP laminates are usually applied for external strengthening in concrete beams or
as confining for concrete columns; FRP strips and rods can be used as NSM
strengthening in flexural concrete members. In this section, a brief review on fire
performance of concrete beams incorporated with FRP reinforcement is provided. Based
on the types and function of FRP reinforcement, this section separately discusses the fire
response of concrete beams reinforced with internal FRP rebars, concrete beams
strengthened with external FRP laminates, and those strengthened with NSM FRP
reinforcement.

2.5.1 Concrete beams reinforced with internal FRP rebars
There are limited studies in the literature on fire performance of concrete beams
reinforced with FRP rebars, and current design standards do not provide guidelines on
55

fire resistance of this type of beams (ACI 440.1 2006). Some of notable studies relating
to fire resistance of concrete beams reinforced with FRP bars are reviewed here (See
Tables 2.3 and 2.4).
Sakashita et al. (1997) carried out fire tests on 11 concrete beams reinforced with
different types of FRP rebars. The tested beams were categorized based on fiber type
(aramid, glass or carbon) and fabrication method (spiral, straight or braided) of FRP rebar.
The test results indicated that beams reinforced with CFRP rebars achieved the highest
fire resistance, followed by the beams reinforced with GFRP rebars, and then the beams
reinforced with AFRP rebars. Also, the beams with spiral or straight fiber rebars yielded
longer fire resistance than those with braided fiber rebars. Through these comparisons,
the authors concluded that concrete beams with FRP rebars might achieve similar fire
resistance as that of conventional steel reinforced concrete beams. However, roomtemperature strength capacity of these beams were not clearly stated in the published
paper (strength of steel and FRP rebars is not specified), and thus the fire resistance might
not have been evaluated under the same loading level (load/capacity ratio).
Abbasi and Hogg (2006) carried out fire tests on two full-scaled concrete beams
(350×400 mm) reinforced with different types of GFRP rebars. The parameters
considered in the tests included resin type (thermoset and thermoplastic) and rebar size
(one beam with only #4 bars, the other with #3, #4 and #6 bars) and shear stirrup (GFRP
and steel stirrup). In the fire tests, both beams exhibited a long plateau on their loaddeflection response, and both beams failed abruptly due to debonding of FRP rebars with
surrounding concrete. The beam with thermoset FRP achieved a fire resistance of 128
minutes, while the beam with thermoplastic FRP achieved a fire resistance of 94 minutes.
56

Thus the authors concluded that with sufficient concrete cover, concrete beams with
GFRP rebars can provide the required fire resistance ratings. Unfortunately, not many
detailed test measurements (e.g. temperatures in rebars) are presented in the paper, and
thus the test data is of limited use for validation of numerical models. Also, the applied
load level on the beam during fire tests (ratio of applied load to room temperature
capacity) was smaller than that encountered in practical situations.
Rafi et al. (2007) carried out fire tests on two simply supported beams reinforced
with CFRP rebars (120×200 mm) under ISO 834 standard fire conditions. Both beams
were tested under a load corresponding to 40% of room-temperature capacity. In the fire
test, the temperature in CFRP rebar exceeded 500°C at around 50 minutes, and the resin
of CFRP rebar got evaporated (indicated by the remaining cracked beams). The two
beams achieved fire resistance of 51 and 63 minutes respectively, and prior to failure,
carbon fibers (in rebars) supported the beam through a “tie-arch” mechanism. Therefore,
the authors concluded that a concrete beam reinforced with CFRP rebars can perform
equally well under fire conditions, as compared to steel reinforced concrete beam, and the
anchorage at the two ends of rebars is vital to develop tie-arch mechanism under fire
conditions.
Besides fire tests, limited numerical studies have been carried out on the fire
performance of concrete beams reinforced with FRP rebars. Two main approaches were
applied in these numerical studies. In the first approach, ACI 440.1 specifications (2006)
are applied to check flexural and shear capacity of the critical section of the beam under
fire conditions (Saafi 2002, Abbasi and Hogg 2005). This sectional analysis is similar to
that of room-temperature capacity evaluation, but strength reduction factors for concrete,
57

steel and FRP reinforcement (resulting from high temperature) are applied in evaluating
moment (or shear) capacity at a given fire exposure time. Based on the results from these
studies, Saafi indicated that a minimum concrete cover of 64 mm to FRP reinforcement is
required to achieve a fire resistance of 2 hours (Saafi 2002). Also, Abbasi and Hogg
(2005) concluded that beams reinforced with FRP rebars provide half the fire resistance
of an equivalent concrete beam with steel reinforcement.
In the second approach, researchers (Rafi et al. 2008, Hawileh and Naser 2012)
carried out finite element analysis for evaluating fire response of FRP or steel reinforced
concrete beams utilizing commercial software packages such as ANSYS. Various
response parameters, including cross-sectional temperature, position of neutral axis, and
mid-span deflections were evaluated under fire conditions. However, thermal and creep
effects of FRP reinforcement and temperature induced bond degradation at FRP-concrete
interface, are not accounted for in the analysis. These factors can significantly influence
the behavior of concrete beam with FRP rebars under fire conditions.
The above literature review indicates that there is limited information on fire
response of concrete beams reinforced with FRP rebars. Most of the previous studies
involved undertaking standard fire tests or simplified numerical approaches on concrete
beams reinforced with FRP rebars to check the adequacy of beams to satisfy fire
resistance ratings. The critical factors that influence fire resistance of RC beams, such as
realistic fire scenario, load level, bond degradation, and restraint conditions, are not yet
addressed.

58

Table 2.3 Experimental studies on fire response of concrete beams reinforced with internal FRP rebars
Dimension
Reference
(mm)
Sakashita
et al.
(1997)

200×300
×4800
(11 beams)

FRP rebar
Strength
Type
(MPa)
AFRP,GFRP
-CFRP, Steel

Abbasi
350×500
and Hogg ×4250
(2006)
(2 beams)

GFRP

120×200
Rafi et al.
×1750
(2007)
(3 beams)

CFRP
Steel

586-760
(Beam 1)
1000
(Beam 2)
1676
(CFRP)
530 (steel)

fc’
(MPa)

Loading

Results

Fire resistance: CFRP RC beam>GFRP RC beam>AFRP
2-point load
RC beam, beam with spiral or straight fiber rebar> beam
(24kN)
with braided rebar
Both beams failed abruptly due to debonding of FRP
4-point load rebars with concrete.
42
(10kN)
Fire resistance: beam with thermoset FRP (128 mins),
beam with thermoplastic FRP (94 mins)
Fire resistance: 51 or 63 mins for CFRP RC beam, 79
4-point load
33-35
mins for steel RC beam. Anchorage of rebar is vital to
(24kN)
develop tied-arch mechanism under fire conditions.
36

Table 2.4 Numerical studies on fire response of concrete beams reinforced with internal FRP rebars
Reference
Saafi (2002)
Abbasi and
Hogg (2006)
Rafi et al.
(2008)
Hawileh and
Naser (2012)

Numerical approach or model
Applied sectional analysis to check
flexural and shear capacity of the beam
under fire conditions
Proposed a semi-empirical temperature
profile and strength reduction factors.
Carried out finite element analysis using
ANSYS. Model was validated against
their own test results.
Carried out finite element analysis using
ANSYS. Model was validated against
test data by Abbasi and Hogg (2006)

Results
Minimum concrete cover for FRP rebar should be 64 mm
Proposed an analytical method for predicting strength capacity of beam
under fire conditions.
Material properties used in model provided satisfactory simulation results.
The location of neutral axis remained unchanged for FRP reinforced beam
under fire conditions.
The developed FE model can capture the behavior of RC beams under fire
conditions. Concrete cover thickness and fire scenario have significant
influence on fire response of FRP reinforced beam.

59

2.5.2 RC beams strengthened with external FRP laminates
Since the last decade, several researchers have studied the fire response of RC
beams strengthened with external FRP. The fire resistance of external FRP strengthened
RC beams was evaluated for various configurations and fire scenarios, and the critical
factors influencing this fire resistance were also evaluated through experimental or
numerical studies (Ahmed and Kodur 2011, Williams et al. 2008, Firmo et al. 2012). The
review of these studies is presented as follows (See Tables 2.5 and 2.6).
Blontrock et al. (2000) tested two RC beams and six CFRP strengthened RC
beams under ISO standard fire exposure to investigate the effect of temperature on bond
degradation between FRP and concrete. The beams were provided with fire insulation of
Promatech-H or Promatech-100. Fire test results showed that fire insulation is necessary
to minimize strength loss in FRP and to maintain low deflections in the beam during fire
exposure. Also, the authors concluded that it is critical to maintain the adhesive
temperature below glass transition temperature (about 80-90°C) in order to keep an
effective bond between FRP and concrete.
Williams et al. (2008) conducted fire tests on four full-scaled FRP strengthened
T-beams. The beams were protected with different insulation systems, and were tested
under service load while exposing to ASTM E119 standard fire. In these fire tests, Tg of
FRP was reached in the early stages of fire (about 60-90 minutes), but this did not lead to
failure of the beam based on strength or critical temperature (rebar temperature) limit
state. The beams achieved four hours fire resistance rating under ASTM E119 fire
exposure.

60

Ahmed and Kodur (2011) presented results from fire resistance experiments on
five rectangular reinforced concrete beams. Four of these RC beams were tested after
being strengthened with CFRP laminates and protected with fire insulation, while the
remaining one was tested as a control RC beam. The beams were tested by exposing them
to fire and service load (about 50% of room temperature capacity). The test variables
included type of fire exposure, anchorage zone, insulation type, and restraint conditions.
Fire test results indicated that anchorage configuration plays a critical role in limiting the
deflections of the strengthened beam after debonding of the FRP occurs at Tg ±10°C. The
authors concluded that FRP-strengthened RC beams supplemented with insulation
possess sufficient fire resistance under ASTM E119 standard fire or a design fire. It was
also found that the fire-induced axial restraint force can significantly increase the fire
resistance.
Firmo et al (2012) studied the efficiency of different fire protection systems
through fire tests on CFRP strengthened RC beams. The fire protection systems
comprised of calcium silicate boards and layers of vermiculite/perlite cement based
mortar applied along the beam soffit. The anchorage zones of the CFRP laminates were
particularly insulated to evaluate the benefits of this construction detail. Fire test results
indicated that if the strengthening system were left unprotected, CFRP laminate debonded
after 23 minutes into fire exposure. However, if the fire insulation was applied, the
debonding time was significantly delayed (60-89 minutes for 25 mm fire insulation, 137167 minutes for 40 mm fire insulation). The post-fire assessment indicated that CFRP
laminates transforms into a “cable” fixed at the anchorage zones. When one of the
anchorage zones debonds, the entire strengthening system will fail totally.
61

Besides fire resistance test, some researchers also evaluated fire resistance of RC
beams strengthened with external FRP through numerical studies. Williams et al. (2008)
developed a 2-D heat transfer model that employs an explicit finite difference
formulation and heat transfer equations to determine temperature at each time step. The
model is capable of predicting temperature distribution in FRP-strengthened rectangular
and T-shaped beams exposed to standard fire scenarios. The model is validated by
comparing model predictions with full-scaled fire test conducted at National Research
Council, Canada (Williams et al. 2008). The temperature predictions within beam cross
section were reasonably good as compared to fire test data. However, the model
underestimates the temperature at the interface of FRP and insulation for the entire fire
duration. Further, this model does not account for strength degradation of beam with
temperature, and thus fire resistance cannot be evaluated only using this thermal model.
Hawileh et al. (2009) used finite element software, ANSYS, to study the thermal
and structural response of FRP-strengthened T-beam under standard fire exposure. The
model was validated against measured data from fire test conducted by Williams et al.
(2008), and the predictions have reasonable agreement with experimental data. However,
the model does not account for several important factors such as various strain
components due to thermal and creep effects, fire induced bond-slip at FRP-concrete
interface, as well as the effect of fire induced axial restraint force in the analysis.
Ahmed and Kodur (2010) presented a numerical approach for modeling the bond
degradation in fire exposed FRP-strengthened RC beams. The numerical procedure was
incorporated into a macroscopic finite element model which is capable of accounting
high temperature material properties, different fire scenarios, bond degradation and
62

failure limit states. The validity of the model was established by comparing predictions
from the program with data from fire tests on FRP strengthened RC beams. Results from
the analysis indicated that significant bond degradation occurs close to glass transition
temperature of the adhesive. The time at which bond degradation occurs depends on the
fire insulation thickness and glass transition temperature of the adhesive. However,
variation of adhesive thickness does not significantly influence fire resistance of FRPstrengthened RC beams.
The above review indicates that external FRP strengthening system is highly
susceptible to fire exposure. When the temperature in adhesive exceeds its Tg, the
debonding mostly likely occurs between FRP laminate and concrete. Thus, the anchorage
zones of FRP laminates are vital to maintain its strengthening effect. Also, it is evident
that thermal insulation is necessary to achieve a satisfactory fire resistance for RC beams
strengthened with external FRP laminates.

63

Table 2.5 Experimental studies on fire response of RC beams strengthened with external FRP laminates
Reference

Dimension
Steel rebar
(mm)

Blontrock 200×300
et al.
×2850
(2000)
(No.= 8)

FRP
laminates

200×1.2mm
2ϕ16mm
CFRP
(591MPa)
(2800 MPa)

Flange:
100×1 mm
Williams 1220 ×150
2ϕ20mm
CFRP
Web:
et al.
(500MPa)
300×250
(745 MPa)
(2008)
(L=3900)
Ahmed
and
Kodur
(2011)

254×406
×3660
(No.= 4)

100×120
Firmo et
×1350
al. (2012)
(No.=5)

203×2 mm
3ϕ19mm
CFRP
(420MPa)
(834 MPa)

50×1.2 mm
4 ϕ 6mm
CFRP
(524MPa)
(2742 MPa)

fc’
(MPa)

Load

Insulation

57

40.6 kN
Plat or U2-point
shape
load

41

34
kN/m,
UDL

U-shape

52

70 kN,
2-point U-shape
load

32

10.2 or
16.3kN
U-shape
3-point
load

64

Fire

Results

ISO
834

Fire insulation is necessary during fire
exposure. It is critical to maintain the adhesive
temperature below glass transition temperature
in order to keep an effective bond between
FRP and concrete

Tg of FRP was reached in the early stages of
ASTM fire, but the beam did not fail based on
E119 strength or critical temperature limit state. The
beams achieved four hours fire resistance
Anchorage plays a critical role in limiting the
deflections of the strengthened beam. FRPASTM strengthened beams with insulation possess
E119 sufficient fire resistance. Fire-induced axial
restraint force can significantly increase the
fire resistance.
CFRP laminate debonded after 23 minutes if
without insulation. CFRP laminates
ISO
transformed into a “cable” fixed at the
834
anchorage zones. FRP strengthening failed
when one anchorage zones debonded.

Table 2.6 Numerical studies on fire response of RC beams strengthened with external FRP laminates
Reference Numerical approach or model
Results
Williams et Use 2-D heat transfer model that employs finite Temperature predictions are reasonably good as compared to
al. (2008) difference method and heat transfer equations.
fire test data, but the model underestimates the temperature at
the interface of FRP and insulation.
Hawileh et Use ANSYS to study the thermal and structural response The predictions have reasonable agreement with the
al. (2010) of FRP-strengthened T-beam under standard fire experimental data. However, the model does not account for
exposure.
several important factors such as bond, creep etc.
Ahmed and Use a macroscopic finite element model which accounts Significant bond degradation occurs close to glass transition
Kodur
for high temperature material properties, realistic fire temperature of the adhesive leading to initiation of FRP
(2010)
scenarios, and bond degradation of FRP.
delamination.
Table 2.7 Experimental studies on fire response of RC beams strengthened with NSM FRP reinforcement
Reference

Cross Steel
section rebar

Rein et al.
-(2007)

254×
Burke et
102
al. (2012)
mm
Palmieri
et al.
(2012)

200×
300
mm

NSM
FRP

fc’

Load

Insulation

Fire

Results

NSM strengthening provided a better performance than
EBR system. For the beam protected by intumescent
real
CFRP rod,
coating, NSM FRP strengthening stayed in place. If
--Plat
-fire
2500 MPa
protected by the gypsum board, NSM FRP strengthening
remained intact.
NSM FRP with epoxy adhesive yielded much higher
strength than those with cementitious grout at ambient
2 ϕ 6,
CFRP strip, 46
20 kN no
200°C temperature. But at high temperatures, the slabs with
667
2068 MPa MPa
cementitious grout achieved higher duration than those
MPa
with epoxy adhesive.
Fire insulation fell off on some beams and NSM FRP
36 or
reinforcement attained high temperatures. But all tested
2ϕ16,
CFRP rod 40
40.5 kN Plat or U- ISO
beams sustained service loads for at least 2 hours. A U550
834
or strips
MPa 2-point shape
shaped fire protection is more efficient than that of a flat
MPa
load
protection at the bottom surface of the beam only.
65

2.5.3 RC beams strengthened with NSM FRP reinforcement
Since NSM FRP strengthening is relatively a new technique for civil construction,
the literature on fire response of NSM strengthened RC members is extremely scarce
(See Table 2.7). Rein et al. (2007) performed fire tests to compare the fire performance of
two different strengthening systems, EBR and NSM. For each type of strengthening,
three specimens were fabricated. One was left unprotected, one was painted with an
intumescent coating, and the remaining one was protected by a gypsum board box. The
test results indicated that NSM FRP system had a better performance than EBR system.
For the beam protected by intumescent coating, NSM FRP strengthening still stayed in
place, although the adhesive was glazed and contained transverse cracks. While for one
protected by the gypsum board, NSM FRP strengthening system remained intact in the
grooves. However, this test did not record the temperature in the strengthened beams, and
the loading was not specified in the literature either. Thus, this experimental study cannot
provide comprehensive evaluation of fire response of NSM FRP strengthened RC beams.
Burke et al. (2013) tested 13 reinforced concrete slabs under elevated temperature
conditions (up to 200ºC, not fire exposure), 11 of which were strengthened in flexure
with a single NSM FRP tape. Epoxy and cementitious grout were used on different slabs
to study the influence of different adhesive on the behavior of NSM FRP system at both
ambient and elevated temperatures. The test results indicated that provision of epoxy
adhesive on NSM FRP reinforcement yielded much higher strength capacity as compared
with cementitious grout at ambient temperature, and this was attributed to better bond
from epoxy adhesive. However, at elevated temperatures (at about 200ºC), the slabs with
cementitious grout achieved higher duration (failure time) than those with epoxy
66

adhesive. Based on the test results, the authors inferred that insulated NSM FRP
strengthened slabs provide required fire resistance for building applications.
Palmieri et al. (2012) conducted fire tests on ten RC beams strengthened with
various NSM FRP configurations, in conjunction with fire insulation, to evaluate fire
performance. In these fire tests, fire insulation on some of the beams fell off, and NSM
FRP reinforcement attained very high temperatures (about 850ºC). However, all tested
beams sustained service loads for at least 2 hours under ISO 834 standard fire exposure.
Also, it was found that a U-shaped fire protection (extending to the sides of the beam) is
more efficient than that of a flat protection at the bottom surface of the beam only.
The above review clearly indicated that there are a number of knowledge gaps on
fire response of NSM FRP strengthened RC beams. No experimental studies are
conducted to evaluate fire performance of unprotected NSM FRP strengthened RC beams
(without insulation). Further, no information is documented on the behavior of NSM
strengthened RC T-beams under standard or realistic fire conditions. Also, no numerical
studies are carried out to evaluate critical factors governing the fire response of NSM
strengthened RC beams. Therefore, extensive studies are still required to develop a
comprehensive understanding on the behavior of NSM FRP strengthened RC beams
under fire conditions.

2.6 Codes and Standards for FRP strengthened RC members
Guidelines for design of FRP strengthened RC structures are available in various
standards (ACI 440.2 2008, CSA S806 2002, Fib Bulletin 14 2007). In the latest version
of ACI 440.2R guidelines (2008), design specifications on NSM FRP strengthening
67

system are incorporated, including size of NSM groove (refer to Figure 2.2), NSM bond
strength, flexural strengthening design approach, etc. For evaluating flexural strength of
NSM FRP strengthened RC members, ACI specification applies an approach analogy to
that of external bonded FRP. A reduction factor for preventing debonding failure of NSM
FRP is recommended on ultimate strain of FRP as follows.
εfd = 0.7 εfu

(2.11)

where εfd is debonding strain of FRP reinforcement, εfu is design rupture strain of FRP
reinforcement. Utilizing Eq. 2.11, tensile strength NSM FRP can be obtained and the
flexural strength capacity of RC member can be evaluated based on force equilibrium and
strain compatibility principles. Also, a reduction strength factor of FRP ѱf, which is in
addition to the flexural strength reduction factor ϕ, is recommended to address reliability
of FRP contribution to flexural strength.
Although providing design guidelines of NSM FRP strengthening at room
temperature, current codes and standards do not specify fire design guidelines for FRP
strengthened RC members, or simply neglect the strength contribution of FRP
reinforcement in the event of fire. ACI 440.2R (2008) recommends that the nominal
resistance of FRP strengthened RC member at elevated temperature Rnθ should satisfy
the combination effect of dead load and live load, which is
Rnθ ≥ SDL+DLL

(2.12)

This resistance Rnθ does not account for the contribution of the FRP systems unless FRP
temperature can be demonstrated to remain below a critical temperature for FRP. Also,
68

ACI 440.2 (2008) recommends that the lowest Tg of FRP or epoxy adhesive can be taken
as the critical temperature of an FRP strengthening system. Similarly, FIB Bulletin 14
(2007) suggests that without fire protection, the contribution of FRP strengthening should
be totally neglected. In the case of strengthened elements with fire protection, FRP
strengthening is considered only when the adhesive temperature does not exceed the limit
of 50-100°C. However, based on previous studies presented in Section 2.5, these design
recommendations are overly conservative.
A review of current design guidelines in codes indicates that no specific fire
design provisions exist for evaluating fire response of NSM FRP strengthened RC
members due to lack of information. There are only limited guidelines for fire endurance
of external FRP strengthened RC members, but they are too conservative. Due to superior
performance of NSM FRP system under fire conditions, a different evaluation method for
fire resistance should be updated in the codes and standards. Also, from the purpose of
fire safety design, a rational design methodology is needed to simply and accurately
access fire resistance of FRP strengthened concrete members.

2.7 Summary
Based on the above literature review, it is evident there is very limited
information on the fire response of NSM FRP strengthened RC members. At material
level, available test data on high temperature properties are mainly for external FRP
laminates or internal FRP rebars, and they cannot be used for modeling fire performance
of NSM FRP strengthened RC beams. At structure level, limited fire resistance tests have
been carried out, and a number of key issues, such as fire resistance of unprotected RC
69

beams with NSM strengthening, fire resistance of NSM FRP strengthened T-beams, are
not yet addressed. Further, there is no numerical model for predicting fire resistance of
NSM FRP strengthened beam, and thus there is lack of effective tools used for parametric
studies on some critical influencing factors. Due to these knowledge gaps, in current
codes and standards, no specific provisions are provided for structural fire design of NSM
FRP strengthened RC beams. Therefore, for widespread application of NSM FRP
technique for strengthening of RC beams, comprehensive experimental and analytical
studies are required for developing rational design methodologies on NSM FRP
strengthened RC members.

70

CHAPTER 3

HIGH TEMPERATURE MATERIAL PROPERTY
3.1 General
For evaluating fire response of NSM FRP strengthened RC members, high
temperature dependant properties of constituent materials, namely, concrete, reinforcing
steel, NSM FRP, are required. The thermal and mechanical of concrete and reinforcing
steel are well established. However, there is lack of data on properties of NSM FRP
reinforcement at elevated temperatures. These properties, namely, tensile strength and
elastic modulus, bond strength and modulus, and thermal expansion, are different from
that of FRP used as internal and external reinforcement, due to the difference in
composition and cross sectional shapes.
To generate data on high temperature material properties of NSM FRP at elevated
temperatures, a series of tensile strength, bond strength, and thermal expansion tests were
carried out. Data from these tests is utilized to develop empirical relations for tensile
strength and modulus, bond strength and modulus, and thermal expansion of NSM FRP
reinforcement over a wide temperature range.

3.2 Tensile Strength Tests
As part of experimental studies, a number of tension tests were carried out on
NSM FRP strips and rods over a wide temperature range. Data from tests are utilized to

71

evaluate tensile strength and elastic modulus of NSM FRP at various temperatures.
Details on test procedure and results are presented as follows.

3.2.1 Preparation of test specimens
The experimental program consisted of tension tests on 25 CFRP strips and CFRP
rods at various temperatures. 13 of these test specimens were CFRP strips, while
remaining 12 were CFRP rods. CFRP strips were of 4.5 mm thickness and 13.5 mm
width, and CFRP rods were of 6.4 mm diameter. The nominal tensile strength and
modulus of CFRP strip, as specified by the manufacturer, is 2790 MPa and 155 GPa
respectively, and the ultimate strain is 0.018. For CFRP rod, the corresponding nominal
tensile strength, elastic modulus and ultimate strain are 2070 MPa, 124 GPa and 0.017
respectively. CFRP specimens for tests were provided by FYFE Co. LLC. Other
properties of FRP reinforcement used in the test program are given in Table 3.1.
Table 3.1 Properties of NSM CFRP reinforcement as specified by manufacturer
Tensile properties
Fiber
NSM
Dimension Density
content
Strength Modulus Ultimate
3
reinforcement
(mm)
(g/cm )
(%)
(MPa)
(GPa)
strain
Strip

2790

155

0.018

13.5×4.5

1.81

62

Rod

2070

124

0.017

dia. 6.4

N/A

60

It is well established that CFRP reinforcement possesses high tensile strength at
ambient conditions. However, in a tension test, two ends of CFRP are susceptible to
crushing under the pressure of gripping. Thus strong anchors have to be provided at the
two ends, to facilitate gripping of CFRP specimen. The provision of proper anchors
ensures failure to occur in the central region of the specimen, rather than at ends (in the
72

anchorage zone). A specialized anchorage system was implemented while preparing
CFRP strip/rod specimens for tension tests. The anchor system was developed following
ACI 440.3 specifications (2006) and those recommended by Wang et al. (2007). This is
achieved through filling high strength adhesive into a circular steel tube (confinement), as
shown in Figure 3.1a.
In this experimental program, both high strength epoxy (Tyfo S epoxy) and
expansive cement (RockFrac NEDA) were applied as filling materials to evaluate their
relative bond performance. Tyfo S epoxy is a two-component matrix material used in
bonding applications and is marketed by FYFE Co. LLC. This epoxy was prepared by
adding component A (modified epoxy resin) to component B (hardener) in a volumetric
ratio of 100:42 (or a weight ratio of 100:34.5). The added ingredients were mixed for 5
minutes using a mixer at a speed of 400-600 RPM until two components are uniformly
blended. Another filling material used in the fabrication of anchorage system is RockFrac
NEDA expansive cement, which is used as non-explosive demolition agent and is
marketed by RockFrac Company. The cement mortar was prepared by adding RockFrac
cement into cold water (30% of the overall weight), and then thoroughly mixing cement
and water to get a uniform mortar.
Commercially available steel pipes were selected as confinement for filling
materials, to ensure sufficient bond is generated between filling material and CFRP
specimen. The nominal dimensions of steel pipes are 42 mm in outer diameter and 1.6
mm in thickness, and the pipes were cut into tubes of 356 mm length. These dimensions
are as per recommendations of ACI 440.3 standard (2006) and previous researchers
(Wang et al. 2007). To increase friction between filling material and tube, 102 mm long
73

thread was fabricated inside the surface of the tube. To prevent sliding between CFRP
and filling material, some small dents were created on CFRP strip or rod, and steel wires
were bound to these dents, as shown in Figure 3.1b. Through this procedure a higher
interaction (friction) was generated between CFRP and anchor system.
When epoxy (or cement) is filled into the tube, CFRP strip or rod had to be
aligned vertically and centrally in the steel tube, to avoid any eccentric forces generated
during tension test. For this a steel frame was fabricated to align CFRP and tube in the
vertical direction, as shown in Figure 3.1c. The steel tubes sit on a wooden board and
they were clipped by two aluminum plates. A wooden plug, with a hole in the center, was
installed at the bottom of the tube so that CFRP specimen can be placed centrally. CFRP
specimen was also fixed at the top of steel frame to ensure it was aligned vertically. Once
the epoxy gets hardened in the steel tube, CFRP specimen is turned around for casting
anchor system at the other end.

(a) Epoxy filling

(b) Wires on FRPs

(c) Steel frame

Figure 3.1 Fabrication of anchor system for FRP specimens

74

(d) Test specimen

3.2.2 Test set-up
Room temperature tensile strength tests on NSM CFRP specimens were carried
out using Hydraulic Materials Test System (MTS), since MTS machine is capable of
providing high compression pressure to grip the two ends of test specimens, as well as
applies higher tension load so as to reach high strength and stiffness of CFRP specimens
at room temperature. CFRP strip and rod specimens for room temperature tests were
specially prepared to fit MTS machine set-up. The test apparatus and specimens for room
temperature tests are shown in Figure 3.2.

MTS

CFRP CFRP
strip
rod
Figure 3.2 Test apparatus and specimens for room temperature test
For high temperature tests, a different test set-up was developed, and an
illustration of this set-up is depicted in Figure 3.3. In this set-up, two ends of CFRP
specimen (with anchor system), are clipped to two pairs of clamping brackets
respectively, which are connected to top and bottom beams. The CFRP specimen is
loaded in tension by adjusting the distance between these two beams. Two hydraulic
jacks, sitting on the bottom steel beam, can directly apply specified loading to the top
beam through an extension rod. When hydraulic jacks apply an increasing load, the top
75

beam moves upward and thus CFRP specimen gets stretched longitudinally. The top
beam is always maintained perfectly horizontal to minimize eccentric loading occurring
during the test. The heating device comprised of a small scale furnace which is placed
between two pairs of clamping brackets. Through this set-up, tensile strength test can be
conducted by heating the CFRP specimen to a desired temperature and then subjecting it
to tensile loading.

Steel bracket

Furnace
LVDT
Inside
furnace

Hydraulic
lack

Figure 3.3 Test setup for FRP tension test at elevated temperatures
During the test, CFRP specimen is heated to a target temperature, and then the
heating is continued for additional 20 to 30 minutes to ensure the entire specimen attains
target temperature. To accurately monitor the temperature of CFRP specimen, two
thermocouples are installed on the surface of CFRP specimen at two different locations
(mid-height and quarter height), and the average of these two thermocouple readings is
taken as the actual temperature of the specimen. The heating rate of furnace is set to be at
5-10°C/min, depending on the target temperature: a faster rate is used for higher target
temperatures. The progression of measured CFRP temperature with time is shown in
76

Figure 3.4. It can be seen in the figure that in each case, temperature gradually increases
to a target temperature, and then the specimen is maintained at this target temperature for
about 20 minutes. This ensures that the specimen and furnace reach thermal equilibrium
conditions and that the internal and surface temperatures of the specimen were
sufficiently close to the target temperature.
700

Temperature (°C)

600
500
400

600°C
500°C
400°C
300°C
200°C
100°C

300
200
100
0

0

20

40

60
Time (min)

80

100

120

Figure 3.4 Temperature progression in FRP during high temperature tension tests
Following the specimen attaining a target temperature, tension test is carried out
using hydraulic jacks. To measure elongation of CFRP in tension tests, a linear variable
differential transformer (LVDT) is placed between the upper and the lower clamping
brackets. The variation of distance between these two brackets is taken as elongation of
CFRP specimen placed between two anchors, since the elongation of CFRP in anchor
parts is negligible. The elongation measurements start as soon as loading is applied, and
the displacement of the upper pair of brackets is recorded until CFRP specimen fails. The
reliability of loading equipment and elongation measurements are verified through two
77

preliminary tests, one using steel strand and the other using CFRP strip. In these two
tests, strain gauges were placed along the longitudinal direction of the specimen, and the
measurement of strain gauges was compared with the readings from loading cell. As
shown in Figure 3.5, in steel strand test, tensile stress in specimen kept increasing until
steel entered yielding phase. While in CFRP strip test, tensile stress in specimen
increased linearly. It can be seen that the stress values based on load reading match well
with those obtained from strain gauges (product of strain and modulus), and thus the
measurement from instrumentation is considered to be reliable.
700

Load cell - steel strand test
Strain gauge 1 - steel strand test
Strain gauge 2 - steel strand test
Load cell - FRP strip test
Strain gauge - FRP strip test

Stress (MPa)

600
500
400
300
200
100
0

0

10

20
30
Time (min)

40

50

Figure 3.5 Comparison of measured stresses using loading cell with strain gauges

3.2.3 Results and discussion
Data recorded in tension tests is utilized to evaluate tensile strength and elastic
modulus of NSM CFRP at various temperatures. The tensile strength was calculated by
dividing the maximum load at failure by the actual cross-sectional area of test specimen,
while elastic modulus was evaluated as the slope of linear part of stress-strain curve. At
78

each target temperature, two tension tests were conducted, and the average of two values
was taken as tensile strength and elastic modulus of CFRP. Results from these tests at
various temperatures are tabulated in Tables 3.2 and 3.3 for CFRP strips and rods
respectively.
The tensile strength and elastic modulus of NSM CFRP strip, based on room
temperature tests, were found to be 1641 MPa and 150.8 GPa respectively, and the
corresponding values for CFRP rod are 1577 MPa and 130.9 GPa respectively. The
measured room temperature elastic modulus of CFRP strips and rods are very close to
those specified in manufacturer data (2.7% error for strip and 5.6% error for rod).
However, room temperature tensile strength obtained from tension tests is relatively
lower than manufacturer specified nominal strength. This is mainly attributed to the fact
that CFRP resin fractures at a relatively low load. In the room temperature tests, failure of
CFRP specimen gets initiated through cracking of resin. With increase in load, CFRP
specimen gradually split into bunch of fibers, and some of these fibers were fractured or
pulled out from anchors at the end. This resulted in drop in tension load due to reduction
in the amount of fibers in a CFRP specimen. Although CFRP specimen does not break
(fracture) totally, the peak tension load is attained when majority of resin cracks. In fact,
the strength specified in the manufacturer data is essentially the strength of carbon fibers,
but in tension test CFRP specimens hardly reach this strength due to fracture of resin.
Thus, the tensile strength obtained in the test is taken as the actual room temperature
strength of CFRP.
Results and observations from strength tests are tabulated in Tables 3.2 and 3.3. It
can be seen in these two tables that strength and elastic modulus of NSM CFRP strip and
79

rod decrease with increase in temperatures. The variation of tensile strength of CFRP
strip and rod with temperature is plotted in Figures 3.6a and 3.7a. The trends in both
figures indicate that the degradation of tensile strength in CFRP can be grouped into three
stages. In 20-200°C temperature range, tensile strength of CFRP decreases gradually at a
slow pace, and CFRP strip and rod retain about 80% of original strength at 200°C. In
current practice, CFRP is assumed to lose significant strength past its glass transition
temperature (around 80°C). However, data from these strength tests clearly indicate that
CFRP resin remains intact till about 200°C, and thus CFRP retains much of its initial
strength. In 200-400°C temperature range, CFRP strip and rod experience faster
degradation of their strength, and this is mainly due to decomposition of polymer resin at
around 300°C. As noted from observations (see Tables 2 and 3), resin starts melting at
300°C, but does not get totally decomposed, hence CFRP splits into bunches of fibers
and these fibers primarily resist tension load. Based on linear interpolation, the tensile
strength of CFRP strips and rods drop to 50% of their original strength at about 305°C
and 330°C respectively. This temperature can be treated as critical temperature for CFRP
strip or rod. The critical temperature analogy used for conventional steel reinforcing bars
is defined as the temperature at which steel loses 50% of its room temperature strength.
In the third stage (400-600°C), majority of polymer resin gets decomposed, and only
individual fibers contribute to load resistance. The strength of CFRP rod and strip
degrades at a very high rate at this stage and reaches about 10% of their original strength.
The amount of strength retention is highly dependent on the extent of oxidation of carbon
fibers.

80

Table 3.2 Tensile strength and elastic modulus of CFRP strips at various temperatures
Average % of
Elastic Average % of
Temp. Strength
strength initial modulus modulus initial Failure mode
(°C) (MPa)
(MPa) strength (GPa)
(GPa) modulus
CFRP split into a
1724
141.2
bunch of fibers, and
20
1641
100
150.8
100
then fibers got
fractured or were
1559
160.5
pulled out
CFRP split into a
1431
160.1
bunch of fibers, and
100
1461
89.0
135.9
90.1
then fibers got
fractured around the
1491
111.7
mid-height
CFRP split into a
1532
137.5
bunch of fibers, and
200
1122
76.2
123.5
81.9
fibers fractured around
968
109.5
the mid-height
Resin melted and fibers
705
89.0
300
768
50.5
79.9
52.9
fractured around the
831
70.7
mid-height
Majority of resin got
585
51.5
400
717
43.7
70.0
46.4
decomposed, fibers
850
88.5
were stretched apart
Little resin left and
657
8.1
500
512
31.2
33.1
22.0
fibers were stretched
367
58.1
apart
No resin left, fibers got
600 175
175
10.6
---separated and stretched
apart

81

Table 3.3 Tensile strength and elastic modulus of CFRP rods at various temperatures
Average % of Elastic Average % of
Temp. Strength
strength initial modulus modulus initial
Failure mode
(°C) (MPa)
(MPa) strength (MPa) (MPa) modulus
CFRP split into a bunch
1536
127.2
of fibers, and then fibers
20
1577
100
130.9
100
got fractured or were
1618
134.6
pulled out
CFRP split into a bunch
1536
991.0
of fibers, and then fibers
100
1399
88.7
115.0
87.8
got fractured around the
1261
130.9
mid-height
CFRP split into a bunch
1199
916.2
of fibers, and then fibers
200
1274
80.8
96.9
74.0
got fractured around the
1349
102.1
mid-height
Resin melted and fibers
1114
105.3
300
927
58.8
93.9
71.7 got fractured around the
741
82.4
mid-height
Majority of resin got
400
484
484
30.7
69.4
69.4
53.0 decomposed, fibers
were stretched apart
Little resin left and
223
65.9
500
312
19.8
52.9
40.4 fibers were stretched
401
39.9
apart
No resin left, fibers got
600
126
126
8.0
26.6
26.6
2.0 separated and stretched
apart
It can be seen in Figures 3.6 and 3.7 that the measured strength and modulus data
at elevated temperatures is relatively scattered as compared to those obtained at room
temperature. This is mainly attributed to two factors, variation of heat flux in a specimen
and sliding (slip) occurring between CFRP and anchors. Since heating rate of furnace is
controlled manually, the heat flux introduced by furnace is different from one test to
another, and this results in variation in specimen temperature at the time of test. Also, in
some high temperature tests, there was slight sliding that occurred between CFRP and
epoxy at the anchors, which also lead to variations in the measured strength. The use of
82

expansive cement in anchors generates higher bond performance as compared to that of
epoxy, and only negligible slip occurred in specimens with expansive cement anchors.
180
160

1600

Elastic modulus (GPa)

Tensile strength (MPa)

2000

140
120

1200

100

800
Test data
Average values

400
0

0

80
60
40

Test data
Average values

20
0

100 200 300 400 500 600
Temperature (°C)

0

100 200 300 400 500 600
Temperature (°C)

(a) Tensile strength

(b) Elastic modulus

Figure 3.6 Variation of tensile strength and elastic modulus of CFRP strips with

1800
1600
1400
1200
1000
800
600
400
200
0

160
140
Elastic modulus (GPa)

Tensile strength (MPa)

temperature

Test data
Average values
0

100 200 300 400 500 600
Temperature (°C)

(a) Tensile strength

120
100
80
60
40

Test data
Average values

20
0

0

100 200 300 400 500 600
Temperature (°C)

(b) Elastic modulus

Figure 3.7 Variation of tensile strength and elastic modulus of CFRP rods with
temperature
83

The stress-strain relationships for CFRP strips and rods at various temperatures
are shown in Figures 3.8 and 3.9 respectively. It can be seen that CFRP strip and rod
exhibit almost linear stress-strain response at both ambient and high temperatures. Also,
the ultimate strain of CFRP decreases with increase in temperature. Thus the ductility of
CFRP reinforcement decreases at higher temperatures, which is contrary to that occurring
in conventional steel reinforcing bars. The slope of stress-strain curves at different
temperatures is taken as the elastic modulus of CFRP specimens, and they are plotted in
Figures 6b and 7b. It can be seen in Figures 6b and 7b that the decrease in elastic
modulus follows similar trend as that of tensile strength. However, at most target
temperatures, relatively higher percentage of elastic modulus is retained as compared to
that of tensile strength. Based on the observations in tests, degradation of elastic modulus
is more dependant on the state of polymer resin. Prior to decomposition of polymer resin
(300°C), the integrity of CFRP specimen is well maintained, and thus higher level of
elastic modulus is retained. Once polymer resin melts and evaporates, CFRP specimens
turn into a bunch of separate fibers, and thus elastic modulus gets significantly reduced.

84

2000

Stress (MPa)

1500
1000

20°C
100°C
200°C
300°C
400°C
500°C

500
0

0

0.002 0.004 0.006 0.008 0.01
Strain

0.012 0.014 0.016

Figure 3.8 Stress-strain response of CFRP strips at various temperatures
2000

Stress (MPa)

1500
1000

20°C
100°C
200°C
300°C
400°C
500°C

500
0
0.000

0.002

0.004

0.006 0.008
Strain

0.010

0.012

0.014

Figure 3.9 Stress-strain response of CFRP rods at various temperatures
The failure modes of CFRP strips and rods at various temperatures are illustrated
in Figures 10 and 11. The failure pattern of CFRP specimens in 20-300°C range are quite
similar, wherein CFRP splits into bunches of thin fibers due to cracking of polymer resin.
These fibers then gradually are stretched or pulled out, and eventually CFRP specimen
85

loses its integrity as well as strength. Beyond 300°C, polymer resin starts to decompose,
and carbon fibers also oxidize at temperatures above 400°C. It can be seen in Figures 10
and 11 that the fibers get more softened and separate out in 400-600°C temperature
range. In these tests, the specimens eventually failed due to stretching of fibers at the
mid-height.

20°C
100°C
200°C

300°C

400°C

500°C
600°C
Figure 3.10 Failure modes of CFRP strips at various temperatures

86

20°C
100°C
200°C

300°C

400°C
500°C
600°C
Figure 3.11 Failure modes of CFRP rods at various temperatures

3.2.4 Relations for tensile strength and modulus with temperature
Data generated from the above tests is utilized to develop empirical relations for
strength and modulus of NSM CFRP reinforcement as a function of temperature. These
relations are expressed in terms of temperature dependant reduction factors, which are
normalized to room temperature values. A review of literature shows that there is very
little information on degradation of mechanical properties of CFRP after resin
decomposition. Mouritz and Gibson (2006) proposed the following general relation for
the variation of mechanical properties of FRP with temperature.

87

P − PR
P +P
' 
U
tanh(k (T − Tg ))  R n
P(T ) = R − U

2
2



(3.1)

P(T) represents a particular property, either tensile or compressive strength, or elastic
n

modulus; R is a power law factor to account the residual resin content. For tensile
strength and elastic modulus, n can be considered to be zero, since tensile strength is
mainly dependant on the strength of fibers after the decomposition of polymer resin, and
n

thus R = 1. PU and PR are unrelaxed (low temperature) and relaxed (high temperature)
values of that property, respectively. Tg’ is the critical temperature of FRP, corresponding
to a 50% reduction in the property value. k is a constant describing the extent of
relaxation. This relation takes into account the effect of decomposition of FRP occurring
at high temperatures on mechanical properties, and thus can be used over a wide range of
temperatures. By dividing Eq. 3.1 by PU, the retention factor for tensile strength and
elastic modulus at a given temperatures can be obtained
1 + PR / P
1 − PR / P
U tanh( k (T − T ' ))
F (T ) = U −
g
2
2

(3.2)

F(T) is the retention (%) factor of mechanical properties at temperature T (°C).
The above equation is taken as the basis for developing an expression for strength
and modulus retention factors for NSM CFRP. As discussed above, the resin of CFRP
strips and rods gets completely evaporated at 600°C. Therefore, the strength and modulus
at 600°C were used as PR, and the strength and modulus at room temperature (20°C)
were used as PU. The critical temperature (Tg’) corresponding to 50% reduction in tensile
strength and modulus of NSM CFRP strip is 305°C and 340°C respectively, and the
88

corresponding values for NSM CFRP rod are 330°C and 320°C respectively. Then k is
the only coefficient to be determined in Eq. 3.2.
A regression analysis was carried out using “Solver” function in Excel (2010) to
determine k. The “Solver” is an advanced program in Excel which is able to obtain an
optimum function to match a specified dataset. The prerequisite for using this Solver
function is to provide a basic format of a function and coefficients to be determined. In
the current analysis, Eq. 3.2 is the basic format of the function and k is the coefficient to
be determined. Then a regression analysis was carried out so as to achieve a minimum
error value between predictions from empirical formula (Eq. 3.2) and the above measured
test data. Based on the regression analysis results, the following relations were arrived for
strength and modulus retention factors in CFRP strip and rod as a function of temperature.
CFRP strip:

0.56 − 0.44 tanh(0.0052(T − 305))
Strength: f (T ) =

(3.3)

0.51 − 0.49 tanh(0.0035(T − 340))
Modulus: E (T ) =

(3.4)

0.54 − 0.46 tanh(0.0064(T − 330))
Strength: f (T ) =

(3.5)

0.51 − 0.49 tanh(0.0033(T − 320))
Modulus: E (T ) =

(3.6)

CFRP rod:

The comparison of predicted strength and elastic modulus from proposed
empirical relations with measured values in above discussed tests is plotted in Figures
3.12 and 3.13. It can be seen in Figure 3.12 that the proposed empirical relations closely
match with measured data for tensile strength of CFRP strip and rod, and the average
error between predicted strength and test data is 7% and 6.3% respectively. The elastic
modulus predictions, as shown in Figure 3.13, also show reasonable agreement with test
89

data, and the average error is 10% and 11.2% for CFRP strips and rods respectively. This
slight larger error in elastic modulus of CFRP strip and rod is mainly due to relatively
scattered data obtained in tests.

Strength retention (%)

1.2

Test data- strip
Empirial formula- strip
Test data- rod
Empirical formula- rod

1
0.8
0.6
0.4
0.2
0

0

200

400
Temperature (°C)

600

800

Figure 3.12 Comparison of tensile strength predicted by empirical formula with test data

Modulus retention (%)

1.2

Test data - strip
Empirical formula - strip
Test data - rod
Empirical formula - rod

1
0.8
0.6
0.4
0.2
0

0

100

200

300
400
Temperature (°C)

500

600

700

Figure 3.13 Comparison of elastic modulus predicted by empirical formula with test data

90

3.2.5 Summary of tension test results
Temperature has significant influence on tensile strength and stiffness properties
of NSM CFRP reinforcement. NSM CFRP strips and rods retain much of their tensile
strength and modulus till about 200°C. This is mainly due to the fact that polymer resin
of CFRP remains intact up to 200°C. However, beyond 300°C, tensile strength and
elastic modulus of NSM CFRP decrease at a faster pace due to decomposition of polymer
resin. At 600°C, NSM CFRP only retains about 10% of its original strength.
CFRP strips and rods exhibit linear stress-strain response at both ambient and
high temperatures. However, ultimate (failure) strain of CFRP decreases with increase in
temperature, which is contrary to that occurring in reinforcing steel. NSM CFRP strips
and rods exhibit slightly better resistance to high temperature as compared to
conventional CFRP rebars and laminates. At last, empirical relations for strength and
elastic modulus of CFRP strip and rod is proposed over a wide temperature range. These
relations can be used in evaluating fire response of concrete structures strengthened with
NSM FRP reinforcement.

3.3 Bond Strength Tests
This section presents results from an experimental study on the effect of
temperature on bond strength and modulus of near-surface mounted (NSM) fiberreinforced polymer (FRP) strengthened concrete. A series of NSM FRP specimens,
fabricated using different types of epoxy adhesive and FRP reinforcement, were tested to
evaluate bond strength in 20-400°C temperature range. Details of test procedure and
results are presented as follows.
91

3.3.1 Preparation of test specimens
The experimental program consisted of 36 pull-out tests on NSM FRP specimens
at various temperatures, as shown in Table 3.4. The NSM FRP specimens were made
with two cross sectional shapes of CFRP types, strip and rod, embedded in two types of
adhesives, namely Tyfo S epoxy and Tyfo T300 epoxy. The specimen preparation for
bond strength tests comprised of three steps; casting of concrete block (Figure 3.14(a)),
fabrication of FRP anchor (Figures 3.14(b) and 3.14(c)), and then fabrication of NSM
FRP system (Figure 3.14(d)). The concrete blocks, of 150×150×400 mm size, were cast
from a batch of pre-mixed concrete. The concrete mix comprised of Type I Portland
cement, sand and carbonate based coarse aggregate. The measured compressive strength
of concrete was 48 MPa on 28th day, and reached 50 MPa on 90th day.
Table 3.4 Bond test program on NSM FRP system
Test
NSM
Temperature
Reinforcement
groups
adhesive
(°C)
I
Tyfo T300 CFRP strip (4x13.5 mm) 20-400
II
Tyfo T300 CFRP rod (dia. 6mm)
20-300
III
Tyfo S
CFRP strip (4x13.5 mm) 20-400
IV
Tyfo S
CFRP rod (dia. 6mm)
20-300

(a) Concrete block (b) Steel frame for anchor (c) Filling cement
Figure 3.14 Fabrication of NSM FRP bond test specimen
92

(d) Test specimen

The concrete blocks were strengthened with two shapes of NSM FRP
reinforcement, CFRP strips and CFRP rods. CFRP strips were of 4.5 mm thickness and
13.5 mm width, and CFRP rods were of 6.4 mm diameter. The nominal tensile strength
and modulus of CFRP strip, as specified by the manufacturer, are 2790 MPa and 155 GPa
respectively. While the nominal tensile strength and modulus of CFRP rod are 2070 MPa
and 124 GPa respectively. The high strengths of CFRP strips and rods ensure that bond
failure occurs prior to rupture of CFRP reinforcement. During preparation of NSM FRP
specimens, one end of CFRP strip (or rod) was bonded to concrete blocks, and the other
end was installed with a strong anchor, to facilitate gripping of CFRP strip (or rod) in the
pull-out test. The anchor system was developed as per ACI 440.3 specifications (2004)
and those recommended by Wang et al. (2007). This is achieved through filling
expansive cement (RockFrac NEDA) into a circular steel tube (confinement), as shown in
Figures 3.14(b) and 3.14(c).
After preparing concrete blocks and FRP anchors, concrete blocks were
strengthened with NSM CFRP strips or rods. For this a groove was cut on the surface of
casted concrete block. ACI 440.2 (2008) specifications recommend the groove size to be
a minimum of 1.5 times the diameter of FRP rod. For FRP strips, the groove size needs to
be at least 3.0ab×1.5bb, where ab is the smallest bar dimension and bb is the length of the
other edge, as shown in Figure 3.15. Therefore, two types of groove sections were cut on
the surface of concrete blocks utilizing an electric saw. A groove size of 10×25 mm was
cut for placing CFRP strips (4.5×13.5 mm in section), while a groove size of 13×13 mm
was cut for CFRP round bars (6.4 mm in diameter). The bond length was set to be 150
mm for all specimens.
93

bb
ab

1.5db
1.5db

1.5bb
3.0ab

Figure 3.15 Groove size for installation of NSM FRP specified in ACI 440.2 (2008)
Two types of epoxy based adhesive, Tyfo S epoxy and Tyfo T300 epoxy, were
used as groove fillers (adhesive). Tyfo S epoxy is a two-component matrix material and
is marketed by FYFE Co. LLC. Tyfo S epoxy is recommended for its excellent bond
properties at ambient conditions, and is widely used in externally bonded FRP
strengthening systems. The specified glass transition temperature of Tyfo S epoxy is
82°C, and hence it might not exhibit good bond performance at elevated temperatures.
An improvement over Tyfo S epoxy is Tyfo T300 epoxy, which has a higher glass
transition temperature of 120°C. Thus Tyfo T300 epoxy might exhibit better bond
behavior in fire resistance applications, but this is not quantified to date.
The concrete blocks were strengthened with CFRP strips or rods following the
recommendations of Hughes Brothers, Inc. (2011). The grooves cut in concrete blocks
were first filled with epoxy approximately till half depth. Then NSM FRP strip or rod
was centered and inserted into the groove. Finally, the remaining space of the groove was
filled with epoxy. The epoxy was allowed to cure for at least seven days before
undertaking bond strength tests. A fabricated NSM FRP strengthened test specimen is
shown in Figure 3.14(d).

94

3.3.2 Test set-up
For undertaking high temperature bond tests, a specialized set-up was designed
and the test set-up is shown in Figure 3.16. The test equipment comprises of tension
testing machine and an electric furnace to generate high temperature. In the tension
testing machine, one end of the specimen, the concrete block, is held by a steel cage,
which is connected to the top beam. The other end of the specimen, FRP with anchor
system, is clipped to a pair of clamping brackets which are connected to the bottom
beam. The bond specimen is loaded in tension by adjusting the distance between the top
and the bottom beams. Two hydraulic jacks, sitting on the bottom steel beam, can directly
apply specified load to the top beam through an extension rod. When hydraulic jacks
apply an increasing load, the top beam moves upward and thus tensile force is applied on
the NSM FRP specimen. During the test, the top beam is always maintained in a perfectly
horizontal position to minimize onset of eccentric loading during the movement. The
heating device comprises of a small scale electric furnace which can heat the entire steel
cage and concrete block. Through this set-up, bond strength test can be conducted by
heating NSM FRP system to a desired temperature and then subjecting it to tensile
loading.

95

Inside
furnace

Steel
cage

Furnace

LVDT

Steel
bracket

Hydraulic
lack

Figure 3.16 Test set-up for evaluating bond strength of NSM systems at high
temperatures
During the test, NSM FRP specimen is heated to a target temperature, and then
the heating is continued for additional 20 to 30 minutes to ensure the test specimen and
furnace reach thermal equilibrium conditions. To accurately monitor the temperature
difference between inside and outside of NSM epoxy, two thermocouples are embedded
into NSM groove as well as on the surface of concrete block. The heating rate in the
furnace is set to be at 5-10°C/min, depending on the target temperature: a higher heating
rate is used for higher target temperatures.
Following the specimen attaining a target temperature, a pull-out test is carried
out through the application of load using hydraulic jacks. To measure slip that occurs
during a pull-out test, a linear variable differential transformer (LVDT) is placed between
the top beam and the clamping brackets. The variation of distance between them is taken
as the slip between CFRP reinforcement and concrete block, since the elongation of
CFRP in anchor parts is negligible. The elongation measurements start as soon as loading
96

is applied, and the displacement of the top beam is recorded until CFRP strip or rod is
pulled out.

3.3.3 Results and discussion
Data recorded in pull-out tests is utilized to evaluate bond strength and modulus
of NSM FRP specimen at various temperatures. The bond strength (τmax) and bond
modulus (E) are evaluated using as:

τ max = Pmax / A

(3.7)

E =τ / ∆ε slip
∆

(3.8)

where Pmax is the maximum load recorded in the tension test, A is the area of contact
surface between CFRP and NSM epoxy, Δτ and Δεslip are the relative bond stress and slip
strain on linear part of bond stress-strain curve.
The slip strain is evaluated as

ε slip = s / Lbond

(3.9)

where s is the slip measured in the test, and Lbond is the bond length of test specimen.
At each target temperature, two pull-out tests were carried out, and the average of
two values was taken as bond strength and modulus of NSM FRP system. Results from
these tests at various temperatures are tabulated in Tables 3.5 to 3.8 for CFRP strip and
rod with Tyfo T300 and Tyfo S epoxy respectively.

3.3.3.1 Bond strength and modulus at room temperature
97

The bond strengths of NSM CFRP specimens with Tyfo T300 epoxy at room
temperature are found to be 7.04 and 10.33 MPa for CFRP strips and CFRP rods
respectively, and the corresponding values with Tyfo S epoxy are 3.57 and 3.42 MPa
respectively. The bond strength of CFRP strip and rod with Tyfo T300 epoxy is
significantly higher than that casted with Tyfo S epoxy. The main reason for this
difference can be attributed to different failure patterns that occurred in these two types of
epoxy. In NSM CFRP specimens fabricated with Tyfo T300 epoxy, bond failure occurred
at epoxy-concrete interface, and a thin layer of concrete got detached from concrete
blocks with CFRP strip or CFRP rod. This indicates that Tyfo T300 epoxy possesses
good adhesion with CFRP strip or CFRP rod in use, and this helps to develop a stronger
bond at FRP-epoxy interface. Thus failure in this case is through progression of cracking
in concrete and this leads to development of higher bond strength.
In contrast, in NSM FRP specimens fabricated with Tyfo S epoxy, failure
occurred through pull-out of CFRP strips or rods, and the bond at epoxy-concrete
interface was barely affected. This indicates that shear stress between CFRP and Tyfo S
epoxy is relatively lower than those at concrete-epoxy interface, and thus failure occurs
through debonding between CFRP and epoxy. A comparison of bond modulus, evaluated
for NSM CFRP with two types of adhesive, also indicates that Tyfo T300 possess higher
bond modulus than that of Tyfo S epoxy.

98

Table 3.5 Bond strength and modulus of Tyfo T300 epoxy
for NSM CFRP strip at various temperatures
Bond Avg. bond % of
Bond Avg. bond % of
Temp. Force
strength strength initial bond modulus modulus initial bond Failure mode
(°C) (kN)
strength (MPa) (MPa)
(MPa) (MPa)
modulus
Fracture of
45.12 8.22
227.32
concrete edge
20
7.04
100.0
181.07
100.0
or cracking of
32.08 5.85
134.81
epoxy
Debonding at
18.25 3.33
127.22
3.94
56.0
119.01
65.7 bar-epoxy
100
25.01 4.56
110.80
interface
Debonding at
8.53 1.56
42.60
200
1.35
19.3
44.95
24.8 bar-epoxy
6.33 1.15
47.29
interface
Debonding at
6.62 1.21
20.72
300
1.15
16.3
29.15
16.1 bar-epoxy
6.00 1.09
37.57
interface
Debonding at
2.96 0.54
11.97
400
0.65
9.3
13.97
7.7
bar-epoxy
4.21 0.77
15.97
interface
Table 3.6 Bond strength and modulus of Tyfo T300 epoxy
for NSM CFRP rod at various temperatures
Bond Avg. bond % of
Bond Avg. bond % of
Temp. Force
strength strength initial bondmodulus modulus initial bondFailure mode
(°C) (kN)
(MPa) (MPa)
strength (MPa) (MPa)
modulus
Fracture of
34.15 11.15
197.75
concrete edge
10.33
100.0
186.54
100.0
20
or cracking of
29.13 9.51
175.32
epoxy
Debonding at
24.29 7.93
154.02
100
7.09
68.7
142.56
76.4 bar-epoxy
19.16 6.25
131.09
interface
Debonding at
7.09 2.31
43.45
200
3.18
30.8
43.65
24.0 bar-epoxy
12.41 4.05
43.84
interface
Debonding at
4.10 1.34
39.69
300
1.24
12.0
32.67
17.9 bar-epoxy
3.49 1.14
25.65
interface
99

Table 3.7 Bond strength and modulus of Tyfo S epoxy
for NSM CFRP strip at various temperatures
Bond Avg. bond % of
Bond Avg. bond % of
Temp. Force
strength strength initial bondmodulus modulus initial bondFailure mode
(°C) (kN)
strength (MPa) (MPa)
(MPa) (MPa)
modulus
Debonding at
18.38 3.35
93.49
20
3.57
100.0
90.87
100.0 bar-epoxy
20.83 3.80
88.26
interface
Debonding at
8.58 1.56
55.84
100
2.24
62.8
62.67
69.0 bar-epoxy
16.04 2.92
69.49
interface
Debonding at
4.81 0.88
37.54
200
1.07
29.9
39.55
43.5 bar-epoxy
6.92 1.26
41.56
interface
Debonding at
3.64 0.66
44.18
300
0.81
22.7
31.79
35.0 bar-epoxy
5.27 0.96
19.40
interface
Debonding at
4.03 0.73
27.55
400
0.67
18.8
23.19
25.5 bar-epoxy
3.33 0.61
18.83
interface
Table 3.8 Bond strength and modulus of Tyfo S epoxy
for NSM CFRP rod at various temperatures
Bond Avg. bond % of
Bond Avg. bond % of
Temp. Force
strength strength initial bond modulus modulus initial bond Failure mode
(°C) (kN)
strength (MPa) (MPa)
modulus
(MPa) (MPa)
Debonding at
11.10 3.62
76.72
20
3.42
100.0
71.17
100.0 bar-epoxy
9.87 3.22
65.61
interface
Debonding at
4.68 1.53
43.35
100
1.94
56.6
54.80
77.0 bar-epoxy
7.19 2.35
66.24
interface
Debonding at
4.03 1.32
30.45
200
1.13
33.0
28.18
39.6 bar-epoxy
2.88 0.94
25.91
interface
Debonding at
1.46 0.48
13.86
300
0.61
17.8
16.04
22.5 bar-epoxy
2.27 0.74
18.21
interface

100

3.3.3.2 Bond strength and modulus at elevated temperature
The bond strength and modulus of NSM FRP strengthening system at elevated
temperatures were evaluated using measured failure load and displacement. The variation
of bond strength and bond modulus of NSM FRP is shown in Figures 3.17 and 3.18, by
plotting normalized bond strength and modulus as a function of temperature. It can be
seen that in both cases of Tyfo T300 and Tyfo S epoxy, bond strength and modulus of
NSM strengthening system degrade quickly with increasing temperature, and this
degradation can be grouped into two stages. In 20-200°C temperature range, bond
strength decreases at a relatively faster pace, and NSM FRP system only retains 20-30%
of its original bond strength at 200°C. This rapid deterioration is mainly due to softening
of epoxy beyond glass transition temperature (around 70°C), and thus the adhesion
between FRP and epoxy gets degraded. Beyond 200°C, epoxy adhesive experiences
melting and decomposition, and thus bond properties further deteriorate with temperature.
Since NSM FRP system has already lost most of its bond strength and stiffness at around
200°C, the rate of degradation at this stage is relatively low. Observations during bond
tests indicate that epoxy starts to burn at around 400°C and this damages NSM bond.
Thus bond strength becomes negligible at 400°C for CFRP strips and 300°C for CFRP
rods. Therefore, no further tests were conducted beyond these temperature levels.
A comparison of bond test data plotted in Figures 3.17(a) and 3.18(a) indicates
that CFRP rods possess slightly higher bond strength than those of CFRP strips. This can
be attributed to the fact that CFRP rod is embedded in concrete block on all surfaces, and
this helps to develop higher confinement in epoxy adhesive. However, for the same type
of epoxy, measured bond forces are very close for CFRP strips and CFRP rods (see
101

Tables 2-5). This indicates that at high temperatures, shape of FRP reinforcement (strip
or rod) does not significantly influence bond properties of NSM FRP system.

Bond strength retention (%)

120

Degradation trend - CFRP strip
Degradation trend- CFRP rod
Test data - CFRP strip
Test data - CFRP rod

100
80
60
40
20
0

0

100

200
300
Temperature (°C)

400

500

(a) Bond strength

Bond modulus retention (%)

120

Degradation trend- CFRP strip
Degradation trend- CFRP rod
Test data - CFRP strip
Test data - CFRP rod

100
80
60
40
20
0

0

100

200
300
Temperature (°C)

400

500

b. Bond modulus
Figure 3.17 Variation of bond strength and elastic modulus of NSM CFRP strip and rod
with Tyfo T300 epoxy with temperature
102

Bond strength retention (%)

120

Degradation trend- CFRP strip
Degradation trend- CFRP rod
Test data - CFRP strip
Test data - CFRP rod

100
80
60
40
20
0

0

100

200
300
Temperature (°C)

400

500

(a) Bond strength

Bond strength retention (%)

120

Degradation trend- CFRP strip
Degradation trend- CFRP rod
Test data - CFRP strip
Test data - CFRP rod

100
80
60
40
20
0

0

100

200
300
Temperature (°C)

400

500

(b) Bond modulus
Figure 3.18 Variation of bond strength and bond modulus of NSM CFRP strip and rod
with Tyfo S epoxy with temperature
A review of trends plotted in Figures 3.17 and 3.18 infer that NSM CFRP with
Tyfo T300 epoxy possesses higher bond strength and modulus than those of Tyfo S
103

epoxy at elevated temperatures. This higher bond strength in NSM CFRP with Tyfo T300
epoxy can be attributed to better thermal insulation effect facilitated by Tyfo T300 epoxy.
As shown in Figure 3.19, temperature rise in Tyfo T300 epoxy is relatively lower than
that in Tyfo S epoxy, and this mainly results from higher glass transition temperature of
Tyfo T300 epoxy. Thus, higher retention of bond strength is achieved NSM CFRP
specimens with Tyfo T300 epoxy. Also, Tyfo T300 epoxy possesses relatively better
adhesion with CFRP strips or rods, as found in the ambient temperature tests. Thus at
elevated temperatures, this better adhesion also helps to achieve higher bond strength.

Temperature inside epoxy (°C)

200
150
100
T300 - 100°C
T300 - 200°C
T300 - 300°C
T300 - 400°C

50
0

0

20

40
Time (mins)

60

80

(a) Tyfo T300 epoxy
Figure 3.19 Variation of temperature inside Tyfo T300 and Tyfo S epoxy as a function of
heating time

104

Figure 3.19 (cont’d)

Temperature inside epoxy (°C)

250
200
150
TS - 100°C
TS - 200°C
TS - 300°C
TS - 400°C

100
50
0

0

20

40
Time (mins)

60

80

(b) Tyfo S epoxy
The failure mode of NSM CFRP specimens with Tyfo T300 and Tyfo S epoxy in
high temperature pull-out tests are shown in Figures 3.20 and 3.21 respectively. It can be
seen that all NSM CFRP specimens failed through debonding at FRP-epoxy interface at
high temperatures, and both CFRP strips and rods were pulled out from NSM adhesive.
This failure mode is in contrast to that experienced at room temperature, and this is also
an indicator of lower bond strength in NSM FRP system at elevated temperatures. As can
be seen in Figures 3.20 and 3.21, at 100°C and 200°C, CFRP strips or rods were directly
pulled out, and there was no obvious damage either in NSM epoxy or in concrete block.
This indicates that the NSM epoxy gets softened, leading to significant decrease in the
shear resistance at CFRP-epoxy interface. Further, in tests at 300°C, the color of epoxy
turned black, and this infers that epoxy underwent chemical reaction (charring) and
started decomposing. When temperature raised to 400°C, epoxy experienced significant
pyrolysis, and NSM CFRP system was severely damaged as shown in Figures 3.20 and
105

3.21. Thus, no bond (strength) was left in NSM CFRP system at temperatures beyond
400°C.

20°C

100°C

200°C

300°C

400°C

(a) CFRP strips

20°C

100°C

200°C

300°C

(b) CFRP rods
Figure 3.20 Failure modes of NSM CFRP specimens with Tyfo T300 epoxy

20°C

100°C

200°C
(a) CFRP strips
106

300°C

400°C

20°C

100°C

200°C

300°C

(b) CFRP rods
Figure 3.21 Failure modes of NSM CFRP specimens with Tyfo S epoxy
3.3.3.3 Bond stress-slip relations
The bond stress-slip relationships for NSM CFRP system, with Tyfo T300 and
Tyfo S epoxy, are shown in Figures 3.22 and 3.23 respectively. It can be seen that all
NSM CFRP systems exhibit similar stress-slip response in pull-out tests, regardless of
epoxy type and reinforcement type. The measured bond stress-slip response can be
grouped under two distinct stages: pre-peak stage and post-peak stage. In pre-peak stage,
the bond stress increases at a high rate and quickly reaches its peak value, and the slip
between CFRP and concrete is quite small. In this stage, there is good adhesion between
CFRP and epoxy adhesive, and the measured slip is roughly equivalent to elastic
deformation of CFRP and epoxy adhesive.
Past the peak point (post-peak stage), the bond stress deteriorates, and this is
mainly due to onset of cracking in epoxy adhesive. In this stage, NSM system might
regain some of its lost bond strength, and then bond strength gradually decreases until
FRP is pulled out. This gradual decrease can be attributed to interlock action between
CFRP and epoxy adhesive, and this interlock action remains effective until FRP is totally
pulled out.
107

Bond stress (MPa)

10
20°C
100°C
200°C
300°C
400°C

8
6
4
2
0

0

5

10
15
Slip (mm)
(a) NSM CFRP strip

20

25

12
20°C
100°C
200°C
300°C

Bond stress (MPa)

10
8
6
4
2
0

0

5

10
15
Slip (mm)
(b) NSM CFRP rod

20

25

Figure 3.22 Bond stress-slip relations for NSM CFRP specimens with Tyfo T300 epoxy
at various temperatures

108

4

20°C
100°C
200°C
300°C
400°C

Bond stress (MPa)

3.5
3
2.5
2
1.5
1
0.5
0

0

5

10
15
Slip (mm)

20

25

(a) NSM CFRP strip
4

20°C
100°C
200°C
300°C

Bond stress (MPa)

3.5
3
2.5
2
1.5
1
0.5
0

0

5

10
15
Slip (mm)

20

25

(b) NSM CFRP rod
Figure 3.23 Bond stress-slip relations for NSM CFRP specimens with Tyfo S epoxy at
various temperatures

109

It can be seen from Figures 3.22 to 3.23 that the bond stress-slip responses for
both CFRP strips and CFRP rods almost follow the same trend at various temperatures.
However, at elevated temperatures, both bond stress and bond modulus decrease
significantly, and thus the ascending phase and descending phase of bond stress-slip
curves are not obvious at high temperatures. This also leads to more evenly distributed
bond stress along the bond length.

3.3.4 Relations for bond strength and modulus with temperature
Data generated from the above tests is utilized to develop empirical relations for
bond strength and bond modulus of NSM CFRP system as a function of temperature. The
above test results indicated that NSM adhesive (epoxy) is the primary factor influencing
bond strength and modulus at various temperatures, and shape of CFRP reinforcement
does not have significant influence on the degradation of bond properties. Thus empirical
relations were developed for NSM CFRP reinforcement with Tyfo T300 epoxy and Tyfo
S epoxy respectively, and these relations are expressed in terms of temperature dependant
reduction factors. These reduction factors of high temperature bond strength and modulus
are normalized to their corresponding room temperature values.
So far no bond strength-temperature relations are available for NSM FRP
strengthening system. A review of literature indicated that the following relations for
bond degradation in concrete member reinforced with internal FRP rebars is available
(Katz and Berman 2000, Bisby et al. 2005).

τ (T )= 0.5(1 − τ r ) tanh(k (T − a)) + 0.5(1 + τ r )

110

(3.10)

where τ(T) represents normalized bond strength at temperature T, τr represents
normalized residual bond strength. k is a constant related to degree of cross-link of
polymer epoxy. a is a constant related to glass transition temperature of polymer epoxy.
Bond degradation in concrete with internal FRP rebars mainly results from
temperature induced softening of FRP epoxy, which is similar to debonding mechanism
of NSM FRP system based on the observations and data obtained from this test program.
Thus, the above proposed relation (Eq. 3.10) for bond degradation in concrete with
internal FRP rebars is modified to account for NSM CFRP system.
A regression analysis was performed using “Solver” function in Excel (2010) for
developing modified expressions for bond strength and modulus retention factors of
NSM FRP system. The “Solver” is an advanced program in Excel which is able to obtain
an optimum function to match a specified dataset. The prerequisite for using this Solver
function is to provide a basic format of a function and coefficients to be determined. The
decreasing sigmoidal expression of Eq. 3.10 is taken as the basic format. The retention of
bond strength and modulus at 400°C is used as τr, since NSM FRP systems lose most of
their bond strength at that temperature. Thus k and a are the only coefficients to be
determined in Eq. 3.10.
Then a regression analysis was carried out so as to achieve a minimum error value
between predictions from empirical formula (Eq. 3.10) and the above measured test data.
Based on the regression analysis results, the following temperature dependant relations
were arrived at for bond strength and bond modulus retention factors of NSM CFRP with
Tyfo T300 and Tyfo S epoxy respectively.
111

Tyfo T300 epoxy:

0.55 − 0.45 tanh(0.011(T − 119))
Bond strength: τ (T ) =

(3.11)

0.59 − 0.41tanh(0.01(T − 143))
Bond modulus: E (T ) =

(3.12)

0.55 − 0.45 tanh(0.012(T − 129))
Bond strength: τ (T ) =

(3.13)

0.6 − 0.4 tanh(0.009(T − 143))
Bond modulus: E (T ) =

(3.14)

Tyfo S epoxy:

A comparison of predicted bond strength and modulus from empirical relations (Eq. 3.13
and Eq. 3.14) with measured values from above discussed tests is plotted in Figures 3.24
and 3.25. It can be seen in Figure 3.24 that the proposed empirical relations reasonably
agree with measured data for bond strength of Tyfo T300 and Tyfo S epoxy, and the
average error between predicted bond strength and test data is 6.7% and 8.2%
respectively. The bond modulus predictions, as shown in Figure 3.25, also show good
agreement with test data, and the average error is 6.3% and 6.8% for Tyfo T300 and Tyfo
S epoxy respectively. It can be seen that Tyfo T300 epoxy exhibits slightly higher
degradation in bond strength and bond modulus than those of Tyfo S epoxy. This is
mainly attributed to the fact that Tyfo T300 epoxy possesses relatively higher bond
strength at room temperature. However, in comparison to actual bond strength at various
temperatures, Tyfo T300 epoxy exhibits better bond performance than Tyfo S epoxy.

112

120
Empirical formula - Tyfo T300

Bond strength retention (%)

100

Empirical formula - Tyfo S
Test data - Tyfo T300

80

Test data - Tyfo S

60
40
20
0

0

100

200
300
Temperature (°C)

400

500

Figure 3.24 Comparison of predicted bond strength from proposed empirical relations
with measured data from tests
120

Empirical formula - Tyfo T300
Empirical formula - Tyfo S
Test data - Tyfo T300
Test data - Tyfo S

Bond modulus retention (%)

100
80
60
40
20
0

0

100

200
300
Temperature (°C)

400

500

Figure 3.25 Comparison of predicted bond modulus from proposed empirical relations
with measured data from tests
113

3.3.5 Summary of bond test results
Based on the above bond tests, bond strength of NSM FRP system are mainly
dependant on the type of epoxy adhesive, rather than shape of FRP reinforcement (strip
or rod). At elevated temperatures, the failure mode of NSM CFRP system with Tyfo
T300 epoxy is through pull-out of CFRP strips or rods. This is contrast to room
temperature failure mode, which is through detachment of concrete layer. The bond
strength and modulus of NSM CFRP system decrease by about 80% of their original
values at 200°C, and becomes negligible at 400°C. NSM CFRP system with Tyfo T300
epoxy exhibits higher bond strength and bond modulus than those of NSM CFRP system
in the entire 20-400°C range.
Bond stress-slip response of NSM CFRP system exhibits two distinct stages: prepeak stage and post-peak stage. Bond stress-slip responses at both room and high
temperatures (in 20-400°C range) follow a similar pattern. However, the peak value
(bond strength) and the slope (bond modulus) are lower at elevated temperatures.
At last, the proposed temperature dependant relations for degradation of bond
strength and bond modulus of NSM CFRP system can be used for evaluating fire
response of concrete structures strengthened with NSM CFRP reinforcement.

3.4 Thermal Expansion Tests
Thermal expansion of FRP varies in the longitudinal and transverse directions
depending on the types of fiber, resin, and volume fraction of fiber. Previous studies on
thermal expansion of FRP were mainly focused on internal FRP rebars, but no studies
were conducted on thermal expansion of NSM FRP strips. This section provides detailed
114

test procedure and results on thermal expansion test of typical FRP reinforcement for
NSM application.

3.4.1 Preparation of test specimens
To evaluate thermal expansion of FRP reinforcement at elevated temperatures, a
set of thermal expansion tests were conducted utilizing Thermal Mechanical Analyzer
(TMA). Four types of commercially available FRP reinforcement, provided by two
manufacturers, are tested in this program. They are Aslan GFRP 100 rod, Aslan CFRP
200 rod, Tyfo CFRP strip and Tyfo CFRP rod. All these FRP products are used for NSM
strengthening applications. The dimensions and properties of FRP samples in use are
tabulated in Table 3.9.
Table 3.9 NSM FRP specimens used for thermal expansion test
FRP specimens
Aslan GFRP 100
Aslan CFRP 200
Tyfo CFRP strip
Tyfo CFRP rebar

Dimensions (mm)
Section
Length
dia. 9
10/20
dia.13
10/20
13.5×4.5
10/20
dia.6
10/20

Fiber content (%)

Tg (°C)

>70 (weight)
N/A
62 (volumetric)
60 (volumetric)

>110
>110
71
71

Based on ISO 11358 (1999) and ASTM E831 (2012) standard, the specimens
used for thermal expansion test should be of 5-10 mm in length and width, and the two
ends of test specimens should be parallel. Thus, FRP specimens were cut into around 10
mm in length, and the transverse dimension (width or diameter) was trimmed to be within
10 mm. To ensure reliability of measurements, thermal expansion tests are repeated at
least once.

115

3.4.2 Test apparatus and test procedure
For thermal expansion measurements, thermo-mechanical analyzer (TMA)
apparatus was used in the test, as shown in Figure 3.26. TMA utilizes a movable-core
linear variable differential transducer (LVDT), which generates an output signal directly
proportional to the specimen’s dimension change. TMA can be used for measuring
dimensional changes in a specimen from room temperature to 1000°C. A flat-tipped
standard expansion probe is placed on the specimen, and a small static force is applied to
it so that the probe stays on the specimen. The specimen is subjected to a temperature
increase regiment according to a user-defined temperature ramp, and the probe movement
records the sample expansion or contraction (Kodur and Khaliq 2011).
Before the test, FRP specimen is placed on a pedestal in the moveable furnace of
the TMA and the expansion probe is set on the specimen, as shown in Figure 3.26. Once
specimen is placed in position, the test can be run and controlled by computer, which
records dimensional change with increasing temperatures. Based on the recommendation
from TMA manufacturer (TA 2007), the heating rate of thermal expansion test was set to
be 3°C/min. The temperature range in test was constrained to 20-300°C, since FRP starts
to decompose beyond 300°C and then this might damage the test equipment.

116

sample

furnace

Figure 3.26 TMA apparatus and setup for thermal expansion test
3.4.3 Results and discussion
Measured dimensional changes of NSM FRP specimens were recorded to
evaluate their thermal expansion in a wide temperature range. The variation of transverse
dimension of FRP specimens is shown in Figure 3.27, by plotting a unit dimensional
change as a function of temperature. It can be seen in Figures 3.27(a) and 3.27(b) that the
transverse dimension of FRP keeps increasing at elevated temperatures, regardless of
fiber type (glass or carbon) or cross section shape (strip or rod). This is mainly attributed
to the fact that thermal expansion in transverse direction is dominated by the properties of
polymer matrix of FRP, and polymer expands significantly at elevated temperatures. As
shown in Figure 3.27(a), Aslan GFRP exhibits a relatively larger thermal expansion than
that of Aslan CFRP, which might result from more sensitive response of glass fibers to
thermal effect as compared to carbon fibers. For Tyfo rods and strips investigated, their
thermal expansion responses were very similar throughout the tests. This is mainly due to
similar fiber content (61%) and transverse dimensions (6 mm for rods and 4.5 mm for
strips) of these specimens.

117

25

Aslan GFRP100 - T1
Aslan GFRP100 - T2
Aslan CFRP200 - T1
Aslan CFRP200 - T2

ΔL/L (10-3)

20
15
10
5
0

0

50

100

150
200
Temperature (°C)

250

300

350

(a) Thermal expansion of Aslan GFRP and Aslan CFRP
30
Tyfo rod - T1

ΔL/L (10 -3)

25

Tyfo rod - T2
Tyfo strip - T1

20

Tyfo strip - T2

15
10
5
0

0

50

100

150
200
Temperature (°C)

250

300

350

(b) Thermal expansion of Tyfo rods and Tyfo strips
Figure 3.27 Thermal expansion of NSM FRP specimens in transverse directions
Unlike thermal response in transverse direction, the variations of NSM FRP in
longitudinal direction are relatively small. It can be seen in Figures 3.28(a) and 3.28(b),
the dimensional changes in longitudinal direction are mostly negative values for CFRP
118

specimens, which indicates that CFRP actually experiences shrinking at elevated
temperatures. For Aslan GFRP specimen, it still expands in longitudinal direction at
elevated temperature, but the elongation per unit length gets significantly deceased. This
lower expansion is due to the fact that longitudinal thermal expansion is dominated by the
properties of fibers in FRP. Fibers, especially carbon fibers, usually have very small
thermal deformation (Bank 1993). This leads to negligible thermal expansion of FRP
composite in longitudinal direction. Since the epoxy of FRP gets softened at elevated
temperatures, FRP specimens can easily buckle in longitudinal direction. Thus the
longitudinal thermal expansion data usually varies considerably in the test. The test
results plotted in Figure 3.28 indicate that longitudinal dimensional change of FRP
3

fluctuated around (-3~1)×10 per unit length.
1
0.5
0
ΔL/L (10-3)

-0.5

50

100

150

200

250

300

350

-1

-1.5
-2

-2.5
-3
-3.5
-4

Aslan GFRP100 - L1
Aslan GFRP100 - L2
Aslan CFRP200 - L1
Aslan CFRP200 - L2
Temperature (°C)
(a) Thermal expansion of Aslan GFRP and Aslan CFRP

Figure 3.28 Thermal expansion of NSM FRP specimens in longitudinal directions

119

Figure 3.28 (cont’d)
0.5

50

0

100

150

200

250

300

350

ΔL/L (10 -3)

-0.5
-1

-1.5

Tyfo rod - L1
Tyfo rod - L2
Tyfo strip - L1
Tyfo strip - L2

-2

-2.5
-3

Temperature (°C)
(b) Thermal expansion of Tyfo rods and Tyfo strips

Coefficient of thermal expansion (CTE) is a most widely used parameter for
accessing thermal elongation of materials. Based on the recommendation from ISO
11358 standards (1999), the coefficient of thermal expansion is calculated using the
following equation:

=
α

dL 1
×
dT L0

(5.1)

where L0 is the sample length at room temperature, dL is the change in length at
temperature T, and dT is the change in temperature. ACI 440.1 specification (2006)
provides a set of CTE values for various types of FRP. However, these data was
generated in a limited temperature range, and they were mainly for internal reinforcing
bars. Thus, the data generated in this test was analyzed to compute CTE over a wide
temperature range for NSM FRP reinforcement, as tabulated in Table 3.10.

120

It can be seen in Table 3.10 that CTE of NSM FRP in transverse direction has
consistent variation at elevated temperatures. For all the specimens investigated,
transverse CTE attained relatively large values if larger temperature range was applied.
-6

Transverse CTE of Aslan GFRP attains 70×10 /°C, whereas that of CFRP varies in a
-6

range of (30~80)×10 /°C for three different specimens. This level of thermal expansion
in transverse direction does not cause significantly internal stress between FRP and
concrete, since polymer matrix of FRP gets softened and melted beyond 300°C.
However, in longitudinal direction, thermal expansion might affect effective
stress in NSM FRP when exposed to high temperatures. It can be seen that in Table 3.10
that in low temperature ranges (50°C or 100°C), data on longitudinal CTE has relatively
larger variation for different specimens. Thus the data obtained from lower temperature
range might not be reliable, and test results on larger temperature range are selected to
evaluate the response of FRP under extreme conditions such as fire. Based on the test
results in Table 3.10, longitudinal CTE of CFRP can be considered to be around -5×10
6

-

-6

/°C in 20-300°C temperature range, and the corresponding values of GFRP is 3×10 /°C.

3.4.4 Summary of thermal expansion tests
Coefficient of thermal expansion (CTE) of NSM FRP varies significantly
depending on direction and composition. NSM GFRP has positive CTE (expansion) in
both transverse and longitudinal directions. However, NSM CFRP expands in transverse
direction at elevated temperatures, but shrinks in longitudinal direction. At relatively
higher temperatures, GFRP and CFRP experience larger thermal expansion (or shrinking),
121

in both transverse and longitudinal directions. Based on measured data, CTE of GFRP
and CFRP are recommended over a large temperature range (20-300°C) to evaluate the
effect of thermal expansion to NSM FRP strengthened RC members.
Table 3.10 Transverse and longitudinal CTEs for various NSM FRP reinforcement

NSM FRP specimens
Test 1
Aslan
Test 2
GFRP100
Average
Test 1
Aslan
Test 2
CFRP200
Average
Test 1
Tyfo
Test 2
CFRP rod
Average
Test 1
Tyfo
CFRP
Test 2
strip
Average

Longitudinal direction
Transverse direction
-6
-6
(10 /°C)
(10 /°C)
ΔT = ΔT = ΔT = ΔT = ΔT =
ΔT =
50°C 100°C 280°C 50°C 100°C 280°C
3.5
1.3
2.6
28.2
52.9
74.8
5.3
1.7
2.8
28.0
49.9
68.5
4.4
1.5
2.7
28.1
51.4
71.7
-10.3
-8.4
-13.0
10.6
12.1
18.3
-9.5
-9.7
-6.3
16.4
28.8
44.1
-9.9
-9.1
-9.6
13.5
20.5
31.2
-1.7
-2.9
-4.3
37.6
56.9
67.4
-5.9
-7.5
-10.3
35.9
60.0
68.3
-3.8
-5.2
-7.3
36.7
58.5
67.8
0.6
-0.8
-3.7
40.5
59.4
82.9
-0.4
-1.2
-1.2
26.4
51.1
73.0
0.1
-1.0
-2.5
33.4
55.2
77.9

3.5 Summary
Material property tests were performed to characterize various properties of NSM FRP at
elevated temperatures. A large set of data was generated to gauge the effect of
temperature on mechanical and deformation properties of NSM FRP, including tensile
strength and modulus, bond strength and modulus, and thermal expansion. Data
generated from these tests was utilized to develop empirical relations for mechanical and
bond properties of NSM CFRP system as a function of temperature. The proposed
empirical relations are capable of predicting mechanical and bond properties over a wide

122

temperature range. Thus, these relations can be used as input data in numerical models
for evaluating fire response of NSM FRP strengthened members.

123

CHAPTER 4

FIRE RESISTANCE EXPERIMENTS
4.1 General
The literature review presented in Chapter 2 clearly shows that there is lack of
experimental data on fire response of NSM FRP strengthened RC beams. No experiments
have been carried out to evaluate fire resistance of NSM FRP strengthened RC beams
without insulation. Critical factors influencing fire resistance such as load level,
anchorage of FRP reinforcement, and fire induced axial force have not been quantified.
To fill these knowledge gaps, fire resistance tests were undertaken on four NSM FRP
strengthened T-beams. One beam was tested without any fire insulation, while the
remaining three were protected with U-shaped insulation. These tests were aimed at
generating reliable test data for validation of numerical models. Full details of the fire
experiments, including beam fabrication, instrumentation, test procedure and measured
response parameters, are presented in this chapter.

4.2 Preparation of Test Specimens
The test program consisted of design and fabrication of four NSM FRP
strengthened RC T-beams and testing them under ASTM E119 standard fire conditions.
The fabrication of test specimens comprised of three steps, namely, fabrication of RC Tbeams, installation of NSM FRP, and installation of fire insulation.

124

4.2.1 Design and fabrication of RC T-beams
Four RC beams of T cross-section, representing beam-slab assembles in buildings,
were designed as per AIC 318 (2011) specifications. The dimensions of T-beams were
selected to be close to typical building geometries. The flange of T-beams is of 432 mm
in width and 127 mm in thickness, and the web is of 229 mm in width and 279 mm in
depth. The beams have three 19 mm diameter rebars as flexural reinforcement and four
13 mm diameter rebars as compressive reinforcement. The stirrups used as shear
reinforcement were of 6 mm diameter, and were spaced at 150 mm over the length of the
beam and bent at the top flange at 135° into the concrete core. 13 mm diameter transverse
rebars were placed at a spacing of 305 mm on the top of stirrups to prevent the failure of
overhangs of beam flange (ACI 318 2011). The steel used for the main reinforcing bars
and stirrups had specified yield strengths of 414 MPa and 280 MPa, respectively. The
elevation and cross sectional details of T-beams are shown in Figure 4.1.
The above designed RC T-beams were fabricated at the Civil Infrastructure
Laboratory in Michigan State University (MSU). Plywood forms were first designed and
assembled to have the same internal dimensions as those of tested beams, as shown in
Figure 4.2(a). Then the reinforcement cage (Figure 4.2(b)) was assembled and placed in a
plywood form. All four beams were casted from one batch of concrete, which was
supplied from a local batch mix plant to achieve good quality control. During pouring,
concrete was vibrated and finished using concrete trowel to obtain smooth finishing
surface. The concrete mix was designed to achieve a compressive strength of 41 MPa on
28th day. Type I Portland cement and carbonate based coarse aggregate were used in
concrete batch mix. The measured compressive strength of concrete on 28th day was 48
125

MPa, and reached 50 MPa on 90th day. Batch proportions of concrete mix are given in
Table 4.1.
The casted beams were cured and sealed within the forms for three days, as
shown in Figure 4.2(d). Thereafter, the beams were lifted out from the forms and stored
in the laboratory, under a condition of 25°C temperature and 40% relative humidity.
Table 4.1 Batch proportion of concrete
3
Cement, kg/m

309

3
Fine aggregate, kg/m

908

3
Course aggregate, kg/m

1015

3
Fly ash, kg/m

42

3
Slag, kg/m

59

3
Water, kg/m

160

Water cement ratio (w/c)

0.32

Air

6.5%

Moisture in fine aggregate

4%

Moisture in coarse aggregate

1%

Slump, mm

100

3
Unit weight of concrete, kg/m

85.3

Compressive strength fc’(specified), MPa

41.4

Compressive strength fc’(28 days), MPa

48

Compressive strength fc’(90 days), MPa

50

126

P
A

B

A

P

B

C

127
406 279
152

610

1219
1402

854
3962

C
610

152
1219
1402

(a) Elevation

102

432
228

102

clear cover
thickness 51

127

#4 transverse
38
rebar@305mm

4#4

#2 stirrups@152mm

3#6

clear cover
thickness 51

51

228

38

406
279

51

(b) Cross section of RC beam

T2

216

T1
TC6 SG5 TC32
SG3 SG6
TC33
TC9
102

TC31

SG1
102
64
38

TC2
TC5
N3 S3 SG2
114
Section A

TC7

TC10
102
TC11
SG4
TC12
102
N1 S1 N2
114
Section B

TC34
TC17
TC18
TC16
114
Section C

(c) Instrumentation
Figure 4.1 Elevation, cross-section, and instrumentation of FRP strenghtened RC beams
127

(a) Preparation of wood forms

(b) Assembling reinforcement cage

(c) Casting of concrete

(d) Curing of fabricated T-beams

Figure 4.2 Steps in fabrication of RC beams

4.2.2 NSM FRP strengthening
4.2.2.1 Design of flexural strengthening
The flexural capacity of RC T-beams, which was computed to be 116 kN-m as
per ACI 318 (2011), was enhanced by about 50% through strengthening using NSM
CFRP strips. Typically in field application, the beam are strengthened to achieve 20-50%
of additional capacity. To achieve this enhanced capacity, two Tyfo NSM CFRP strips
were installed at the tension side of T-beam. Tyfo NSM CFRP strips are of high tensile
strength and modulus, pull-formed, epoxy-carbon composite, and is usually applied
together with Tyfo TC epoxy or thickened Tyfo S epoxy in NSM strengthening
128

applications. The cross-sectional area of NSM strip in use is 13.5 mm × 4.5 mm, and the
length of strips is 3.18 m, which corresponds to outer dimension of the furnace. Thus the
ends of NSM strips are thermally protected by the walls of furnace. This configuration
was adopted to simulate the situation where anchorage zones of NSM strips are provided
with thick insulation layers, or NSM strips are inserted into the partition walls (Firmo et
al. 2010). Detailed properties of NSM CFRP strips are provided in Table 4.2.
The resulting moment capacity of NSM FRP strengthened RC beams was
calculated to be 173 kN-m as per specifications prescribed in ACI 440.2 (2008). Detailed
calculations of moment capacity of tested NSM FRP strengthened RC beams are
presented in Appendix B.
Table 4.2 Properties of Tyfo NSM CFRP strips
Property
Dimension
Ultimate tensile strength in
primary fiber direction
Elongation at rupture
Tensile modulus

Typical test value
13.5mm × 4.5mm

Design value
13.5mm × 4.5mm

2.79 GPa

2.51 GPa

1.8%
155 GPa

1.67%
139.6 GPa

4.2.2.2 Installation of NSM FRP strips
The installation of NSM FRP strips is as per the field application procedure
provided by manufacture. Detailed installation procedures are listed as follows.
•

Step 1: The beams were flipped upside down for ease of cutting the grooves. Two
grooves, for placing two FRP strips, were cut on the soffit of each beam. The
dimensions and spacing of grooves were as per ACI 440.2 specification (2008).
The depth and width of the groove were 25 mm and 14 mm respectively, and the

129

clear edge distance between groove and beam edge was 70 mm, as shown in
Figure 4.3.
•

Step 2: After the cutting was finished, the grooves were cleaned using compressed
air.

•

Step 3: Before installation of NSM strips, Tyfo S epoxy, marketed by FYFE
company, was prepared as filling adhesive. Generally Tyfo S epoxy is made by
mixing two components (epoxy resin and hardener), as described in Section 3.2.1.
When used in NSM applications, a third component, fumed silica (Cab-O-Sil),
was added into epoxy, to thicken the adhesive as well as to provide stronger
adhesion to CFRP strips during installation. These three components were mixed
thoroughly using a mixer.

•

Step 4: After the epoxy adhesive was uniformly blended, the adhesive was filled
in the groove to its half depth.

•

Step 5: An NSM CFRP strip was inserted into each NSM groove, and special
attention was paid to position the CFRP strip at the center of the groove.

•

Step 6: After positioning the CFRP strip, the entire groove was filled with epoxy
adhesive.

•

Step 7: After filling the grooves, the epoxy adhesive was cured for three weeks to
achieve good bond between FRP strips and concrete substrate.

Various steps in the installation of NSM FRP is illustrated in Figure 4.4.

130

25
70 14 60 14

ϕ19 steel
rebar

70

13.5×4.5
rectangular CFRP strip
Figure 4.3 Location and dimensions of NSM grooves (Units: mm)

(a) Cut groove at beam soffit

(c) Fill groove with epoxy

(b) Clean the groove

(d) NSM FRP strengthened beams

Figure 4.4 Installation of NSM FRP strengthening on RC T-beams

4.2.3 Fire insulation on T-beams
4.2.3.1 Fire insulation properties
131

To study the effect of fire insulation, three of the above strengthened beams were
provided with Tyfo® CFP fire insulation. This Tyfo® CFP system, an improved version
of previously developed Tyfo® AFP system (Fyfe 2013), comprises of three components;
VG Primer, VG Dash Coat and WR-AFP. VG Primer is a special glue agent, which is
applied on the concrete surface to provide better bond between concrete substrate and
insulation material. VG Dash Coat is basically a sand coating, and it can roughen the
concrete surface and thereby improve the adhesion of insulation material to the substrate.
WR-AFP is the primary insulation material of Tyfo® CFP system. It possesses
characteristics of lightweight, low thermal conductivity, and good crack resistance.
Tyfo® CFP system is non-combustible and non-flammable, and it provides up to
4 hours fire resistance rating. The density and bond strength of CFP insulation, as
3

specified by manufacturer, is 458 kg/m and 0.079 MPa, respectively (Fyfe 2013). The
thermal conductivity and specific heat of CFP insulation are found to be 0.1936 W/m-K
and 0.2698 MJ/kg-K, based on the tests conducted by Kodur and Shakya (2013).

4.2.3.2 Installation of fire insulation
The fire insulation on NSM FRP strengthened beams was applied by professional
contractors from Fyfe Company. The installation procedure is illustrated in Figure 4.5.
The first step of installation was spraying a layer of VG primer on cleaned concrete
surface (see Figure 4.5(a)). The VG primer layer is to be applied uniformly to cover the
entire beam substrate, since any defects could result in debonding of insulation. Then a
thin layer of dash coat was sprayed on VG primer layer (see Figure 4.5(b)); this is mainly
used to roughen concrete surface to ensure better adherence of insulation layer. After
132

applying the above two layers, the beams were cured for 2-3 hours so as to generate good
bond between insulation and concrete substrate.
Thereafter, Tyfo® WR-AFP, which is usually in powdered form, was mixed with
appropriate amount of clear water and spray-applied on beams using a hopper gun, as
shown in Figure 4.5(c). The mixed material was applied in lifts of approximately 8-10
mm thickness to accelerate the drying procedure before next lift was sprayed. During
application, the thickness of insulation was measured at several places along the beam
length to maintain uniform thickness throughout the depth and length of beam web. The
finished insulation system was 25 mm thick at the bottom surface of beam web and
extended to 200 mm on two sides of web (see Figure 4.6). The insulation was cured for
21 days to ensure that full bond strength of insulation material is developed. The
complete insulated beams are shown in Figure 4.5d.

(a) Application of a VG primer layer

(b) Spray a dash coat layer

(c) Spray a WR-AFP layer

(d) Insulated beams for curing

Figure 4.5 Steps in application of fire insulation on NSM FRP strengthened RC beams
133

Figure 4.6 Layout of fire insulation scheme on NSM FRP strengthened RC beams

4.2.4 Instrumentation
The instrumentation mounted in strengthened T-beams included thermocouples,
strain gauges and displacement transducers. To monitor temperature progression within
beams, Type-K Chromel-alumel thermocouples were installed at three different sections
in each beam. During the fabrication of RC T-beams, each beam was instrumented with
23 thermocouples so that temperatures at various locations of concrete and steel rebar can
be recorded during the tests. During the installation of NSM FRP, thermocouples were
bonded at mid-span, quarter span, as well as two ends of FRP strip, to monitor the
variation of temperature in FRP strips and anchorage zones. Some other critical locations,
such as unexposed surface (beam top), beam-insulation interface, were also installed with
thermocouples, as shown in Figure 4.1(c).
Normal temperature strain gauges were mounted to compression and tension
rebars. These strain gauges were bonded to flat finished surface of steel rebar, and
protected with a small piece of duct tape to minimize damage during the casting of
134

concrete. The location and numbering of thermocouples and strain gauges in the crosssection are shown in Figure 4.2c.
In addition, three Linear Variable Differential Transducers (LVDTs) were
installed at unexposed surface (top) along the centerline of each beam, one at mid-span
and two at loading cells to measure the deflections of beam during fire tests. For the
beam with axial restraint, one additional LVDT was applied at one support of the beam to
record variation of axial displacement in the beam.

4.3 Test Apparatus
The fire resistance tests on NSM FRP strengthened beams were carried out using
the structural fire testing furnace in the Civil Infrastructure Laboratory at Michigan State
University. The test furnace, shown in Figure 4.7, has the capacity to supply both heat
and loading that are representative to those in a typical building exposed to fire. The
furnace consists of a steel frame supported by four steel columns, with a fire chamber that
is 2.44 m wide, 3.05 m long, and 1.78 m high. Six natural gas burners are located within
the furnace and provide thermal energy, and the maximum heat (power) can reach 2.5
MW. Six Type-K thermocouple probes placed as per ASTM E119 (2008), are distributed
throughout the test chamber, and they are used to monitor the furnace temperature during
a fire test. During the fire test, these furnace temperatures are used to manually adjust
fuel supply, and maintain a temperature time curve consistent with a pre-determined
standard or design fire scenario. In this way, the furnace temperature can be maintained
along a desired curve. Two small view ports on either side of the furnace wall are

135

provided for visual monitoring of the fire-exposed specimens during a test. The furnace
facilitates two beams at a time, and different load levels can be applied on each beam.

Loading
Frame

Actuator
860
3660

1680

Beam

NSM FRP

Furnace
2440

(a) Furnace and loading frame

(b) Schematic for front view of furnace

Figure 4.7 Structural fire test furnace at MSU Civil and Infrastructure Laboratory
The axial restraint was applied on one beam during the fire test (Beam III). The
devices used for simulating axial restraint are as shown in Figure 4.8. One end of the
beam was loaded through a hydraulic jack, ENERPAC RC-506, and the other end of
beam was connected to steel frame through a short steel beam. The loading capacity of
hydraulic jack is 498 kN, and the maximum stroke is 159 mm.

(a) Axial restraint at one beam end

(b) Axial restraint at the other beam end

Figure 4.8 Installation of axial restriant on NSM FRP strengthened RC beam (Beam III)
136

Data from the test which included temperatures, displacement, strains, and forces,
was collected through “Darwin Data DA100/DP120-13” data acquisition system. This
system is capable of recording 70 thermal couple channels, 10 strain gauge channels, and
10 LVDT channels. All these channels were connected to data acquisition system and the
measurements in the tests were recorded in “.CSV” file using “DAQ32” computer
program.

4.4 Test Conditions and Procedure
During each fire experiment, two NSM FRP strengthened RC T-beams were
tested simultaneously under loading and fire conditions, and thus two fire experiments
were carried out (on four beams). In both fire tests, the beams were simply supported at
ends with an unsupported length of 3.66 m, of which 2.44 m was exposed to fire in the
furnace. ASTM E119 standard fire was applied in both fire tests. The experimental
program and variables studied in fire tests are shown in Table 4.3.
In the first fire test, one uninsulated RC beam (Beam I) and one insulated RC
beam (Beam II) were tested. This is to gauge the fire resistance of NSM FRP
strengthened RC beam without any protection, as well as to investigate the effect of
insulation to fire response of strengthened RC beams. In the second fire test, the effect of
boundary conditions was evaluated through adding axial restraint to one of the two tested
beams. Also, different loads were applied in two fire tests and thus the effect of load level
was studied.
All four beams were subjected to two-point loading in fire tests, and each point
load was 1.4m away from the end support, as shown in Figure 4.1(a). Concentrated loads
137

of 62 kN and 80 kN (loading at one point) were applied in the first and second fire test
respectively, and they represent 50% and 65% of nominal capacity of the strengthened
beam at room temperature. This nominal capacity was determined as per ACI 440.2R
(2008) that requires the effective strain in NSM FRP should be limited to certain level to
prevent the debonding of FRP from concrete substrate. Thus, the moment capacity was
computed with this limiting strain to obtain the superimposed loading. Details of
calculations are provided in Appendix B.
In fire tests, the loading was applied approximately 30 minutes before the start of
the test until steady condition (no increase in deflection with time) was reached. This was
selected as the initial condition for the deflection of the beam.
Table 4.3 Variables studied in fire tests on NSM FRP strengthened T-beams
Fire tests
st

1 test
nd

2

test

Beam
Insulation
specimens
Beam I
None
Beam II
U-shaped

Load (ratio)
62 kN (50%)
62 kN (50%)

Beam III

U-shaped

80 kN (65%)

Beam IV

U-shaped

80 kN (65%)

Boundary
conditions
Simply supported
Simply supported
Simply supported
with axial restraint
Simply supported

4.5 Material Tests
Material tests on constituent materials of NSM strengthened T-beams, including
concrete, steel rebar, FRP strip, were carried out to obtain respective strength properties.
To determine compressive strength of concrete, concrete cylinders prepared from the
same batch mix, as that used for fabricating concrete beams, were tested at 7, 28 days, 90
days, and on the day of fire testing. Average compressive strength of concrete is tabulated
in Table 4.4. The 28-day and 90-day compressive strength of the concrete was 48 and 50
MPa, respectively, which is higher than the design compressive strength of 41.4 MPa.
138

Table 4.4 Compressive strength of concrete
Test date
Concrete
compressive
strength (MPa)

Design strength

7-day

28-day

90-day

Test day

41.4

35.7

48.0

49.7

53.1

The yield strength and ultimate strength of steel rebars were obtained through
tensile strength tests using 810 universal material testing system (MTS). Two tensile tests
were undertaken on rebar samples of 19 mm diameter. The average yield strength,
ultimate strength and ultimate strain were found to be 455 MPa, 674 MPa and 0.18,
respectively. The stress-strain curves for the tested rebars are shown in Figure 4.9.
The mechanical properties of NSM CFRP strip and bond properties of NSM
adhesives (Tyfo S epoxy), were also evaluated through tests. Details on test procedure
and results of these tests are presented in Chapter 3.
800
700
Stress(MPa)

600
500
400

Rebar - 1
Rebar - 2

300
200
100
0

0

2

4

6

8 10 12 14 16 18 20 22
Strain (%)

Figure 4.9 Stress-strain relations of steel rebars used for flexural reinforcement

139

4.6 Test Results and Discussion
A large set of test data was collected in fire resistance tests, including
temperatures at various locations, strains in compression and tension rebars, mid-span
deflections of beams, and axial restraint forces. This data was utilized to evaluate the
comprehensive fire behavior of NSM FRP strengthened RC beams. Also, the response
parameters of NSM FRP strengthened RC beams were compared with published test data
on conventional RC beam and externally bonded FRP strengthened RC beam. Detailed
information on observations taken during fire tests, thermal response, structural response,
and residual strength capacity of these beams are discussed in the following sections.

4.6.1 Test observations
During fire tests, visual observations were recorded from two viewing windows
on each opposite side of the furnace walls. Important events during the tests, including
insulation cracking, epoxy burning, beam cracking, were recorded through photographs
and videos. Tables 4.5 and 4.6 provide a summary of observations at critical moments in
two fire tests.
In the first fire test, NSM epoxy on uninsulated beam (Beam I) started burning
after only 10 minutes into fire exposure. This is mainly due to highly combustible nature
of epoxy, and results of direct exposure to fire. Burning of epoxy on Beam I lasted for
about 50 minutes. The polymer matrix of CFRP strips mostly burned out, and some
carbon fibers were exposed at the beam soffit, as shown in Table 4.5 (80 minutes).
However, since the anchorage zones of NSM FRP strips were protected by furnace wall,
most carbon fibers stayed inside of NSM grooves, and no significant detachment of these
140

fibers was seen during the test. At later stages of fire, some cracks developed on Beam I,
however, the beam did not fail for 210 minutes of fire exposure.
Compared to Beam I, epoxy in Beam II did not burn in the early stage of fire
exposure, as U-shaped fire insulation well protected this beam (from bottom and sides).
There was a little burning of epoxy at beam soffit starting at 60 minutes, and this is due to
onset of cracking in fire insulation. Throughout the fire test, epoxy burning in Beam II
did not cease and it turned more severe at later stage of the test. However, Beam II did
not fail during 210 minutes of fire exposure, but this insulated beam exhibited much
better performance than that of uninsulated beam (Beam I).
In the second set of fire test, Beams III and IV were subjected to higher loading
(65% of room temperature moment capacity) than that in Beams I and II. Thus, cracking
of insulation occurred earlier in these two beams as compared to Beam II, and thus the
burning of epoxy was more severe. At later stage of the test (160 minutes), one piece of
fire insulation fell off from the soffit of Beam IV (without axial restraint), and epoxy at
that unprotected area quickly burned out. In contrary, the insulation on Beam III
remained attached to soffit and sides of beam during the entire fire exposure, and this is
mainly attributed to relative smaller deflection resulting from axial restraint at the
supports. At last, Beams III and IV did not fail during 210 minutes of fire exposure. The
critical observations at various timelines, together with photos, are presented in Tables
4.5 and 4.6.

141

Table 4.5 Visual observation for Beams I and II in the first fire resistance test
Time (mins) Observations

State of the specimens

0

Beams were loaded to 50% of their
room temperature capacity. ASTM
E119 standard fire started.

10

NSM epoxy on Beam I started
burning.

25

The entire beam soffit of Beam I was
engulfed in fire.

35

Vertical cracks occurred in the
insulation of Beam II.

60

Cracking of insulation appeared at
bottom of Beam II, and epoxy on
Beam II started burning.

80

Burning of epoxy in Beam I stopped.
Some carbon fibers exposed at beam
soffit.

100

Burning of epoxy was observed at
multiple spots at the bottom of Beam
II.

190

Visible cracks appeared on Beam I

142

Table 4.6 Visual observation for Beams III and IV in the second fire resistance test
Time (mins) Observations

State of the specimens

0

Beams were loaded to 65% of their
room temperature capacity. ASTM
E119 standard fire started.

30

NSM epoxy on Beam IV started
burning.

55

Cracking of insulation appeared on
Beam III, and epoxy at beam soffit
started burning.

65

More cracks occurred in the insulation
of Beam IV, and burning of epoxy got
severe.

80

More cracks occurred in the insulation
of Beam III, and burning of epoxy
occurred at multiple spots.

160

One piece of insulation at the bottom
of Beam IV fell off, and the epoxy
around the protected area burned
severely.

190

On Beam III, burning of epoxy got
severe.

195

NSM epoxy at the place where
insulation fell off on Beam IV
completely burned out.
143

4.6.2 Thermal response
During the fire test, temperatures at various locations within beam cross section
were recorded to evaluate thermal response of NSM FRP strengthened RC beams. This
section presents details on temperature progression at critical points including that on
NSM FRP, insulation/concrete interface, steel rebars, and various depths of concrete.

4.6.2.1 Furnace temperatures
Figure 4.10 presents the temperature-time curve of ASTME E119 standard fire
and measured average furnace temperatures in two fire tests. The beams were exposed to
ASTME E119 standard fire for 210 minutes. Overall, it can be seen that furnace
temperatures reasonably match the required standard fire temperature, and the
discrepancy between average furnace temperature and ASTM E119 fire is within 5%
range throughout fire duration. This ensures that two sets of beams were tested under
similar fire exposure conditions, and test results of these beams are comparable.
1200
Temperature (°C)

1000
800
600

Measured temperature curve - Test 1

400

Measured temperature curve - Test 2
Specified temperature curve - ASTM E119

200
0

0

30

60

90
120
Time (mins)

150

180

210

Figure 4.10 Measured and specified time-temperature curve during fire tests
144

4.6.2.2 NSM FRP temperatures
Temperature in NSM FRP strips is an important indicator of the condition of FRP
under fire exposure. In this test program, thermocouples were bound to CFRP strips at
various locations and inserted into NSM grooves. Figure 4.11 shows temperature rise in
NSM FRP strip for each tested beam. In Beam I, it can be seen that temperature in FRP
jumped to 600°C at about 20 minutes into fire, and then reached 800°C at about 40
minutes. This quick rise in temperature is mainly caused by severe burning of epoxy in
NSM grooves, as shown in Table 4.5. The burning of epoxy spread along the entire
length of the beam, and thus FRP temperatures at mid-span and quarter span were equally
high during the test. Thus in later stage of fire exposure, CFRP strips turned into carbon
fibers to support the beam. In the anchorage zone, since the epoxy and FRP strips were
not exposed to fire directly, temperature in FRP strips at both ends remained lower than
100°C. This cool anchorage ensures NSM FRP continued to contribute to load bearing
capacity of Beam I, even though temperature in some places of FRP strips went beyond
800°C.
Owing to the protection from U-shaped fire insulation, temperatures rise in FRP
in Beam II was in a much slower rate than that in Beam I. As shown in Figure 4.11(a),
the temperature at quarter span of FRP increased at a slow pace for the entire fire
duration. After 210 minutes of fire exposure, FRP temperatures measured at quarter span
only reached 400°C. However, FRP temperatures at mid-span were much higher in fire
test. After 40 minutes, due to cracking occurred in the insulation, temperature at mid-span
of FRP jumped to 800°C within 10 minutes, and remained in 800-900°C range in the rest
fire duration. However, this localized high temperatures did not lead to debonding of
145

NSM FRP strips in the test, since temperatures in other parts of NSM FRP strips
remained low.
The temperature rise in NSM FRP in Beams III and IV was similar to that in
Beam II, since the same U-shaped fire insulation was applied on these three beams. As
shown in Figure 4.11(b), FRP temperatures in these two beams remained lower than
300°C until 100 minutes, both at middle and quarter span. At 100 minutes, NSM FRP in
both beams attained high temperatures (800°C), and this is directly related to crack
formation in the insulation. Depending on the size of crack and location of thermal
couples, NSM FRP temperatures can be significantly different. Temperatures in NSM
FRP in Beam III were relatively lower than those in Beam IV. This lower temperature is
mainly attributed to the fact that presence of axial restraint on Beam III minimized the
cracks generated in the insulation, and thus heat penetration through insulation was
reduced.
Temperatures at insulation/concrete interface were also recorded at various
locations along the length of insulated beams (Beams II-IV), as shown in Figure 4.12. It
can be seen that temperatures at insulation/concrete interface are similar for three
insulated beams: temperature rise is relatively faster in first 40 minutes of fire exposure,
and then gradually increases until the end of fire exposure. Compared with NSM FRP
temperature curves in Figure 4.11, temperatures at insulation/concrete interface (outside
of groove) were slightly higher than those in NSM FRP (inside of groove). This indicates
NSM epoxy and concrete cover have certain thermal protection effect to NSM FRP.
However,

if

epoxy

in

NSM

groove

started

burning,

the

temperatures

at

insulation/concrete interface also jumped to high level (800-900°C). Thus temperatures at
146

NSM FRP and at insulation/concrete interface were essentially the same as fire
temperatures.
1400

Beam I - Middle span
Beam I - Anchorage zone
Beam II - Quarter span

Temperature (°C)

1200

Beam I - Quarter span
Beam II - Middle span
Beam II - Anchorage zone

1000
800
600
400
200
0

0

30

60

90

120
150
Time (mins)

180

210

240

(a) Beam I and Beam II
1200

Beam III - Middle span
Beam III - Anchorage zone
Beam IV - Quarter span

Temperature (°C)

1000

Beam III - Quarter span
Beam IV- Middle span
Beam IV - Anchorage zone

800
600
400
200
0

0

30

60

90

120
150
Time (mins)

180

210

240

(b) Beam III and Beam IV
Figure 4.11 Variation of NSM FRP temperatures with fire exposure time in Beams I-IV
147

1400

Beam II - Middle span
Beam III - Middle span
Beam IV - Middel span

Temperature (°C)

1200

Beam II - Quarter span
Beam III - Quarter span
Beam IV - Quarter span

1000
800
600
400
200
0

0

30

60

90

120
150
Time (mins)

180

210

240

Figure 4.12 Variation of temperatures at insulation/concrete interface with fire exposure
time in Beams II-IV

4.6.2.3 Steel rebar temperatures
Since FRP reinforcement usually experiences faster degradation on strength and
stiffness during fire exposure, strength retention in steel rebars plays a critical role on fire
resistance of FRP strengthened RC beams. Therefore, temperatures in rebars were
monitored throughout the fire tests. Figure 4.13 shows variation of rebar temperature as a
function of fire exposure time for four tested beams. It can be seen that rebar
temperatures in Beam I increased at much higher rate than those in other beams. At 210
minutes, corner rebar in Beam I reached about 600°C, and this already exceeds the
temperature limit (593°C) specified in ASTM E119 (2012). However, temperatures in
middle rebar attained 400°C, indicating it still possessed most of the original strength.
That’s one reason why Beam I did not fail in the fire test.
148

For Beam II, rebar temperatures were much lower than those in Beam II at any
given fire exposure time, mainly due to protection of fire insulation. It can be seen that
temperatures in corner and middle rebars remained below 300°C during entire fire
exposure, so there was not much strength degradation in steel rebars of Beam II. This
indicated that U-shaped fire insulation can effectively reduce heat progression within the
beam.
In the case of Beams III and IV, temperature in steel rebars rose at slightly higher
rate than that in Beam II, as shown in Figure 4.13(b). This can be attributed to cracking
developing and widening on insulation layer which resulted from higher loading (65% of
load ratio). At later stage of fire exposure, the cracks in the insulation got enlarged, and
one piece of insulation in Beam IV even fell off during the test, and this introduced more
heat transfer into the beam. However, both corner and middle rebar temperatures still
remained below 350°C throughout the fire exposure, which indicated only little strength
loss occurred in steel rebars.

149

700

Beam I - Corner rebar
Beam I - Middle rebar
Beam I - Top rebar
Beam II - Corner rebar
Beam II - Middle rebar
Beam II - Top rebar

Temperature (°C)

600
500
400
300
200
100
0

0

30

60

90

120
150
Time (mins)

180

210

240

180

210

240

(a) Beams I and II
350

Beam III - Corner rebar
Beam III - Middle rebar
Beam III - Top rebar
Beam IV - Corner rebar
Beam IV - Middle rebar
Beam IV - Top rebar

Temperature (°C)

300
250
200
150
100
50
0

0

30

60

90

120
150
Time (mins)

(b) Beams III and IV
Figure 4.13 Variation of steel rebar temperatures with fire exposure time in Beams I-IV

150

4.6.2.4 Concrete temperatures
The variation of concrete temperatures at various depths is plotted in Figure 4.14,
as a function of fire exposure time. The locations monitored during fire exposure include
concrete at quarter depth, mid-depth, and three quarters depth from beam soffit. As
expected, concrete at locations closer to fire exposure attained relatively higher
temperature. In Beam I, temperatures at various depths of concrete increased to 100°C at
about 30-40 minutes, and then sustained a plateau at around 100°C for more than 30
minutes. This is due to the fact that moisture in concrete absorbs significant heat during
evaporation process. After this moisture got evaporated, temperature in concrete
continued to increase. At last stage of fire exposure, concrete temperature at quarter depth
from beam soffit reached 430°C. However, temperatures in the upper half concrete,
which is the primary compression zone of beam, still remained below 300°C.
Temperature rise in concrete in insulated beams (Beams II-IV) was very slow
throughout fire exposure duration. It can be seen that in Figure 4.14(b) that there is no
significant temperature gradient developed over the depth of concrete, and the highest
temperature attained in concrete is only 200°C. This is mainly attributed to the fact that
U-shaped insulation covers the entire web of beam, and thus thermal propagation within
concrete section is considerably reduced. Based on temperature-strength relationship
specified in ASCE (Lie 1992) and Eurocode (2004), there is no strength and stiffness loss
in concrete until 400°C. Thus, in all four tested beams, concrete retained most of the
nominal strength and stiffness throughout fire exposure duration.

151

450

Beam I - 1/4h from bottom
Beam I - 1/2h from bottom
Beam I - 3/4h from bottom
Beam II - 1/4h from bottom
Beam II - 1/2h from bottom
Beam II - 3/4h from bottom

Temperature (°C)

400
350
300
250
200
150
100
50
0

0

30

60

90

120
150
Time (mins)

180

210

240

180

210

240

(a) Beams I and II
300

Beam III - 1/4h from bottom
Beam III - 1/2h from bottom
Beam III - 3/4h from bottom
Beam IV - 1/4h from bottom
Beam IV - 1/2h from bottom
Beam IV - 3/4h from bottom

Temperature (°C)

250
200
150
100
50
0

0

30

60

90

120
150
Time (mins)

(b) Beams III and IV
Figure 4.14 Variation of concrete temperatures with fire exposure time at various
locations in Beams I-IV
152

4.6.3 Structural response
4.6.3.1 Deflections
Structural response of four NSM FRP strengthened RC beams is compared in
Figure 4.15, by plotting the variation of mid-span deflection as a function of fire exposure
time. Previously test data on an unstrengthened RC beam tested by Dwaikat and Kodur
(2009) and an externally FRP strengthened RC beam tested by Ahmed and Kodur (2011)
are also plotted in the figure to compare relative fire response of RC beams with different
FRP strengthening. These two beams are of 254×406 mm rectangular sections, which are
slightly wider than tested T-beams. However, all beams are in the same depth and
comprise of same flexural reinforcement, and further all beams were tested exposed to
ASTM E119 fire. Thus, the behaviors of these beams are comparable. The configurations
of unstrengthened RC beam, external FRP strengthened RC beam, as well as NSM FRP
strengthened T-beams, are shown in Table 4.7.
Table 4.7 Configuration and test conditions of RC beams with various FRP strengthening
Beam configuration
Cross section
Steel rebars
Figure
(mm)
Beam I
3 ϕ 19 mm in
Flange
Beam II
tension
432×127
4 ϕ 13 mm in
Web
Beam III
228×279
compression
Beam IV
3 ϕ 19 mm in
Unstrengthened tension
254×406
RC beam
2 ϕ 13 mm in
compression
3 ϕ 19 mm in
External FRP
tension
strengthened
254×406
2 ϕ 13 mm in
RC beam
compression

Beams

153

Load ratio Fire insulation
50%
50%
65%
65%

None
25mm U-shape
25mm U-shape
25mm U-shape

54%

None

50%

25mm U-shape

The variation of mid-span deflection as a function of fire exposure time for four
tested T-beams is plotted in Figure 4.15. It can be seen that the uninsulated Beam I
experienced much faster deflection than those of insulated beams (Beams II to IV). Due
to direct exposure to fire, NSM epoxy in Beam I started burning at 10 minutes into fire.
Thus the bond between FRP and concrete member in Beam I was severely affected at the
early stage of the fire exposure, and FRP strength and stiffness also decreased
significantly. These are two main factors resulting in much larger deflections in Beam I.
Thereafter, the deflection keeps increased during the fire exposure, due to temperature
induced strength degradation in steel rebar and concrete. To prevent sudden failure of
beam, the loading on Beam I was released a little in the final stage of the test, and thus
the deflection in Beam I almost stopped increasing. Finally Beam I did not fail for 210
minutes of fire exposure.
Due to the protection of fire insulation, Beams II-IV underwent lower deflections
as compared to Beam I. Beams II retained a small amount of deflection in the entire fire
exposure duration, and this mainly results from low temperatures in steel rebar and NSM
FRP (refer to Section 4.6.2). For Beams III and IV, the mid-span deflections also
remained in a low level in the first 90 minutes. However, after 90 minutes, these two
beams experienced accelerating deflections, and this is mainly due to bond degradation of
NSM FRP resulting from burning of epoxy. Since the loading on Beams III and IV is
relatively large (65% of room temperature capacity), more cracks developed in the
insulation, and thus more epoxy burning is induced on these two beams. However, Beam
III yielded smaller deflection as compared to Beam IV. This is mainly attributed to the
counteracting moment developed through axial restraint force, which reduced the
154

moment applied by external loading. This effect is similar to that of prestressed strands to
a concrete beam.
The comparative deflection response of RC beams with different FRP
strengthening is also plotted in Figure 4.15. It can be seen that deflection response of
NSM FRP strengthened RC beam without insulation (Beam I) is similar to that of
unstrengthened RC beam tested by Dwaikat and Kodur (2009). However, NSM FRP
strengthened RC beam experienced smaller deflection than that of unstrengthened RC
beam throughout fire duration. This can be attributed to the “cable action” that was
developed through remaining NSM CFRP strips. It is established that carbon fibers
possess good temperature resistance and can retain most of their strength even at 1000°C
(Davies et al. 2004, Sauder et al. 2004). Therefore, even polymer matrix of CFRP strips
melted and decomposed under fire conditions, carbon fibers can hold RC beam and limit
its further deflections, as long as anchorage zones of NSM FRP remain intact (Rafi et al.
2008, Ahmed and Kodur 2011). Finally, the unstrengthened RC beam failed at 180
minutes, but NSM FRP strengthened RC beam (Beam I) did not fail for 210 minutes of
fire exposure. This also indicated that carbon fibers in Beam I still contribute to load
bearing capacity of the beam.
Beam II and the beam tested by Ahmed and Kodur (2011) are FRP strengthened
RC beams with U-shaped fire insulation. These two beams were tested under similar fire
and loading conditions as shown in Table 4.7. Thus the behavior of these two beams is
comparable. It can be seen in Figure 4.15 that deflection response of two beams is very
similar, and this is attributed to the fact that both beams were thermally protected and
thus steel and FRP retained most of their room temperature strength. External FRP
155

strengthened RC beam experienced slightly smaller deflection than that of NSM FRP
strengthened RC beam. This can be attributed to the fact that relative larger stiffness
provided by external FRP laminates than those of NSM FRP strips. Overall, similar
response of these two beams also proves the reasonability of fire test results.

0

0

30

60

Time (min)
90
120

150

180

210

Deflection (mm)

-10
-20
-30
-40
-50

Beam I
Beam II
Beam III
Beam IV
Dwaikat 2009
and Kodur 2009
Ahmed and Kodur 2011

-60
Figure 4.15 Comparison of mid-span deflections of NSM FRP strengthened RC beams
with unstrengthened RC beam and external FRP strengthened RC beam

4.6.3.2 Axial restraint force
In the second fire test, axial restraint force and axial displacement at beam support
(Beam III) were recorded during the fire test, in order to quantify the influence of axial
restraint to fire response of NSM FRP strengthened RC beam. It can be seen in Figure
4.15 that fire induced axial force gradually increased with fire exposure time, and this is
mainly due to fire induced expansion of strengthened beam against axial restraint. At
later stages of fire exposure, the measured axial restraint force decreased slightly with fire
156

exposure time. This is mainly attributed to the fact that the beam was slightly detached
with the restraint device resulting from relatively larger beam deflection at last stage of
fire exposure. However, the effect of axial restraint is still demonstrated through
comparative behavior of Beam III and Beam IV. Beam III, which has axial restraints at
two ends, achieved smaller deflection and the insulation layer remained attached to beam
substrate throughout fire test. While the simply supported Beam IV experienced
relatively larger deflection, and this leads to a piece of insulation falling off at later stage
of fire exposure.
The variation of axial displacement at the beam support (Beam III) with
temperature is also plotted in Figure 4.16. It can be seen that the axial displacement
gradual increased with fire exposure time, which indicates that beam slightly expanded in
axial direction. Based on the measurement of axial restraint force and displacement, the
axial restraint stiffness can be estimated to be 5-10 kN/mm, which is similar to the axial
restraint encountered in beam-column frame in buildings.
35

8
Axial displacement (mm)

Axial force (kN)

25

7
6
5

20

4

15

3

10

2

5

1

0

0

0

30

60

90
120
Time (mins)

150

180

210

Figure 4.16 Variation of axial force and displacement with fire exposure time
157

Axial displacement (mm)

Axial force (kN)

30

4.6.3.3 Strain in longitudinal reinforcement
The strains in longitudinal reinforcement of the tested beams were monitored
utilizing conventional strain gauges since the pre-loading stage. The measured strain at
central section of four tested beams is plotted as a function of time in Figures 4.17 and
4.18. It can be seen there is slightly irregular variation of strains measured in the
compression and tension rebars, and this is probably due to incremental loading in the
pre-loading stage. After 20 to 30 minutes, the tension and compression strains gradually
became stable. It can be seen that Beams III and IV attained relatively higher strain levels
than those of Beams I and II, due to higher loads applied on the beams. However, for the
beams under the same loading level, the strains reached similar values, which also proved
effectiveness of strain gauge data.
The strain gauges installed in the beam are regular strain gauges, and they are
only functional under 80°C. After fire tests started around 10-15 minutes, all the strain
gauges were damaged. Thus strain data in Figure 4.17 stopped after about 40 minutes.

4.6.4 Fire resistance
Time to reach failure under fire exposure is defined as the fire resistance of a
structural member. In this experimental program, strength and deflection limit specified
in current design standards (ASTM 2012, BSI 2009) were applied to determine failure of
beam. According to these limiting criteria, all four NSM FRP strengthened beams did not
fail for 210 minutes of fire exposure. This infers these NSM FRP strengthened RC beams
possess at least three hours of fire resistance under ASTM E119 standard fire.

158

1000
800
Mirostrain (10-6)

600
Tention rebar strain - Beam I
Compressive rebar strain - Beam I
Tension rebar strain - Beam II
Compression rebar strain - Beam II

400
200
0

15

30

45

60

75

-200
-400
-600

Time (mins)

Figure 4.17 Strain measured in tension and compression rebars in Beams I and II during
the test (starting from pre-loading stage)
1400
1200
Mirostrain (10-6)

1000
Tention rebar strain - Beam III
Compressive rebar strain - Beam III
Tension rebar strain - Beam IV
Compression rebar strain - Beam IV

800
600
400
200
0

10

20

30

40

50

-200
-400

Time (mins)

Figure 4.18 Strain measured in tension and compression rebars in Beams III and IV
during the test (starting from pre-loading stage)

159

In current design provisions, the fire resistance of FRP strengthened RC beams is
considered to be the same as that of original unstrengthened RC beam, and the
contribution of FRP strengthening is usually neglected if no fire insulation is provided
(ACI 440.2 2008, FIB Bulletin 14 2007). However, in these fire experiments, although
Beam I was unprotected and NSM epoxy experienced severe burning, carbon fibers still
provided tensile strength to the beam through “cable action”. As a comparison, an
unstrengthened RC beam with similar configuration and load level failed in 180 minutes
(Dwaikat and Kodur 2009). This indicates that anchorage zone is vital to achieve
relatively higher fire resistance in NSM FRP strengthened RC beams. As long as
anchorage zone remains intact, NSM FRP can still contribute to moment capacity even
when the beam is not insulated. On the other hand, the axial restraint, which represents
typical boundary conditions in buildings, is proved to be beneficial to fire resistance of
NSM FRP strengthened RC beams in the fire test. The beam with axial restraint retains
relatively smaller deflections, and cracking in the insulation is also reduced. Considering
the above factors, it is likely that NSM FRP strengthened RC beams possess satisfactory
fire resistance for building applications.

4.7 Residual Strength Tests of NSM FRP Strengthened RC Beams
Since all four tested NSM FRP strengthened RC beams did not fail in the fire
resistance tests, all four beam specimens were utilized to study the residual strength of
these beams. The test is aiming at evaluating the degradation of load bearing capacity of
NSM FRP strengthened RC beams after fire exposure. Details on procedure and results of
residual strength test are presented in the following sections.
160

4.7.1 Test procedure
For the residual strength test, fire exposed Beams I, II and III were allowed to
cool down for 24 hours. However, Beam IV was loaded to failure right after 210 minutes
of fire exposure, in order to evaluate the residual flexural capacity of fire exposed beams
prior to cooling. Beams I, II and IV were tested under simply supported conditions.
However, since Beam III was axially restrained during the fire test, and this axial restraint
was also applied in residual strength test. The variables studied in residual strength are
tabulated in Table 4.8.
In the residual strength test, each beam was loaded to failure under two-point
loading (as in fire tests), and the load was increased gradually at 5 kN/min until failure
occurred. Similar to the fire tests, the displacements at mid-span and loading points were
recorded throughout the loading range.
Table 4.8 Test variables and results in residual strength tests on fire exposed beams
Specimen

Insulation

Beam I

No

Beam II

U-shaped

Beam III

U-shaped

Beam IV

U-shaped

Boundary
condition
Simply
supported
Simply
supported
Axially
restrained
Simply
supported

Cooling
time

Failure load

24 hours

113 kN

24 hours

129 kN

24 hours

132 kN

No cooling

123 kN

Failure mode
Yielding of
steel rebar
Crushing of
top concrete
Crushing of
top concrete
Crushing of
top concrete

4.7.2 Results and discussion
The measured load-deflection response for four tested beams is plotted in Figure
4.19. All four beams exhibit similar load-deflection response. The load-deflection
response is linear till almost full capacity is attained, and then follows a long plateau
161

stage. This behavior is more similar to the response of an unstrengthened RC beam,
rather than a NSM FRP strengthened RC beam, which has an obvious increase in load
capacity after steel rebar enters yielding stage. This load-deflection response indicates
NSM FRP strengthening has lost its effectiveness when exposed to fire, mainly resulting
from temperature induced bond degradation at FRP-concrete interface. However, a close
examination shows that Beams II and III achieved higher residual strength (129 kN and
132 kN) than that of Beam I (113 kN), and this indicates that NSM FRP in Beams II and
III contributes to a limited extent to flexural strength capacity of the beam. This is mainly
due to the fact that bond at FRP-concrete interface was not completely lost in insulated
beams due to relatively low temperatures in NSM FRP.
Beam IV was loaded to failure right after 210 minutes of fire exposure without
any cooling, and the residual capacity is 123 kN. This residual strength capacity is lower
than that in Beam II, which was tested after full cooling. Also, the stiffness of Beam IV is
slightly smaller than those of Beams II and III as shown in Figure 4.19. As discussed in
thermal response section, temperatures in steel rebars in Beam IV reached about 350°C.
At this temperature level, modulus of elasticity of steel rebars already has about 20%
degradation based on temperature-property relations specified in Eurocode 2 (2004), so
the stiffness of the whole beam also decreased in some extent correspondingly. While
Beam II experienced one day cooling and temperatures in steel rebars were low. Thus
Beam II exhibited relatively larger stiffness as compared to that of Beam IV in residual
strength tests.

162

160
140
120
Load (kN)

100
80
60

Beam I
Beam II
Beam III
Beam IV

40
20
0

0

20

40

60
80
Deflection (mm)

100

120

140

Figure 4.19 Load-deflection response of Beams I-IV in residual strength tests
The failure patterns of four NSM FRP strengthened beams in residual strength
tests are illustrated in Figure 4.20. It can be seen that Beam I failed due to yielding of
steel reinforcement, which is a typical failure mode in unstrengthened RC beams.
However, Beams II, III and IV failed due to crushing of top concrete, and this is more
like a failure occurred in NSM FRP strengthened RC beams. A closer observation
indicates that major part of FRP strips in Beams II-IV still stayed inside of NSM grooves,
as shown in Figure 4.21. This also indicated that NSM FRP in Beams II to IV still
possess some strengthening effect even after 210 minutes of fire exposure.

163

(a) Beam I

(b) Beam II

(c) Beam III

(d) Beam IV

Figure 4.20 Failure patterns of Beams I-IV in residual strength tests

164

(a) Beam I

(b) Beam II

(c) Beam III

(d) Beam IV

Figure 4.21 Response of NSM FRP strips after failure in residual strength tests

4. 8 Summary
Fire resistance tests were carried out on four NSM FRP strengthened RC beams
of T cross section. Three of these strengthened beams were provided with fire insulation,
while one beam was tested without any fire insulation. Besides visual observations,
temperature and deflection responses were recorded to study fire response of NSM FRP
strengthened RC beams. The observations and recorded data allowed to evaluate

165

comparative performance of NSM FRP strengthened RC beams under different loading
and boundary conditions.
All four tests beams did not fail after 210 minutes of fire exposure, judging from
strength and deflection criteria. One of these NSM FRP strengthened RC beams was
without any fire insulation, and it also did not fail for 210 minutes, indicating NSM FRP
strengthened RC beam can achieve sufficient fire resistance through proper design. In
addition, comparison of tested beams indicates that presence of fire insulation and axial
restraint significantly enhances fire resistance of NSM FRP strengthened RC beams.
Results from these fire tests provide a better understanding on the behavior of NSM FRP
strengthened RC beams under fire conditions. The data generated from these tests is
further utilized for validating numerical models developed for tracing the fire response of
NSM FRP strengthened RC beams.

166

CHAPTER 5

NUMERICAL MODEL
5.1 General
Undertaking fire tests is usually expensive and time consuming. In lieu of fire
tests, numerical approach can be applied to evaluate the behavior of a structural member
under fire exposure. There have been no numerical studies for evaluating fire response of
NSM FRP strengthened RC beams. A sophisticated numerical model, based on finite
element approach, is critical for undertaking detailed fire resistance studies on NSM FRP
strengthened RC beams. Such a model should account for high temperature properties of
constituent materials, various strain components, fire induced bond degradation, and
realistic loading and boundary conditions.
A numerical model, initially developed for tracing the fire behavior of RC beams
externally strengthened with FRP (Kodur and Ahmed 2010), is extended to simulate the
fire performance of RC beams strengthened with NSM FRP reinforcement. The updated
model is capable of evaluating fire response of RC beams with various cross-sections,
FRP strengthening and insulation schemes. Details of this numerical model are presented
in this chapter.

5.2 Macroscopic Finite Element Model for Fire Resistance Analysis
The behavior of RC beams exposed to fire can be simulated using general purpose
finite element software such as ANSYS or ABAQUS. In these microscopic finite element
167

based models, a structural member is generally discretized into a three dimensional mesh,
and coupled (or uncoupled) thermal and structural analyses are carried out to trace the
fire response of structural members. However, such an analysis is highly complex and
requires use skills for discretizing and analyzing results. Also, most of the commercial
finite element programs do not account for various strain components (such as creep
strain and transient strain in concrete) as well as temperature induced bond degradation at
FRP-concrete interface.
As an alternative, macroscopic finite element approach can be used for tracing the
fire behavior of RC structural members. In macroscopic finite element model, a sectional
analysis is carried out at a number of cross-sections along the length of the member and
moment-curvature relationships are generated for these sections to trace the behavior of
structural member under a given fire exposure and loading condition. Recently, such
macroscopic computer models have been successfully applied to evaluate fire response of
RC beams with various configurations (Kodur and Dwaikat 2008, Kodur and Ahmed
2010). In this chapter, such a macroscopic model is further extended to account for the
features of NSM FRP strengthened RC beams.

5.2.1 General approach
The numerical model presented here is based on macroscopic finite element
approach, and utilizes sectional moment-curvature relationships to trace the response of
NSM FRP strengthened RC beams from pre-loading stage to collapse under fire
conditions. In the model, an RC beam is discretized into a number of segments along its
length, and cross-sectional area of each segment is subdivided into a number of elements,
168

as shown in Figure 5.1. The mid-section of each segment is assumed to represent the
overall behavior of the segment. Fire resistance analysis is carried out by incrementing
time in steps. At each time step, the analysis is performed through three stages, namely,
(1) evaluating fire temperatures, (2) carrying out heat transfer analysis to determine
temperature distribution along cross-section, and (3) conducting structural analysis to
determine moment capacity and deflection of beam. The analysis is carried out at various
time increments till failure occurs in the beam under any given fire exposure and loading
conditions. A flowchart illustrating the steps associated in the model for fire resistance
analysis of NSM FRP strengthened beam is presented in Figure 5.2.

w

NSM
NSMFRP
FRP

Insulation
Insulation

Fire exposure
Fire exposure

Fire exposure
Fire exposure

(a) Layout and cross section of beam

w
1

2

3

4

5

6

7

8

9

NSM FRP

10

11

12

Insulation

NSM FRP

Insulation
Fire exposure
Fire exposure

(b) Discretization into segments

Finer
mesh

Finer mesh

Fire exposure
Fire exposure
(c) Discretization into elements

Figure 5.1 Typical beam layout and discretization of beam into segments and elements

169

Start

Discretization
of beam

Calculation of fire temp.
High temperature
thermal properties
Bond-slip evaluation

Calculation of cross-sectional
temp. for segment i
Initial total strain at the top
most fiber of concrete

Calculate stress in FRP
Calculate shear stress at
FRP-concrete interface
Check if bond
No No
strength is adequate
slip
Yes
Calculate slip strain

High temperature
mechanical properties

Initial curvature
Calculation of strains
(thermal/mechanical/creep/slip)
Calculate strains and stresses
Check sectional
force equilibrium
Yes
Record curv. and
corresponding moment
(point on the M-κ curve)
Ultimate
curvature*
Yes

* Either crushing of

concrete or rupture of
FRP

Segment = n**

** n = total number of

beam segments

***Limit states:

1) Applied moment > moment
capacity
2) Deflection > L/20
2
3) Rate of deflection > L /9000d
(mm/min)

No Increment
curvature

No Increment
strain
No

Yes

Segment
i = i+1

Nonlinear stiffness
analysis of beam
Calculate deflection of beam
Check failure***
End

No Increment
time

Yes

Figure 5.2 Flowchart illustrating the steps associated in the numerical model
170

5.2.2 Fire temperatures
The fire temperature in the model is evaluated following a standard fire curve
such as ASTM E119 (2012) and ISO 834 (2012) fire, or a design fire curve based on
specific compartment characteristic. The time-temperature relations for ASTM E119
(2012) and ISO 834 (2012) standard fires can be calculated using the following equations:
ASTM E119: T f = + 750(1 − e−3.79533 t ) + 170.41 t
To
ISO 834: T f = 10 (8t + 1)
T0 + log

(5.1)
(5.2)

For a design fire, a decay phase follows after reaching the peak value of fire
temperature, and the decay rate mainly depends on a number of factors such as material
properties of fuel, size of ventilation, and thermal properties of lining material (Buchanan
2002). User can define any time-temperature relations based on a specific compartment,
or utilize design fires specified in current Eurocode 1 (2002) or SFPE Handbook (2008).

5.2.3 Thermal analysis
Thermal analysis on an NSM strengthened RC beam is carried out utilizing finite
element approach. The given beam is discretized into a number of segments along beam
length, and the central section of the segment, which is assumed to represent the behavior
of each segment, is further divided into number of elements. as depicted in Figure 5.1. A
finer mesh is applied in the vicinity of critical zones (steel rebar, NSM FRP, and
insulation) along the beam cross section to achieve better accuracy in the numerical
analysis.

171

Knowing fire temperatures at various time steps, two-dimensional heat transfer
analysis is carried out to evaluate cross-sectional temperature in each segment. It is
assumed that the beam is exposed to fire from three sides (bottom and two side surfaces),
and fire temperature is uniform along the length of segment. Thus the calculation is
performed over a unit length of each segment. Steel reinforcement is not specifically
considered in the thermal analysis because it does not influence the temperature
distribution in the beam cross section (Lie and Irwin 1993).
Based on the conservation of energy, the governing equation for heat transfer
within the beam cross section is given as:
k ∇ 2T + Q =
ρc

∂T
∂t

(5.3)

where, k is the thermal conductivity, ρc is the heat capacity, T is the temperature, t is the
fire exposure time; and Q is internal heat generation.
It has been established that heat transfer occurring from fire to the surface of
beam is through convection and radiation (Buchanan 2002). Conduction is the
predominant heat transfer mechanism within the beam. The heat flux due to convention
and radiation on the fire exposed surfaces can be evaluated through the following
equations:
= hrad (T − TE )
qrad

(5.4)

= hcon (T − TE )
qcon

(5.5)

where, qrad and qcon represent radioactive and convective heat fluxes respectively, and
hrad and hcon represent radioactive and convective heat transfer coefficient respectively.
172

TE is external temperature surrounding the boundary. Hence the total heat flux on the
beam boundary (qb) can be given by the following equation:
= ( hcon + hrad )(T − TE )
qb

(5.6)

Using Fourier’s Law, the governing heat transfer equation on the boundary of the beam
can be written as:

 ∂T
∂T 
−h
k
ny +
nz  =(T − TE )
∂z 
 ∂y

(5.7)

where, ny and nz are components of the vector normal to the boundary in the plane of the
cross-section, and
h = hcon + hrad

(5.8)

The beam is exposed to fire from bottom and two side surfaces, while the top surface of
beam remains cool. Thus two types of boundary conditions should be considered for
thermal analysis, namely:
1) Fire exposed boundaries where the heat flux is governing by:

 ∂T
∂T 
−h f
k
ny +
nz  =(T − T f )
∂z 
 ∂y

(5.9)

2) Unexposed boundaries where the heat flux is governing by:

 ∂T
∂T 
−hc
k
ny +
nz  =(T − T0 )
∂z 
 ∂y

(5.10)

where, hf and hc are heat transfer coefficient of the fire side and room temperature side
respectively, and Tf and T0 are fire and room temperature respectively.
173

Galerkin finite element formulation is applied to solve Eq. 5.3. In this
formulation, the material property matrices (stiffness matrix Ke, mass matrix Me) and the
equivalent nodal heat flux (Fe) are generated for each element. These matrices are given
by following equations (William 1990):

Ke =

 ∂N ∂N T ∂N ∂N T 
T
k
∫A  ∂x ∂x + ∂y ∂y dA + ∫Γ Nα N ds




M e = ∫ ρ cNN T dA

(5.12)

A

=
Fe

(5.11)

∫A NQdA + ∫Γ NαTα ds

(5.13)

where, N is the vector of the shape functions, k is the thermal conductivity, α is hc or hf
depending on the boundary condition Г, Q is heat source; s is distance along the
boundary, A is the area of the element, and Tα is fire or ambient temperature depending
on boundary condition Г.
Once the matrices of elements are computed, they are assembled into a global
system of differential equations which is expressed as:


MT + KT =)
F (t

(5.14)

where, K is global stiffness matrix, M is global mass matrix, F is equivalent nodal heat
flux, and Ṫ is temperature derivative with respect to time (t).
͘
The above equation is solved using finite difference algorithm of trapezoidal
family (θ algorithm) in the time domain. This algorithm computes temperature
distribution at any time step (n+1) using the information available at preceding time step
(n), and can be written as (William 1990):
174



= Tn (θ Tn +1 + (1 − θ )Tn )
Tn +1

(5.15)

Multiplying both side of Eq. (5.15) by M and using Eq. (5.14) at the beginning
and the end of the time interval (tn, tn+1), the following equation can be obtained:

( M + hθ K )Tn +1 = ( M − h(1 − θ ) K )Tn + h(θ Fn +1 + (1 − θ ) Fn )

(5.16)

where, h is time step, Tn and Tn+1 are temperatures at the beginning and the end of time
step respectively. Fn and Fn+1 are the equivalent nodal heat flux at the beginning and the
end of time step, and θ is a constant between 0 and 1.
For unconditional stability of numerical calculations, θ has to be equal to or
greater than 0.5 (William 1990). By knowing the temperatures at ambient conditions, Eq.
5.16 can be applied to obtain the time history for temperature at the following time step,
and this can be repeated for subsequent time steps. In each time step, an iterative process
is required to solve Eq. 5.16 due to the nonlinearity of both material properties and
boundary conditions. More details on the finite element formulation for solving the heat
and mass transfer equations are provided in Appendix C. The obtained nodal temperature
from Eq. 5.16 is utilized to calculate the temperature in each element by averaging the
four nodal temperatures of rectangular elements. For steel rebars the temperature is
assumed to be that at the center of the rebar.

5.2.4 Structural analysis
5.2.4.1 General analysis procedure
After generating cross sectional temperature of the beam at various time steps,
structural analysis is performed to evaluate the fire resistance of NSM FRP strengthened
175

RC beams. In structural analysis, the calculation is conducted using the same mesh as
used for thermal analysis. The strains and stresses in each element are represented by the
corresponding values at the center of the element. The temperatures in each element
obtained from thermal analysis are used as input, and segmental M-κ relationships are
developed to trace the structural behavior of NSM FRP strengthened RC beams at
various time steps. The structural analysis proposed here is based on the following
assumptions.
•

Plane sections before bending remain plane after bending.

•

Beam has a constant cross-section.

•

The failure of beam is through flexural strength limit and the beam does not fail
in shear strength limit.

• There is no bond-slip between steel reinforcement and concrete at various
temperatures.
•

FRP reinforcement exhibits linear stress-strain relationship at various
temperatures up to failure.
At each time step, the structural analysis is performed by first estimating fire

induced axial force and slip at NSM FRP/concrete interface in each beam segment. Then
M-κ relationship for each beam segment is generated based on force equilibrium and
strain compatibility principles. At last, nonlinear stiffness analysis is conducted to
evaluate the structural response (moment capacity, deflection, stress) of NSM FRP
strengthened RC beam at each time step. Details on structural analysis and calculations
are described in the following sections.

176

5.2.4.2 Evaluating temperature induced slip and axial restraint force
In NSM FRP strengthened RC beam, bond at the interface of NSM FRP, adhesive
and concrete plays a critical role in transferring stresses from concrete substrate to FRP
reinforcement. With increase of temperature in NSM adhesive, bond properties
deteriorate rapidly and this introduces slip at FRP-adhesive-concrete interface. Eventually,
the NSM adhesive loses its effectiveness in transferring stresses and thus debonding of
NSM FRP occurs.
In the numerical model, temperature induced slip and bond degradation is
accounted for introducing a slip strain in NSM FRP reinforcement. When slip occurs,
strain resulting from slip is added into the total strain of FRP, and thus the effective
mechanical strain (loading resistance) is reduced. To evaluate slip strain at various
temperatures, the amount of slip that occurs in each segment is to be calculated. For this a
bond-slip relation proposed by Sena Cruz and Barros (2004) is incorporated into the
numerical model, and is given by:
α

 s 
τ
= τ m ⋅   , s ≤ sm
 sm 

 s 
τ
= τm ⋅ 
 sm 

(5.17)

−α '

, s > sm

(5.18)

where, τ and s represent shear stress and corresponding slip developed at FRP-concrete
interface, and τm and sm are peak bond stress and corresponding slip, respectively. α and
α’ are parameters defining the shape of curves, and their values follow the data reported
by Sena Cruz and Barros (2004). τm and sm are a function of temperature, and the
177

variation of bond strength (τm) and corresponding slip (sm) of NSM FRP reinforcement
with temperature is plotted in Figure 5.3, which is obtained from high temperature bond

Bond stress (MPa)

test data presented in Chapter 3.
9
8
7
6
5
4
3
2
1
0

20°C
100°C
200°C
300°C
400°C

0

5

10
15
Slip (mm)

20

25

Figure 5.3 Bond stress-slip relations of NSM FRP strip at various temperatures
Equations for evaluating bond-slip in a segment can be derived by applying for
equilibrium at the FRP-concrete interface and can be written as:

τ i (t ) ⋅ ( PFRP ⋅ = (σ i +1 (t ) − σ i (t )) ⋅ ( AFRP )
Li )

(5.19)

where, σi(t) is the stress in FRP reinforcement for segment i at time step t, PFRP and
AFRP are perimeter and area of FRP reinforcement respectively, Li is the length of
segment i, the shear stress τi(t) is assumed to be uniformly distributed along the segment
length, and the average shear stress τi at the FRP-concrete interface can be calculated
using Eq. 5.19.

178

Knowing τi(t), the slip of FRP reinforcement at each time step can be evaluated as
given in Eqns. 5.17 and 5.18. Then the slip strain in FRP reinforcement can be obtained
as:

ε slip = s / Li

(5.20)

Epoxy adhesive
Concrete
τ

τ

τ

τ

AFRP· σi

τ

CFRP
rod(stips)
AFRP·(σi+1)

τ

Concrete

Figure 5.4 Force equilibrium at NSM FRP-concrete interface in the ith segment (vertical
view)
In addition to the slip at NSM FRP reinforcement, temperature inducted axial
restraint force also influences the behavior of NSM FRP strengthened RC beams. This is
mainly attributed to the fact that RC beams can experience considerable expansion when
exposed to severe temperatures. Generally beams in buildings are restrained by columns
or shear walls, and thus significant axial restraint force can develop at the supports under
fire conditions. This needs to be properly accounted in the numerical analysis. For this an
approach recommended by Dwaikat and Kodur (2008) used for predicting axial forces in
RC beam, is applied to determine fire induced axial restraint force in NSM FRP
strengthened beams.

179

The total axial restraint force (P) that develops in the beam can be calculated from
summation of compressive and tensile forces in each element of the beam (segment),
which is given as:
P = T + C = ∑ σ m Am

(5.21)

where, σm is stress at the center of each element, and Am is area of the corresponding
element. Since stress in each element can be computed using a given central total strain
and the curvature of beam, the axial force in each beam segment (Pi) can be related to the
corresponding central total strain (ε0i) and the curvature (κi) as follows:

Pi = φ (ε 0i , κ in )

(5.22)

In this numerical model, axial restraint force in each beam segments is assumed to
be constant at a given time step. At the beginning of each time step, the curvature in
beam segment, is equal to the curvature computed in the preceding time step (n-1), and
for a small increment in time step, the difference in curvature is usually very small. With
these assumptions, Eq. (5.22) can be expressed in terms of central total strain (εo) and
curvature (κ) for each beam segment i as

= φ (ε 0i , κ in ) ≈ φ (ε 0i , κ in −1 )
Pi

(5.23)

The total central strain in each segment is used to check the compatibility conditions, and
the value of axial force (P) is modified until compatibility and equilibrium conditions are
satisfied. The compatibility conditions along the span of the beam need to be satisfied to
the following conditions:

∑ li − L − ∆ = 0
180

(5.24)

where L is length of the beam, and Δ is total axial expansion in beam length. li is
projected length of deformed segment i, and it can be calculated as follows.

li=

( si )2 − ( win − win )2 ≈ ( si )2 − ( win −1 − win −1 )2
2
1
2
1

(5.25)

where si is the length of deformed segment i, win −1 and win −1 are deflections at the
2
1
th

beginning and the end of beam segment in the (n-1) time step, and win and win are
2
1
th

deflections at the beginning and the end of beam segment in the n time step, as
illustrated in Figure 5.5.
Since si = (1+ε0i) Li, Eq. 5.24 can be expressed as

∑

(1 + ε 0i )2 L2 − ( win −1 − win −1 )2 − L − ∆ = 0
i
2
1

(5.26)

To satisfy both force equilibrium and strain compatibility, the axial restraint force
(P) that develops in the fire exposed beam is calculated through the following iterative
procedure (Ahmed 2010):
•

n-1

Assume a value of 'P' (axial restraint force) for known value of curvature (κi

)

from preceding time step (n-1). In the first time step (at room temperature), P = 0.
•

Compute central total strain (εoi) in each segment i of beam.

•

Calculate axial displacement (Δ) for a known value of spring stiffness (k).

•

Check compatibility using Eq. (5.26)

•

Update axial force (P) until Eq. (5.26) is satisfied within a pre-determined
tolerance value.
181

Once the axial restraint force is computed through iterative procedure stated above, M-κ
relationships are to be generated for further structural analysis. Accounting for fire
induced axial restraint force is critical in fire resistance analysis of NSM FRP
strengthened RC beams.

th

th

(a) Deflected beam at the (n-1) and n time steps

(b) Typical beam segment
Figure 5.5 Illustration of axial restraint force calculations
182

5.2.4.3 Generation of moment-curvature (M-κ) relationships
After temperature induced slip and axial restraint force in the beam are calculated,
the M-κ relationships of each beam segment are generated through an approach
analogous to analysis of a prestressed concrete beam. The calculation starts with an
assumed value of strain at the top fiber of concrete (εc) and curvature (κ), and the total
strain (εt) in each element of concrete, FRP and rebar can be evaluated as:

ε= ε c + κ y
t

(5.24)

where εt is the total strain in any given element, εc is the strain at the top most fiber in
concrete, κ is the curvature, y is the distance from the top layer (concrete) to the center of
the given element. During fire exposure, a concrete member experiences strain due to
thermal, mechanical (loading) and creep effects. In concrete (element), the resulting total
strain is the sum of thermal, mechanical, transient and creep strains. However, in
reinforcing steel bars, the total strain is the sum of thermal, mechanical and creep strains.
In the case of NSM FRP reinforcement, the total strain is the sum of thermal, mechanical,
creep and slip strains. Thus, the mechanical strain in each element of concrete, FRP and
steel rebar is respectively evaluated as,

ε mec =ε tc − ε thc − ε crc − ε trc (in concrete)

(5.25)

ε mes =ε ts − ε ths − ε crs (in steel)

(5.26)

ε mef =ε tf − ε thf − ε crf − ε slip (in FRP)

(5.27)

where εtc, εthc, εmec, εcrc, εtrc represent total, thermal, mechanical, creep, and transient
strains respectively in concrete element; εts, εths, εmes, εcrs represent total, thermal,
183

mechanical, and creep strains respectively in steel rebar; and εtf, εthf, εmef, εcrf, εslip
represent total, thermal, mechanical, creep and slip strains respectively in FRP
reinforcement. The expressions and associated reference for evaluation of strain
components in constituent materials is tabulated in Table 5.1.
The above computed mechanical strains are utilized to obtain stress and force in
each element, utilizing relevant time-dependant stress-strain relations of concrete, steel
and FRP. These relations are given in Appendix A. An iterative procedure is applied to
evaluate the curvature and stress for a given (assumed) concrete strain (εc), till force
equilibrium and strain compatibility are satisfied, as shown in Figure 5.6. The moment
and curvature corresponding to that strain level are computed to represent one point on
M-κ curve. For each time step, various points on the M-κ curve are generated until
concrete strain at the top most fiber reaches its limiting (failure) strain. With these timedependant M-κ relationships, the structural behavior of NSM FRP strengthened beam can
be further traced through nonlinear beam analysis.

steel rebar in
compression

y
steel rebar
in tension

εc
εs'

σc

N.A.

εs
εf

Axis of zero
mechanical
strain

σs
σf

Cs
Cc
Tc
Ts
Tf

Ct= Cs+ Cc

T=Tf+Ts+Tc

Total strain diagram
C=T
NSM FRP
Internal forces
Force equilibrium
Cross section
Stress diagram

Figure 5.6 Force equilibrium and strain compatibility in an RC beam strengthened with
NSM FRP

184

5.2.4.4 Beam analysis
The M-κ relationships, slip in NSM FRP and axial restraint force generated for
various segments form the basis for tracing the response of NSM FRP strengthened beam
exposed to fire. With time-dependant M-κ relationships, the secant stiffness of each
segment can be determined based on the moment level reached in that particular segment,
and then nonlinear stiffness analysis is performed to evaluate the deflection response of
NSM FRP strengthened RC beam.
Each node in the idealized beam is assumed to have two degrees of freedom,
namely; rotation and vertical displacement. The deflection of the bam is calculated
through a stiffness approach and utilizing an iterative procedure described by Cambell
and Kodur (1990). The first step in this stiffness analysis is to apply a unit load to
determine the moment and corresponding curvature in each beam segment. The initial
stiffness (EI0), evaluated based on stiffness at elastic condition, is applied in this step as
shown in Figure 5.6. The segment with the maximum moment is selected as the critical
segment of the beam.
Then a target curvature in the key beam segment is selected on pre-generated M-κ
curve. Utilizing unit load analysis, a scaling factor is computed by dividing the target
curvature with unit load curvature in the key segment. The unit load curvatures in all
beam segments are scaled by this scaling factor. Based on scaled curvatures, the secant
rigidity can also be updated from segmental M-κ relationships. An iterative procedure,
illustrated in Figure 5.6, is employed until convergence of segmental secant stiffness is
achieved within certain tolerance. Once the tolerance is achieved, the above procedure is
repeated for next assumed target curvature (Dwaikat 2009, Ahmed 2010).
185

Table 5.1 Strain components in concrete, steel, and FRP
Material

Strain
Expression and reference (source)
component
effective strain for resisting external load
ε
mec

εthc

= [0.004(T 2 − 400) + 6(T − 20)] ×10−6 (Lie 1992)
ε thc

σ
ted (T − 293) (Harmathy 1993)
fc,T

ε crc = β1
εcrc

-6 -0.5

β1 =6.28×10 s

-3

-1

(constant) ,d =2.658×10 K (empirical

constant), T = current concrete temperature (K), t = time (s), fc,T =
concrete strength at temperature T, and σ = stress in the concrete

Concrete

∆ε tr k2
=

εtrc

σ

fc,20

∆ε th (Anderberg and Thelandersson 1976)

k2 = a constant that ranges between 1.8 and 2.35 (k2 = 2 in the
analysis), Δεth = change in thermal strain, Δεtr = change in transient

εmes
εths

strain, fc,20 = concrete strength at 20°C
effective strain for resisting external load

= [0.004(T 2 − 400) + 6(T − 20)] ×10−6 T < 1000°C (Lie 1992)
ε ths

ε crs
= (3Z ε t2 )1/3θ 1/3 + Zθ (Harmathy 1967)
0
4.7


6.755 ×1019 σ / f y
σ / f y ≤ 5 /12 

Z =

16 10.8(σ / f y )
) σ / f y > 5 /12 
1.23 ×10 (e



(

Steel

εcrs

)

θ = ∫ e−∆H / RT dt , ΔH/R=38900K, t = time (hours),

ε t 0 = 0.016(σ / f y )1.75 , σ = stress in steel as function of
εmef
εthf

temperature, and fy = yield strength of steel (room temperature).
effective strain for resisting external load

10 × −6
GFRP: ε thf =10 (T − 20) CFRP: 0
t

FRP

σ

0

kT

ε crf = ∫ Bσ 0.01e− H / kT sinh(
εcrf

εslip

)dt

B =×10−4 T 1.55 ⋅ t 0.25 T is FRP temperature (K), σ is the
2.03

stress in FRP (MPa), t is the fire exposure time (s), and k is
Boltzmann’s constant. H is the activation energy which follows the
reported experimental data
See section 5.2.4.2
186

After each iteration procedure, stiffness matrix and the loading vector are
computed for each longitudinal segment and assembled in the form of a nonlinear global
stiffness equation, and solved to compute deflections at that time step:
[ K g ] ⋅ [δ ] =
[ P]

(5.28)

where: Kg = global stiffness matrix, δ = nodal displacements.
P = Pf + Ps

(5.29)

where, Pf is equivalent load vector due to applied loading and Ps is equivalent nodal
vector due to P effect.
The effect of the second order moments, developed due to the axial restraint force,
is calculated using the following equation:
[ Ps ] = −[ K geo ][ P ]

(5.30)

where, [Kgeo] is geometric stiffness matrix, [δ] is nodal displacements, and [Ps] is
equivalent nodal load vector due to P-δ effect.
Various response parameters, including temperature and stress in rebar, mid-span
deflection, and moment capacity, generated from the program, are utilized to evaluate
failure of the beam at each time step. The time step at which failure of the beam is
attained is taken to be the fire resistance of the beam. The beam is said to attain failure
when any of the below limiting criterion is reached:
1. The moment due to applied service load exceeds the capacity of the beam (ASTM,
2012).

187

2. The deflection of the beam exceeds L/20 (where L is the length of beam) at any fire
exposure time (BS 476, 1987).
2

3. The rate of deflection exceeds the limiting deflection rate [L /9000d (mm/min), where
d is the effective depth of beam] (BS 476, 1987).

M

Second iteration

First
EI
iteration EI11 1 12
EI13
EI0
1
1 1
Curvature
normalization
M3
M2
M1
Target curvature
(a) Segments in idealized beam and bending moment diagram

k

(b) M-κ of beam segment

Figure 5.7 Illustration of curvature controlled iterative procedure for beam analysis

5.3 Computer Implementation
The macroscopic finite element model described in above is developed into an
executable computer program using FORTRAN language. In this section, input and
output data as well as material properties used in this program are discussed in detail.

5.3.1 Input data

188

The input data for this numerical program comprises of four components, namely,
geometric properties, material properties, fire and loading conditions, and analysis
options.
•

Geometric properties: mainly refer to elevation and cross-sectional dimension of
beam, locations of steel and FRP reinforcement, and layout and thickness of
insulation.

•

Material properties: include thermal and mechanical properties of constituent
materials, such as concrete, reinforcing steel, FRP, and insulation. The variation
of thermal and mechanical properties of these materials with temperature can be
input as a set of factors normalized to the room temperature values.

•

Fire, loading and boundary conditions: For fire exposure, user can select a
standard fire or design fire incorporated in the program, or define a specified
time-temperature curve. The available loading conditions include uniformly
distributed load and concentrated load (one-point or two-point loading) on the
beam. Two types of boundary conditions, simply supported and axially restrained,
can be applied to the beam. The axial restraint stiffness at beam support can be
defined based on specific boundary situations.

•

Analysis options: mainly used for controlling the convergence and accuracy of the
analysis. The available options include curvature increment, criteria of
convergence, and criteria of beam failure.
The sequential order of the input data must be followed in the input file.

Consistent SI units are used throughout the input file.

189

5.3.2 Output results
Thermal and structural response parameters of NSM FRP strengthened RC beam
are output at each time step. Thermal response parameters include cross sectional
temperatures in concrete, steel, and FRP. Structural response mainly includes momentcurvature relationship strength capacity, deflection, etc.
•

Thermal response: temperature in each element is output at each time step. In
addition, temperatures at critical locations, like reinforcing steel, FRP, center of
concrete, are output in separated files.

•

Moment-curvature relationship: M-κ relationships in each segment of beam are
output at various time steps.

•

Moment capacity and deflection: remaining moment capacity of the beam and
mid-span deflections at each time step are generated in output files. The program
automatically stops when the beam reaches failure limit. Thus the time of final
analysis step is taken as the fire resistance of beam.

•

Stress: the stresses in each steel and FRP reinforcement are generated at each
incremental time step. This information can be used to evaluate strength
contribution from steel and FRP reinforcement under fire exposure.
The output results are also in SI units, and each component of output results

(temperatures, strength capacity, etc) are stored in separated files for ease of data analysis.

5.3.3 Material properties
High temperature properties of constitutive materials have significant influence
on thermal and structural response of concrete member exposed to fire. For concrete,
190

high-temperature thermal and mechanical property relations as per Eurocode (2004) and
Lie (1992) provisions are incorporated in the numerical model, and user can select
appropriate properties according to specified concrete strength (normal strength or high
strength) and aggregate type (carbonate or siliceous). The spalling of concrete is not
specifically considered in this model, since FRP strengthening is generally applied on
concrete structures made of normal strength concrete (NSC), and fire induced spallling is
usually not a major concern in NSC beams (Kodur and Phan 2007).
For steel reinforcement, only high-temperature mechanical properties are
accounted for in the analysis. Relevant relations for temperature dependant stress-strain
curves for reinforcing steel, taken from Lie (1992) and Eurocode (2004) standards, is
built into the computer model. Thermal properties of steel rebar are not specifically
considered since they do not significantly affect temperature distribution within the beam
cross section (Lie and Irwin 1993, Kodur and Dwaikat 2008).
Since temperature in epoxy adhesive has critical influence on bond degradation of
NSM FRP, thermal properties of epoxy are incorporated into the numerical model. The
input values of thermal properties of epoxy are determined based on the data reported in
literatures (Chern et al. 2002, Shokralla and Al-Muaikel 2009, Kandare et al. 2010).
Temperature-dependant thermal properties of epoxy are provided in Appendix A.
For NSM FRP, it has been established that FRP follows a linear stress-strain
response both at room temperature (ACI 440.1 2006, FIB 40 2007) and at elevated
temperatures (Bisby 2003, Wang et. al 2007). Thus, temperature dependent stress-strain
response of FRP can be represented through a set of linear relationships. The peak value

191

(tensile strength) and slop (elastic modulus) of these linear relations are taken from the
test data generated in Chapter 3.
The temperature-dependant thermal properties of insulation are also built into the
numerical model. The relations for thermal conductivity and thermal capacity of fire
insulation follow the test data reported by Bisby (2003).
All the temperature dependant thermal and mechanical properties of constitutive
materials, including concrete, reinforcing steel, FRP, epoxy, and insulation, are presented
in Appendix A.

5.4 Validation of Numerical Model
The validity of the above model is established by comparing predictions from the
model with measured response parameters in experiments both at ambient and fire
conditions. The tested beams used in validation are selected from literature (Rasheed et al.
2010, Palmieri 2012) and from fire resistance tests carried out as part of this dissertation.
The response parameters covered in validation include load-displacement response at
ambient conditions, cross-sectional temperatures, mid-span deflections, and fire
resistance of beam. The detailed validation process is described below.

5.4.1 Response at ambient conditions
For room temperature validation, three RC beams (designated as Beam V1, V2
and V3) tested by Rasheed et. al (2010) were analyzed using the above developed model.
The selected beams are of 254×457 mm rectangular cross-section with an effective span
of 4.72 m. Each beam is divided into 40 segments, and the cross-section of each segment
192

is subdivided into 800 elements of 12×11 mm (similar to that in Figure 5.1). The main
flexural reinforcement in the beam comprise of four ϕ 19 mm steel rebars, while two ϕ 9
mm steel rebars form the compressive reinforcement. Beam V1 is a conventional RC
beam (no strengthening), Beam V2 is an RC beam strengthened with eight 16×2 mm
NSM CFRP strips (four grooves, two strips per groove), and Beam V3 is an RC beam
externally strengthened with CFRP laminates. Details of beam configuration and material
properties are shown in Table 5.2.

P
457
457

2360
2360

2360
2360

4880
4880

a. Beam layout

25

25
204
254
Beam V1

44 54 58 54 44
254
Beam V2

254x0.165
CFRP
laminates

457

16x2 CFRP
strips

457

4ϕ19mm

457

2ϕ13mm

254
Beam V3

b. Configuration
Figure 5.8 Configuration of tested beams for room temperature response validation (Units:
mm)

193

Table 5.2 Configuration and properties of RC beams used for validation
Property

Beams V1, V2, V3

Test condition

room temperature

Cross section (mm)

254×457

200×300

Span (m)
Load/moment
capacity ratio
fc' (MPa)
Tension
Steel Compression
rebar
fs (MPa)

4.72

3.0

monotonic

40%

34.5
4ϕ19 mm
2ϕ9 mm

40
2ϕ16 mm
2ϕ10 mm

576
V2: Eight 16×2
CFRP strips
V3: 254×0.165
CFRP laminates
V2: 2068 MPa
V3: 643 MPa

550
V4: 2ϕ12
GFRP bars
V5: 2ϕ9
CFRP bars
GFRP:1350 MPa
CFRP:1900 MPa
V4: Promatect H
V5: Aestuver

FRP

FRP type
(mm)
ff (MPa)

Insulation type

None

Beams V4, V5
ISO 834 standard
fire

Beams I, II, III & IV
ASTM E119
Flange: 432×127
Web: 228×279
3.66
I and II: 50%
III and IV: 65%
53
3ϕ19 mm
4ϕ13 mm
455
two 13.5×4.5 CFRP
strips
2510
Tyfo CFP system

· fc', fs, ff is the compressive strength of concrete, strength of steel, and strength of FRP,
respectively.
The three beams were analyzed under concentrated loading at mid-span, which
was same as in tests. Based on the results from analysis, the moment capacities of Beam
V1, Beam V2 and Beam V3, as predicted by the model, are 262, 391 and 400 kN-m,
respectively, which are slightly lower than the measured values reported in tests (271,
399 and 410 kN-m). The slight difference between predicted and measured strength
capacities is possibly due to the use of elasto-plastic stress-strain response for steel rebars,
which may be lower than actual steel strength in the tested beams.
The predicted and measured load-deflection response for all three beams is
compared in Figure 5.9. It can be seen that in the initial stages, all three beams exhibit a
194

linear response until cracking occurs in the beam (concrete). After that, the mid-span
deflection increases at a higher rate due to decreasing stiffness resulting from cracking in
the concrete beam. At this stage, the stresses in steel and FRP reinforcement increase at a
faster rate until the steel rebars yield, and this can be seen in Figure 5.9 through the
presence of another inflexion point on the load-deflection curve. In Beam V1, which is a
conventional RC beam, the moment capacity reaches its peak once the steel rebar enters
yielding plateau. However, in FRP strengthened beams (Beam V2 and Beam V3), the
moment capacity keeps increasing with increased stress in FRP strips or laminates until
the top concrete crushes.
In all three beams, the measured deflections at final stages are slightly higher than
predicted values, and this is probably due to the fact that confinement effect on concrete
is not considered in the model. Since Beam V2 and Beam V3 were designed to achieve
same moment capacity from strengthening, their load-deflection response is quite similar
under monotonic loading. It can be seen from Figure 5.9 that the overall load-deflection
curves generated from the numerical model match well with measured data from tests.
Thus, the above developed numerical model is deemed to be capable of predicting room
temperature response of RC beams strengthened with NSM FRP reinforcement.

195

350
300

Load (kN)

250
200

Beam V1 - Model
Beam V1 - Test
Beam V2 - Model
Beam V2 - Test
Beam V3 - Model
Beam V3 - Test

150
100
50
0

0

10

20

30
40
50
Displacement (mm)

60

70

Figure 5.9 Load-deflection response in RC beams under monotonic loading (ambient
condition)

5.4.2 Response under fire conditions - Rectangular beams
The validity of the above model in predicting fire response is established by
comparing predictions from the analysis with fire test data on two beams (designated as
Beam V4 and Beam V5) reported by Palmieri et al. (2012). The selected test beams are of
200×300 mm rectangular cross-section with an effective span of 3 m. The beam is
divided into 40 segments, and the cross-section of each segment is subdivided into 700
elements of 10×10 mm. A finer mesh is adopted in the vicinity of NSM FRP and
insulation area, as illustrated in Figure 5.1. The main flexural reinforcement in the beam
comprise of two ϕ 16 mm steel rebars as primary reinforcement, and two ϕ 10 mm steel
rebars as compression reinforcement. Two ϕ 12 GFRP rebars and two ϕ 9 CFRP rebars
are installed as part of NSM strengthening in Beams V4 and V5, respectively. The high
temperature properties of concrete and steel reinforcement follow the relations specified
196

in Eurocode 2 (2004). U-shaped fire protection boards are applied at the bottom surface
and on two side surfaces of both beams. The insulation thickness at beam soffit of Beams
V4 and V5 is 40 and 30 mm respectively and the insulation material is different from
each other. Details of the beam configuration, and properties of concrete, steel and FRP,
as reported from tests, are shown in Figure 5.10 and Table 5.2.

P

P

300

1000

1000

1000

3150

(a) Beam layout

2 ϕ 10

2 ϕ 10
270

15

2 ϕ 16

270

15

2 ϕ 16

30 120
40

120

200
200

Insulation

Beam V4

30
30

200
200

Insulation

Beam V5
(b) Configuration

Figure 5.10 Configuration of tested beams for fire condition response validation (Units:
mm)
The validation process involved comparison of predicted thermal and structural
response parameters from the analysis with measured values in fire tests. For thermal
197

response validation, the predicted FRP and steel rebar temperatures in Beam V4 are
compared with measured temperatures in the fire test in Figure 11(a). It can be seen that
the temperatures in both FRP and steel reinforcement remain low throughout the fire
exposure duration, and this is mainly due to protection from fire insulation. At about 35
minutes, a plateau can be seen on the measured temperatures in FRP, and this is
attributed to large heat consumption during the evaporation of free water in the
surrounding concrete (when concrete temperature reaches about 100ºC). However,
numerical model does not predict this plateau at around 100ºC, since the effect of
moisture in concrete is not fully captured in high temperature thermal properties of
concrete. The analysis predicted slightly unconservative temperatures as compared to
measured values (in 60 to 90 minutes range), and this variation might be due to
differences in high temperature thermal property relations of concrete and insulation used
in the analysis and the actual properties of these materials used in the tested beam. The
temperatures at other locations in concrete could not be compared since the authors did
not report measured concrete temperatures in tests (Palmieri et al. 2012). However, a
closer examination of predicted concrete temperatures from the model at various
locations indicates the expected trend – lower temperatures at further distances from the
fire exposed surface. Overall, the predicted temperature from analysis reasonably agrees
with measured cross-sectional temperature in the test. Similar temperature comparison
for Beam V5 indicates good agreement with measured temperatures.
To validate structural response, the mid-span deflection predicted by the analysis
is compared with measured deflections in fire tests for both beams (V4 and V5) in Figure
5.11 (b). It can be seen that both predicted and measured deflections increase at very slow
198

rate at the initial stage of fire exposure (up to 25 minutes), since FRP reinforcement has
little reduction in its strength and stiffness, mainly due to lower temperature in FRP. With
increase in fire exposure time, FRP and steel reinforcement experience relatively higher
degradation in their strength and modulus, and thus the mid-span deflections in beams
gradually increase as well. At about 90 minutes, the deflections in both beams increase at
a higher rate and this might be due to yielding of steel (rebar).
Beam V4 experienced a relatively larger deflection than that of Beam V5 in the
entire range of fire exposure, and this can be attributed to relatively lower stiffness and
strength provided by GFRP reinforcement in Beam V4, as compared to CFRP
reinforcement in Beam V5. Due to protection from U-shaped fire insulation, no FRP
debonding observed in these two beams during the fire exposure time. Overall, the
deflections predicted from the analysis agree reasonably well with the measured data
from tests throughout the fire exposure time. Therefore, the macroscopic finite element
model and the high-temperature constitutive relations in use are deemed appropriate for
evaluating fire performance of RC beams strengthened with NSM FRP reinforcement.

199

Rebar temperature (ºC)

700

FRP rebar temp.-Test
FRP rebar temp.- Analysis
Steel rebar temp. - Test
Steel rebar temp. - Analysis
Compression rebar - Analysis

600
500
400
300
200
100
0

0

15

30

45

60 75
Time (min)

90

105 120 135

(a) Rebar temperatures (Beam V4)

0

0

15

30

Time (min)
45 60 75

90 105 120 135

Deflection (mm)

-5
-10
-15
-20
-25
-30
-35

Deflection - Test V4
Deflection - Analysis V4
Deflection - Test V5
Deflection - Analysis V5

-40

(b) Mid-span deflection (Beams V4 and V5)
Figure 5.11 Comparison of predicted and measured temperatures and mid-span
deflections for Beams V4 and V5

5.4.3 Response under fire conditions – T-beams
Further validation of the numerical model was undertaken by comparing response
parameters against test data generated on NSM FRP strengthened T-beams as part of this
200

dissertation. Various thermal and structural response parameters, including crosssectional temperatures, mid-span deflections, and axial restraint forces, were compared
against the predictions from numerical model. In the analysis, the geometric and material
properties of NSM FRP strengthened RC beams were taken to be as those given in the
test program described in Chapter 4. Details on beam configuration and test conditions
are shown in Figure 5.12 and Table 5.3.

P

P

127
406 279
152

152
610

1219

3962

610

1219

(a) Beam layout

Clear cover
thickness
51

432
228

102

102
127

4 No. 4

Clear cover
thickness

406

3 No. 6

279

51

Two 13.5x4.5 25 51
NSM FRP strips

51 25
228

Insulation
thickness

(b) Configuration
Figure 5.12 Configuration of tested T-beams for fire response validation (Units: mm)
201

To illustrate the usefulness of numerical model on tracing thermal response,
predicted temperatures from numerical model are compared with measured temperatures
at various locations, including NSM FRP, steel rebars, and concrete at different depth.
Figure 5.13 plots a comparison of temperatures in steel rebar and NSM FRP for four
tested beams. It can be seen that in uninsulated beam (Beam I), the temperature
predictions in steel rebar match well with measured data throughout fire exposure
duration. Temperature predictions in NSM FRP are lower than measured values. This is
mainly attributed to the fact that burning of epoxy in Beam I leads to extremely high
temperatures in NSM FRP in fire test, and heat transfer model does not account for effect
of epoxy burning. However, since FRP lost most of strength beyond 800°C, this
unconservative temperature prediction does not affect structural analysis of FRP
strengthened RC beam.
In the case of insulated beams (Beams II to IV), there are some discrepancies
between predicted and measured temperatures in steel rebar and NSM FRP, as shown in
Figures 5.13(b)-(d). In fire tests, the measured cross-sectional temperatures in Beams III
and IV are slightly higher than those in Beam II, due to large number of cracks that
developed in these two beams resulting from higher load (stress) level. Numerical model
does not account for the effect of crack formation and widening in insulation to thermal
response, and thus gives identical temperature predictions in Beams II to IV, due to their
same configuration and fire exposure. However, these temperature discrepancies are
small, and temperatures in steel rebar and NSM FRP remain in a low range (below 400°C)
throughout fire exposure duration. Thus this discrepancy does not significantly cause
major different in predicted strength degradation in steel rebar or FRP.
202

1400

Corner rebar - Test
Middle rebar - Test
NSM FRP - Test

Temperature (°C)

1200

Corner rebar - Model
Middle rebar - Model
NSM FRP - Model

1000
800
600
400
200
0

0

30

60

90

120
150
Time (mins)

180

210

240

(a) Beam I
600

Corner rebar - Test
Middle rebar - Test
NSM FRP - Test

Temperature (°C)

500

Corner rebar - Model
Middle rebar - Model
NSM FRP - Model

400
300
200
100
0

0

30

60

90

120
150
Time (mins)

180

210

240

(b) Beam II
Figure 5.13 Comparison of predicted and measured temperatures in NSM FRP and steel
rebar for MSU beams

203

Figure 5.13 (cont’d)
600

Corner rebar - Test
Middle rebar - Test
NSM FRP - Test

Temperature (°C)

500

Corner rebar - Model
Middle rebar - Model
NSM FRP - Model

400
300
200
100
0

0

30

60

90

120
150
Time (mins)

180

210

240

(c) Beam III
1000

Corner rebar - Test
Corner rebar - Model
Middle rebar - Test
Middle rebar - Model
NSM FRP - Test
NSM FRP - Model

Temperature (°C)

800
600
400
200
0

0

30

60

90

120
150
Time (mins)

(d) Beam IV

204

180

210

240

To further validate thermal response, the predicted and measured temperatures at
various depth of concrete are compared in Figure 5.14. It can be seen in the early stage of
fire exposure, the measured concrete temperatures usually increase at a faster rate than
those from numerical analysis, especially for Beam I. This is mainly due to fast increase
of fire temperature in the early stage. In the insulated beams (Beams II-IV), concrete
temperatures remain in a low range (below 250°C) throughout fire exposure duration.
This infers that there is not much strength degradation in concrete. A closer examination
of plots shows that predicted and measured temperatures in concrete have some level of
discrepancy for three insulated beams. This is mainly attributed to different levels of
cracking in insulation and concrete resulting from different loading in these beams.
Overall temperature predictions at various locations of beam cross section reasonably
agree with temperature data obtained from fire tests.
500

1/4h from bottom - Test
1/4h from bottom - Model
1/2h from bottom - Test
1/2h from bottom - Model
3/4h from bottom - Test
3/4h from bottom - Model

Temperature (°C)

400
300
200
100
0

0

30

60

90

120
150
Time (mins)

180

210

240

(a) Beam I
Figure 5.14 Comparison of predicted and measured temperatures in concrete for MSU
beams
205

Figure 5.14 (cont’d)
250

1/4h from bottom - Test
1/4h from bottom - Model
1/2h from bottom - Test
1/2h from bottom - Model
3/4h from bottom - Test
3/4h from bottom - Model

Temperature (°C)

200
150
100
50
0

0

30

60

90

120
150
Time (mins)

180

210

240

180

210

240

(b) Beam II
250

1/4h from bottom - Test
1/4h from bottom - Model
1/2h from bottom - Test
1/2h from bottom - Model
3/4h from bottom - Test
3/4h from bottom - Model

Temperature (°C)

200
150
100
50
0

0

30

60

90

120
150
Time (mins)

(c) Beam III

206

Figure 5.14 (cont’d)
250

1/4h from bottom - Test
1/4h from bottom - Model
1/2h from bottom - Test
1/2h from bottom - Model
3/4h from bottom - Test
3/4h from bottom - Model

Temperature (°C)

200
150
100
50
0

0

30

60

90

120
150
Time (mins)

180

210

240

(d) Beam IV
A comparison of predicted and measured mid-span deflections of four NSM FRP
strengthened RC beams is plotted in Figure 5.15. In the case of uninsulated beam (Beam
I), the mid-span deflection increased in a higher rate from the beginning of fire exposure.
At 20 minutes, a small drop occurred in time-deflection curve of Beam I, which is
probably caused by the slip of NSM FRP strips. The numerical model is capable of
capturing this variation due to slip occuring in NSM FRP. Thereafter, the beam exhibited
increasing deflections due to strength/stiffness degradation in steel rebar and FRP,
however the beam did not fail for 210 minutes of fire exposure. Overall the deflection
response obtained from numerical model matches measured data in Beam I in most fire
exposure duration, and the predicted fire resistance also compares well with test data.
For the beams with fire insulation (Beams II-IV), the mid-span deflections
remained low throughout fire exposure duration, especially for Beam II. This is mainly
207

due to lower temperatures in steel rebar, NSM FRP and in concrete. Beams III and IV
were tested under a relatively higher loading (65%), and thus the deflections in these two
beams increased at a faster rate during at later stage of fire exposure (after 160 minutes).
Predicted deflections from numerical analysis are slightly smaller than those measured
from tests, and this is probably because the numerical model does not account for the
effect of crack widening in fire insulation. However, numerical model can properly
simulate the axial restraint effect to structural behavior of the beam. It can be seen in
Figure 5.15 that Beam III exhibits smaller deflections than those in Beam IV, and this is
mainly due to the fire induced axial force which develops counter acting moment and
thus reduces total moment on Beam III. Overall predicted deflections from the model
have a good agreement with measured values throughout fire duration.

0

0

30

60

Time (mins)
90
120

150

180

210

240

Deflection (mm)

-10
-20
-30
-40
-50

Beam I - Test
Beam I - Model
Beam II - Test
Beam II - Model
Beam III - Test
Beam III - Model
Beam IV - Test
Beam IV - Model

-60
Figure 5.15 Comparison of predicted and measured mid-span deflection in T-beams
The predicted axial restraint force is also compared with measured force in the
test, as shown in Figure 5.16. It can be seen that predicted axial restraint force reasonably
208

matches the data obtained from test. In the later stage of fire exposure (after 165 minutes),
the measured axial force starts to decrease. This is probably due to faster increase in
deflections after 165 minutes, and this might have caused slight detachment between
concrete beam and restraint devices. However, in the numerical model, the predicted
axial force keeps increasing due to thermal expansion of beam. Overall the axial restraint
force and its influence on structural response of FRP strengthened beam are well traced

Axial force (kN)

by the numerical model.
45
40
35
30
25
20
15
10
5
0

Axial force - Test
Axial force - Model

0

30

60

90 120 150
Time (mins)

180

210

240

Figure 5.16 Comparison of predicted and measured axial forces in T- beams

5.5 Summary
In this chapter, a macroscopic finite element model available in literature is
extended for evaluating fire response of NSM FRP strengthened RC beams. Fire
resistance analysis in the model is conducted through three stages, namely, fire growth,
thermal propagation and structural analysis. Various response parameters including cross
sectional temperature, moment capacity and deflection, can be evaluated. The model
209

accounts for various cross sections, high temperature properties of constituent materials,
as well as temperature induced bond-slip at NSM FRP/concrete interface.
The validity of this numerical model was established through comparing
predictions from the model with test data on NSM FRP strengthened RC beam at both
ambient and fire conditions. The comparison shows that predictions from numerical
model have a good agreement with the measured values from fire resistance tests. This
indicates that the developed macroscopic finite element model is capable of evaluating
the fire response NSM FRP strengthened RC beams under various fire, loading, and
boundary conditions. Therefore, this validated model can be further applied to undertake
parametric studies to quantify the critical factors governing the fire resistance of NSM
FRP strengthened RC beams.

210

CHAPTER 6

PARAMETRIC STUDIES
6.1 General
The fire response of FRP strengthened RC beams is influenced by a number of
factors. Many of these influencing factors are interdependent and this makes fire
resistance prediction quite complex. Thus the effect of these factors on fire response of
FRP strengthened RC beam needs to be quantified through parametric studies. In this
chapter, the numerical model validated in Chapter 5 is applied to evaluate the effect of
various factors influencing fire response of NSM FRP strengthened RC beams and
identify critical parameters. This is done through a set of parametric studies, wherein the
response of NSM FRP strengthened RC beam is evaluated by varying each parameter
over a wide range. The results from parametric studies can be utilized to develop design
guidelines on fire response of RC beams strengthened with NSM FRP reinforcement.
Details on procedure and results of parametric studies are discussed in the following
sections.

6.2 Critical Factors Influencing Fire Resistance
Critical factors influencing fire resistance of RC beams with external FRP
laminates or internal FRP rebars have been evaluated in previous studies (Ahmed and
Kodur 2010, Yu and Kodur 2013). However, there are no studies in the literature to
quantify the factors influencing on fire response of NSM FRP strengthened RC beams.
211

Previous studies on fire response of FRP strengthened RC beams indicate that
temperature-induced FRP degradation is a primary factor causing the failure of
strengthened beams under fire conditions. Thus the influence of FRP strengthening type,
NSM FRP locations, and reinforcement ratio of FRP to steel needs to be gauged. Further,
concrete strength, external loading and boundary conditions, and fire exposure have
critical influence on fire response, and they are also main factors to be investigated. In
addition, fire insulation can significantly enhance the behavior of FRP strengthened RC
beam under fire conditions. However, the thickness and layout of insulation have to be
optimized for performance and economy. Therefore, an optimal insulation scheme is also
developed for NSM FRP strengthened RC beams.

6.3 Parametric Studies
The influence of various parameters to fire response is evaluated through
numerical analysis on a typical NSM FRP strengthened RC beam in buildings. The
configuration, material properties, and boundary conditions of this beam are varied over a
wide range and thus the influence of each parameter to fire response can be evaluated.
Specific parameters in the study include FRP strengthening type, NSM FRP location,
reinforcement ratio of NSM FRP and steel, load level, axial restraint stiffness, concrete
strength, fire scenario, insulation layout. The details on the influence of each parameter
are presented in the following sections.

6.3.1 Beam configuration and parameters in study
A simply supported RC beam with NSM FRP, designated as Beam A, was
selected as the primary beam for parametric studies. This beam is of 254×457 mm
212

rectangular cross-section with a span length of 4.72 m. The primary reinforcement is
composed of four ϕ 19 mm steel rebars, while the compression reinforcement is two ϕ
12.7 mm steel rebars. Four 16×4 mm CFRP strips are used as NSM strengthening at
tension face of the beam. The beam is subjected to a uniform distributed load, which is
equivalent to 50% of the room temperature capacity of beam. In the analysis, the
configuration parameter and boundary conditions of this o beam were varied in a wide
range, and thus a number of beams were generated for parametric studies. The detailed
information on geometric and material properties is shown in Table 6.1 and Figure 6.1.
Table 6.1 Geometric and material properties of FRP strengthened RC beams
used in parametric study
Property
Cross-section (mm)
Span (m)
Magnitude
Loading
Load type
Aggregate

Values
254×457
4.72
70 kN/m, 50% load ratio
Uniformly distributed load
Carbonate

Concrete

fc’ (MPa)

34.5

Steel rebar

Cover thickness
Top rebar
Bottom rebar

25 mm
4 ϕ 19
2 ϕ 12.7

fy (MPa)

576

Dimension

Four 16 × 4 mm strips

fFRP (MPa)

2068

EFRP (GPa)

131

Groove size
Dimension

25 × 10 mm
254 × 0.165 mm laminates

fFRP (MPa)

634

EFRP (GPa)

46.4

NSM CFRP

External
CFRP

213

w

2ϕ13mm

457
457

4ϕ19mm

457

254

4880
4880

NSM FRP strips
Figure 6.1 Configuration and elevation of NSM FRP strengthened RC beam (Beam A)
for parametric study (Units: mm)
To quantify the influence of various factors to fire resistance of RC beams
strengthened with NSM FRP, eight groups of analysis were carried out using the
numerical model validated in Chapter 5. In each group of analysis, one parameter was
varied within a practical range, while all other properties were kept constant.
•

In Group 1 beams, the type of FRP strengthening was varied, and the fire
response of an RC beam under different configurations, namely, unstrengthened,
strengthened with externally bonded FRP, and strengthened with NSM FRP, was
compared under the same loading level. The amount of FRP strengthening was
selected such that the same level of moment capacity is achieved in different
strengthening arrangement.

•

In Group 2 beams, the location of NSM FRP was varied from corner of beam
soffit to middle, to demonstrate the influence of NSM reinforcement location on
fire response of the strengthened beams.

•

In Group 3 beams, the area of FRP strips or the strength of steel rebar was varied,
and thus the reinforcement ratio of steel rebar and FRP strips is different in each
beam. The purpose of this analysis is to quantify the influence of the
214

reinforcement ratio of FRP to steel on fire resistance of NSM FRP strengthened
RC beams.
•

In Group 4, the compressive strength of concrete was varied from 35 to 60 MPa,
to study the influence of concrete strength to fire response of NSM FRP
strengthened beams.

•

In Group 5, the load level on the strengthened beam was varied from 40-70% of
room temperature capacity, to quantify the influence of load level on fire
resistance of NSM FRP strengthened beams.

•

In the analysis of Group 6 beams, axial restraint at the supports of beam was
varied from zero to 200 kN/mm, to evaluate the influence of axial restraint on fire
response.

•

In Group 7 beams, the beams were exposed to four different fire scenarios to
study the response of NSM FRP strengthened RC beams under different fire
scenarios.

•

Finally in Group 8, NSM FRP strengthened RC beam (Beam A) was provided
with fire insulation, and the insulation thickness and its geometric layout were
varied to develop an optimum insulation scheme.
Detailed range for each parameter is tabulated in Table 6.2. The primary beam,

Beam A, in each group is also marked in the table.

6.3.2 Material properties
The range of properties of constituent materials used for parametric studies is
consistent with those used in field applications. At room temperature, the compressive
215

’

strength of concrete (fc ) is 34.5 MPa, and the yield strength of steel (fy) is 576 MPa. The
high temperature properties of concrete and steel rebar are assumed to vary as per ASCE
relations (Lie 1992). CFRP laminate (used in Beam I-2 as shown in Table 6.2) has a
strength of 634 MPa, and elastic modulus of 46.4 GPa; while CFRP strips used in NSM
strengthened beams has a strength of 2068 MPa, and elastic modulus of 131 GPa. The
high temperature tensile strength properties and bond strength properties of NSM CFRP
follow the empirical relations proposed in Chapter 3, and the variations of those
properties for external FRP laminates follow the empirical relations reported by Bisby et
al. (2005). For VG (Vermiculite-Gypsum) fire insulation, the temperature-dependant
thermal capacity and thermal conductivity are assumed to follow the properties reported
in the literature (Bisby 2003).
The detailed material properties for concrete, steel rebar, and NSM FRP are
tabulated in Table 6.1. Temperature-dependant property relations are provided in
Appendix A.

216

Table 6.2 Critical factors investigated in parametric study
Factor
FRP
strengthening
NSM FRP
location

Designation
Beam I-1

Variable
RC beam

Beam I-2

External CFRP strengthened RC beam

Beam I-3

NSM CFRP strengthened RC beam (Beam A)

Beam II-1

Uniformly distributed at beam soffit (Beam A)

Beam II-2

Close to corner at beam soffit

Beam II-3

At middle of beam soffit

Beam III-1
Reinforcement
ratio of FRP to Beam III-2
steel
Beam III-3
Concrete
strength

Load level

Axial restraint

Fire scenario

Insulation
layout

Beam IV-1
Beam IV-2
Beam IV-3
Beam V-1
Beam V-2
Beam V-3
Beam V-4
Beam VI-1
Beam VI-2
Beam VI-3
Beam VI-4
Beam VI-5
Beam VII-1
Beam VII-2
Beam VII-3
Beam VII-4
Beam VIII-1
Beam VIII-2
Beam VIII-3
Beam VIII-4
Beam VIII-5
Beam VIII-6
Beam VIII-7

4 ϕ 19 rebar and 4 16×4mm FRP strips
(fy = 576 MPa, ff = 2076 MPa) (Beam A)
4 ϕ 19 rebar and 4 16×4mm FRP strips
(fy = 461 MPa, ff = 2076 MPa)
4 ϕ 19 rebar and 4 16×2mm FRP strips
(fy = 576 MPa, ff = 2076 MPa)
fc’ = 34.5 MPa (Beam A)
fc’ = 50 MPa
fc’ = 60 MPa
Load is equivalent to 40% of room temperature capacity
Load is equivalent to 50% of room temperature capacity
(Beam A)
Load is equivalent to 60% of room temperature capacity
Load is equivalent to 70% of room temperature capacity
k = 0 (Beam A)
k = 5 kN/mm
k = 50 kN/mm
k = 100 kN/mm
k = 200 kN/mm
ASTM E119 (Beam A)
ASTM Hydrocarbon fire
Design fire I
Design fire II
No insulation (Beam A)
Insulation thickness = 15 mm, depth = 75 mm
Insulation thickness = 25 mm, depth = 75 mm
Insulation thickness = 35 mm, depth = 75 mm
Insulation thickness = 25 mm, depth = 50 mm
Insulation thickness = 25 mm, depth = 75 mm
Insulation thickness = 25 mm, depth = 100 mm
217

6.3.3 Discretization and analysis details
For numerical analysis, the beam is discretized into 40 segments along its length,
with smaller segments at critical regions moment such as mid-span and a smaller length
of segment is divided around mid-span, as depicted in Figure 6.2. The central section of
the segment, which is assumed to represent the behavior of each segment, is further
divided into number of elements. A finer mesh is applied in critical zones (steel rebar,
NSM FRP, and insulation) along the beam cross section to achieve better accuracy in the
numerical analysis. All beams have simply supported conditions and are loaded with
uniformly distributed load along the span. This applied load is equivalent to 50% of the
room temperature capacity of each beam, which is calculated as per ACI 318 (2011) and
ACI 440.2 (2008) provisions. The beams are exposed to ASTM E119 standard fire for
four hours till failure is attained. Cross-sectional temperatures, moment capacity and
deflections are output at each time step (five minutes) to evaluate fire response of FRP
strengthened RC beams.

6.3.4 Failure criteria
Based on the discussion in Chapter 5, three limiting criteria are applied to
evaluate the fire resistance of NSM FRP strengthened RC beam, namely moment
capacity, mid-span deflection, and rate of deflection. Steel rebar temperature limit is not
considered as one failure criteria, since NSM FRP might contribute to strength capacity
of the beam to some extent even at later stage of fire exposure. Also, this criteria is not
sensitive to the failure caused by load level and boundary conditions. Partial debonding
of NSM FRP or external FRP laminate does not define the failure of FRP strengthened
218

beams, since both literature review and experimental studies indicate the strengthened
beams still possess good load resistance after FRP debonding. Overall, the strength
capacity, deflection, and rate of deflection are the most realistic criteria for evaluating the
failure of NSM FRP strengthened beams under fire conditions.

w
NSM FRP
L/2

L/2

Fire exposure

(a) Original beam layout and cross section

w
1

2

3 4 5 --

NSM FRP

L/2

L/2

Finer
mesh
Fire exposure

(b) Discretization along beam length and cross section
Figure 6.2 Layout of NSM FRP strengthened RC beam and discretization along beam
length and cross section
6.4 Results of Parametric Studies
Results from fire resistance analyses are utilized to gauge the influence of critical
factors on fire response of NSM FRP strengthened RC beams. Various output parameters,
including temperature in steel rebar and FRP, deflection, moment capacity, and fire
resistance, are generated to quantify the influence of each factor. Table 6.3 provides a
comparison of results from parametric studies. Detailed analysis results for each factor
are discussed in the following sections.

219

Table 6.3 Summary of fire resistance values for the beams in parametric studies
Ratio of
2
3
4
Insulatio FR
LR Fire scenario
k
FRP to
Parameter
1
(%)
(kN/mm) n
(min)
steel
Beam I-1
0.81
50 ASTM E119
0
No
160
FRP
Beam I-2
0.81
50 ASTM E119
0
No
90
strengthening
Beam I-3
0.81
50 ASTM E119
0
No
110
Beam II-1
0.81
50 ASTM E119
0
No
110
NSM FRP
Beam II-2
0.81
50 ASTM E119
0
No
105
location
Beam II-3
0.81
50 ASTM E119
0
No
115
Beam III-1
50 ASTM E119
0
No
110
0.81
Ratio of FRP
Beam III-2
50 ASTM E119
0
No
80
1.01
to steel
Beam III-3
50 ASTM E119
0
No
135
0.41
Beam IV-1
0.81
50 ASTM E119
0
No
110
Concrete
Beam IV-2
0.81
50 ASTM E119
0
No
115
strength
Beam IV-3
0.81
50 ASTM E119
0
No
120
Beam V-1
0.81
0
No
140
40 ASTM E119
Load level
Beam V-2
0.81
0
No
110
50 ASTM E119
Beam V-3
0.81
0
No
95
60 ASTM E119
Beam V-4
0.81
ASTM E119
0
No
65
70
Beam VI-1
0.81
50 ASTM E119
No
110
0
Beam VI-2
0.81
50 ASTM E119
No
115
5
Axial
Beam VI-3
0.81
50 ASTM E119
No
125
50
Beam VI-4
0.81
50 ASTM E119
No
135
100
restraint
Beam VI-5
0.81
50 ASTM E119
No
140
200
Beam VII-1
0.81
50 ASTM E119
0
No
110
Beam VII-2
0.81
50 Hydrocarbon
0
No
75
Fire scenario
Beam VII-3
0.81
50 Design I
0
No
80
Beam VII-4
0.81
50 Design II
0
No
155
Beam VIII-1
0.81
50 ASTM E119
0
110
No
Insulation
Beam VIII-2
0.81
50 ASTM E119
0
190
15
thickness
Beam VIII-3
0.81
50 ASTM E119
0
235
25
(mm)
Beam VIII-4
0.81
50 ASTM E119
0
255
35
Beam VIII-5
0.81
50 ASTM E119
0
200
50
Insulation
depth
Beam VIII-6
0.81
50 ASTM E119
0
235
75
(mm)
Beam VIII-7
0.81
50 ASTM E119
0
250
100
1. Ratio of FRP to steel is the ratio of product of cross sectional area and tensile strength
of FRP to that of steel.
2. LR means load ratio.
3. Axial restraint stiffness
4. Fire resistance
Beam
designation

220

6.4.1 Effect of FRP strengthening
Three beams, designated as Beam I-1, Beam I-2 and Beam I-3, were analyzed for
evaluating comparative fire response of RC beam with different FRP strengthening.
Beam I-1 is a conventional RC beam with four ϕ 19 mm steel rebars as tensile
reinforcement, while Beams I-2 and I-3 are Beam I-1 strengthened with externally
bonded (EB) FRP laminates and NSM FRP strips respectively. Beams I-2 and I-3 are
designed to yield similar flexural capacity and based on the room-temperature analysis,
the nominal flexural capacities of Beams I-1, I-2 and I-3 are 246, 392, and 393 kN·m,
respectively. Elevation and configuration of three beams are shown in Figure 6.3.

w
457
457
4880
4880

25

25
204
254
Beam I-1

254x0.165
CFRP
laminates

457

4ϕ19mm

457

2ϕ13mm

254
Beam I-2

16x2
CFRP
strips

457

(a) Elevation

44 54 58 54 44
254
Beam I-3

(b) Cross section
Figure 6.3 RC beams analyzed for studying the effect of FRP strengthening (Unit: mm)
The thermal response of three beams (Beams I-1, I-2 and I-3) is compared in
Figure 6.4, by plotting steel and FRP reinforcement temperatures as a function of fire
221

exposure time. The temperature at the center of steel rebar and FRP strip and the average
temperature of FRP laminate are selected for comparison. It can be seen that the steel
rebar temperatures in Beams I-1 and I-3 are identical, since the rebars are located at the
same location and the concrete cover depth is identical. However, the temperature rise in
steel rebar in Beam I-2 is slower than those in Beams I-1 and I-3. This can be attributed
to the fact that FRP laminates slow down the heat transfer from fire zone to the bottom
surface of the beam due to relatively lower thermal conductivity of FRP laminate.
Temperatures in FRP reinforcement are significantly different in Beams I-2 and I3 during the entire fire exposure time, as plotted in Figure 6.4. In Beam I-2 (with
externally strengthened FRP), the temperature of FRP laminate increases at a faster rate
from the start of fire exposure, and reaches the critical temperature of CFRP (around
350ºC) in 13 minutes. This is due to direct exposure of FRP laminate to fire. In Beam I-3
(NSM FRP strengthened RC beam), the temperature rise in NSM FRP strip is at a much
lower rate than that of FRP laminate in Beam I-2, and this can be attributed to thermal
protection effect provided through concrete cover and near surface adhesive on FRP.
NSM FRP in Beam I-3 also reaches critical temperature in about 30 minutes of fire
exposure, and NSM strips retain more strength throughout fire exposure duration.
Therefore, the type of strengthening (external or NSM) influences the rate of temperature
rise in steel and FRP reinforcement under fire conditions.

222

1000

Temperature (°C)

800
600
Corner rebar - Beam I-1
Corner rebar - Beam I-2
Corner rebar - Beam I-3
FRP laminate (avg.) - Beam I-2
Corner FRP strip - Beam I-3
Middle FRP strip - Beam I-3

400
200
0

0

30

60

90
120
Time (mins)

150

180

Figure 6.4 Effect of FRP strengthening type on temperature rise in steel rebar and FRP
To illustrate the comparative structural response of these three beams with
different strengthening system, the variation of moment capacity with fire exposure time
is plotted in Figure 6.5. For the control beam (Beam I-1), there is no drop in the moment
capacity till about 55 minutes, and this is mainly due to the fact that there was no strength
loss in steel rebars since the temperature in rebar stays quite low (below 350ºC). At about
60 minutes, the temperature in corner steel rebar increases to about 400ºC and
consequently steel rebars start to lose some of their strength and elastic modulus
properties. Thereafter, the moment capacity in Beam I-1 decreases gradually till failure
occurs. For the RC beam with externally bonded FRP laminate (Beam I-2), the moment
capacity decreases drastically in initial stages of fire exposure, and this can be attributed
to significant drop in the strength of FRP laminates due to a faster rise in FRP
temperature, which reaches about 500°C at 15 minutes. At about 20 minutes, the
contribution of FRP to the strength of the beam ceases, and then this beam behaves
similar to that of control RC beam. As to NSM strengthened beam, Beams I-3 retains
223

much higher moment capacity than that of Beam I-2 during the entire fire exposure time.
The main reason for this higher moment capacity can be attributed to lower loss of
strength in NSM strips, which is due to slower temperature rise resulting from concrete
cover to NSM FRP strips. Also, the bond between NSM FRP strips and concrete remains
effective for a longer duration and thus NSM FRP strips continue to contribute to some
level of moment capacity till about two hours. Therefore, NSM strengthened beam
achieves higher fire resistance than that of externally strengthened beam.
450

Moment (kN-m)

400
350
300
250
200
150

Beam I-1
Beam I-2
Beam I-3

100
50
0

0

30

60

90
120
Time (mins)

150

180

Figure 6.5 Effect of FRP strengthening type on variation of moment capacity of RC
beams
To further illustrate the variation in structural response, mid-span deflection in
three beams is plotted as a function of fire exposure time in Figure 6.6. At the initial
stages of fire exposure, the resulting deflections in all three beams are similar, due to the
same level of loading and similar fire exposure conditions. After about 30 minutes,
Beams I-2 and I-3 experience deflections at an accelerated rate as compared to the control
beam (Beam I-1). This can be attributed to deteriorating stiffness in Beams I-2 and I-3
224

that results from decreasing elastic modulus in FRP reinforcement at elevated
temperature. After about 90 minutes into fire exposure, temperature in inner steel rebars
reaches about 400ºC and this induces higher degradation in strength and elastic modulus
of steel rebars (400ºC). This in turn results in significant rise in deflection in all three
beams until failure occurs. Overall, at the same load level (applied moment to capacity
ratio), the conventional RC beam (Beam I-1) exhibits the highest fire resistance (160
minutes), while the RC beam with externally bonded FRP (Beam I-2) exhibits the lowest
fire resistance of 95 minutes. The beam strengthened with NSM FRP strips (Beam I-3)
has a fire resistance of 110 minutes. Of the two FRP strengthened beams, NSM FRP
strengthened beam exhibits better structural response than the one with externally bonded
FRP.
Time (mins)
0

0

30

60

90

120

150

180

Deflection (mm)

-20
-40
-60
-80
-100

Beam I-1
Beam I-2
Beam I-3

-120
-140
Figure 6.6 Effect of FRP strengthening type on the variation of mid-span deflection of
RC beams

225

6.4.2 Effect of NSM FRP location
The strength degradation in NSM FRP reinforcement plays a critical role on fire
resistance of strengthened beams as seen from above analysis. Thus, the location of NSM
FRP rods or strips within beam cross-section is an important factor governing fire
response, since temperature rise in NSM FRP strip/rod depends on their locations. Three
NSM FRP strengthened RC beams, designated as Beam II-1, II-2, and II-3, were studied
as part of this parametric study. In Beam II-1, four FRP strips are evenly distributed at the
beam soffit. Beams II-2 and II-3 have the same amount of NSM FRP strips, but NSM
FRP strips are located around corner area at beam soffit in Beam II-2, and around middle
area at beam soffit in Beam II-3 respectively, as shown in Figure 6.7. Results from fire
resistance analysis on Beams II-1 to II-3 are used to illustrate the comparative fire
response of RC beams with NSM FRP at various locations.

w
457
457
4880
4880

44 54 58 54 44
254
Beam II-1

44

166 44
254
Beam II-2

16x2
CFRP
strips

457

16x2
CFRP
strips

457

16x2
CFRP
strips

457

(a) Elevation

98 58 98
254
Beam II-3

Figure 6.7 RC beams analyzed for studying the effect of NSM FRP location (Units: mm)
226

Temperature (°C)

1000
800
600
400
Beam II-2
NSM strip - corner position

200
0

NSM strip - inner position
Beam II-3
0

30

60

90
120
Time (mins)

150

180

Figure 6.8 Effect of FRP location on temperatures rise in FRP
The variation of temperatures in NSM FRP strips as a function of fire exposure
time is plotted in Figure 6.8. It can be seen the temperatures in NSM FRP are different
from one beam to another, and they are highly dependent on the location of FRP strips. In
Beam II-3, the temperature in NSM FRP strips increases at a slower rate than that in
Beam II-2, and this is mainly due to the location of FRP strip at middle of the beam soffit,
which is farther from fire-exposed side surfaces. The slower temperature rise in NSM
FRP strips in Beam II-3 helps to retain strength during fire exposure, and this leads to
higher fire resistance of NSM FRP strengthened beams. Therefore, the location of NSM
FRP affects fire response of NSM FRP strengthened beams. The temperature rise in steel
rebar is identical in all three beams, since the location of steel rebar remains the same.
The structural response of Beams II-1, II-2 and II-3 is shown in Figure 6.9, by
plotting the variation of their moment capacity as a function of fire exposure time. It can
be seen in Figure 6.9, the degradation of moment capacity in three beams is similar, and
the slight difference among these beams is attributed to different level of contribution
227

from NSM FRP strips. The beam with FRP strips at the center of beam soffit (Beam II-3)
is able to retain more strength in FRP, and thus attains higher moment capacity. This
difference in moment capacity produces 5-10 minutes variation of fire resistance. Beam
II-1 achieves fire resistance of 110 minutes, while Beams II-2 and II-3 yield fire
resistance of 105 and 115 minutes, respectively. Thus, besides satisfying the basic
requirement of spacing and groove size the location of NSM FRP strips should be placed
close to mid-portion of beam soffit for achieving higher fire resistance.
400
Beam II-1

Moment (kN-m)

350

Beam II-2

300

Beam II-3

250
200
150

0

30

60

90
120
Time (mins)

150

180

Figure 6.9 Effect of FRP location on the variation of moment capacity of NSM
strengthened RC beams

6.4.3 Effect of reinforcement ratio of FRP and steel rebar
The flexural strength in NSM FRP strengthened RC beams is provided by steel
rebars and NSM FRP reinforcement. Under fire conditions, since NSM FRP
reinforcement experiences much faster degradation in strength and stiffness properties,
steel rebars contribute to higher percentage of flexural capacity at higher temperatures.
228

Thus, reinforcement ratio of steel rebar to that of NSM FRP influences the fire resistance
of NSM FRP strengthened RC beams.
Since tensile strength and elastic modulus of NSM FRP and steel rebar are quite
different, a comparison of product of rebar area and tensile strength of NSM FRP and
steel rebar is a better measure to reflect the relative contribution of these two
reinforcement to flexural capacity. Thus, this parameter (product of rebar area and tensile
strength) was varied over a practical range in the analysis to study the influence of
reinforcement ratio of NSM FRP and steel rebar. As shown in Table 6.4, Beam III-1 is
reinforced with four ϕ 19 mm steel rebars and four 16 × 4 mm FRP strips, and tensile
strength of steel and FRP is 576 and 2068 MPa respectively. Beam III-2 has the same
size of steel rebars and FRP strips, but tensile strength of steel rebar is 461 MPa (80% of
576 MPa), so the reinforcement ratio of steel rebar is actually lower than Beam III-1.
Beam III-3 has the same tensile strength of steel and FRP, but the area of FRP strips is 16
× 2 mm, and thus the reinforcement ratio of steel rebar is higher than that of Beam III-1.
The characteristics of NSM FRP and steel rebar, and moment contribution of steel and
FRP for these three beams are compared in Table 6.4.

229

Table 6.4 Configuration and moment capacity contribution of NSM FRP
and steel rebar in Beams III 1-3
Ratio of product of area and strength
Beams
Beam
III-1
Beam
III-2
Beam
III-3

FRP
/steel

NSM FRP

Steel rebar

4 16×4mm
strips
ff =2068MPa
4 16×4mm
strips
ff =2068MPa
4 16×2mm
strips
ff =2068MPa

4 ϕ 19 mm
rebars
0.81
fy = 576 MPa
4 ϕ 19 mm
rebars
1.01
fy = 461 MPa
4 ϕ 19 mm
rebars
0.41
fy = 576 MPa

Room temperature
Fire
Moment
resistance
FRP
rebar
capacity
contribution contribution (mins)
(kN-m)
393

38.7%

61.3%

110

325

41.5%

58.5%

80

333

29.1%

70.9%

135

The above three beams were analyzed under the same level of applied loading,
(50% of room temperature moment capacity) to demonstrate the influence of FRP to steel
reinforcement ratio on fire resistance of NSM FRP strengthened RC beams. The thermal
response of three beams is identical, due to the same locations of steel rebar and FRP
strips. The structural response of these beams is compared in Figure 6.10, by plotting the
variation of moment capacity with fire exposure time. It can be seen in Figure 6.10 that
Beams III-2 and III-3 possess similar flexural moment capacity at ambient conditions.
However, under fire conditions, the moment capacity of Beam III-2 decreases much
faster than that of Beam III-3. This is mainly attributed to the fact that NSM FRP strips in
Beam III-2 lose strength rapidly. Therefore, the contribution of FRP strips to moment
capacity (41.5%) decreases significantly. While in Beam III-3, NSM FRP strips
contribute less percentage to moment capacity (29.1%). Even though FRP strips lose
most of strength, the major part of moment capacity, which is provided by steel rebars,
230

decreases at a very low pace. Analysis results indicate that Beam III-2 fails at 80 minutes
(fire resistance), while Beam III-3 fails at 135 minutes. Beam III-1 has a moderate
reinforcement ratio of FRP (38.7%), and thus fails at 110 minutes. Based on comparative
response of three beams, higher reinforcement ratio of NSM FRP leads to lower fire
resistance in NSM FRP strengthened RC beams.

Moment capacity (kN-m)

400
350
300
250
200
150

Beam III-1
Beam III-2
Beam III-3

100
50
0

0

30

60
90
Time (mins)

120

150

Figure 6.10 Effect of reinforcement ratio of FRP and steel rebar on the variation of
moment capacity of NSM strengthened RC beams

6.4.4 Effect of concrete compressive strength
The effect of concrete compressive strength on fire response of NSM FRP
strengthened RC beam is evaluated through fire resistance analysis on beams with
concrete strength ranging from 35-60 MPa. In the analysis, the temperature dependent
thermal and mechanical properties of concrete are assumed to follow those of normal
strength concrete as recommended in Eurocode 2 (2004). This study is limited to the

231

scope of normal strength concrete, so any fire induced spalling is not included in the
analysis. Therefore, thermal response of these beams is the same throughout fire exposure.
Figure 6.11 shows the effect of compressive strength of concrete on fire response
of NSM FRP strengthened RC beams, where variation of moment capacity is plotted
against fire exposure time. It can be seen that the room temperature capacity of
strengthened beams increases with the increase in concrete strength. This is due to the
fact that NSM FRP strengthened beams usually fail in compression zone, and higher
concrete strength helps in utilizing more strength of NSM FRP strips. However, at high
temperatures, the effect of concrete strength becomes minor, since high temperature
moment capacity of strengthened beams mainly depends on degradation of strength in
steel rebar and FRP strip. As mentioned earlier, thermal response of the beams is same.
Therefore, steel rebar and FRP strips retain the same strength and stiffness, the moment
capacity of these beams also deceases in a similarly pattern. Overall, the results from this
analysis indicate that compressive strength of concrete is not a critical factor influencing
fire response of NSM FRP strengthened RC beams.

Moment capacity (kN-m)

500
400
300
200

Concrete strength - 34.5MPa
Concrete strength - 50MPa
Concrete strength - 60MPa

100
0

0

30

60
Time (mins)

90

120

Figure 6.11 Effect of concrete compressive strength on the variation of moment capacity
of NSM strengthened RC beams
232

6.4.5 Effect of load level
The level of loading on RC beam can significantly influence the structural
behavior under fire conditions. Higher load level leads to quick degradation in flexural
capacity and stiffness of beam, and introduces larger deflection in beam. Also RC beams
can fail before strength limit state is reached, due to exceeding deflection limits. In this
section, numerical analysis was carried out on an NSM FRP strengthened RC beam under
40, 50, 60 and 70% load ratios, to study the influence of load level. The load ratio is
calculated as the ratio of bending moment due to applied load under fire conditions to
room temperature nominal capacity of the beam. The effect of load ratio on the fire
response of NSM FRP strengthened RC beam is illustrated in Figures 6.12.
Since material properties and heat transfer within beam cross-section are not
affected by load level, the thermal response of these beams remains identical. However,
load ratio significantly influences fire resistance of NSM FRP strengthened RC beam
based on strength capacity and deflection criteria. Overall the fire resistance decreases
with increasing load ratio. This can be attributed to the fact that beams at higher load
levels experience higher internal stresses, and this in turn leads to significant degradation
in strength and stiffness properties of constitutive materials. Therefore, the beams with
higher load ratios (more than 50%) experience much larger deflections, as shown in
Figure 6.12. Finally the beams fail under fire conditions due to reaching the moment
capacity limit.
Also, relatively higher load level produces large curvatures in the beam, and thus
NSM FRP reinforcement fails earlier than the beams under smaller loading. This also
accelerates the failure of NSM FRP strengthened beams under fire conditions. Thus, in
233

structural fire design of NSM FRP strengthened beams, the influence of loading level
needs to be accounted for, and load ratio under fire conditions should be limited to 50%.
Time (mins)

Deflection (mm)

0

0

30

60

90

120

150

-20
-40
-60
-80
-100
-120
-140

Load ratio - 40%
Load ratio - 50%
Load ratio - 60%
Load ratio - 70%

Figure 6.12 Effect of load level on the variation of mid-span deflections of NSM
strengthened RC beams

6.4.6 Effect of axial restraint
Reinforced concrete beams in buildings are generally subjected to some level of
axial restraint from adjoining frame members. The restraint can have significant influence
on fire response of RC beams (Dwaikat and Kodur 2008). Therefore, it is important to
account for the influence of axial restraint in evaluating fire resistance of NSM FRP
strengthened RC beam. To study this influence, a typical RC beam strengthened with
NSM FRP strips (Beam VI-1) is analyzed with different levels of axial restraint at the
beam ends. The axial restraint stiffness is varied over a range that covers typical
boundary conditions encountered in buildings. For instance, a stiffness of 5 kN/mm
represents the restraint provided by a typical beam column connection, while a stiffness
234

of 200 kN/mm represents the restraint provided by a shear wall (Dwaikat and Kodur
2008). In the analysis, the beam is exposed to ASTM E119 standard fire and subjected to
a uniformly distributed load, which corresponds to 50% of room temperature capacity.
Fire response of NSM FRP strengthened RC beams with axial restraint is
illustrated in Figure 6.13, by plotting mid-span deflection in beam as a function of fire
exposure time. It can be seen that the beam with larger axial restraint stiffness undergoes
smaller deflection under fire exposure, and also yields higher fire resistance. This high
fire resistance can be attributed to fire-induced axial forces that develop at the beam ends.
When exposed to fire, a concrete beam undergoes thermal expansion along the beam
length, and then an axial restraint forces (compression) get developed at the ends of the
beam. Since this fire induced axial force acts at the mid-depth of cross-section, which is
at a lower level than the location of neutral axis of beam, axial force will produce a
counter acting moment and the total moment applied on the beam is reduced, as
illustrated in Figure 6.14. Correspondingly, the deflection of beam also decreases, due to
fire induced axial force. Larger restraint stiffness produces larger axial force and larger
counter acting moment, and thus the deflection is even smaller and the fire resistance is
further enhanced.

235

0

0

30

Time (mins)
60
90

120

150

Deflection (mm)

-20
-40
-60
-80
-100
-120

k = 0 kN/mm
k = 5 kN/mm
k = 50 kN/mm
k = 100 kN/mm
k = 200 kN/mm

-140
Figure 6.13 Effect of axial restraint on the variation of mid-span deflections of NSM FRP
strengthened RC beams

w
k

k

w
Neutral axis locations of different
sections along the span
F

F

Figure 6.14 Illustration of axial restraint force under fire conditions
As shown in Figure 6.13, the mid-span deflections in different cases are quite
close at the initial stages of fire exposure, this is due to similar strength degradation in
FRP strips and steel rebars in each beam. After 45 minutes into fire exposure, the simply
supported beam (k = 0 kN/mm) experiences larger deflection, while the beams with axial
restraint undergo smaller deflections due to the effect of counter-moment. After 90
236

minutes, all beams start to experience accelerating deflections, due to significant strength
and stiffness loss in steel rebar. Analysis results indicate that the simply supported beam
achieves a fire resistance of 110 minutes, while the beams with axial restraint achieve
higher fire resistance by about 5-30 minutes, as shown in Figure 6.13.
The development of axial restraint force in beams with different levels of restraint
stiffness is plotted in Figure 6.15, as a function of fire exposure time. As expected, higher
axial restraint stiffness produces higher axial force throughout fire exposure duration. It
can be seen that at the initial stage of fire exposure, the axial forces increase at a faster
rate than that at later stages. This can be attributed to rapid thermal expansion along the
beam in the early stage. However, after 60 minutes into fire exposure, there is no major
increase in axial forces. This is mainly due to temperature induced degradation in
strength and stiffness of constituent materials (concrete, steel rebars and FRP strips), and
this in turn leads to decrease of beam stiffness. With the increase of mid-span deflections
(critical section) under fire conditions, the neutral axis of beam moves down and the
counter-moment generated from axial restraint also reduces. Therefore, the axial restraint
forces have marginal benefit at the later stages of fire exposure.

237

1200

k = 5 kN/mm
k = 50 kN/mm
k = 100 kN/mm
k = 200 kN/mm

Axial force (kN)

1000
800
600
400
200
0

0

30

60
90
Time (mins)

120

150

Figure 6.15 Variation of axial force in NSM FRP strengthened RC beams as a function of
fire exposure time
ACI 216.1 specifications (2007) also indicates that restrained concrete beams can
achieve higher fire resistance than that of unrestrained beams, yet the extent of influence
of restraint conditions is not fully quantified. The numerical studies herein quantify the
increase in fire resistance for strengthened RC beams under various levels of axial
restraint.

6.4.7 Effect of fire scenario
Previous fire resistance tests on RC beams strengthened with NSM FRP were
mainly evaluated under standard fire exposure, which may not represent the true response
of these beams under realistic fire conditions. Thus, an NSM strengthened RC beam was
analyzed under various fire exposure conditions to evaluate the effect of fire scenarios on
fire resistance. Figure 6.16 shows time-temperature curves for different fire scenarios
used in the analysis, which are ASTM E119 standard fire, ASTM hydrocarbon fire, and
238

two design (realistic) fires. The time-temperature relations of two design fires are
generated based on Eurocode 1 provisions (Eurocode 1 2002), and they represent a wide
range of compartment characteristics including fuel load and ventilation. Design fire I
represents a severe fire in a library or a storage room with sufficient ventilation and a
large amount of combustible material. The peak temperature is assumed to be 1250ºC,
and then the decay phase lasts for 200 minutes. Design fire II represents a typical fire in a
residential compartment. The NSM FRP strengthened beam in the analysis is unprotected
(no fire insulation), and it is subjected to a uniformly distributed load along the whole
span.
1400
1200
Temperature (ºC)

1000
800
600

ASTM E119
ASTM Hydrocarbon
Design fire I
Design fire II

400
200
0

0

30

60

90

120 150 180 210 240 270
Time (min)

Figure 6.16 Standard and design fire temperature curves used in parametric study
The comparative thermal response of RC beam under different fire scenarios is
shown in Figure 6.17, by plotting the temperature in corner FRP strips as a function of
fire exposure time. It can be seen that the temperature rise in FRP strips highly depends
on the type of fire exposure. After 60 minutes into fire, FRP strips under exposure to
hydrocarbon fire and Design fires I attain much higher temperature than that under
239

ASTM E119 fire and Design fire II, due to much higher severity of these two fires. FRP
temperature under ASTM Hydrocarbon fire keeps increasing during the entire of fire
exposure, while the one under Design fire I starts to decrease in the later stage of fire. For
Design fire I, once the decay phase starts, the heat propagation within beam ceases, and
thus the rise in rebar temperatures gradually stops and starts to decrease. However, under
Design fire I, FRP strips already went beyond 800ºC prior to the decay phase, which
infers that FRP strips lost most of its strength and stiffness before the start of the decay
phase.
1200

Temperature (°C)

1000
800
600
Corner strip - ASTM E119
Corner strip - ASTM Hydrocarbon
Corner strip - Design I
Corner strip - Design II

400
200
0

0

30

60

90
120
Time (mins)

150

180

Figure 6.17 Effect of fire exposure on temperature rise in corner FRP strip
To compare structural response of the above beams under different fire scenarios,
the variation of mid-span deflection with fire exposure time is plotted in Figure 6.18. The
mid-span deflections in hydrocarbon fire and Design fires I (severe fires) are similar, and
they experience much faster rise than the other two cases. This is mainly due to faster
degradation of strength and stiffness of steel rebar and FRP strips in these severe fires. It
can be seen that the strengthened beam achieves a fire resistance of about 75 minutes
240

under severe fire, and the failure is governed by strength limit criteria. However, under
moderate fire (Design fire II), the deflection rate of the beam is relatively small, and the
beam has in a low deflection for 120 minutes. This is mainly due to high retention of
beam stiffness resulting from relatively slower heat propagation within beam crosssection. These results indicate that NSM strengthened RC beams can achieve high fire
resistance of 150 minutes under moderate fire exposure conditions, even without any fire
insulation.

0

0

30

Time (mins)
60
90
120

150

180

Deflection (mm)

-20
-40
-60
-80
-100
-120
-140
-160
-180

ASTM Hydrocarbon fire
ASTM E119 fire
Design fire I
Design fire II

Figure 6.18 Effect of fire exposure on the variation of mid-span deflections in NSM FRP
strengthened RC beams

6.4.8 Effect of insulation layout
Results from the above analysis clearly indicate that NSM FRP strengthened RC
beam possess a relatively higher fire resistance than that of externally bonded FRP beams.
However, structural members in building might need to provide up to four hours of fire
resistance, depending on occupancy and impotence of the building. Thus fire insulation
241

has to be applied on NSM FRP strengthened RC beam. To develop optimum fire
insulation schemes, a parametric study was carried out on a typical NSM FRP
strengthened RC beam (Beam VIII-1) with various insulation schemes. The thermal
properties of fire insulation are assumed to follow those of VG insulation reported by
Bisby (2003) and included in the Appendix A.
When an RC beam is exposed to fire, temperature-induced strength and stiffness
degradation in FRP and steel reinforcement (tension) dominates the response of
strengthened beam. Thus, the best way to enhance fire performance is to provide
optimum fire protection on the bottom and side surfaces of the beam. Thus insulation
thickness and depth of insulation on side surfaces are the two most important parameters.
Two sets of analysis are carried out on Beam VIII-1 to study the effect of insulation (See
Figure 6.19). In the first set, the insulation thickness at the beam soffit and two sides
(Beam VIII-1) were varied from 15 to 35 mm, while the depth of insulation on two sides
of beam were kept constant at 75 mm (three times of concrete cover thickness). In the
second set, the depth of insulation on side surfaces was varied from 50 to 100 mm, and
the thickness of insulation on side and bottom surfaces of beam was kept constant at 25
mm. The detailed information on insulation layout is shown in Figure 6.19 and Table 6.5.
Table 6.5 Effect of insulation layout on fire response of NSM FRP strengthened beams
Factors in study
Uninsulated beam

Beams

Beam VIII-1
Beam VIII-2
Effect of insulation
Beam VIII-3
thickness
Beam VIII-4
Beam VIII-5
Effect of insulation
Beam VIII-6
depth
Beam VIII-7

Insulation
thickness (mm)
-15
25
35
25
25
25
242

Insulation
depth (mm)
-75
75
75
50
75
100

Fire resistance
(mins)
110
190
235
255
200
235
250

Beam
VIII-1

15

Beam
VIII-2

25

Beam
VIII-3

75
25

75
15

35

Beam
VIII-4

75
35

(a) Beams analyzed for evaluating the effect of insulation thickness

Beam
VIII-1

25
50
25

Beam
VIII-5

25
75
25

Beam
VIII-6

25
100

Beam
VIII-7

25

(b) Beams analyzed for evaluating the effect of insulation depth
Figure 6.19 RC beams analyzed for studying the effect of fire insulation scheme
The analysis indicates that steel rebars in the insulated beam remain lower than
400°C and do not lose strength in most fire duration. Thus the temperature in NSM FRP
has dominant influence on the fire response of the strengthened beam. Figure 6.20
illustrates the effect of insulation thickness on the temperature in corner NSM FRP strips.
The temperature rise is plotted against fire exposure time for four cases, one without any
insulation and the other three with varying insulation thickness at beam soffit. It can be
seen that the application of insulation significantly slows down the temperature rise in
NSM FRP strip, and this in turn leads to slower degradation of strength and stiffness in
NSM FRP strip. When the thickness of insulation increases from 15 to 25 mm, the
temperature in NSM FRP decreases significantly at any given fire exposure time. Even
after 4 hours of fire exposure, the temperature in NSM FRP remains below 600ºC. This
indicates for the most fire durations, NSM FRP possesses some level of strength and
243

contributes to moment capacity of beam. However, when the thickness of insulation
increases from 25 to 35 mm, there is no major advantage (rebar temperature or fire
resistance) from added insulation, since fire resistance of the insulated beam is almost
four hours of fire exposure and this is sufficient for meeting needed fire resistance in
buildings. This analysis infers that beyond an optimum insulation thickness, increasing
insulation thickness does not help in achieving any significant increase in fire resistance,
as indicated in Table 6.5. Therefore, for this type of fire insulation and beam
configuration, an optimum thickness of fire insulation is 25 mm.

Temperature (°C)

1000
800
600
400

No insulation
15mm thickness
25mm thickness
35mm thickness

200
0

0

30

60

90 120 150
Time (mins)

180

210

240

Figure 6.20 Effect of insulation thickness on temperature rise in NSM FRP strips
The above analysis was also applied to Beam VIII-1 by varying depth of
insulation on side surface (c) of the beam from 50 mm to 100 mm, and keeping the
insulation thickness constant at 25 mm. The variation of predicted temperatures in corner
NSM FRP strips are plotted in Figure 6.21. It can be seen that increasing depth of
insulation from 50 mm to 75 mm lowers corner FRP temperatures by about 80ºC (at 4
hours fire exposure), while further increasing in the depth of insulation to 100 mm does
not lower NSM FRP temperature significantly. This is because the 75 mm depth of
244

insulation is three times of concrete cover and it is high enough to decrease the heat
transfer from two sides of beam. Higher depth of insulation does not produce more
protective effect. From the point of view of structural response (see Table 6.5), the beam
with 75 mm depth of insulation on side surfaces achieved a fire resistance of 35 minutes
higher than the case of 50 mm depth of insulation. While beyond 150 mm, the increase in
fire resistance is marginal (only 15 minutes). Therefore, an optimum insulation scheme is
a U-shaped insulation which comprises of 25 mm insulation in thickness and 75 mm in
depth on two sides of beam. This analysis clearly illustrates usefulness of the numerical
model in developing an optimum insulation scheme for NSM FRP strengthened RC
beams.

Temperature (°C)

1000
800
600
400

No insulation
50mm depth
75mm depth
100mm depth

200
0

0

30

60

90 120 150 180 210 240
Time (mins)

Figure 6.21 Effect of insulation depth on temperature rise in NSM FRP strips

6.5 Summary
This chapter presents results of parametric studies on critical factors influencing
fire response of NSM FRP strengthened RC beams. Based on the analysis results, FRP
strengthening type, reinforcement ratio of steel and FRP, load level, axial restraint, fire
245

scenario, and insulation scheme have significant influence on the fire resistance of NSM
FRP strengthened RC beam. While NSM FRP location and concrete strength have
moderate influence on fire resistance. The results obtained in parametric studies helps to
develop design guidelines for fire resistance of NSM FRP strengthened RC beams.
However, since geometric and material properties of FRP strengthened RC beams vary in
a wide range, a simple and reliable design approach is needed to access fire resistance of
various NSM FRP strengthened RC beams. Development and verification of such design
methodology are presented in Chapter 7.

246

CHAPTER 7

RATIONAL DESIGN METHODOLOGY
7.1 General
As discussed in Chapter 2, there are only limited design guidelines on fire design
of FRP strengthened RC members. These design guidelines recommend neglecting the
contribution of FRP to capacity under fire conditions (ACI 440.2 2008, FIB Bulletin 14
2007). However, results from previous studies clearly indicate this assumption to be over
conservative, especially for NSM FRP strengthened RC beams and beams protected with
fire insulation. Thus, rational design methodology is needed for evaluating fire response
of FRP strengthened RC beams.
To overcome this drawback, a simplified approach is developed for predicting the
fire response of FRP strengthened RC beams. This approach is derived by applying
current fire design approach for RC beams but incorporating the effect of FRP and fire
insulation in fire resistance calculations. The proposed approach comprises of two main
steps, namely; evaluating temperatures in concrete, FRP, and steel rebar of strengthened
RC beams, and calculating moment capacity of FRP strengthened RC beam at a given
fire exposure time. Simplified equations are developed for evaluating temperatures in
concrete, steel rebar, and FRP reinforcement (NSM or EBR) and then procedure for
calculating moment capacity of FRP strengthened RC beams is outlined.
The validity of the proposed simplified approach is established by comparing
predicted fire response parameters with those obtained from fire resistance tests and
247

detailed numerical studies. The applicability of this approach is also illustrated through
practical design examples.

7.2 Simplified Approach for Predicting Temperatures in RC Members
Fire resistance of FRP strengthened RC beams is mainly influenced by
temperature-induced strength degradation in FRP, steel rebar, and concrete. Thus,
accurate estimation on cross-sectional temperature is a key step in evaluating fire
response of FRP strengthened RC beams.
For an FRP strengthened RC beam without any external fire insulation,
temperature progression within the beam cross-section can be taken to be very much
similar to that of original RC beam, since the amount of FRP (either NSM FRP or
external FRP) is too small to influence heat transfer in an RC member. However, in an
FRP strengthened RC beam with fire insulation, temperature progression in concrete,
steel and FRP reinforcement is significantly reduced by insulation layer, and thus crosssectional temperatures within concrete beam are much lower than those of an uninsulated
beam. Therefore, separate equations are needed for evaluating temperatures in
uninsulated and insulated beam respectively. Detailed procedure for developing these
simplified equations is presented in this section.

7.2.1 An approach for predicting temperature in an uninsulated RC member
7.2.1.1 General
For predicting temperature in a fire exposed RC member, a number of design
graphs and charts are available in codes and standards (ACI 216 2007, Eurocode 2 2004).
248

However, these graphs usually provide very conservative temperature predications, as
these are developed based on standard fire test data or results of analysis on specific types
of concrete (Kodur et al. 2013). Also, in both ACI 216.1 and Eurocode 2, the temperature
profiles are provided in time intervals of 0.5 hour or 1 hour, so an interpolation is
required for evaluating temperature at other time intervals, which might increase
inaccuracy of temperature predictions.
A review of literature indicates that there are few simplified expressions for
evaluating the cross-sectional temperature in an RC member as a function of depth and
fire exposure time (Hertz, K. 1981, Wickstrom 1986). The most notable of these
simplified temperature expressions is the empirical relation proposed by Wickstrom, for
normal-weight aggregate concretes (Wickstrom 1986). According to Wickstrom’s
method, the temperature (Tc) in an RC member (slab) exposed to fire from one side at a
given depth x (in meters) and time th (in hours) can be calculated as:
Tc = η x ⋅η w ⋅ T f

(7.1)

ηx
= 0.18ln(th / x 2 ) − 0.81

(7.2)

η w = 1 − 0.0616th −0.88

(7.3)

In Eqns. 7.1-7.3, ηw is the ratio between concrete surface temperature and the fire
temperature, ηx is the heat transfer factor induced through one fire-exposed surface, and
Tf is the fire temperature. For obtaining temperatures at corner locations of a structural
member, the heat conduction occurring in two directions (x and y) is to be accounted for

249

through ηx and ηy, in which ηy is calculated similar to ηx in Eq. 7.2. The temperature Tc
resulting from fire exposure from both x and y directions is
= [η w (η x + η y − 2η xη y ) + η xη y ]T f
Tc

(7.4)

where, ηx and ηy are the heat transfer factors induced by each side of fire exposure.
Wickstrom’s empirical equation provides only a rough estimation of cross-sectional
temperatures, since it does not account for different growth rates of fire temperatures
(Buchanan 2002). Also, this equation does not include the influence of aggregate type
(siliceous or carbonate), newer concrete types (high strength concrete) and variation of
thermal properties with temperature, and hence may not be applicable for different
concrete types (Kodur et al. 2013). Therefore, there is a need for simple and reliable
approach for evaluating cross-sectional temperatures in a fire-exposed RC member.
Unlike the case of steel structural members, the temperature profiles in RC
members have a large spatial variation within the cross section. This makes it quite
complex to derive a simplified expression for temperatures formula based on heat transfer
principles. Developing an expression based on nonlinear regression analysis on a
database of cross-sectional temperatures is a more feasible approach, and the procedure
of developing such expression is outlined below.

7.2.1.2 Generation of temperature data for regression analysis
The simplified equations for predicting temperatures in an RC member are
developed through a nonlinear regression analysis on a large database generated using
finite element analysis (FEA). To generate temperature data for regression analysis,
250

twenty representative RC beams are analyzed using the finite element program described
in Chapter 5. Since temperature rise in fire-exposed RC members is mainly influenced by
cross-sectional geometry, concrete strength, aggregate type and fire exposure conditions
(Thomas and Webster 1953, Ali et al. 1996, Kodur et al. 2004), selected RC beams are
varied over a wide range and the ranges of these parameters are tabulated in Table 7.1.
As shown in Table 7.1, the width of beam section was varied from 200 to 500mm,
while the depth was varied from 400 to 700mm, thus giving a width to depth ratio
ranging from 0.4 to 0.8. The twenty beams were classified into four groups, Group I to
Group IV, to account for the effect of different concrete types. Group I and Group III
were assumed to be made of normal strength concrete (NSC), while Group II and IV
were assumed to be made of high strength concrete (HSC). Further, Group I and II were
of carbonate aggregate (CA) concrete, while Group III and IV were of siliceous aggregate
concrete (SA). Temperature dependant thermal conductivity and thermal capacity of
these concretes vary according to the relations given in ASCE manual (Lie 1992) or by
Kodur et al. (2008). In the FEA, each beam was exposed to ASTM E119 fire exposure
from three sides for 4 hours, and the cross-sectional temperatures at 30 locations were
recorded at various time intervals. In total, 1200 temperature data points with
corresponding time and location information (5×30×8) were generated for each group of
beams.

251

Table 7.1 Characteristics of RC members for regression analysis
Group

I

II

III

IV

Cross-sectional dimensions
Concrete
Aggregate
Strength
Dimension of beam(mm) b/h
200×500
0.4
300×400
0.75
NSC
Carbonate
300×500
0.6
300×700
0.43
400×500
0.8
200×500
0.4
300×400
0.75
HSC
Carbonate
300×500
0.6
300×700
0.43
400×500
0.8
200×500
0.4
300×400
0.75
NSC
Siliceous
300×500
0.6
300×700
0.43
400×500
0.8
200×500
0.4
300×400
0.75
HSC
Siliceous
300×500
0.6
300×700
0.43
400×500
0.8

7.2.1.3 Cross section division for 1-D and 2-D heat transfer area
Due to the complexity associated with 3D heat transfer analysis, and variation of
thermal properties of concrete with temperature, the cross-sectional temperatures are
often evaluated based on 1-dimensional (slabs) or 2-dimensional (beams or columns) heat
transfer analysis. However, there is no specific criteria for categorizing 1-D or 2-D heat
transfer area division within a concrete member.
A parametric study was conducted to investigate the relationship between
temperatures and distance from each fire-exposed beam surface individually. Figure 7.1
illustrates the variation of cross-sectional temperatures with depth to the bottom (y) at
252

different fire exposure times. It can be seen that at a given width (z), the cross-sectional
temperature decreases dramatically with increasing depth (y) up to the mid-depth of the
section (h/2). Beyond half of beam depth (y/h>0.5), the temperatures barely increase with
y and almost remain constant. This means the heat transfer from the bottom mainly
influences the temperatures in the lower half of the beam, but has little effect on the
temperatures in the upper half of the beam. In the horizontal direction (z), the temperature
deceases with the distance from the surface (z) significantly until z/b approaches to 0.5,
as shown in Figure 7.2. This indicates the heat transfer from the surface of fire exposure
mostly influences temperature in half of depth or width of the beam till three or four
hours of fire exposure.
700

z=37.5mm
z=67.5mm
z=97.5mm
z=127.5mm
z=150mm

Temperature(°C)

600
500
400

Y

300

Fire

200

Z

100
0

0.00

0.25

0.50
y/h

0.75

1.00

(a) 1.5 hours
Figure 7.1 Variation of temperature with depth from the bottom of an RC beam at various
times (section 300×500mm)

253

Figure 7.1 (cont’d)
900

z=37.5mm
z=67.5mm
z=97.5mm
z=127.5mm
z=150mm

Temperature(°C)

800
700
600

Y

500
Fire

400

Z

300
200

0.00

0.25

0.50
y/h

0.75

1.00

(b) 3 hours

800

y=462.5mm
y=312.5mm
y=162.5mm
y=127.5mm
y=82.5mm
y=37.5mm

Temperature(°C)

700
600
500
400
300

Y
Fire
Z

200
100
0

0.1

0.2

0.3
z/b

0.4

0.5

(a) 1.5 hours
Figure 7.2 Variation of temperature with distance from the side surface of an RC beam at
various times (section 300×500mm)
254

Figure 7.2 (cont’d)
1000

y=462.5mm
y=312.5mm
y=162.5mm
y=127.5mm
y=82.5mm
y=37.5mm

Temperature(°C)

900
800
700
600

Y
Fire

500

Z

400
300
200

0.1

0.2

0.3
z/b

0.4

0.5

(b) 3 hours
Thermal analysis was carried out on all RC beams listed in Table 7.1. It is found
that for beams with width ranging from 200 to 500mm and the depth ranging from 400 to
700mm, cross-sectional temperature is dominated by the distance (depth and width) from
the fire exposed surfaces, but barely influenced by z/b and y/h ratio. Based on the
influencing area of each fire exposure side, the division criteria for different heat transfer
areas in these beams can be given as follows: for the portion of the section where z/b<0.5
and y/h<0.5, 2-D heat transfer occurs, since the resulting temperature is the effect of heat
transfer from the bottom and side surfaces. For the portion of the section where z/b<0.5
and y/h>0.5, 1-D heat transfer occurs since the resulting temperature is affected by heat
transfer from one side. The section within z/b>0.5, can also be divided into 1-D and 2-D
heat transfer area according to the symmetry of geometry and fire-exposure, as shown in
Figure 7.3. Similarly, by considering the fire exposure conditions and section properties,
the columns, slabs and walls could also be divided into 1-D and 2-D heat transfer areas
255

for temperature calculation, as shown in Figure 7.3. For concrete members with width (or
depth) smaller than 200mm, the above criteria may not be applicable, since the crosssectional temperatures of these members is influenced by heat transfer from multiple fire
exposed surfaces.

Y

1D Heat 1D Heat
Transfer Transfer

Y

2D Heat 2D Heat
Transfer Transfer

2D Heat
Transfer
2D Heat
Transfer

2D Heat
Transfer
2D Heat
Transfer

Y
1D Heat
Transfer

Slab/Wall
Z
(1-side fire exposure)
Column(4-side fire exposure)
Beam(3-side fire exposure)
Z

Figure 7.3 Cross section idealization for heat transfer analysis in concrete members
exposed to different fire conditions

7.2.1.4 Nonlinear regression analysis
A nonlinear regression analysis on temperature data with corresponding fireexposed time and cross-sectional locations was carried out using “solver” function in
Microsoft Excel (2010). The “solver” function is able to calculate the optimum
coefficients to match the original data with a given format of formula and applied
“constraint” criteria. The extent of “optimum”, which is the error between the predictions
and original data, highly depends on the format of formula and constraint criteria.
256

Therefore, the basic format of the equations and constraint criteria were to be developed
first before undertaking regression analysis.
Based on trial analysis and sensitivity studies, the general format of the
temperature equation subjected to regression is deduced by applying similar analogy to
the temperature equation proposed by Wickstrom (1986). The equation for temperatures
controlled by 1-D heat transfer can be expressed as:

Tc = c1 ⋅η z ⋅ (at n )

η z = a1 ⋅ ln

t

1.5

z

+ a2 ⋅ z + a3

(7.5)
(7.6)

where, Tz is the temperature resulting from 1-D heat transfer in °C, ηz is the heat transfer
factor induced through one fire-exposed surface, c1 is the coefficients to account for
concrete type, t is the fire exposure time in hours, z is the distance from the point in
concrete section to fire exposure surface in meters, a1, a2 and a3 are the coefficients to be
n

traced in the regression analysis. at is the temperature under standard fire exposure
(Dwaikat and Kodur 2013). For ISO 834 fire, a = 935 and n = 0.168, and for ASTM
E119 fire, a = 910 and n = 0.148.
For 2-D heat transfer, the temperature equation is obtained by combining the heat from
each side of fire exposure:
Tc = c2 ⋅ (b1 ⋅ (η z ⋅η y ) + b2 ⋅ (η z + η y ) + b3 )(at n )

(7.7)

where, Tyz is the temperature resulting from 2-D heat transfer in °C, c2 are the
coefficients to account for concrete type, ηz and ηy are the heat transfer factors resulting
257

from y and z side fire exposure, ηy is calculated in the same manner as that of ηz in Eq.
7.2. b1, b2 and b3 are the coefficients to be traced in the regression analysis. The default
value of c1 and c2 is 1.0 for normal strength carbonate aggregate concrete. In the
regression analysis, the regression on Eq. 7.1 was carried out at first to find the value of
a1, a2 and a3, and then these obtained values were used to get b1, b2 and b3 for 2-D heat
transfer formula.
In reality, the regression analysis can hardly match all the data points closely.
Therefore, it is necessary to fit the data points in the critical range with the smallest
discrepancy, and that have reasonable match in other regions using “constraint” criteria.
It is well established that the compressive strength of concrete and yield strength of
reinforcing steel are not influenced up to 300°C, and that these strengths become
negligible after reaching 800°C (ACI 216 2007, Eurocode 2 2004). Therefore, the
regression result has to be highly reliable or slightly conservative in temperature-sensitive
zone of 300-800°C. Further, the regression results in 20-300°C could be set as a
secondary target since the variation in this temperature range does not significantly
influence the strength of concrete and steel reinforcement. To achieve this objective, the
following constraint criteria were applied in the regression analysis:
a.

When temperature is in 300-800°C range, the average of errors between temperatures
by FEA and predicted temperatures by regression equations should be controlled
within 10%.

b.

For temperature higher than 800°C, predicted temperature using regression equations
should not be smaller than those from FEA.
258

c.

For temperature in 100-300°C, the average of errors between temperatures by FEA
and predicted temperatures by regression equations should be controlled within 15%.

d.

For temperature from FEA smaller than 100°C, predicted temperatures by regression
equations should not be lower than those from FEA by more than 50°C. When
predicted temperature is lower than 20°C, it is taken as 20°C.

With the above developed equations and constrains, a regression analysis was conducted
for 1-D and 2-D heat transfer equations for each types of concrete. The final formulae
used for calculating temperature at a given point in an RC member are obtained as
follows.
For 1-D heat transfer: Tc = c1 ⋅η z ⋅ (at n )
where, η z 0.155ln
=

t

z1.5

− 0.348 z − 0.371

(7.8)
(7.9)

For 2-D heat transfer: Tc = c2 ⋅ (−1.481 ⋅ (η z ⋅η y ) + 0.985 ⋅ (η z + η y ) + 0.017)(at n ) (7.10)
where c1 are 1.0, 1.01, 1.12 and 1.12 for NSC-CA, HSC-CA, NSC-SA and HSC-SA,
respectively; c2 are 1.0, 1.06, 1.12 and 1.20 for NSC-CA, HSC-CA, NSC-SA and HSCSA, respectively.

7.2.1.5 Regression analysis results
The temperature predictions from proposed equations (Eqns. 7.8 and 7.10) are
compared with the regression data obtained from detailed finite element analysis. These
comparisons are plotted in Figure 7.4 for 4 RC groups of beams made of NSC-CA, HSCCA, NSC-SA and HSC-SA. In these figures, a point below “-10% margin” line indicate
259

that the predicted temperature from equations is to be higher than that obtained in FEA
by more than 10%. If a point lies above “+10% margin” line, the predicted temperature
from equations is smaller than that obtained in FEA by more than 10%. It can be seen
that for all four concrete types, most data points lie within ±10% margin zone, especially
for temperatures higher than 300°C. Therefore, the proposed equations are capable of
predicting cross-sectional temperatures of RC members exposed to standard fire to a
good degree. It is noted that there are a few points in the zone above “+10% margin” line,
indicating unconservative temperature predictions. These points correspond to sections
with smaller width (200×500 mm) and this inaccuracy could be attributed to the fact
those cross-sectional temperatures result from heat transfer from three fire-exposed
surfaces due to the smaller width, while the proposed formulas account for heat transfer

800

+10% margin

600
400
-10% margin

200
0

0

200 400 600 800
Predicted temperature(°C)

Temperature from FEA (°C)

Temperature from FEA(°C)

from one or two fire-exposed sides, which is true in most practical situations.

(a) 1-D heat transfer (NSC-CA)

+10% margin

800
600
400

-10% margin

200
0

0

200 400 600 800
Predicted temperature(°C)
(b) 2-D heat transfer (NSC-CA)

Figure 7.4 Comparison of predicted temperatures from the proposed equations with those
from FEA

260

800

+10% margin

600
400
-10% margin

200
0

0

Temperature from FEA (°C)

Temperatire from FEA (°C)

Figure 7. 4 (cont’d)
800
600
400

0

200 400 600 800
Predicted temperature(°C)

600
400
-10% margin

200
0

0

200 400 600 800
Predicted temperature (°C)

0

200 400 600 800
Predicted temperature (°C)

(d) 2-D heat transfer (HSC-CA)

1000
Temperature from FEA (°C)

Temperature from FEA (°C)

+10% margin

-10% margin

200

(c) 1-D heat transfer (HSC-CA)

800

+10% margin

(e) 1-D heat transfer (NSC-SA)

+10% margin

800
600
400

-10% margin

200
0

0

200 400 600 800 1000
Predicted temperature (°C)
(f) 2-D heat transfer (NSC-SA)

261

Figure 7. 4 (cont’d)

Temperature from FEA (°C)

+10% margin

600
400
-10% margin

200
0

0

200 400 600 800
Predicted temperature (°C)

Temperature from FEA (°C)

1000

800

(g) 1-D heat transfer (HSC-SA)

+10% margin

800
600
400

-10% margin

200
0

0

200 400 600 800 1000
Predicted temperature (°C)
(h) 2-D heat transfer (HSC-SA)

7.2.1.6 Verification of temperature equations using test results
The validity of the proposed equations is established by comparing the predicted
temperatures (using Eqns. 7.8 and 7.10) with the measured temperatures from fire tests
on RC beams, columns and slabs. In total, 5 beams, 5 columns and 1 slab tested in the
literature (Kodur et al. 2006, Raut and Kodur 2011, Lin 1981, Dwaikat and Kodur 2009,
Kodur and Bisby 2005, Dotreppe and Franssenm 1985, Kodur et al. 2004), were selected
for this validation. The properties of selected RC members cover different concrete types
(NSC-CA, HSC-CA, NSC-SA and HSC-SA) and width-depth ratios (ranging from 0.33
to 1.0). The tested beams, columns and slab were subjected to three-side, four-side and
one-side fire exposure, respectively. The details of tested members used for validation are
shown in Table 7.2.
The predicted temperatures using Eqns. 7.8 and 7.10, for NSC-CA, are compared
with measured values in fire tests in Figure 7.5. It can be seen that the predicted rebar
262

temperatures are generally in good agreement with the measured values in the beams and
columns. In the initial stage, the predicted rebar temperatures are slightly higher than the
measured ones in fire tests, due to relatively larger discrepancy in 20-300°C range in the
regression analysis. In Figures 7.5e and 7.5f, the temperatures in the slabs, calculated
using 1-D heat transfer equation, are also compared to measured temperatures in the test.
It can be seen the predictions agree with the test results throughout the slab thickness,
which demonstrates that the proposed 1-D heat transfer equation can well handle the slab
temperature problem.
To check the validity of the proposed equations over a wide range of scenarios,
the predicted temperatures are compared against the measured temperatures in fire test on
RC members made of different types of concrete (HSC-CA, NSC-SA and HSC-SA). The
comparisons are plotted in Figures 7.6-7.8. Since the proposed equations utilizes factors
(c1 and c2) to account for different aggregate types and concrete types, the cross-sectional
temperatures predicted by those equations have a close match with the measured
temperatures. Also, by using 1-D or 2-D equations, the temperatures in both rebar and
concrete at various depths could be predicted with a good accuracy. Thus, Eqns. 7.8 and
7.10 are suited to predict cross-sectional temperatures in structural members made of
different types of concrete.

263

Table 7.2 Sections of RC members used in validation of temperature equations
Cross-sectional dimensions
Concrete
Group
Aggregate Finite element analysis
Test
Strength
Dimension (mm) b/h
Dimension (mm)
Column 406×406
(Kodur et al. 2006)
B400×700
0.57
Column 203×203
(Raut and Kodur 2011)
Beam 229×533
(Lin 1981)
I
NSC Carbonate
Beam 254×408
B250×450
0.56
(Dwaikat and Kodur
2009)
Slab 152
(Kodur and Bisby 2005)
Column 203×203
B400×700
0.57
(Raut and Kodur 2011)
II
HSC Carbonate
Beam
B250×450
0.56 254×408 (Dwaikat and
Kodur 2009)
Beam 200×600
B400×700
0.57
(Dotreppe and
Franssenm 1985)
III
NSC
Siliceous
Column 305×305
B250×450
0.56
(Kodur et al. 2003)
B400×700
IV

HSC

Siliceous

0.57

B250×450

0.56

Column 305×305
(Kodur et al. 2003)

b/h
1.0
1.0
0.43
0.62
-1.0
0.62
0.33
1.0

1.0

In Figures 7.5-7.8, the temperature predictions using Wickstrom’s equation [1986]
are also plotted. It can be seen that at the location of rebars, the predicted temperatures
using Wickstrom’s equation are much higher than the measured values in fire tests, while
at mid-depth of concrete, Wickstrom’s equation predicts lower temperatures than the
measured ones. One possible reason for this discrepancy is due to the fact that
Wickstrom’s equation does not account for the variation resulting from thermal
264

properties of different concrete types (NSC-CA, HSC-CA, NSC-SA and HSC-SA). Such
large discrepancy on cross-sectional temperatures could affect fire resistance calculations
of an RC member. Therefore, the proposed equations can provide better estimate of

1000

800

Rebar temperature (°C)

Reber temperature (°C)

temperatures, and thus are more suited for fire resistance evaluation.

600
400
Test
Proposed Eq.
Wickstrom's Eq.

200
0

0

800
600
400
Test
Proposed Eq.
Wickstrom's Eq

200
0

30 60 90 120 150 180 210
Time (min)

0

60

(a) RC column
800
Rebar temperature (°C)

Rebar temperature (°C)

240

(b) RC column

800
600

600

400

400

200
0

120
180
Time(min)

Test
Proposed Eq.
Wickstrom's Eq.
0

Test
Proposed Eq.
Wickstrom's Eq.

200

30 60 90 120 150 180 210
Time (min)
(c) RC beam

0

0

15

30 45 60 75
Time (min)

90

(d) RC beam

Figure 7.5 Validation of the proposed approach by comparing predicted and measured
temperatures for NSC-CA members

265

Figure 7.5 (cont’d)
1000
Temperature (°C)

900

B

800

A

700

75mm
50mm

600
500
400

A-Test
A-Proposed Eq.
A-Wickstrom's Eq.
B-Test
B-Proposed Eq.
B-Wickstrom's Eq.

300
200
100
0

0

30

60

90 120
Time (min)

150

180

210

(e) RC slab
600

A-Test
A-Proposed Eq.
A-Wickstrom's Eq.
B-Test
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

500
400
300
200

B

100
0

A

0

30

60

90 120
Time (min)

(f) RC slab

266

30mm
15mm

150

180

210

Rebar temperature(°C)

800
700
600
500
400
300

Test
Proposed Eq.
Wickstrom's Eq.

200
100
0

0

20

40

60

80 100 120 140 160 180

Time(min)
(a) RC beam
1400

Rebar-Test
Rebar-Proposed Eq.
Rebar-Wickstrom's Eq.
Center-Test
Center-Proposed Eq.
Center-Wickstrom's Eq.

Temperature (°C)

1200
1000
800
600
400
200
0

0

30

60

90

120

150

180

210

Time (min)
(b) RC column
Figure 7.6 Validation of the proposed approach by comparing predicted and measured
temperatures for HSC-CA members

267

Rebar temperature(°C)

700
600
500
400
300
200

Test
Prediction
Wickstrom

100
0

0

30

60
90
Time (min)

120

(a) RC beam
1600

A-Test
A-Proposed Eq.
A-Wickstrom's Eq.
B-Test
B-Proposed Eq.
B-Wickstrom's Eq.

1400
Temperature(°C)

1200
1000
800

Y

101
B 19
A

600
400

Z

200
0

0

60

120
180
Time (min)

240

300

(b) RC column
Figure 7.7 Validation of the proposed approach by comparing predicted and measured
temperatures for NSC-SA members

268

1600

A-Test
A-Proposed Eq.
A-Wickstrom's Eq.
B-Test
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature(°C)

1400
1200
1000
800

Y

101
B 19
A

600
400

Z

200
0

0

30

60

90 120 150 180 210
Time (min)

Figure 7.8 Validation of the proposed approach by comparing predicted and measured
temperatures for HSC-SA members
7.2.1.7 Verification of temperature equations using FEA Results
The above developed simplified equations for temperature predictions are further
validated by comparing temperature predictions with those obtained from FEA. To
demonstrate the applicability of the proposed equations to a wide range of situations, the
selected dimensions of concrete members for FEA are different from those of the tested
concrete members used in Section 7.2.1.2, since test specimens are generally of smaller
dimensions. As shown in Table 7.2, the cross section of beams used for validation are
400×700 mm and 250×450 mm, and the high-temperature material properties of these
two beams are varied to take into account for NSC-CA, HSC-CA, NSC-SA and HSC-SA.
Two points in each beam, located in 1-D and 2-D heat transfer area, respectively, are
selected for comparisons between predictions by proposed equations and FEA.
The comparison of temperature predictions using proposed equations and FEA is
shown in Figures 7.9-7.12. It can be seen that for all beams under consideration, the
269

proposed equations are able to accurately predict cross-sectional temperatures in the
entire range of fire exposure. Since the two points in each beam are using 1-D and 2-D
heat transfer equations, respectively, the reasonability of cross-sectional division are also
validated. Comparing to the test results validation, the predictions by the proposed
equation have better agreement with FEA results. This is probably due to the fact that the
proposed equation is derived based on the results from finite element analysis.
The predicted temperatures using Wickstrom’s equation are also compared to
FEA results in Figures 7.9-7.12. Wickstrom’s equation gives the same temperature
predictions for the beams with different concrete types as can be seen in the figures, and
this is due to the fact that Wickstrom’s equations does not account for specific concrete
type. The predicted temperatures from Wickstrom’s equation are in better agreement for
siliceous aggregate concrete members, but for carbonate aggregate concrete the
predictions are too conservative.

270

1400

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1200
1000
800
600

Y

B(150,600)

400

A(60,60)

200
0

0

30

60

Z

90 120 150 180 210 240
Time (min)
(a) Beam 400×700 mm

1400

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1200
1000
800
600

Y
B(50,250)
A(50,50)

400

Z

200
0

0

30

60

90 120 150 180 210 240
Time (min)
(b) Beam 250×450 mm

Figure 7.9 Validation of the proposed approach by comparing predicted temperatures
with FEA results for NSC-CA members

271

1400

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1200
1000
800

Y

B(150,600)

600

A(60,60)

400
200
0

0

30

60

90 120 150
Time (min)

180

210

Z

240

(a) Beam 400×700 m
1200

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1000
800

Y
B(50,250)

600

A(50,50)

400

Z

200
0

0

30

60

90 120 150
Time (min)

180

210

240

(b) Beam 250×450 mm
Figure 7.10 Validation of the proposed approach by comparing predicted temperatures
with FEA results for HSC-CA members
272

1400

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1200
1000
800

Y

B(150,600)

600
400

A(60,60)

200
0

0

30

60

90 120 150
Time (min)

180

210

Z

240

(a) Beam 400×700 mm
1200

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1000
800

Y
B(50,250)

600

A(50,50)

400

Z
200
0

0

30

60

90 120 150
Time (min)

180

210

240

(b) Beam 250×450 mm
Figure 7.11 Validation of the proposed approach by comparing predicted temperatures
with FEA results for NSC-SA members
273

1400

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1200
1000
800

Y

600

B(150,600)

400

A(60,60)

200
0

0

30

60

90 120 150
Time (min)

180

210

Z

240

(a) Beam 400×700 mm
1200

A-FEA
A-Proposed Eq.
A-Wickstrom's Eq.
B-FEA
B-Proposed Eq.
B-Wickstrom's Eq.

Temperature (°C)

1000
800

Y
B(50,250)

600

A(50,50)
Z

400
200
0

0

30

60

90 120 150
Time (min)

180

210

240

(b) Beam 250×450 mm
Figure 7.12 Validation of the proposed approach by comparing predicted temperatures
with FEA results for HSC-SA members
274

7.2.2 An approach for predicting temperatures in an insulated RC member
The above simplified approach for evaluating temperature in RC members is
extended to cover the temperature predictions in an insulated RC member. Unlike a
conventional RC member, temperature profiles in an insulated RC member are influenced
by properties of both concrete and fire insulation. Since there is a large difference
between thermal properties of concrete and insulation, also the heat flux on the boundary
of concrete and insulation is different, predicting temperature in an insulated concrete
member becomes a more complicate problem. So far there is no simplified approach for
evaluating temperature in an insulated concrete member.
This section provides development of simplified approach for evaluating
temperature profiles in an insulated RC member. A simple expression for converting
insulation layer to equivalent concrete layer is firstly derived. Then regression analysis on
a large amount of temperature data, collected using detailed thermal analysis on RC
members, is conducted to obtain the final temperature equations. Since FRP or steel
reinforcement does not significantly affect the temperature rise in an insulated RC
member, the proposed equations are suitable for evaluating temperatures in RC members
with various configurations, such as NSM or external FRP strengthened RC members,
concrete members with internal FRP rebar, etc. Detailed derivation and regression
procedure are presented as follows.

7.2.2.1 Converting fire insulation layer to equivalent concrete layer
For an FRP strengthened RC member (with or without fire insulation),
temperatures at critical locations such as FRP and steel rebar, dominate the behavior of
275

strengthened members under fire conditions. Thus temperatures in concrete, steel and
FRP need to be known, while temperature in insulation layer is not of much interest. It is
well established that thermal properties of concrete and insulation primarily influence
temperature rise within a concrete member. Thermal properties of steel rebar and FRP
(laminate, strip or rod) does not significantly affect temperature rise in RC member due
to their small cross sectional areas as compared to concrete section (Lie and Irwin 1993).
Thus, if the insulation layer on concrete member is converted to equivalent concrete layer,
temperature profile in an insulated concrete section can be evaluated using the same
temperature equation as that for uninsulated RC sections (Eqns. 7.8 and 7.10).
Figure 7.13 shows a typical RC beam protected by a U-shaped fire insulation. The
thickness of insulation on sides and bottom of the beam are zi and yi respectively.
Assuming that fire insulation layer can be replaced by an equivalent concrete layer with
the thickness of zec and yec on sides and bottom respectively, and temperature profiles
remain the same within beam cross section after this alternation. Based on the heat
transfer principles, the following equations can be obtained within the insulation or its
equivalent concrete layer.

ki
∂Ti
Q
∇ 2Ti =
−
∂t ( ρ c)i
( ρ c )i

(7.11)

kc
∂Tec
Q
∇ 2Tec =
−
∂t
( ρ c )c
( ρ c )c

(7.12)

where ki and (ρc)i are thermal conductivity and heat capacity of insulation respectively,
and kc and (ρc)c are thermal conductivity and heat capacity of concrete respectively; Q is
276

the heat source; Ti and Tec are the temperatures in insulation and equivalent concrete

respectively; t is the time; and ∇ is the second order derivative of temperature (Ti or Tec)
with respect to the distance to fire exposed surface (z or y).

Concrete
beam

zec zc

zi zc
Fire
insulation

Concrete
beam

ρccc , kc

ρccc , kc
yc
yi

yc
ρccc , kc

yec

Equivalent
concrete layer

An insulated concrete section
Figure 7.13 Illustration of the equivalent concrete depth method

Eqns. 7.11 and 7.12 represent temperature distributions within insulation layer or
equivalent concrete layer. At the boundary of the insulation layer (z = zi), temperatures
remain same before and after alternation (see Figure 7.13). Thus Eq. 7.13 can be obtained.

kc ∂ 2Tec
( ρ c)c ∂z 2

ki ∂ 2Ti
≈
( ρ c)i ∂z 2

z=zec

z=zi

(7.13)

where z is the distance from fire exposed surface. Since 1-D heat transfer dominates
temperature distribution within insulation or concrete layer due to their small thickness,
temperature equation resulting from 1D heat transfer (Eq. 7.8) can be used. Tec in Eq.
7.13 can be expressed as:
= (0.155ln
Tec

t

1.5

z

− 0.348 z − 0.371) ⋅ (at n ) ≈ (0.155ln

277

t

1.5

z

− 0.371) ⋅ (at n ) (7.14)

n

where at is the standard fire temperature (Dwaikat and Kodur 2013). For ISO 834 fire, a
= 935 and n = 0.168, and for ASTM E119 fire, a = 910 and n = 0.148. Assume that
temperature distribution within insulation is similar to that within concrete, and then Tec
in Eq. 7.13 can be expressed as
t
Ti ≈ (a1 ln
− a2 ) ⋅ (at n )
1.5
z

(7.15)

where a1 and a2 are the coefficients describing temperature distribution within insulation
layer. Importing Eqns. 7.14 and 7.15 into Eq. 7.13, the following relation between the
thickness of insulation layer (zi) and concrete layer (zec) can be obtained
zec
k c ( ρ c )i
0.155 kc ( ρ c)i
= η
≈ λη
zi
a1 ( ρ c)c ki
( ρ c)c ki

(7.16)

where λ and η are the coefficients to be determined. Notice that Eq. 7.16 describes an
approximate relation between insulation thickness (zi) and the equivalent concrete
thickness (zec). Since thermal properties of insulation and concrete vary with temperature
(or fire exposure time), λ is assumed to be as a function of time (t) in hours, accounting
for the influence of fire exposure time. Finally, the following expression is arrived:
zec α β kc ( ρ c)i
= t
( ρ c)c ki
zi

(7.17)

where α and β are the coefficients to be determined. Once the values of α and β are
obtained, the insulation thickness can be converted to an equivalent concrete thickness.
For example, Figure 7.13 shows a point (Point A) located in an insulated RC beam. The
distances from Point A to side and bottom surface of beam are zc and yc respectively, and
278

insulation thickness on side and bottom surface of beam are zi and yi respectively. Using
the equivalent concrete depth method, the distance from Point A to fire exposed surface
can be expressed as:
zc ' =zc + zec =zc + zi α t β

k c ( ρ c )i
( ρ c)c ki

(7.18)

yc ' =yc + yec =yc + yi α t β

k c ( ρ c )i
( ρ c)c ki

(7.19)

Then zc’ and yc’ can be applied into equations used for predicting temperatures in an RC
member (Eqns. 7.8 and 7.10) to obtain temperature profiles in an insulated RC member,
as shown below.
For 1-D heat transfer: Tc = c1 ⋅η z ⋅ (at n )

ηz
where, = 0.155ln

t

( z ')1.5

− 0.348 z ' − 0.371

(7.20)
(7.21)

For 2-D heat transfer: Tc = c2 ⋅ (−1.481 ⋅ (η z ⋅η y ) + 0.985 ⋅ (η z + η y ) + 0.017)(at n ) (7.22)
Where t is the fire exposure time in hours, z’ is the distance from the point in concrete
section to fire exposed surface using the equivalent concrete depth method (Eqns. 7.18
and 7.19), the meaning of other symbols is illustrated in Section 7.2.1.3.
Eqns. 7.18-7.22 provide a simplified approach for evaluating temperatures within
an insulated RC beam, including the cases of FRP-strengthened members with insulation.
The only unknowns to be determined are α and β in Eqns. 7.18 and 7.19. These two
unknowns are obtained through nonlinear regression analysis on a large database
generated using finite element analysis (FEA).
279

7.2.2.2 Regression analysis
A regression analysis similar to that in Section 7.2.1 was carried out to obtain
empirical equations for predicting temperatures in an insulated RC beam. To generate
temperature data for regression analysis, three representative RC beams with two types of
insulation were analyzed using finite element program described in Chapter 5. The
characteristics of these RC beams were varied over a wide range and are shown in Table
7.3 and Figure 7.14. The width of beam section was varied from 200 to 300mm, while the
depth was varied from 300 to 500mm. Two types of fire insulation, Aestuver and Tyfo
VG insulations, are assumed to be applied on the beams. The variation of thermal
properties of fire insulation with temperatures follows previously reported values (Bisby
2003), and they are summarized in Appendix A. Five different points within beam
section were selected in each beam, and they are typical locations of steel and FRP
reinforcement, as shown in Figure 7.14. In the finite element analysis, each beam was
subjected to ASTM E119 fire exposure from three sides for 4 hours, and temperature data
at each time interval of 0.5 hours was output for regression analysis. In total, 240
temperature data points with corresponding time and location information (3×2×5×8)
were generated for regression analysis.

280

Table 7.3 Characteristics of insulated RC beams used in the regression analysis

2

Corner steel rebar
AESTUVER
Middle steel rebar
200×300mm
250×400mm k = 0.185W/m-K
NSM FRP strip
3
300×500mm (ρc) = 650kJ/m -K 1/4 length of FRP laminate
Middle of FRP laminate
Corner steel rebar
Tyfo VG
Middle steel rebar
200×300mm k = 0.116W/m-K
250×400mm
NSM FRP strip
3
(ρc) = 413kJ/m -K
300×500mm
1/4 length of FRP laminate
Middle of FRP laminate

3ϕ16

25

300

2ϕ10

2ϕ13
3ϕ19

25
2ϕ6.4 200x0.5 FRP
FRP rods laminates

2 16x4
FRP strips

Fire exposure
time
0.5h, 1h,
1.5h, 2h,
2.5h, 3h,
3.5h, 4h
0.5h, 1h,
1.5h, 2h,
2.5h, 3h,
3.5h, 4h

300

250

200
25

Point

38

400

1

Fire insulation

2ϕ13
4ϕ19

25
250x1 FRP
laminates

500

Case
Section
No.

38
4 16x4 300x1.5 FRP
FRP strips laminates

(a) Beams analyzed for regression analysis

2ϕ10
3ϕ16

350

25

25
2ϕ6.4 200x0.5 FRP
FRP rods laminates

38

2ϕ13
4ϕ19

500

350

200

38
4 16x4 300x1.5 FRP
FRP strips laminates

(b) Beams analyzed for validation of temperature equations
Figure 7.14 FRP strengthened RC beams used in FEA for regression and validation
(Units: mm)
281

A regression analysis was performed using “Solver” function in Excel (2010) to
develop an expression for converting insulation to an equivalent concrete layer (Eq. 7.17).
The “solver” function is able to calculate the optimum coefficients to match the original
data with a given format of formula and applied “constraint” criteria. To ensure better
accuracy of the final equation, the errors between predicted temperatures using formula
and temperatures obtained from FEA were controlled within 10%, or 15% conservative.
α and β in Eqns. 7.17 are the coefficients to be determined in the regression analysis.
Then a regression analysis was carried out so as to achieve minimum error
between predicted temperature (using Eqns. 7.18-7.22) and temperature obtained from
FEA. Based on the regression analysis results, α and β are determined to be 4.5 and 1.75
respectively, and thus the relation between insulation and its equivalent concrete is
zec = zi 4.5 t 1.75

k c ( ρ c )i
( ρ c)c ki

(7.23)

The temperature predictions using equivalent concrete method (Eqns. 7.18 to 7.22)
are compared with temperature data generated from FEA. These comparisons are plotted
in Figures 7.15 - 7.17 for three insulated RC beams (two types of insulation). In these
figures, a point below “-10% margin” line indicate that the predicted temperature is to be
higher than that obtained in FEA by more than 10%. If a point lies above “+10% margin”
line, the predicted temperature is smaller than that obtained in FEA by more than 10%. It
can be seen that for three insulated RC beams, most data points lie within ±10% margin
zone. Therefore, the proposed equivalent concrete method is capable of predicting
temperatures in insulated RC beams exposed to standard fire to a good degree. It is noted
that there are a few points outside “±10% margin” line, indicating the errors are larger
282

than 10%. However, most of these points are below “-10% margin” line, and they
provide conservative predictions of steel and FRP rebar temperatures.

Temperature from FEA (°C)
Temperature from simulation (°C)

900
+10% margin
+10% margin

800
800
700

600
600
500

400
400

-10% margin
-10% margin

300

200
200
100
00

0
0

400
600
800
100 200 300 400 500 600 700 800 900
200
Predicted temperature (°C)
Predicted temperature(°C)

Figure 7.15 Comparison of predicted temperatures from the proposed equations (Eqns.
7.18-7.22) with those from FEA (Beam 200×300mm)

Temperature from FEA (°C)
Temperature from simulation (°C)

900
800
800

+10% margin
+10% margin

700
600
600
500

400
400

-10% margin
-10% margin

300

200
200
100
00

0 100 200 300 400 500 600 700 800 900
600
800
0
200
400
Predicted temperature (°C)
Predicted temperature(°C)

Figure 7.16 Comparison of predicted temperatures from the proposed equations (Eqns.
7.18-7.22) with those from FEA (Beam 250×400mm)
283

Temperature from FEA (°C)
Temperature from simulation (°C)

900

+10% margin
+10% margin

800
800
700

600
600
500

400
400

-10% margin
-10% margin

300

200
200
100
00

0
0

400
600
800
100 200 300 400 500 600 700 800 900
200
Predicted temperature(°C)
Predicted temperature (°C)

Figure 7.17 Comparison of predicted temperatures from the proposed equations (Eqns.
7.18-7.22) with those from FEA (Beam 300×500mm)

7.2.2.3 Verification of temperature equations using test results
The validity of the proposed approach is established by comparing the predicted
temperatures using Eqns. 7.18-7.22 with the measured temperatures from fire tests
reported in the literature. The validation focuses on the accuracy of temperature
prediction in FRP and steel reinforcement, since these temperatures apply critical
influence on fire response of FRP strengthened RC beams. Details of tested members
selected for validation are tabulated in Table 7.4.
Figures 7.18-7.21 show the comparison of predicted steel and FRP temperatures
from the proposed approach with those recorded in the fire tests. It can be seen that the
predicted temperatures are mostly in good agreement with the measured values in
insulated RC beams, especially on temperature predictions in steel rebar. This is very
important to FRP strengthened RC members, since steel rebars provide primary
284

contribution to moment capacity under fire conditions. For temperatures in FRP, the
predicted FRP temperatures are slightly lower than the measured ones, especially in the
initial fire exposure. This is mainly due to quick rise in fire temperatures in early stage,
leading to significant temperature increase in FRP at beam soffit. Also, if fire insulation
cracks during the fire test (such as the case in MSU beam II), the measured FRP
temperatures can suddenly jump to a high level. Since the proposed temperature
equations do not account for these uncertain factors such as insulation cracking, predicted
temperatures using equations are relatively lower than measured temperatures in the fire
tests.
A further examination on Figures 7.18-7.21 indicates there is relatively larger
discrepancy between predicted and measured temperatures in 20-100°C range. This is
because this temperatures range is not primary objective in the regression analysis. As
mentioned in Section 7.2.1, the regression analysis cannot match all the data closely.
Thus the regression analysis was performed to fit the data points in the critical
temperature range. Since temperature variation in 20-100°C range does not significantly
influence the strength in steel and FRP, the accuracy of temperature predictions in this
range is set as a secondary target in the regression analysis. However, this does not
significantly affect further structural analysis of FRP strengthened RC beams. Overall
predicted temperatures have a good agreement with measured data in most fire duration,
and this demonstrates the validity of the equivalent concrete approach for predicting
temperatures in an insulated RC beam.

285

300
Steel rebar - Test
Steel rebar - Formula
External FRP - Test
External FRP - Formula

Temperature(ºC)

250
200
150
100
50
0

0

15

30

45
60
Time (mins)

75

90

105

Figure 7.18 Validation of the proposed approach by comparing predicted and measured
temperatures (Blontrock et al. 2000)
400

Steel rebar - test
Steel rebar - Formula
External FRP - Test
External FRP - Formula

Temperature(ºC)

350
300
250
200
150
100
50
0

0

30

60

90

120 150
Time (mins)

180

210

240

270

Figure 7.19 Validation of the proposed approach by comparing predicted and measured
temperatures (Williams et al. 2008)

286

400

Steel rebar - Test
Steel rebar - Formula
NSM FRP - Test
NSM FRP - Formula

350
Temperature(ºC)

300
250
200
150
100
50
0

0

15

30

45

60
75
Time (mins)

90

105

120

135

Figure 7.20 Validation of the proposed approach by comparing predicted and measured
temperatures (Palmieri et al. 2012)
500

Corner steel rebar - Test
Corner steel rebar - Formula
Middle steel rebar - Test
Middle steel rebar - Formula
NSM FRP - Test
NSM FRP - Formula

Temperature (°C)

400
300
200
100
0

0

30

60

90

120
150
Time (mins)

180

210

240

Figure 7.21 Validation of the proposed approach by comparing predicted and measured
temperatures (MSU Beam II)

287

7.2.2.4 Verification of temperature equations using FEA results
The proposed equations are further validated through comparing temperature
predictions with those obtained from FEA. To demonstrate the applicability of the
equations in a wide range of situations, the selected concrete beams for validation are
different from those used in regression analysis, as shown in Table 7.3 and Figure 7.14.
The cross-sections of beams used for validation are 200×350 mm and 350×500 mm, and
two types of fire insulation are applied on selected beams respectively. In each selected
beam, temperatures in corner and middle steel rebars, NSM FRP strip, and center and
average temperature of external FRP laminates are evaluated for comparison.
A comparison of predicted temperatures from proposed equations (Eqns. 7.187.22) with those from FEA is plotted in Figures 7.22 - 7.25. It can be seen that predicted
temperatures reasonably match with those obtained from FEA. In a few cases, mainly in
the cases of FRP laminates or strips, the predicted temperatures are conservative (higher)
as compared to FEA results. This can be attributed to the fact that proposed equations do
not account for the variation of thermal properties of insulation at high temperatures.
Also, temperature prediction in 20-200°C range has relatively larger discrepancy with
FEA results, as shown in Figure 7.25(a). This is mainly due to the fact that 20-200°C
range is not primary target in the regression analysis as explained earlier. However, the
discrepancy between predicted temperatures and FEA results is mostly within in 10%.
Thus these equations are applicable in design situation. Overall the comparison of
predicted temperatures with data from FEA results indicates the proposed equations are
capable of evaluating temperatures in insulated RC beams.

288

600

Temperature (°C)

500
400
300
Corner steel rebar - FEA
Corner steel rebar - Formula
Middle steel rebar - FEA
Middle steel rebar - Formula

200
100
0

0

30

60

90

120 150
Time (mins)

180

210

240

270

(a) Steel rebar temperatures
700

Temperature (°C)

600
500
400
300

NSM FRP - FEA
NSM FRP - Formula
FRP average - FEA
FRP average - Formula
FRP middle - FEA
FRP middle - Formula

200
100
0

0

30

60

90

120
150
Time (mins)

180

210

240

270

(b) FRP temperatures
Figure 7.22 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 200×350mm with Aestver insulation)
289

600

Corner steel rebar - FEA
Corner steel rebar - Formula
Middle steel rebar - FEA
Middle steel rebar - Formula

Temperature (°C)

500
400
300
200
100
0

0

30

60

90

120 150
Time (mins)

180

210

240

270

(a) Steel rebar temperatures
600

Temperature (°C)

500
400
300
NSM FRP - FEA
NSM FRP - Formula
FRP average - FEA
FRP average - Formula
FRP middle - FEA
FRP middle - Formula

200
100
0

0

30

60

90

120
150
Time (mins)

180

210

240

270

(b) FRP temperatures
Figure 7.23 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 200×350mm with VG insulation)
290

400

Corner steel rebar - FEA
Corner steel rebar - Formula
Middle steel rebar - FEA
Middle steel rebar - Formula

Temperature (°C)

300

200

100

0

0

30

60

90

120 150 180
Time (mins)

210

240

270

(a) Steel rebar temperatures
500

Temperature (°C)

400
300
200

NSM FRP - FEA
NSM FRP - Formula
FRP average - FEA
FRP average - Formula
FRP middle - FEA
FRP middle - Formula

100
0

0

30

60

90

120 150
Time (mins)

180

210

240

270

(b) FRP temperatures
Figure 7.24 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 350×500mm with Aestver insulation)
291

350

Corner steel rebar - FEA
Corner steel rebar - Formula
Middle steel rebar - FEA
Middle steel rebar - Formula

Temperature (°C)

300
250
200
150
100
50
0

0

30

60

90

120 150
Time (mins)

180

210

240

270

180

210

240

270

(a) Steel rebar temperatures
400

NSM FRP - FEA
NSM FRP - Formula
FRP average - FEA
FRP average - Formula
FRP middle - FEA
FRP middle - Formula

350
Temperature (°C)

300
250
200
150
100
50
0

0

30

60

90

120
150
Time (mins)

(b) FRP temperatures
Figure 7.25 Validation of the proposed approach by comparing predicted temperatures
with FEA results (Beam 350×500mm with VG insulation)

292

7.3 Evaluating Moment Capacity of FRP-strengthened RC Beams
Once temperatures in steel and FRP reinforcement are obtained, flexural capacity
of fire exposed FRP strengthened RC beam can be evaluated at any given fire exposure
time, utilizing similar procedure as that for room temperature moment capacity as
specified in ACI 440.2 (2008). To apply these equations for evaluating moment capacity
at a given fire exposure time, corresponding strength loss in concrete, FRP and steel
reinforcement due to temperature rise needs to be accounted. This section provides
detailed procedure for evaluating moment capacity of FRP strengthened RC beam at any
give fire exposure time, and a flow chart is also provided for better illustrating step by
step calculations.

7.3.1 Degradation of steel and FRP properties
Temperature induced strength degradation in steel and FRP reinforcement have
significant influence on resisting moment capacity of an FRP strengthened RC beam at a
given fire exposure time. For steel rebars, the degradation of strength and elastic modulus
at evaluated temperature has been well studied and documented. In this research,
temperature-property relations specified as per Eurocode 2 (2004), are applied for
evaluating the strength and elastic modulus of steel rebar at any give temperature (or fire
exposure time).
For FRP reinforcement (EBR laminates or NSM rods and strips), there is very
limited information on the degradation of mechanical properties at elevated temperature.
It has been known that FRP exhibits a linear stress-strain response both at room
temperature (ACI 440.1 2006, FIB Bulletin 14 2007) and at elevated temperatures (Wang
293

et. al 2007, Bisby et al. 2005, Yu and Kodur 2013). Thus, temperature dependent stressstrain response of FRP can be represented through a set of linear relationships. In this
section, it is assumed that high temperature strength and modulus of external FRP
laminates follow the empirical relations proposed by Bisby et al. (2005), and those of
NSM FRP follow the empirical relations proposed in Chapter 3.
The temperature dependant property relations of reinforcing steel and FRP, are
summarized in Appendix A.

7.3.2 Effective concrete width under fire exposure
For an RC beam exposed to fire exposure, concrete in compression zone is not
usually protected by fire insulation. Thus concrete in compression zone experiences
certain level of strength and stiffness degradation, especially at the area close to fire
exposed surface (sides of the beam). However, concrete in compression zone experiences
different strength degradation depending on the specific location. Thus it is difficult to
account for concrete strength degradation in the calculation moment capacity. To
evaluate the effect of concrete degradation on moment capacity of RC beam, a method of
“effective concrete width”, similar to that in Eurocode 2 (2004), is utilized in this study.
This method assumes that concrete elements still possess full room temperature strength,
but the width of concrete section is reduced due to high temperatures on fire exposure
surface.
Although providing a concept of “effective concrete width”, Eurocode 2 (2004)
does not provide specific values of effective concrete width for various concrete members.
In this study, the effective concrete width is quantified over a wide range of beam
294

sections. For this purpose a set of RC beams (as shown in Table 7.4) were analyzed
utilizing finite element program presented in Chapter 5. For each analyzed beam, the
strength degradation in each concrete element in compression zone (the upper half beam)
is evaluated at various fire exposure times. The average strength degradation of all these
elements (in percentage) is calculated as the reduction factor of concrete width. Summary
on these reduction factors for various beam sections is tabulated in Table 7.4. The
effective concrete width of other beam sections can be obtained through linear
interpolation on these known values.
Table 7.4 Factors for calculating effective concrete width for various RC beams
exposed to ASTM E119 standard fire
Time
(minutes)
0
15
30
45
60
75
90
105
120
135
150
165
180
195
210
225
240

150×200
100
99.7
91.1
83.0
75.5
69.1
61.7
63.3
68.2
69.5
66.6
61.7
56.4
52.4
49.8
48.3
47.1

Effective width factors (%)
200×300
250×400
300×500
100
100
100
99.9
99.9
99.9
97.2
98.2
97.4
95.6
96.0
94.0
91.9
92.8
91.2
88.8
90.7
88.1
86.4
88.0
86.1
83.5
86.2
83.5
80.6
83.8
82.2
78.5
82.3
80.2
75.2
80.1
78.8
72.1
78.0
77.2
69.8
76.8
75.7
66.7
74.6
74.6
63.0
72.8
73.3
59.7
70.6
71.9
56.8
68.9
70.6

295

400×600
100
99.9
98.2
95.6
93.3
91.4
88.9
87.7
86.3
84.7
83.5
82.4
81.2
80.4
79.3
78.3
77.8

7.3.3 Evaluating moment capacity at a given fire exposure time
Knowing temperature dependent strength properties of steel rebar (fy,T) and FRP
(ff,T, Ef,T) and effective concrete width (bT), the moment capacity of FRP strengthened
RC beams at any give fire exposure time can be calculated. Based on ACI 440.2
provisions (2008), there are two primary failure modes that occur in FRP strengthened
RC beams:
•

Crushing of top concrete before FRP debonding

•

Rupture of FRP laminate after steel yielding

Thus moment capacity of FRP strengthened beams can be evaluated using different
formulas for these two failure modes. Figure 7.26 illustrates stress and internal force on
cross section of an NSM FRP strengthened RC beam.

εc
N.A.

σc

fc’abT

Cc,T

Neutral axis

steel
σs,T(fy,T)
rebar in
fy,TAs
εs
tension
T=Tf,T+Ts,T
εf
ff,TAf
σf,T(ff,T)
NSM FRP
Total strain diagram
Internal forces C = T
Cross section
Stress diagram
Force equilibrium
Figure 7.26 Force equilibrium and strain compatibility of NSM FRP strengthened RC
beam at a given fire exposure time
At a given fire exposure time, if the beam fails due to crushing of top concrete,
top concrete is considered to reach its compression strain limit (εc = εcu= 0.003), while
strains in steel and FRP reinforcement can be calculated using the strain compatibility
principles as follows

296

εs

ε
= cu
d −c
c

εf

ε
= cu
h−c
c

(7.24)

(7.25)

Since the strain hardening effect is usually neglected in the design codes, the steel stress
is assumed to be that of yield strength as long as εs ≥ εsy. The stress in FRP reinforcement
can be calculated as
f f ,T = E f ,T ε f

(7.26)

Based on the force equilibrium principle, the following equation can be obtained,
0.85 f= As f y ,T + A f f f ,T
c ' abT

(7.27)

εf and a are the only unknowns in Eqns. 7.24 - 7.27, and thus the values of εf and a can be
identified.
Then the flexural moment capacity at a given fire exposure time can be calculated as
M n= As f y ,T (d − 0.5a ) + A f f f ,T (h − 0.5a )
,T

(7.28)

If the beam fails due to rupture of FRP reinforcement, FRP reaches its strain limit
(εf = εfe = κmεfu). κm is strain reduction factor specified in ACI 440.2 (2008) to prevent
the debonding failure of FRP reinforcement. Equating tension and compression forces,
0.85 f= As f y ,T + A f ( E f ,T ε fe )
c ' abT

(7.29)

Solving Eq. 7.29 for the depth of the equivalent rectangular stress block a,

a=

As f y ,T + A f ( E f ,T ε fe )
0.85 fc ' bT

(7.30)

Then the flexural moment capacity of FRP strengthened beam can be obtained using
297

M n= As f y ,T (d − 0.5a ) + A f ( E f ,T ε fe )(h − 0.5a )
,T

(7.31)

For an FRP strengthened RC beam exposed to fire, the remaining strength of
constituent materials is known for any given fire exposure time, based on the above
described procedures. However, a preliminary calculation is needed to decide whether the
moment capacity is governed by crushing of top concrete or rupture of FRP. In this
preliminary calculation, Eq. 7.27 is applied firstly to obtain the equivalent stress block a.
Then the strain level in FRP can be evaluated using

εf
=

ε cu
c

(h − c)

(7.32)

If εf > εfe, FRP reinforcement will reach its strain limit before crushing of top concrete,
and thus the rupture of FRP governs the failure mode, and the moment capacity of the
beam can be calculated using Eqns. 7.29-7.31. While if εf < εfe, crushing of top concrete
governs the failure mode, and the moment capacity of the beam can be calculated using
Eqns. 7.24-7.28.
Knowing moment capacity of FRP strengthened beams at any given fire exposure
time, the fire resistance of the beam can be evaluated by comparing moment capacity
with applied moment resulting from external loading. At room temperature, considering
only deal loads and live loads for the strength limit state, most design codes (ASCE 7
2010, Eurocode 1 2002) specify two load combinations as follows
Mu = 1.4D
or

Mu = 1.2D + 1.6L

298

(7.33)
(7.34)

where, Mu is the ultimate load (moment) resulting from factored dead and live loads. D is
the dead load, L is the live load.
However, in the event of fire, the applied loading is much lower than the
maximum design loads specified for ambient conditions, since fire is a rare (accidental)
event. ASCE 7 (2010) recommends loading under fire conditions to be evaluated as
Mfire = 1.2D + 0.5L

(7.35)

Where, Mfire is the loading (moment) under fire exposure.
Thus combining Eqns. 7.24-7.35, the following criteria should be applied to evaluate
failure of FRP strengthened RC beam:
At room temperature: M u ≤ φ M n

(7.36)

Under fire exposure: M fire ≤ M n,T

(7.37)

where, ϕ is the strength reduction factor specified in ACI 440.2R (2008). Under fire
conditions, no reduction factor is applied.
Utilizing the above simplified equations, moment capacity of an FRP
strengthened RC beam can be calculated at any given fire exposure time. When the
moment due to external loading exceeds moment capacity, the beam fails under fire
conditions, and the corresponding time is the fire resistance of an FRP strengthened beam.
A flowchart illustrating the approach for evaluating fire resistance of an FRP
strengthened beam is plotted in Figure 7.27. To further illustrate detailed procedure of the
proposed approach, two design examples on fire resistance evaluation, one NSM FRP
strengthened RC beam without insulation and one external FRP strengthened RC beam
with insulation, are provided in Appendix D.
299

High temp.
material prop.

Select a fire exposure time
Determine temperature in
steel, FRP and concrete

Determine remaining
strength in steel and FRP and
effective concrete width
Evaluate reduced moment
capacity of the beam (Mn,t)

Determine moment due to
external loading (Mfire)
Mfire > Mn,t

NO

YES
Determine fire resistance
Figure 7.27 A flowchart illustrating rational design approach for evaluating fire resistance
of FRP strengthened beam
7.4 Validation of the Proposed Approach
The validity of the above proposed approach is established by comparing the
predicted response of beams with results from fire tests and FEA. To demonstrate
usefulness of the proposed approach, the selected FRP strengthened beams cover those
with various strengthening types (NSM or EBR) and fire protection (with and without
insulation). Details on these selected beams are tabulated in Table 7.5.
The comparison of predicted fire response with those from fire tests is plotted in
Table 7.5. Since the variation of moment capacity with fire exposure time cannot be
300

directly measured in fire tests, the measured fire resistance (failure times) of tested beams
is compared with those predicted from the proposed approach. It can be seen in Table 7.5
that the proposed approach provides good predictions on fire resistance of insulated RC
beams with FRP strengthening, while predictions in the uninsulated beams are relatively
conservative. In the uninsulated beams selected for comparison (Firmo et al. 2012, MSU
Beam I in Chapter 4), the anchorage area of FRP laminates or strips was protected by
furnace walls. Thus during the fire tests, a cable action was developed through cool ends
of FRP, and this provided extra support to RC beams even FRP reached very high
temperatures. The proposed approach does not account for this cable action effect, and
thus predicts a lower fire resistance. In fact, since the extra moment capacity or fire
resistance resulting from the cable action depends on a number of factors, and it is almost
impossible to quantify its influence. Thus, the fire resistance predictions from the
proposed approach are appropriate to be used in design situations.
The predictions from proposed approach are further validated through comparing
the predicted fire response with those obtained from FEA results. The beams in section of
200×350mm and 350×500mm were analyzed in finite element program to compare their
moment capacities with predictions using proposed approach, as shown in Figures 7.277.28. It can be seen that the predicted moment capacity is usually slightly lower than
those from FEA results. This can be attributed to rough estimation on effective concrete
width as well as conservative predictions on steel and FRP temperatures. Thus the
discrepancy between predicted and analyzed moment capacity is reasonable. Moreover,
the predicted fire resistance well matches FEA results, as shown in Table 7.5.

301

The calculation using proposed approach indicates that at ambient conditions,
crushing on top concrete usually governs the failure of beams, for both EBR and NSM
strengthening. This is because FRP laminates or strips possess quite large tensile strength
and modulus, and top concrete reaches its failure strain (0.003) before FRP breaks. While
at high temperature, FRP reinforcement usually loses most of strength, and strengthened
beams usually develop relatively larger curvatures. Thus, FRP reinforcement easily
reaches its failure strain before top concrete crushing, and rupture of FRP governs the
failure of strengthened beams.
Table 7.5 Comparison of fire resistance using proposed approach with
fire tests and FEA results
Source
of data

Fire
tests

Selected beam
Firmo et al. (2012)
MSU Beam I
Blontrock et al.
(2000)
Williams et al.
(2008)
Palmieri et al. (2012)

EBR
NSM

No
No

Fire resistance (mins)
Test /
Proposed
FEA
approach
60
15
180
>210*

EBR

Yes

>90*

>90

EBR

Yes

>240*

>240

NSM

Yes

>120*

>120

FRP
Fire
strengthening insulation

MSU Beam II
NSM
Beam 200×350
EBR
Beam 200×350
NSM
Beam 350×500
EBR
Beam 350×500
NSM
FEA
Beam 200×350
EBR
Beam 200×350
NSM
Beam 350×500
EBR
Beam 350×500
NSM
* The beam did not fail in tests till reported time.

302

Yes
No
No
No
No
Yes
Yes
Yes
Yes

>210*
105
125
90
120
240
240
240
240

>210
105
120
90
120
240
240
240
240

Moment capacity (kN-m)

120
110
100
90
80
NSM - Formula
NSM - FEA
EBR - Formula
EBR - FEA

70
60
50
40

0

30

60
90
Time (mins)

120

150

(a) Beams without insulation

Moment capacity (kN-m)

120
110
100
90
80
NSM - Formula
NSM - FEA
EBR - Formula
EBR - FEA

70
60
50
40

0

30

60

90

120 150 180
Time (mins)

210

240

270

(b) Beams with insulation
Figure 7.28 Validation of the proposed approach by comparing predicted moment
capacity with FEA results (Beam 200×350mm with VG insulation)

303

Moment capacity (kN-m)

450
400

NSM - Formula
NSM - FEA
EBR - Formula
EBR - FEA

350
300
250
200

0

30

60
90
Time (mins)

120

150

(a) Beams without insulation

Moment capacity (kN-m)

450
400
350
300

NSM - Formula
NSM - FEA
EBR - Formula
EBR - FEA

250
200

0

30

60

90

120 150 180
Time (mins)

210

240

270

(b) Beams with insulation
Figure 7.29 Validation of the proposed approach by comparing predicted moment
capacity with FEA results (Beam 350×500 mm with VG insulation)

304

7.5 Limitations of Applicability
Although the proposed approach is applicable over a large range of parameters,
the following limitations are to be applied since these equations are developed based on
these types of FRP strengthened RC members in the analysis.
1) The proposed approach is applicable for evaluating temperatures or fire resistance in
FRP strengthened RC members exposed to standard fire only. These equations are not
applicable for design fires, which have a cooling phase following the growth phase.
2) The temperature predictions on FRP laminates or strips using proposed equations
does not account for uncertainty factors influencing fire insulation, such as cracking
of insulation, or uneven insulation thickness.
3) The proposed approach does not account for the cable action developed through cool
anchorage of FRP reinforcement. In the cases where anchorage zones are protected,
the proposed approach gives conservative predictions.
4) The proposed simplified approach for moment capacity is applicable to simply
supported RC beams only, since the effect of axial restraint resulting from fire is not
taken into account.

7.6 Summary
This chapter presents a simplified approach for assessing fire resistance of FRP
strengthened RC beams exposed to standard fire. This approach is developed by applying
an analogy as that of room temperature design as specified in ACI 440.2 (2008), but the
temperature induced strength degradation in concrete, reinforcing steel, and FRP, are
accounted for in evaluating moment capacity at any give fire exposure time. The
305

proposed approach is capable of predicting temperatures at various locations, and it also
accounts for various parameters such as FRP strengthening type and insulation properties.
The validity of the proposed approach is established by comparing temperature and fire
resistance predictions with those obtained from fire tests and finite element analysis. The
applicability of the proposed approach in design situation is also illustrated through
detailed examples. Overall the proposed approach provides a simple and rational method
for evaluating fire response of FRP strengthened RC beams exposed to standard fires.

306

CHAPTER 8

CONCLUSIONS AND RECOMMENDATIONS
8.1 General
This dissertation presents a comprehensive study on the behaviour of NSM FRP
strengthened RC beams under fire conditions. Both experimental and numerical studies
were carried out to evaluate the fire resistance of NSM FRP strengthened RC beams and
the critical influencing factors. As part of experimental studies, a large number of
property tests were carried out to develop data on variation of thermal and mechanical
properties of NSM FRP as a function of temperature. Data from these tests was utilized to
develop empirical temperature-property relations for NSM FRP over a wide temperature
range. Further, full-scale fire resistance tests were carried out on four NSM FRP
strengthened RC T-beams. Data from fire tests was utilized to gauge the effect of
insulation, load level, and axial restraint on fire resistance of NSM FRP strengthened
beams.
As part of numerical studies, a numerical model, previously developed for
externally bonded FRP strengthened RC beams, was extended to model the response of
NSM FRP strengthened RC beams under realistic fire, loading and restraint conditions.
This model is based on a macroscopic finite element approach, and utilizes time
dependent moment-curvature relationships to trace the response of FRP strengthened RC
beam from pre-loading to failure under fire conditions. The model accounts for high
temperature properties of constituent materials, various strain components, and fire
307

induced bond degradation and axial restraint force. The validity of the modal was
established by comparing predicted response parameters with measured data in fire tests
carried out at MSU and also those reported in literature.
The validated numerical model was further applied to conduct a set of parametric
studies to quantify the influence of critical factors on fire response of NSM FRP
strengthened RC beams. Results generated from parametric studies were utilized to
develop a rational design methodology for evaluating fire resistance of NSM FRP
strengthened RC beams. This methodology comprised of two steps, namely, evaluating
cross-sectional temperatures and calculating moment capacity of beam at any given fire
exposure time. For accessing temperature profiles in an FRP strengthened RC beam, a set
of empirical temperature equations was developed by taking into account various
influencing factors. For accessing moment capacity of FRP strengthened RC beams at
any given fire exposure time, an approach similar to that at room temperature is utilized
but temperature dependant strength properties of concrete, steel and FRP are substituted
in place of room temperature properties. The proposed approach accounts for various
factors influencing fire response of FRP strengthened RC beams, and thus provides a
useful tool for structural fire design of FRP strengthened RC beams.

8.2 Key Findings
Based on the information presented in this dissertation, the following key conclusions are
drawn:
1. There is very limited information on fire response of NSM FRP strengthened RC
beams. Since the behavior of NSM FRP strengthened RC members is quite
308

different from that of external FRP strengthened RC members, currently available
data for external FRP strengthened beams cannot be directly applied to NSM FRP
strengthened beams.
2. NSM CFRP strips and rods retain much of tensile strength and modulus (up to
80%) till about 200°C. Beyond 200°C, tensile strength and elastic modulus of
NSM CFRP decrease at a faster pace due to decomposition of polymer resin. At
600°C, NSM CFRP retains only about 10% of its original strength.
3. Bond strength and modulus of NSM FRP system decrease significantly with
temperature, and only 20% of the original bond strength is retained at 200°C.
Bond strength and modulus continue to degrade in 200-400°C range, and reaches
almost zero at 400°C. Bond stress-slip response of NSM FRP follows a similar
pattern at both room and high temperatures. However, the peak value (bond
strength) and the slope (bond modulus) are smaller at high temperatures.
4. Coefficient of thermal expansion (CTE) of NSM FRP varies significantly
depending on direction and composition. NSM GFRP has positive CTE
(expansion) in both transverse and longitudinal directions. NSM CFRP expands in
transverse direction at elevated temperatures, but shrinks in longitudinal direction.
GFRP and CFRP experience larger thermal expansion (or shrinking) at higher
temperatures.
5. NSM FRP strengthened beam can provide about three hours of fire resistance,
even without fire insulation. Presence of cooler anchorage enables the remaining
NSM FRP strips (or carbon fibers) to contribute to load carrying capacity of the
beam through a “cable” action under fire conditions. In addition, provision of fire
309

insulation or axial restraint enhances fire resistance of NSM FRP strengthened RC
beams.
6. The proposed macroscopic finite element model is capable of tracing the response
of NSM FRP strengthened RC beams from pre-fire stage to collapse under fire
conditions. The model accounts for rectangular and T cross sections, high
temperature properties of constitutive materials (concrete, steel rebars, NSM FRP
and insulation), bond degradation at NSM FRP-concrete interface, as well as axial
restraint at beam supports. Thermal and structural response predictions from the
model compare well with those measured in tests at both ambient and fire
conditions.
7. Results from parametric studies indicate that type of FRP strengthening,
reinforcement ratio of steel and FRP, load level, axial restraint, fire scenario, and
insulation scheme have significant influence on the fire response of NSM FRP
strengthened RC beam. However, location of NSM FRP and compressive strength
of concrete only have moderate influence on fire response. Specifically:
• NSM FRP strengthened RC beam possesses higher fire resistance than that of
external FRP strengthened RC beam, but lower fire resistance than that of
conventional RC beam.
• Higher reinforcement ratio of FRP leads to lower fire resistance of NSM FRP
strengthened RC beam.
• Type of fire exposure has significant influence on the fire resistance of NSM
FRP strengthened RC beam. Under most design fire scenarios, NSM FRP

310

strengthened RC beam can sustain up to three hours of fire resistance even
without fire insulations.
• Higher load level lowers the fire resistance of NSM FRP strengthened RC
beam. Presence of axial restraint enhances fire resistance.
• Provision of fire insulation significantly increases fire resistance, and an
optimal fire insulation scheme is also proposed for an NSM FRP strengthened
RC beam.
• Placing NSM FRP at inner locations (center of beam soffit) or using higher
concrete strength slightly increases the fire resistance of NSM FRP
strengthened RC beam.
8. The proposed approach for evaluating temperature and moment capacity can be
applied to assess fire response of NSM FRP strengthened RC beams under
standard fire exposure. This approach is capable of predicting cross sectional
temperatures, stress levels in steel and FRP, effective concrete width, and moment
capacity at any given fire exposure time. The simplicity and wide range of
applicability of the proposed approach make it attractive for incorporation in
design standards.

8.3 Recommendations for Future Research
Although this study has advanced the state-of-the-art with respect to fire response
of NSM FRP strengthened RC beams, further research is required to fully characterize
the complex behaviour of NSM FRP strengthened RC beams exposed to fire. The
following are some of the key recommendations for future research in this area:
311

•

Due to a large variety of available NSM adhesive materials, more experimental
data is needed to evaluate the effect of NSM adhesive, especially cementitious
based adhesives on fire response of NSM FRP strengthened RC beams.

•

Further fire resistance experiments are needed to develop data on fire response of
NSM FRP strengthened RC beams with different configurations including cross
sectional type, reinforcement ratio of NSM FRP and steel, and insulation layout.

•

Further experimental and numerical studies are needed to obtain complete
understanding on the cable action developed through NSM FRP. The moment
contribution from this cable action needs to be quantified for evaluating fire
resistance of NSM FRP strengthened RC beams.

•

Further work is required to incorporate more advanced features into numerical
model, such as accounting for cracking in insulation or concrete, effect of FRP
charring resulting from pyrolysis process, as well as accounting for prestressed
concrete members with FRP reinforcement.

•

More work is needed to extend the proposed design methodology to account for
the response of FRP strengthened RC beams exposed to design fire scenario (with
cooling phase).

8.4 Research Impact
Due to sensitivity of FRP materials to high temperatures, the performance of FRP
strengthened RC members under fire conditions is a primary concern for applications in
buildings, where fire resistance of a structural member is a major design requirement.
Recently emerged NSM FRP strengthening is considered to possess higher fire resistance
312

than that of conventional strengthening methods such as externally bonded FRP.
However, there is very limited information on fire response of NSM FRP strengthened
members. The studies presented in this dissertation provide a comprehensive evaluation
on the behavior of NSM FRP strengthening under fire conditions, from material level to
structural behaviour of strengthened beams. A fundamental understanding on fire
response of NSM FRP strengthened RC beams is established, and the effects of critical
influencing factors, such as tensile and bond strength properties, loading and restraint
conditions, are quantified through experimental and numerical studies. These studies
have indicated that NSM FRP strengthened RC beams have higher fire resistance than
that of external FRP strengthened RC beams. With proper design and protection, NSM
FRP strengthened RC beam without any fire protection can achieve fire endurance for
more than three hours. For the cases with fire insulation, NSM FRP strengthened RC
beam can achieve up to four hours of fire resistance.
In addition, the numerical model presented in this study provides an effective
alternative for evaluating fire response of NSM FRP strengthened RC beams. This model
accounts for critical influencing factors such as high temperature properties of constituent
materials and bond degradation at FRP-concrete interface. Thus the model can be used to
perform detailed fire resistance analysis on NSM FRP strengthened RC beams.
Further, a rational design approach, in form of a set of simplified equations, is
proposed in this study. This approach is capable of predicting various response
parameters such as cross sectional temperatures and moment capacity of beam at any
given fire exposure time. Thus, a quick and reliable evaluation on fire resistance of FRP
strengthened RC beams can be obtained even without conducting complex fire tests or
313

finite element analysis. The applicability of this approach covers a wide range of beam
sections and insulation schemes, so it is attractive for incorporation in codes and
standards. Overall the research presented in this dissertation facilitates wider use of FRP
in strengthening of concrete members in buildings and other structures where fire safety
is a major design requirement.

314

APPENDICES

315

APPENDIX A
Material Properties at Elevated Temperatures
This appendix provides a summary of high temperature property relationships of
constituent materials of FRP strengthened beam, including concrete, reinforcing steel,
FRP, epoxy, and insulation. The information presented here is used in numerical model
and parametric studies.

A.1 Concrete
A.1.1 Thermal properties
A.1.1.1 Thermal capacity (ρc,TCc,T)
The following property-temperature relations are proposed by Lie (1992) in ASCE
handbook.
3

For siliceous aggregate concrete, with Tc in °C and ρc,TCc,T in J/m -°C
0 ≤ Tc ≤ 200: ρc,T c= (0.005Tc + 1.7) × 106
c,T
200 ≤ Tc ≤ 400: ρc,T cc,= 2.7 ×106
T
400 ≤ Tc ≤ 500: ρc,T cc,T (0.013Tc − 2.5) ×106
=
500 ≤ Tc ≤ 600: ρc,T cc,T =
(−0.013Tc + 10.5) ×106
Tc ≥ 600: ρc,T cc,= 2.7 ×106
T
316

3

For carbonate aggregate concrete, with Tc in °C and ρc,TCc,T in J/m -°C
0 ≤ Tc ≤ 400: ρc,T= 2.566 ×106
cc,T
400 ≤ Tc ≤ 410: ρc,T cc,T= (0.1765Tc − 68.034) ×106
410 ≤ Tc ≤ 455: ρc,T cc,T = Tc + 25.00671) ×106
(−0.05043
455 ≤ Tc ≤ 500: ρc,T= 2.566 ×106
cc,T
500 ≤ Tc ≤ 635: ρc,T cc,T= (0.01603Tc − 5.44881) × 106
635 ≤ Tc ≤ 715: ρc,T cc,T =
(0.005Tc − 100.90225) × 106
715 ≤ Tc ≤ 785: ρc,T cc,T = Tc + 176.07343) ×106
(−0.22103
Tc ≥ 785: ρc,T= 2.566 ×106
cc,T
3

For lightweight concrete, with Tc in °C and ρc,TCc,T in J/m -°C
0 ≤ Tc ≤ 400: ρc,T = 1.930 ×106
cc,T
400 ≤ Tc ≤ 420: ρc,T cc,= (0.0772Tc − 28.95) ×106
T
420 ≤ Tc ≤ 435: ρc,T cc,T = Tc + 46.706) ×106
(−0.1029
435 ≤ Tc ≤ 600: ρc,T = 1.930 ×106
cc,T
600 ≤ Tc ≤ 700: ρc,T cc,T= (0.03474Tc − 18.9140) ×106
710≤ Tc ≤ 720: ρc,T cc,T = Tc + 126.994) ×106
(−0.1737
317

Tc ≥ 720: ρc,T = 1.930 ×106
cc,T
The following property-temperature relations are recommended in Eurocode 2 (2004).
The variations of specific heat (J/kg-°C) of concrete with temperature (Tc in °C) are
20 ≤ Tc ≤ 100: cc,T = 900
100 ≤ Tc ≤ 200: cc,T = 900 + (Tc − 100)
200 ≤ Tc ≤ 400: cc,T = 1000 + (Tc − 200) / 2
400 ≤ Tc ≤ 1200: cc,T = 1100
3

The variations of density (kg/m ) of concrete with temperature (Tc in °C) are
20 ≤ Tc ≤ 115: ρc,T ρ (20°C )
=
115 ≤ Tc ≤ 200: ρc,T = ρ (20°C )(1 − 0.02(T − 115) / 85)
200 ≤ Tc ≤ 400: ρc,T = (20°C )(0.98 − 0.03(T − 200) / 200)
ρ
400 ≤ Tc ≤ 1200: ρc,T = (20°C )(0.95 − 0.07(T − 400) / 800)
ρ
A.1.1.2 Thermal conductivity (kc,T)
The following property-temperature relations are proposed by Lie (1992) in ASCE design
handbook.
For siliceous aggregate concrete, with Tc in °C and kc,T in W/m-°C
0 ≤ Tc ≤ 800: kc,T =Tc + 1.5
−0.000625
318

Tc ≥ 800: kc,T = 1.0
For carbonate aggregate concrete, with Tc in °C and kc,T in W/m-°C
0 ≤ Tc ≤ 293: kc,T = 1.355
Tc ≥ 293: kc,T =Tc + 1.7162
−0.001241
For lightweight concrete, with Tc in °C and kc,T in W/m-°C
0 ≤ Tc ≤ 600: kc,T =Tc + 0.925
−0.00039583
Tc ≥ 600: kc,T = 0.6875
These property-temperature relations are recommended in Eurocode 2 (2004). The
variations of thermal conductivity (W/m-°C) of concrete with temperature (Tc in °C) are
Upper limit: 20 ≤ Tc ≤ 1200: kc,T =/100) + 0.0107(Tc /100)2
2 − 0.2451(Tc
Lower limit: 20 ≤ Tc ≤ 1200: kc,T = Tc /100) + 0.0057(Tc /100)2
1.36 − 0.136(

A.1.1.3 Thermal strain (εc,th)
The thermal strain in concrete specified in ASCE Handbook (Lie 1992) is
= [0.004(Tc 2 − 400) + 6(Tc − 20)] × 10−6
ε c,th

The thermal strain in concrete specified in Eurocode 2 (2004) is
Siliceous aggregate:
20 ≤ Tc ≤ 700: ε c,th = 1.8 ×10−4 + 9 ×10−6 Tc + 2.3 ×10−11Tc3
−
319

700 ≤ Tc ≤ 1200: ε c,th 14 ×10−3
=
Carbonate aggregate:
20 ≤ Tc ≤ 805: ε c,th = 1.2 ×10−4 + 6 × 10−6 Tc + 1.4 × 10−11Tc3
−
805 ≤ Tc ≤ 1200: ε c,th 12 ×10−3
=
A.1.2 Mechanical properties
A.1.2.1 Stress-strain relationship
The stress-strain relationship of concrete specified in ASCE handbook (Lie 1992) is


f'
 c,T

σc = 

 fc',T





 ,ε ≤ ε
max,T 




2
 ε


1 −  max,T − ε   , ε > ε
max,T 
  3ε max,T  

 
 

  ε −ε
max,T
1 − 
  ε max,T
 







fc'

 
 T − 20  
=  fc'  2.011 − 2.353 
fc',T

 1000  
 

0


2

20°C ≤ T ≤ 450°C 


450°C < T ≤ 874°C 


T > 874°C


ε max,T = 0.0025 + (6.0T + 0.04T 2 ) ×10−6
The stress-strain relationship of concrete specified in Eurocode 2 (2004) is

σc =

3ε fc',T

 ε
ε c1,T  2 + 
 ε c1,T





320

3











, ε ≤ ε cu1,T

For εc1(T) < ε ≤ εcu1(T), the Eurocode permits the use of linear as well as nonlinear
descending branch in the numerical analysis. For the parameters in this equation refer to
Table A.1.
Table A.1 Values for main parameters of the stress-strain relationships
of NSC at elevated temperature (Eurocode 2)
Normal strength concrete
T (°C)

Siliceous aggregate

fc',T

fc' (20°C )

Carbonate aggregate

εc1,T

εcu1,T

fc',T

fc' (20°C )

εc1,T

εcu1,T

20

1

0.0025

0.02

1

0.0025

0.02

100

1

0.004

0.0225

1

0.004

0.023

200

0.95

0.005

0.025

0.97

0.0055

0.025

300

0.85

0.007

0.0275

0.91

0.007

0.028

400

0.75

0.01

0.03

0.85

0.01

0.03

500

0.6

0.015

0.0325

0.74

0.015

0.033

600

0.45

0.025

0.035

0.6

0.025

0.035

700

0.3

0.025

0.0375

0.43

0.025

0.038

800

0.15

0.025

0.04

0.27

0.025

0.04

900

0.08

0.025

0.0425

0.15

0.025

0.043

1000

0.04

0.025

0.045

0.06

0.025

0.045

1100

0.01

0.025

0.0475

0.02

0.025

0.048

1200

0

-

-

0

-

-

321

A.2 Reinforcing steel
A.2.1 Thermal strain
The thermal strain in reinforcing steel specified in ASCE Handbook (Lie 1992) is

= [0.004(T 2 − 400) + 6(T − 20)] ×10−6
ε ths
The thermal strain in reinforcing steel specified in Eurocode 2 (2004) is
1.2 ×10−5 T + 0.4 × 10−8 T 2 − 2.416 × 10−4


= 
1.1×10−2
ε ths

2 × 10−5 T − 6.2 × 10−3



20°C ≤ T ≤ 750°C 


750°C < T ≤ 860°C 

20°C ≤ T ≤ 750°C 


A.2.2 Stress-strain relationship
The stress-strain relationship of reinforcing steel specified in ASCE Handbook (Lie 1992)
is
 f (T , 0.001)
εs,


σ s =  0.001
 f (T , 0.001) ε + f (T , ε − ε + 0.001) − f (T , 0.001),
p
s
p
 0.001





εs > ε p 



εs ≤ ε p 

f (T ,= 6.9(50 − 0.04T )[1 − exp((−30 + 0.03T ) x )]
x)

ε p = 4 ×10−6 f y ,20
where: σs and εs are stress (MPa) and strain in steel reinforcement, respectively, and fy,20
is the yield strength of reinforcing steel (MPa) at room temperature.

The stress-strain relationship of reinforcing steel specified in Eurocode (2004) is

322

 ε s Es,T

 f sp,T − c + (b / a )(a 2 − (ε sy ,T − ε s )2 )0.5

 f sy ,T
σs = 

ε s − ε st ,T 

 f sy ,T 1 −
 ε su ,T − ε st ,T 





0.0


ε sp,T =

f sp,T
Es,T

ε s ≤ ε sp,T



ε sp,T < ε s ≤ ε sy ,T 

ε sy ,T < ε s ≤ ε st ,T 


ε st ,T < ε s ≤ ε su ,T 


ε s > ε su ,T


, ε sy ,T = 0.02 , ε st ,T = 0.15 , ε su ,T = 0.2

a 2 = (ε sy ,T − ε sp,T )(ε sy ,T − ε sp,T +

c
Es,T

)

b 2 = sy ,T − ε sp,T ) Es,T + c 2
c(ε

( f sy ,T − f sp,T )2
c =
(ε sy ,T − ε sp,T ) Es,T − ( f sy ,T − f sp,T )
2

The values of fsp,T, fsy,T, and Es,T can be obtained from Table A.2.

323

Table A.2 Values for main parameters of stress-strain relationships of
reinforcing steel at elevated temperatures (Eurocode 2)
Steel temperature T (°C)

fyT / fy

fsp / fy*

EsT / Es*

20

1

1

1

100

1

1

1

200

1

0.807

0.9

300

1

0.613

0.8

400

1

0.42

0.7

500

0.78

0.36

0.6

600

0.4

0.18

0.31

700

0.23

0.075

0.13

800

0.11

0.05

0.09

900

0.06

0.0375

0.0675

1000

0.04

0.025

0.045

1100

0.02

0.0125

0.0225

1200

0

0

0

* fy and Es are yield strength and modulus of elasticity at room temperature.

A.3 FRP
A.3.1 Thermal Properties (proposed by Griffis et al. 1984)
A.3.1.1 Specific heat (cw,T)
In the following equations, specific heat (cw,T) has units of (kJ/kg -°C) and Tw in °C
324

0 ≤ Tw ≤ 325: cw,T = 1.25+

0.95
Tw
325

325 ≤ Tw ≤ 343: cw,T 2.2+
=

2.8
(Tw − 325)
18

343 ≤ Tw ≤ 510: cw,T 5.0+
=

−0.15
(Tw − 343)
167

510 ≤ Tw ≤ 538: cw,T 4.85+
=

−3.59
(Tw − 510)
28

538 ≤ T= 1.265+
w ≤ 3316: cw,T

1.385
(Tw − 538)
2778

Tw ≥ 3316: cw,T = 0

A.3.1.2 Density (ρw,T)
3

In the following equations, density (ρw,T) has units of (g/cm ) and Tw in °C
0 ≤ Tw ≤ 510: ρ w,T = 1.6
−0.35
510 ≤ Tw ≤ 538: ρ w,T =
(Tw − 510)
1.6 +
28

538 ≤ Tw ≤ 120: ρ w,T = 1.25

A.3.1.3 Thermal conductivity (kw,T)
In the following equations, thermal conductivity (kw,T) has units of (W/m-°C) and Tw
in °C
325

0 ≤ Tw ≤ 500: kw,= 1.4 +
T

−1.1
Tw
500

500 ≤ Tw ≤ 650: k w,T =
1.4 +

−0.1
(Tw − 500)
150

Tw ≥ 650: kw,T = 0.2
A.3.2 Mechanical Properties
A.3.2.1 Tensile strength and elastic modulus for internal FRP rebar and external FRP
laminates (proposed by Bisby et al. 2005)
In the following equations, the units of tensile strength (ff,T) and elastic modulus (Ef,T)
are MPa for temperature Tw in °C
1 − aσ
1 + aσ
) tanh(−bσ (Tw − cσ ) +
)
2
2
1 − aE
1 + aE
= E20°C (
E f ,T
) tanh(−bE (Tw − cE ) +
)
2
2
f f ,T
= f 20°C (

where, f20°C and E20°C are tensile strength and modulus of FRP at ambient conditions.
CFRP: aσ = 0.1, bσ = 5.83e − 3, cσ = 339.54

aE = 0.05, bE = 8.68e − 3, cE = 367.41
GFRP: aσ = 0.1, bσ = 8.10e − 3, cσ = 289.14

aE = 0.05, bE = 7.91e − 3, cE = 320.35
AFRP: aσ = 0.1, bσ = 8.48e − 3, cσ = 287.65

aE = 0.05, bE = 7.93e − 3, cE = 290.49

326

A.3.2.2 Tensile strength and elastic modulus for NSM FRP reinforcement (proposed by
Yu and Kodur 2013)
The following equations provide reduction factors of tensile strength and elastic
modulus at elevated temperatures.
For CFRP strip, the reduction factors are

0.56 − 0.44 tanh(0.0052(T − 305))
Strength: f (T ) =
0.51 − 0.49 tanh(0.0035(T − 340))
Modulus: E (T ) =
For CFRP rod, the reduction factors are

0.54 − 0.46 tanh(0.0064(T − 330))
Strength: f (T ) =
0.51 − 0.49 tanh(0.0033(T − 320))
Modulus: E (T ) =
where T is FRP temperature in °C, f(T) and E(T) are reduction factors for tensile strength
and elastic modulus respectively.

A.3.3 Bond Properties
A.3.3.1 Bond properties of internal FRP rebar
The following equations provide the variation of bond strength for internal FRP
rebar at elevated temperatures (proposed by Katz and Berman 2000).

 0.02 
k1

τ = 0.5(1 − τ r ) tanh −
T − k1 (Tg + 0.02 Cr )   + 0.5(1 + τ r )

 Cr 

1,


k1 =1 − 0.025(Tg − 80)

0



327




80 < Tg < 120, 

Tg ≥ 120 

Tg ≤ 80,

where, τ is the normalized bond strength, T is the temperature, τr is the residual bond
strength, Cr is the degree of cross-linking, Tg is the glass transition temperature of
polymer.

A.3.3.2 Bond properties of external FRP laminates
Ahmed (2010) complied the available test data on bond degradation in externally
bonded FRP, and the following temperature dependent bond strength was proposed.
fT
 1 
=  (T − 40) (40°C≤ T ≤ 120°C)
1− 
f 20
 80 

where, f20 and fT are the bond strength at room and higher temperatures respectively, T is
the temperature at the interface of FRP and concrete.

A.3.3.3 Bond properties of NSM FRP reinforcement
The following equations provide reduction factors of bond strength and bond
modulus for NSM FRP over a wide temperature range (20-400°C). These relations are
based on a number of pull-out tests performed by Yu and Kodur (2013).
For Tyfo T300 epoxy, the reduction factors are

0.55 − 0.45 tanh(0.011(T − 119))
Bond strength: τ (T ) =
0.59 − 0.41tanh(0.01(T − 143))
Bond modulus: E (T ) =
For Tyfo S epoxy, the reduction factors are

0.55 − 0.45 tanh(0.012(T − 129))
Bond strength: τ (T ) =
0.6 − 0.4 tanh(0.009(T − 143))
Bond modulus: E (T ) =
328

where T is NSM epoxy temperature in °C, τ(T) and E(T) are reduction factors for bond
strength and bond modulus respectively.

A.4 NSM Epoxy Adhesive
There are no studies conducted to evaluate thermal properties of NSM epoxy
adhesives. However, previous studies on thermal properties of other types of epoxy can
provide a rough estimation on the values of thermal properties. Table A.3 presents some
of previous studies on thermal properties of epoxy at elevated temperatures.
Table A.3 Previous studies on thermal properties of epoxy
Thermal
conductivity
(W/m-°C)

Specific heat
(kJ/kg-°C)

Temperature
range (°C)

0.18-0.32

1.3-2.3

23-223

Epoxy phenolic
resin

0.134

--

30-100

Epoxy resin

0.16

0-2.3

20-450

Epoxy cast resins

0.17-0.21

1.11-2.11

20-200

Reference

Material

Chern et al.
(2002)
Shokralla and
Al-Muaikel
(2010)
Kandare et
al. (2010)
NPL (2013)

Hercules 3501-6
resin

It can be seen in Table A3 that the values of thermal conductivity and specific
heat are reasonably close for different types of epoxy. The values of thermal conductivity
vary in the range of 0.13-0.32 W/m-°C, whereas those of specific heat vary in the range
of 0-2.3 kJ/kg-°C. Thus, the experimental data reported by Chern et al. (2002) is applied
in the numerical model for thermal properties of NSM epoxy adhesives. The temperature
dependent thermal conductivity is:

329

300K ≤ Te ≤ 500K:
04
ke,T = (0.202 + 6.122 × 10−3T − 4.8107 × 10−5 T 2 + 1.248 ×10−7 T 3 − 1.043 ×10−1 T )

where, Te is epoxy temperature in K, ke,T is thermal conductivity of epoxy in W/m-K.
The temperature dependent specific heat is:
300K ≥ Te ≥ 502K: ce,T (5.34T − 456.9)
=
Te ≥ 502K: ce,T= (2867.6 − 13.322T + 4.304 ×10−2 T 2 − 3.776 ×10−5 T 3 )
where, ce,T is specific heat of epoxy in kJ/kg-K.

A.5 Insulation
A.5.1 Tyfo Vermiculite-Gypsum (VG)
This insulation is manufactured by FYFE Co. LLC as fire proofing system for
FRP composites. These thermal properties relationships are based on therogravimetric
analysis (TGA) performed by Bisby (2003).

A.5.1.1 Density
The VG insulation has two primary components, namely, gypsum and vermiculite.
3

3

Based on typical densities of gypsum (865 kg/m ) and vermiculite (128 kg/m ) mixed in
2:1 ratio, the relationships obtained through TGA are:
0 ≤ TVG ≤ 100: ρVG ,T = 351

330

351 − 287
100 ≤ TVG ≤ 200: ρVG ,T =
351 −
(TVG − 100)
200 − 100

TVG ≥ 200: ρVG ,T = 287
3

where, ρVG is density in kg/m and temperature TVG in °C.

A.5.1.2 Specific heat
The two components of insulation (vermiculite and gypsum) have different
specific heat values with temperature variation. For specific heat relationships presented
below, it has been assumed that specific heat of vermiculites remains constant whereas it
changes with temperature for gypsum. The effect of dehydration has been included by
artificially increasing the specific heat around 100°C.
0 ≤ TVG ≤ 20: cVG ,T = 1.1763
1.3058 − 1.1763
20 ≤ TVG ≤ 78: cVG ,T =
1.1763 +
(TVG − 20)
78 − 20
6.9066 − 1.3058
78 ≤ TVG ≤ 125: cVG ,T =
1.3058 +
(TVG − 78)
125 − 78
1.3722 − 1.1763
125 ≤ TVG ≤ 137: cVG ,T =
6.9066 +
(TVG − 125)
137 − 125
1.3722 − 1.0136
137 ≤ TVG ≤ 153: cVG ,T =
1.3722 +
(TVG − 137)
153 − 137
1.0136 − 0.8609
153≤ TVG ≤ 610: cVG ,T =
1.0136 +
(TVG − 153)
610 − 153

1.6976 − 0.8509
610 ≤ TVG ≤ 663: cVG ,T =
0.8509 +
(TVG − 610)
663 − 610
331

1.6976 − 0.9167
663 ≤ TVG ≤ 690: cVG ,T =
1.6976 +
(TVG − 663)
690 − 663

TVG ≥ 690: cVG ,T = 0.9167
where, cVG is specific heat of VG insulation in J/kg-°C and temperature TVG in °C.

A.5.1.3 Thermal conductivity
The thermal conductivity of vermiculite is constant with temperature and that of
gypsum varies with temperature. The variation of thermal conductivity kVG (W/m-°C)
with temperature TVG (°C) is expressed by:
0 ≤ TVG ≤ 100: kVG ,T = 0.1158
0.1158 − 0.0726
100 ≤ TVG ≤ 101: kVG ,T =
0.1158 +
(TVG − 100)
101 − 100

101 ≤ TVG ≤ 400: kVG ,T = 0.0726
0.1224 − 0.0726
400 ≤ TVG ≤ 800: kVG ,T =
0.0726 −
(TVG − 400)
800 − 400
0.2087 − 0.1224
TVG ≥ 800: kVG ,T =
0.1224 −
(TVG − 800)
1000 − 800

A.5.2 Promatect Calcium – Silicate Boards
The following thermal properties relationships are based on reported thermal
properties in the literature or those specified by manufacture (Deuring 1994, Blontrock et
al. 2000, Ahmed 2010).
332

A.5.2.1 Density
The following values of density of Promatech insulation are proposed by Deuring
(1994) and Blontrock et al. (2000).
Promatech-H: ρi = 870
Promatech-100: ρi = 875
Promatech-L: ρi = 500
A.5.2.2 Specific heat
The specific heat (J/kg-°C) for calcium silicate insulating slabs is:
(www.nu-techresources.com/datasheet/PROMATECTH-eng.pdf)
Promatech-H: ci = 920
Promatech-100: ci = 840
Promatech-L: ci = 950
A.5.2.3 Thermal conductivity
The thermal conductivity ki,T of Promatech insulation (J/kg-°C) at various temperatures
Ti (°C) is:
Promatech-H: 0 ≤ Ti ≤ 390: ki,= (1.833e − 4)T + 0.175
T
Ti ≥ 390: ki,T = 0.25
Promatech-100: ki,T = 0.285
333

Promatech-L: 0 ≤ Ti ≤ 100: ki,T= (7.07e − 5)T + 0.083
100 ≤ Ti ≤ 200: ki,T = (4.0e − 5)T + 0.086
200 ≤ Ti ≤ 400: ki,T = (6.0e − 5)T + 0.082
400 ≤ Ti ≤ 500: ki,T = (8.0e − 5)T + 0.074
Ti ≥ 500: ki,T = 0.144

334

APPENDIX B
Design and Load Calculations
This Appendix summarizes the design and load calculations on conventional RC
beam using ACI 318R (2011) and NSM FRP strengthened RC beam using ACI 440.2R
(2008). The cross-section, shear force diagram, and bending moment diagram for the
tested beams are shown in Figure B.1. The design calculations are presented in the
following two sections.

B.1 Design of RC T-beam
1. Configurations and materials
Configurations: See Figure B.1.
Material properties: fc’ = 41.4 MPa, εc = 0.003, fy = 414 MPa
2. Flexural capacity as per ACI-318R (2011)
d 406.4 − 50.8 − 6.4 − 9.5 339.7 mm (Clear concrete cover is 50.8mm)
=
=

Since Neutral axe is located very close to top rebars, the moment contribution of top layer
rebars is neglected.
Based on the force equilibrium principle,
As = 0.85 fc' ⋅ b ⋅ ( β1 ⋅ c)
⋅ fy
854.8mm2 × 414 MPa = × 41.4 MPa × 432mm × (0.75c)
0.85
c = 31.1mm
Based on the strain compatibility principle,
335

εc

=

εt

c d −c
εt
0.003
=
31.1 339.7 − 31.1
εt = 0.0298 > 414 MPa / 201000 MPa = 0.0021, steel yields. The assumption is correct!
Check minimum reinforcement (ACI 318R -10.5.1)
ρmin = 0.0039
=
ρ

As
854.8
=
= 0.0058 > ρ min
b ⋅ d 432 × 339.7

O.K .

Check minimum reinforcement spacing (ACI 318R - 7.6.1)

space= (228.6 − 50.8 − 50.8 − 2 × 6.4 − 3 ×19) / 2
= 28.6 > 25.4 mm or dia. of rebar O.K .
The moment capacity of the beam is
a
M n As f y ⋅ (d − )
=
2

= 854.8 × 414 × (339.7 − 0.5 × 0.75 × 31.1) /106
= 116.1kN ⋅ m

M n = 1.4 Pn
Pn = 82.9 kN and Pu = 74.6 kN

336

432
102
clear cover
thickness

102

228

51

127

#4 transverse
rebar@305mm 38

4#4
4 No. 4

#2 stirrups@152mm

33No. 6
#6

clear cover
thickness

51

38

406
279

51

51
228

(a) Cross section

P

P

127
406 279
152

1402

854
3962

1402

(b) Elevation

M = P×1.4
(c) Bending moment diagram

V=P

V=P
(d) Shear force diagram

Figure B.1 Cross section, elevation and internal force diagram of RC T-beam
337

152

3. Shear capacity as per ACI-318 (#2 stirrups @150mm)
Shear capacity provided by concrete

Vc = 0.16 fc' ⋅ bw ⋅ d = 2 × 41.4 × 228.6 × 339.7 /1000 = 79.9kN
Shear capacity provided by stirrups

=
Vs

Av ⋅ f yt ⋅ d 2 × 31.6 × 241× 339.7
=
= 34.5kN
/1000
s
150

Vn = Vs + Vs = 79.9 + 34.5 = 114.4kN

φVn = 0.75 ×114.4 = 85.8kN > Pu = 74.6kN
Av,min =
0.06 fc' bw s / f yt =
0.75 × 41.4 × 228.6 ×150 / 241/1000
= 0.009 < 2 × 0.049 0.098 O.K .
=
Therefore, using #2 stirrups at 150 mm c/c satisfies shear capacity requirement.
4. T beam configuration check
1) Width of flange (ACI 318R-8.12.2)
width ≤

1
1
× span = × 3658 = 914.5
4
4

O.K .

8×
1016
8 × tslab = 127 = 


overhanging 102 ≤  1
=
 O.K .
 2 × clear dis. to next slab 


2) Flange thickness (ACI 318R - 8.12.4)
thickness = 102 ≥

1
1
× width of web = × 229 = 114
2
2

O.K .

3) Transverse reinforcement shall be spaced not farther apart than 5 times the slab
thickness

338

space = 152 < 5 × slab thickness = 5 ×127 = 635

O.K .

Use #4 rebar @ 150 mm as transverse reinforcement in flange.

B.2 Design of NSM FRP strengthened RC T-beam
1. Material properties
Configurations: See Figure B.2.
Material properties: fc’ = 41.4 MPa, εc = 0.003, fy = 414 MPa
EFRP = 20250 ksi,
εFRP = CE͘·Ka·εfu = 0.95×0.7×0.018 =0.0117 (ACI 440.2R -08 10.1.1)

432
102
clear cover
thickness

102

228

51

127

#4 transverse
rebar@305mm 38

4 No. 4
#4

#2 stirrups@152mm

3 No. 6
3#6

clear cover
thickness

51

two 13.5x4.5
NSM FRP strips

38
279

51

51
228

Figure B.2 Configuration of NSM FRP strengthened RC T-beam

2. Flexural capacity as per ACI 440.2R (2008)

339

406

Based on the force equilibrium principle,
=
As ⋅ f y + AFRP ⋅ f FRP 0.85 fc' ⋅ b ⋅ ( β1 ⋅ c)
854.8mm 2 × 414 MPa + 121mm 2 × (0.0117 ×139.7GPa ) = × 41.4MPa × 432mm × (0.75c)
0.85
c = 47.4 mm <127 mm (within the flange)
Based on the strain compatibility principle,

ε

ε

εf

c
s
= =
c ds − c d f − c

εf
εs
0.003
= =
47.4 339.7 − 47.4 387.4 − 47.4
εs = 0.0165 > 414 MPa / 201000 MPa = 0.0021, steel yields.
εs = 0.0215> 0.0117, FRP fails. Therefore, FRP rupture or debonding controls flexural
failure.
The nominal moment capacity of the beam is
a
a
M n= As f y ⋅ (d s − ) +ψ f AFRP f FRP ⋅ (d f − )
2
2

= 854.8 × 414 × (339.7 − 0.5 × 0.75 × 47.4) /106

+0.85 ×121× (0.117 ×139700) × (387.4 − 0.5 × 0.75 × 47.4) /106
= 175.9kN ⋅ m

The increase in moment capacity is 51.5%

M n = 1.4 Pn
Pn = 125.6 kN and Pu = 113 kN
The load ratio is given as:
LR =

62
×100% = 49.4%
125.6
340

APPENDIX C
Finite Element Formulation
To solve the heat and mass transfer problems, the cross-section of the beam
segment is divided into rectangular elements as shown in Figure 5.1. Since the dependent
variable (the variable to be computed) in the two problems is scalar, Q4 (quadrilateral
element that has four nodes) element is used in the analysis. Due to the nonlinearity of
both problems, the integrations in Eqns. (5.11) through (5.13) are evaluated numerically
using Gaussian quadrate integration technique. The vector of shape functions for Q4
element can be written as:
 (1 − s )(1 − t ) / 4 
 (1 + s )(1 − t ) / 4 

N =
(1 + s )(1 + t ) / 4 


 (1 − s )(1 + t ) / 4 

(C.1)

where: s and t are transformed coordinates as shown in Figure C.1. The analysis is
generally carried out using four Gauss points and the element stiffness matrix (Ke), mass
matrix (Me) and nodal heat or mass flux (Fe) are evaluated at every Gauss point. Those
values of the element matrices at the four Gauss points are summed to form the element
material property matrices which are used for the subsequent steps in the analysis.

341

t

4 (-1,1)

3 (1,1)
s

2 (1,-1)

1 (-1,-1)
Figure C.1 Q4 element in transformed coordinates

342

APPENDIX D
Design Examples
D.1 Example 1 - Fire resistance of NSM FRP strengthened RC beams without fire
insulation
An NSM FRP strengthened RC beam (carbonate aggregate, normal strength) of
span 4.5 m is exposed to a standard ASTM E119 fire and under uniformly distributed
load corresponding to 50% of room temperature capacity. The beam size is 200 mm ×
400 mm and the top surface is protected from fire by the concrete floor slab. The beam
has three 19 mm diameter reinforcing bars at four corners and the clear cover to the
reinforcing bars is 35 mm. The stirrups are of 8 mm dimensions. Two 13.5×4.5 mm
CFRP strips are sued as NSM FRP strengthening. Configuration and material properties
are tabulated in Table D.1. Calculate moment capacity of fire exposed beam as a function
of fire exposure time, and evaluate the fire resistance of beam under such fire and loading
conditions.

400

2ϕ10
3ϕ19
4500

400

200

w

2 13.5x4.5
FRP strips

Figure D.1 Layout and cross section of NSM FRP strengthened RC beam (Beam D1)

343

Table D.1 Properties of Beams D1 and D2
Property
Cross-section (mm)
Span (m)
Loading

Concrete

Steel rebar

Magnitude
Load type
Aggregate
fc’ (MPa)
Cover thickness
Top rebar
Bottom rebar
fy (MPa)
Strengthening
type

Dimension
FRP
strengthening f
FRP (MPa)

VG
insulation

EFRP (GPa)
Groove size
Thermal
conductivity
Specific heat
Density

Beam D1
200×400
4.5
33.8 kN/m, 50%
load ratio
Uniformly
distributed load
Carbonate
41.4
35 mm
3 ϕ 19
2 ϕ 10
414

Beam D2
250×450
6
44.3 kN/m, 50%
load ratio
Uniformly
distributed load
Carbonate
41.4

NSM

EBR

two 13.5×4.5 mm
FRP strips
2068

35 mm
4 ϕ 19
2 ϕ 12.7
414

250×1.0 mm
1133

131
25×10 mm

75.6
-0.116 W/m-K

No insulation

1.176 J/kg-K
3
351 kg/m

Solutions:
Step 1: Calculate temperatures in steel rebars and NSM FRP strips
Applying proposed 1-D and 2-D heat transfer equations to calculate the temperatures in
steel rebar and NSM FRP, respectively.
The distance from the center of corner rebar to two fire exposure side is (35+8+19/2=53)
mm, so y = z = 53 mm. Take the temperature calculation at 1 hour fire-exposure time as
an example. For corner rebar,

344

ηz = =
η y (0.155ln

1

0.0531.5

0.234
− 0.348 0.053 − 0.371) =

Tc =× (−1.481× (0.234 × 0.234) + 0.985 × (0.234 + 0.234) + 0.017)(910 ×10.148 ) = °C
1.0
366
For middle rebar,
= (0.155ln
ηz
= (0.155ln
ηy

1

0.11.5

0.371)
− 0.348 0.1 −= 0.056

1

0.0531.5

− 0.348 0.053 − 0.371) 0.234
=

1.0
261
Tc =× (−1.481× (0.234 × 0.056) + 0.985 × (0.234 + 0.056) + 0.017)(910 ×10.148 ) = °C
For NSM FRP,
= (0.155ln
ηz

1

0.071.5

− 0.348 0.07 = 0.157
− 0.371)

Tc= 1.0 × (−1.481× (0.157 × 0.565) + 0.985 × (0.157 + 0.565) + 0.017)(910 ×10.148 ) 551°C
=
By using spreadsheet the temperatures at other times can be also easily calculated.
The time-temperature curves of rebars and NSM FRP are plotted in Figure D.2.

345

1400

ASTM E119 fire
Middle rebar

Temperature (°C)

1200

Corner rebar
NSM FRP

1000
800
600
400
200
0

0

30

60

90

120 150
Time (min)

180

210

240

Figure D.2 Variation of temperatures in steel rebar and NSM FRP with fire exposure time
in Beam D1

Step 2: Evaluating strength in steel and FRP and effective concrete depth
Knowing the temperature in steel rebars and NSM FRP, the remaining strength in
steel rebar can be evaluated using temperature dependent properties specified in
Eurocode (2004), and the remaining strength in NSM FRP can be obtained utilizing
empirical relations proposed in Chapter 3.
After 1h of fire exposure, the remaining strength in steel is 100% of their room
temperature strength for both corner and middle steel rebars, since their temperature is
lower than 400°C.
The remaining strength f(T) and modulus E(T) in NSM FRP are

f (T ) =
0.56 − 0.44 tanh(0.0052(T − 305))
=0.56 − 0.44 tanh(0.0052(551 − 305)) =0.183
346

E (T ) =
0.51 − 0.49 tanh(0.0035(T − 340))
=
0.51 − 0.49 tanh(0.0035(T − 305)) =
0.202
To evaluate the effective concrete width at compression zone, Table 7.3 is needed. The
effective concrete width for a section of 200×300 can be used in this calculation
(conservative). For 1h fire exposure, the effective concrete width is 91.9% of original
width.

Step 3: Calculate moment capacity of NSM FRP strengthened beam
Based on the force equilibrium principle,
As ⋅ f y ,T + AFRP ⋅ f FRP= 0.85 fc' ⋅ bT ⋅ ( β1 ⋅ c)
,T
854.8mm 2 × 414 MPa + 121mm 2 × (0.0117 × 0.202 ×139.7GPa )

=0.85 × 41.4 MPa × 0.919 × 200mm × (0.75c)
c = 73 mm
Based on the strain compatibility principle,

ε

ε

εf

c
s
= =
c ds − c d f − c

εf
εs
0.003
= =
73
347 − 73 385 − 73
εs = 0.0113 > 414 MPa / 201000 MPa = 0.0021, steel yields.
εs = 0.0128 > 0.0117, FRP failure governs. Eq. 7.24 can be used. Then the moment
capacity of NSM FRP strengthened beam is

347

a
a
M n= As f y ⋅ (d s − ) +ψ f AFRP f FRP ⋅ (d f − )
2
2
= 854.8 × 414 × (347 − 0.5 × 0.75 × 73) /106

+0.85 ×121× (0.0117 × 0.202 ×139700) × (385 − 0.5 × 0.75 × 73) /106
= 125.2kN ⋅ m

By using spreadsheet the moment capacity at other times can also be calculated.
The variation of moment capacity with fire exposure time for NSM FRP
strengthened RC beam is plotted in Figure D.3.

Moment capacity (kN-m)

180
160
140
120
100
80
60
40

0

30

60

90

120 150 180
Time (mins)

210

240

270

Figure D.3 Variation of moment capacity of Beam D1 with fire exposure time

Step 4: Calculate external load and estimate failure time
The moment capacity of NSM FRP strengthened RC beam at room temperature is
calculated to be 168 kN·m as per ACI 440.2 (2008) provisions. Based on the timemoment capacity curve generated in previous step, the beam is estimated to fail at 140
minutes, as shown in Figure D.3. Thus the fire resistance of the beam is 140 minutes.

348

D.2 Example 2 - Fire resistance of External FRP strengthened RC beams with fire
insulation
An external FRP strengthened RC beam (carbonate aggregate, normal strength) of
span 6 m is exposed to a standard ASTM E119 fire and under uniformly distributed load
corresponding to 50% of room temperature capacity. The beam size is 250 mm × 450 mm
and the top surface is protected from fire by the concrete floor slab. The beam has four 19
mm diameter reinforcing bars at four corners and the clear cover to the reinforcing bars is
38 mm. The stirrups are of 8 mm dimensions. One layer of CFRP laminate (250×1 mm)
is used as external FRP strengthening. The beam is protected by U-shaped VG fire
insulation with a thickness of 25mm. Configuration and material properties are tabulated
in Table D.1. Calculate moment capacity of fire exposed beam as a function of fire
exposure time, and evaluate the fire resistance of beam under such fire and loading
conditions.

450

25

2ϕ13
4ϕ19

6000

450

250

w

300x1.5 FRP
laminates

25

Figure D.4 Layout and cross section of external FRP strengthened RC beam (Beam D2)

Solutions:
Step 1: Calculate temperatures in steel rebars and external FRP laminates

349

Applying proposed 1-D and 2-D heat transfer equations to calculate the temperatures in
steel rebar and external FRP, respectively.
Since the beam is protected by fire insulation, the insulation layer needs to be converted
to equivalent concrete layer. It is known that thermal properties of Tyfo VG insulation
(Bisby 2003) and concrete (Lie 1992) as follows.
kVG = 0.116 W/m-K
3

(ρc)VG = 413 kJ/m -K
kc = 1.355 W/m-K
3

(ρc)c = 2566 kJ/m -K
Thus, the thickness of equivalent concrete layer is
zec = t 1.75
zi 4.5

k c ( ρ c )i
1.355 0.413
25 ×
36mm
= 4.5 11.75
×
=
( ρ c)c ki
2.566 0.116

The distance from the center of corner rebar to two fire exposure side is
(36+38+8+19/2=92) mm, so y = z = 92 mm. Take the temperature calculation at 1 hour
fire-exposure time as an example. For corner rebar,

Tc = × (−1.481× (0.08 × 0.08) + 0.985 × (0.08 + 0.08) + 0.017)(910 ×10.148 ) = °C
1.0
150
For middle rebar,
zec = t 1.75
zi 4.5

(0.155ln
ηz =

k c ( ρ c )i
1.355 0.413
25 ×
36mm
= 4.5 11.75
×
=
( ρ c)c ki
2.566 0.116

1

0.1381.5

− 0.348 0.138 − 0.371) =
−0.04

Tc = 1.0 × (−1.481× (−0.04 × 0.08) + 0.985 × (−0.04 + 0.08) + 0.017)(910 ×10.148 ) = 57°C
350

For external FRP (average temperature of FRP laminates is evaluated use the point at
quarter FRP length from fire exposed surface),
= (0.155ln
ηz

1

0.09851.5

− 0.348 0.0985 − 0.371) 0.06
=

Tc= 1.0 × (−1.481× (0.06 × 0.33) + 0.985 × (0.06 + 0.33) + 0.017)(910 ×10.148 ) 339°C
=
By using spreadsheet the temperatures at other times can be also calculated. The
time-temperatures curve of rebars and external FRP are plotted in Figure D.5.
1400

ASTM E119 fire
Middle rebar

1200

Corner rebar
External FRP (avg.)

Temperature (°C)

1000
800
600
400
200
0

0

30

60

90

120 150
Time (min)

180

210

240

Figure D.5 Variation of temperatures in steel rebar and external FRP with fire exposure
time in Beam D2

Step 2: Evaluating the strength in steel and FRP and effective concrete depth
Knowing the temperature in steel rebars and external FRP, the remaining strength
in steel rebar can be evaluated using temperature dependent properties specified in
351

Eurocode (2004), and the remaining strength in external FRP can be obtained utilizing
empirical relations proposed by Bisby et al. (2005).
After 1h of fire exposure, the remaining strength in steel is 100% of their room
temperature strength for both corner and middle steel rebars, since their temperature is
lower than 400°C.
The remaining strength f(T) and modulus E(T) in external FRP are

f (T ) =
0.55 − 0.45 tanh(0.00583(T − 339.54))
= − 0.45 tanh(0.00583(339 − 339.54)) =
0.55
0.55
E (T ) =
0.525 − 0.475 tanh(0.00868(T − 367.41))
= − 0.475 tanh(0.00868(339 − 367.41)) =
0.525
0.64
To evaluate the effective concrete width at compression zone, Table 7.3 is needed. The
effective concrete width for a section of 250×400 can be used in this calculation. For 1h
fire exposure, the effective concrete width is 92.8% of original width.

Step 3: Calculate moment capacity of external FRP strengthened beam
Based on the force equilibrium principle,
As ⋅ f y ,T + AFRP ⋅ f FRP= 0.85 fc' ⋅ bT ⋅ ( β1 ⋅ c)
,T
1134mm 2 × 414 MPa + 250mm 2 × (0.0045 × 0.64 × 75600 MPa )

=0.85 × 41.4 MPa × 0.928 × 250mm × (0.75c)
c = 85.6 mm
Effective strain of FRP is

352

= 0.41
ε fd

fc'
41.4
= 0.41
ε fu
= 0.0045
× 0.015
75600 ×1.0
nE f t f

Based on the strain compatibility principle,

ε

ε

εf

c
s
= =
c ds − c d f − c

εf
εs
0.003
= =
85.6 394 − 85.6 450.5 − 85.6
εs = 0.0108 > 414 MPa / 201000 MPa = 0.0021, steel yields.
εs = 0.0128 > 0.0045, FRP failure governs. Eq. 7.24 can be used. Then the moment
capacity of NSM FRP strengthened beam is
a
a
M n= As f y ⋅ (d s − ) +ψ f AFRP f FRP ⋅ (d f − )
2
2
= 1134 × 414 × (394 − 0.5 × 0.75 × 85.6) /106

+0.85 × 250 × (0.0045 × 0.64 × 75600) × (450.5 − 0.5 × 0.75 × 85.6) /106
= 189.3kN ⋅ m

By using spreadsheet the moment capacity at other times can also be calculated.
The variation of moment capacity with fire exposure time for external FRP
strengthened RC beam is plotted in Figure D.6.

Step 4: Calculate external load and estimate failure time
The moment capacity of external FRP strengthened RC beam is calculated to be 200
kN·m as per ACI 440.2 (2008) provisions. Based on the time-moment capacity curve
generated in previous step, the beam does not fail for four hours of fire exposure. Thus
the fire resistance of the beam is at least four hours.
353

Moment capacity (kN-m)

220
200
180
160
140
120
100
80
60
40

0

30

60

90

120 150 180
Time (mins)

210

240

270

Figure D.6 Variation of moment capacity of Beam D2 with fire exposure time

354

REFERENCES

355

REFERENCES

1.

Abbasi, A. and Hogg, P.J. (2005) “Prediction of the failure time of glass fiber
reinforced plastic reinforced concrete beams under fire conditions.” Journal of
Composites for Construction, ASCE, 9(5), 450-457.

2.

Abbasi, A. and Hogg, P.J. (2006) “Fire testing of concrete beams with fiber
reinforced plastic rebar.” Composite: Part A, 37(8), 1142-1150.

3.

Anderberg, Y. and Thelandersson, S. (1976) “Stress and deformation
characteristics of concrete at high temperatures – Experimental investigation and
material behavior model.” Lund Institute of Technology, Sweden.

4.

Ahmed, A. (2010) “Behavior of FRP Strengthened Reinforced Concrete Beams
under Fire Conditions.” Doctoral Thesis, Michigan State University, East Lansing,
MI, USA.

5.

Ahmed, A. and Kodur, V. (2011) “Effect of bond degradation on fire resistance of
FRP-strengthened reinforced concrete beams.” Composites Part B, 42(2), 226237.

6.

Ahmed, A. and Kodur, V. (2011) “The experimental behavior of FRPstrengthened RC beams subjected to design fire exposure.” Engineering
Structures, 33(7), 2201-2211.

7.

Ali, F.A., Connolly, R.J. and Sullivan, P.J.E. (1996) “Spalling of high strength
concrete at elevated temperature.” Applied Fire Science, 6(3), 3-14.

8.

Alkhrdaji, T., Nanni, A., Chen, G. and Barker, M. (1999) “Upgrading the
transportation infrastructure: solid RC decks strengthened with FRP.” Concrete
International, 21(10), 37-41.

9.

Al-Mahmoud, F., Castel, A., Francois, R. and Tourneur, C. (2011) “Anchorage
and tension-stiffening effect between near-surface-mounted CFRP rods and
concrete.” Cement and Concrete Composites, 33(2), 346-352.

10.

American Concrete Institute Technical Committee 216. (2007) “Code
requirements for determining fire resistance of concrete and masonry construction
assemblies.” ACI 216R-07, Farmington Hills, MI.

356

11.

American Concrete Institute Technical Committee 318. (2011) “Building code
requirements for structural concrete and commentary.” ACI 318R-11, Farmington
Hills, MI.

12.

American Concrete Institute Technical Committee 440. (2006) “Guide for the
design and construction of concrete reinforced with FRP bars.” ACI 440.1R-06,
Farmington Hills, MI.

13.

American Concrete Institute Technical Committee 440. (2008) “Guide for the
design and construction of externally bonded FRP systems for strengthening
concrete structures.” ACI 440.2R-08, Farmington Hills, MI.

14.

American Concrete Institute Technical Committee 440. (2012) “Guide test
methods for Fiber-Reinforced Polymers (FRPs) for reinforcing or strengthening
concrete structures.” ACI 440.3R-12, Farmington Hills, MI.

15.

American Society of Civil Engineers (ASCE). (2013) “Report Card for America's
Infrastructure.” Reston, VA.

16.

American Society for Testing and Materials. (2012) “Standard test methods for
fire tests of building construction and materials.” ASTM E119, West
Conshohocken, PA.

17.

American Society for Testing and Materials. (2013) “Standard Test Method for
Surface Flammability of Materials Using a Radiant Heat Energy Source.” ASTM
E162, West Conshohocken, PA.

18.

American Society for Testing and Materials. (2013) “Standard Test Method for
Specific Optical Density of Smoke Generated by Solid Materials.” ASTM E662,
West Conshohocken, PA.

19.

American Society for Testing and Materials. (2013) “Standard Test Method for
Surface Burning Characteristics of Building Materials.” ASTM E84, West
Conshohocken, PA.

20.

American Society for Testing and Materials. (2012) “Standard test method for
linear thermal expansion of solid materials by thermomechanical analysis.” ASTM
E831, West Conshohocken, PA.

21.

Anagnostopoulos, G., Parthenios, J. and Galiotis, C. (2008) “Thermal stress
development in fibrous composites.” Materials Letters, 62(3), 341-345.

22.

Ashby, M.F. and Jones, D.R.H. (1999) Engineering materials: an introduction to
microstructures, processing and design. Oxford, Pergamon Press.
357

23.

Asplund, S.O. (1949) “Strengthening bridge slabs with grouted reinforcement.”
ACI Structural Journal, 20(4), 397–406.

24.

Bank, L.C. (1993) “Properties of FRP reinforcement for concrete,” FiberReinforced-Plastic (FRP) Reinforcement for Concrete Structures: Properties and
Applications, Developments in Civil Engineering, V.42, Elsevier, Amsterdam, 5986.

25.

Barros, J.A.O., Dias, S.J.E. and Lima, J.L.T. (2007) “Efficacy of CFRP-based
techniques for the flexural and shear strengthening of concrete beams.” Cement
and Concrete Composites, 29(3), 203-217.

26.

Bilotta, A., Ceroni, F., Di Ludovico, M., Nigro, E., Pecce, M. and Manfredi, G.
(2011) “Bond efficiency of EBR and NSM FRP systems for strengthening
concrete members.” Journal of Composite for Construction, 15(5), 757-772.

27.

Bisby, L.A. (2003) “Fire behavior of fibre-reinforced polymer (FRP) reinforced
or confined concrete.” Doctoral Thesis, Queen’s University, Kingston, Canada.

28.

Bisby, L.A., Green, M.F. and Kodur V. (2005) “Response to fire of concrete
structures that incorporate FRP.” Progress in Structural Engineering and
Materials, 7(3), 136-149.

29.

Blaschko, M. (2003) “Bond behavior of CFRP strips glued into slits.”
Proceedings of 6th International Symposium on Fibre-Reinforced Polymer (FRP)
Reinforcement for Concrete Structures (FRPRCS-6), Singapore, 205-214.

30.

Blontrock, H., Taerwe, L., and Vandevelde, P. (2000). “Fire tests on concrete
beams strengthened with fibre composite laminates.” Third PhD Symposium,
Vienna, Austria.

31.

Blontrock, H., Taerwe, L., and Vanwalleghem, H. (2002). “Bond testing of
externally glued FRP laminates at elevated temperature.” Proceeding of the
International Conference Bond in Concrete – from research to standards,
Budapest, Hungary, 648-654.

32.

BNZ
Materials
(1998)
“Structural
Insulation:
Summary
Data.” http://www.bnzmaterils .com/datasi.html (Accessed on Feb. 1, 2013)

33.

Bowles, D.E. and Tompkins, S.S. (1989) “Prediction of coefficients of thermal
expansion for unidirectional composites.” Journal of Composite Materials, 23(4),
370-388.

34.

British Standard Institution. (1987) “Fire tests on building materials and structures
- Part 20: method from determination of the fire resistance of elements of
construction (general principles).” BS476-20, London, UK.
358

35.

Bruggeling, A.S.G. (1992) External prestressing – A state of the Art. External
Prestressing, ACI SP-120, Detroit, Michigan, 61-82.

36.

Buchanan, A. H. (2002). Structural design for fire safety, Wiley, Chichester, UK.

37.

Burke, P.J., Bisby, L.A. and Green, M.F. (2013) “Effects of elevated temperature
on near surface mounted and externally bonded FRP strengthening systems for
concrete.” Cement & concrete composites, 35(1), 190-199.

38.

Campbell, T.I. and Kodur, V.K.R. (1990) “Deformation controlled nonlinear
analysis of prestressed concrete continuous beams.” PCI Journal, 35(5), 42-55.

39.

Canadian Standards Association (CSA) S806-02 (2002) “Design and construction
of building components with fibre-reinforced polymers.” CAN/CSA S806,
Rexdale, Canada.

40.

Chang, Y.F., Chen, Y.H., Sheu, M.S. and Yao, G.C. (2006) “Residual stressstrain relationship for concrete after exposure to high temperatures.” Cement and
Concrete Research, 36(10), 1999-2005.

41.

Cheng F.P., Kodur, V.K.R. and Wang, T.C. (2005) “Stress-strain curves for high
strength concrete at elevated temperatures”, Journal of Materials in Civil
Engineering, 16(1), 84-94.

42.

Chern, B.C., Moon, T.J., Howell, J.R., and Tan, W. (2002). “New experimental
data for enthalpy of reaction and temperature- and degree-of-cure-dependent
specific heat and thermal conductivity of the Hercules 3501-6 epoxy system.”
Journal of Composite Materials, 36(17), 2061-2072.

43.

Deuring, M. (1994) “Brandversuche an nachtraglich verstarkten tragern aus beton.”
Swiss Federal Laboratories for Materials Testing and Research, Dubendorf,
Switzerland.

44.

Dotreppe, J.C. and Franssenm, J.M. (1985) “The use of numerical models for the
fire analysis of reinforced concrete and composite structures.” Engineering
Analysis, 2(2), 67-74.

45.

Dwaikat, M.M.S. and Kodur, V.K.R. (2013) “A simplified approach for predicting
temperatures in fire exposed steel members.” Fire Safety Journal, 55(1), 87-96.

46.

Dwaikat, M. (2009). “Flexural response of reinforced concrete beams exposed to
fire.” Doctoral Thesis, Michigan State University, East Lansing, MI.

359

47.

Dwaikat, M. and Kodur, V.K.R. (2008). “A numerical approach for modeling the
fire induced restraint effects in reinforced concrete beams.” Fire Safety Journal,
43(4), 291-307.

48.

Dwaikat, M. and Kodur, V.K.R. (2009). “Response of Restrained Concrete
Beams under Design Fire Exposure.” Journal of Structural Engineering, ASCE,
135(11), 1408–1417.

49.

De Lorenzis, L. and Nanni, A. (2002) Bond between NSM fiber-reinforced
polymer rods and concrete in structural strengthening. ACI Structural Journal,
99(2), 123–32.

50.

De Lorenzis, L., Rizzon, A. and La Tegola, A. (2002) “A modified pull-out test
for bond of near-surface mounted FRP rods in concrete.” Composites: Part B,
33(8), 589-603.

51.

De Lorenzis, L. and Teng, J.G. (2007) “Near-surface mounted FRP reinforcement
- an emerging technique for strengthening structures.” Composites Part B, 38(2),
119–143.

52.

Di Tommaso, A., Neubauer, U., Pantuso, A., and Rostasy, F. S. (2001).
“Behaviour of adhesively bonded concrete-CFRP joints at low and high
temperatures.” Mechanics of Composite Materials, 37(4), 327-338.

53.

El-Hacha, R and Rizkalla, S.H. (2004) “Near-surface-mounted fiber-reinforced
polymer reinforcements for flexural strengthening of concrete structures.” ACI
Structural Journal, 101(5), 717-726.

54.

European Committee for Standardization. (2002) “EN 1991-1-2: Actions on
structures. Part 1-2: General actions - Actions on structures exposed to fire.”
Eurocode 1, Brussels, Belgium.

55.

European Committee for Standardization. (2004) “EN 1992-1-2: Design of
concrete structures. Part 1-2: General rules - structural fire design.” Eurocode 2,
Brussels, Belgium.

56.

Evseeva, L.E., Tanaeva, S.A. Dubkova, V.I. and Maevskaya, O.I. (2003)
“Influence of thermocycling on the thermophysical properties of epoxy
compositions hardened with phosphorous carbon fibers.” Journal of Engineering
Physics and Thermophysics, 76(1), 222-225.

57.

Fédération Internationale du Béton. (2007) “FRP reinforcement in RC structures.”
FIB Bulletin 40, Lausanne, Switzerland.

360

58.

Firmo, J.P., Correia, J.R. and Franca, P. (2012) “Fire behaviour of reinforced
concrete beams strengthened with CFRP laminates: Protection systems with
insulation of the anchorage zones.” Composites: Part B, 43(3), 1545-1556.

59.

Flynn, D.R. (1999) “Response of High Performance Concrete to fire conditions:
Review of thermal property data and measurement techniques”, NIST GCR 99767, MetSys Corporation, U.S.

60.

Foye, R. L. (1975) “Creep analysis of Laminates.” Composite Reliability, ASTM
STP-580, 381-395.

61.

Franssen J.M., Kodur V.R. and Mason J. (2005) User’s manual for SAFIR 2004:
A computer program for analysis of structures subjected to fire, University of
Liege.

62.

Fujisaki, T., Nakatsuji, T. and Sugita, M. (1993) “Research and development of
grid shaped FRP reinforcement.” International Symposium on Fiber Reinforced
Polymer Reinforcement for Reinforced Concrete Structures, Detroit, Michigan,
Mar. 28-31, 177-192.

63.

FYFE (2012). “Tyfo® WR-AFP for the Tyfo® CFP system.” (Accessed on Feb. 1,
2013) http://www.fyfeco.com/products/pdf/tyfo%20wr-afp.pdf

64.

Gentry, T.R. and Hudak, C.E.(1996) “Thermal compatibility of plastic composite
reinforcements and concrete.” Proceedings of 2nd International Conference on
Advanced Composite Materials in Bridges and Structures, Montreal, Canada,
149-156.

65.

Gorji, M. and Mirzadeh, F. (1989) “Theoretical prediction of the thermoelastic
properties and thermal stress in unidirectional composites.” Journal of Reinforced
Plastics and Composites, 8(3), 232-258.

66.

Griffis, C.A., Masumura, R.A. and Chang, C.I. (1984) “Thermal response of
graphite epoxy composite subjected to rapid heating.” Environmental Effects on
Composite Materials, Vol. 2, Technomic Publishing Company, Lancaster,
Pennsylvania, 245-260.

67.

Harmathy, T.Z. (1967). “A comprehensive creep model.” Journal of Basic
Engineering, 89(3), 496-502.

68.

Harmathy, T.Z. (1993). Fire safety design and concrete, John Wiley & Sons, Inc.,
New York, NY.

69.

Hassan, T. and Rizkalla, S. (2002). “Flexural strengthening of prestressed bridge
slabs with FRP systems.” PCI Journal, 47(1), 76-93.
361

70.

Hawileh, R.A, Naser, M., Zaidan, W. and Rasheed, H.A. (2009) “Modeling of
insulated CFRP-strengthened reinforced concrete T-beam exposed to fire.”
Engineering Structures, 31(12), 3072-3079.

71.

Hawileh, R.A, Naser, M. (2012) “Thermal-stress analysis of RC beams reinforced
with GFRP rebars.” Composites: Part B, 43(5), 2135-2142.

72.

Hertz, K. (1981) “Simple temperature calculations of fire-exposed concrete
constructions.” Report No. 159, Institute of Building Design, Technical
University of Denmark.

73.

Hughes Brothers (2011) http://aslanfrp.com/Aslan200/Resources/Aslan200.pdf
(accessed Feb. 1, 2013)

74.

Intelligent Sensing for Innovative Structures (ISIS) (2001) “Strengthening
reinforced concrete structures with externally-bonded fibre reinforced polymers.”
Design Manual No. 4, Winnipeg, Canada.

75.

International Organization for Standardization (1999) “Plastics –
Thermomechanical analysis (TMA) – Part 2: Determination of coefficient of
linear thermal expansion and glass transitions temperature.” ISO 11359-2, Geneva,
Switzerland.

76.

International Organization for Standardization (2012) “Fire resistance tests –
elements of building construction.” ISO 834, Geneva, Switzerland.

77.

Ishikawa, T., Koyama, K. and Kobayashi, S. (1978) “Thermal expansion
coefficient of unidirectional composites.” Journal of Composite Material, 12(1),
153-168.

78.

Isolatek (n.d.) “Spray-Applied Fire Resistive Materials.” (Accessed on Feb. 1,
2013) http://www.isolatek.com/category_search.asp?categoryID=1

79.

Katz, A., Berman, N. and Bank, L.C. (1999) “Effect of high temperature on bond
strength of FRP rebars.” Journal of Composites for Constructions, 3(2), 73-81.

80.

Katz, A. and Berman, N. (2000) “Modelling the effect of high temperature on the
bond of FRP reinforcing bars to concrete.” Cement and Concrete Composites,
22(6), 433-443.

81.

Kalagiannakis, G. and Van Hemdrijck, D. (2003). “Numerical study on the
nonlinear effects of heat diffusion in composite and its potential in nondestructive testing.” Review of Scientific Instruments, 94(1), 464-465.

82.

Kandare, E., Kandola, B.K., Myler, P. and Edwards, G. (2010) “Thermomechanical responses of fiber-reinforced epoxy composites exposed to high
362

temperature environments. Part I: Experimental data acquisition.” Journal of
Composite Materials, 44(26), 3093-3114.
83.

Khoury, G.A. (1996) “Performance of heated concrete-mechanical properties”,
Contract NUC/56/3604A with Nuclear Installations Inspectorate, Imperial
College, London.

84.

Khoury, G.A. (2000) “Effect of fire on concrete and concrete structures,”
Progress in structural Engineering and materials, 2(4), 429-447.

85.

Kia, H.G. (1988) “Thermal expansion of polyurethane reinforced with continuous
glass fibers.” Polymer Composites, 9(3), 237-241.

86.

Klamer, E. L., Hordijk, D. A., and Janssen, H. J. M. (2005) “The influence of
th
temperature on the debonding of externally bonded CFRP.” Proceedings of 7
International Symposium on Fiber Reinforced Polymer (FRP) Reinforcement for
Concrete Structures (FRP7RCS), Kansas City, 1551-1592.

87.

Kodur, V.K.R. and Ahmed, A. (2010) “Numerical model for tracing the response
of FRP-strengthened RC beams exposed to fire.” Journal of Composites for
Construction, 14(6), 730-742.

88.

Kodur, V.K.R. and Bisby, L.A. (2005) “Evaluation of fire endurance of concrete
slabs reinforced with fiber-reinforced polymer bars.” Journal of Structural
Engineering, 131(1), 34-43.

89.

Kodur, V.K.R., Bisby, L.A. and Green, M.F. (2006) “Experimental evaluation of
the fire behavior of insulated fiber-reinforced-polymer strengthened reinforce
concrete columns.” Fire Safety Journal, 41(7), 547-557.

90.

Kodur, V. K. R. and Dwaikat, M. (2008). “A numerical model for predicting the
fire resistance of reinforced concrete beams.” Cement and Concrete Composites,
30(5), 431-443.

91.

Kodur, V.K.R., Dwaikat, M.M.S. and Dwaikat, M.B. (2008) “High-temperature
properties of concrete for fire resistance modeling of structures.” ACI Materials
Journal, 105(5), 517-527.

92.

Kodur, V.K.R., Dwaikat, M. and Raut, N. (2009) “Macroscopic FE model for
tracing the fire response of reinforced concrete structures.” Engineering
Structures, 31(10), 2368-2379.

93.

Kodur, V.K.R. and Harmathy, T.Z. (2008) “Properties of building materials.”
th
SFPE Handbook of Fire Protections Engineering, 4 edition, National Fire
Protection Association, Quincy, MA, 1167-1195.
363

94.

Kodur, V.K.R. and Phan, L. (2007) “Critical factors governing the fire
performance of high strength concrete systems.” Fire Safety Journal, 42(6), 482488.

95.

Kodur, V.K.R. and Khaliq, W. (2011) “Effect of temperature on thermal
properties of different types of high-strength concrete.” Journal of Materials in
Civil Engineering, 23(6), 793-801.

96.

Kodur, V.K.R., Wang, T.C., and Cheng, F.P. (2004) “Predicting the fire
resistance behavior of high strength concrete columns.” Cement and Concrete
Composites, 26(2), 141-153.

97.

Kodur, V.K.R. and Yu, B. (2013) “Evaluating the fire response of concrete beams
strengthened with near-surface-mounted FRP reinforcement.” Journal of
Composites for Construction, ASCE,17(4), 517-529.

98.

Kodur, V.K.R., Yu, B. and Dwaikat, M.M.S. (2013) “A simplified approach for
predicting temperature in reinforced concrete members exposed to standard fire.”
Fire Safety Journal, Vol. 56, 39-51.

99.

Kumahara, S., Masuda, Y., Tanano, H. and Shimizu, A. (1993). “Tensile strength
of continuous fiber bar under high temperature.” International Symposium on
Fiber Reinforced Polymer Reinforcement for Reinforced Concrete Structures,
Detroit, Michigan, Mar. 28-31, 731-742.

100.

Kumar, A. (2003) “Behavior of RCC beams after exposure to elevated
temperatures” Journal of the Institution of Engineers (India): Civil Engineering
Division, 84(3), 165-170.

101.

Lau, A. and Anson M. (2006) “Effect of high temperatures on high performance
steel fiber reinforced concrete”, Cement and Concrete Research, 36(9), 16981707.

102.

Leone, M., Matthys, S., and Aiello, M. A. (2009). “Effect of elevated service
temperature on bond between FRP EBR systems and concrete.” Composites Part
B, 40(1), 85-93.

103.

Lie, T.T. (1992) “Structural fire protection.” ASCE Manuals and Reports of
Engineering Practice 78, New York, NY.

104.

Lie, T.T. and Irwin, R.J. (1993) “Method to calculate the fire resistance of
reinforced concrete columns with rectangular cross section.” ACI Structural
Journal, 90(1), 52-60.
364

105.

Lie, T.T. and Kodur V.K.R. (1996) “Thermal and mechanical properties of steelfiber-reinforced concrete at elevated temperatures,” Canadian Journal of Civil
Engineering, 23(2), 511-517.

106.

Lin, T.D., Gustaferoo, A.H. and Abrams, M.S. (1981) “Fire endurance of
continuous reinforced concrete beams.” Research and Development Bulletin:
RD072.01B. Portland Cement Association, USA.

107.

Lu, X., Teng, J., Ye, L., and Jiang, J. (2007). “Intermediate crack debonding in
FRP-strengthened RC beams: FE analysis and strength model.” Journal of
Composite for Construction, Special Issue: Recent International Advancements in
FRP Research and Application in Construction, 161–174.

108.

Manzello, S.L., Park, S.H., Mizukami, T. and Bentz, D.P. (2008) “Measurement
of thermal properties of gypsum board at elevated temperatures.” Proceedings of
5th International Conference on Structures in Fire (SIF), Singapore, 656-665.

109.

Meacham B.J. and Custer R.L.P. (1992) “Performance-based fire safety
engineering: an introduction of basic concepts.” Journal of Fire Protection
Engineering, 7(2), 35-54.

110.

Mouritz, A.P. and Gibson, A.G. (2006) Fire Properties of Polymer Composite
Materials, Springer Ltd, Dordrecht, the Netherlands.

111.

Naus, D.J. (2006) “The effect of elevated temperatures on concrete materials and
structures - A literature review.” U.S. Nuclear Regulatory Commission, Office of
Nuclear Regulatory Research, Washington. D.C. 20555-0001.

112.

Neves, I.C., Rodrigues, J.C. and Loureiro, A.P. (1996) “Mechanical properties of
reinforcing and prestressing steels after heating.” Journal of Materials in Civil
Engineering, 8(4), 189-194.

113.

Nomura, S. and Ball, D.L. (1993) “Micromechanical formulation of effective
thermal expansion coefficients of unidirectional fiber composites.” Advanced
Composite Materials, 3(2), 143-152.

114.

Oehlers, D.J., Haskett, M., Wu, C., and Seracino, R. (2008) “Embedding NSM
FRP plates for improved IC debonding resistance.” Journal of Composites for
Construction, 12(6), 635-642.

115.

Palmieri, A., Matthys, S. and Taerwe, L. (2011) “Influence of high temperature
th
on bond between NSM FRP bars/strips and concrete.” Proceedings of the 10
International Symposium of the Fiber-Reinforced Polymer Reinforcement for
Reinforced Concrete Structures, Tampa, FL, 919-930.
365

116.

Palmieri, A., Matthys, S. and Taerwe, L. (2012) “Experimental investigation on
fire endurance of insulated concrete beams strengthened with near surface
mounted FRP bar reinforcement.” Composite Part B, 43(3), 885-895.

117.

Phan, L.T. (1996) “Fire performance of high-strength concrete: A report of the
state-of-the-art.” NISTIR 5934, National Institute of standard and Technology,
Gaithersburg, MD.

118.

Phan, L.T., Lawson, J.R. and Davis, F.L. (2000) “Heating, spalling characteristics
th
and residual properties of high performance concrete.” 15 Meeting of UJNR
Panel on Fire Research and Safety, Vol. 2, NIST, USA.

119.

Pirgon, O., Wostenholm, G.H. and Yates, B. (1973) “Thermal expansion at
elevated temperatures – IV Carbon-fiber composite.” Journal of Physics D:
Applied Physics, 6(1), 309-321.

120.

Priestley, M.J.N., Seible, F., Xiao, Y., and Verma, R. (1994) Steel jacket retrofit
of squat RC bridge columns for enhanced shear strength – Part I – Theoretical
considerations and test design. ACI Structural Journal, 91(4), 394-405.

121.

Rafi, M.M., Nadjai, A. and Ali, F. (2007) “Fire resistance of carbon FRP
reinforced concrete beams.” Magazine of Concrete Research, 59(4), 245-255.

122.

Rafi, M.M., Nadjai, A. and Ali, F. (2008) “Finite element modeling of carbon
fiber-reinforced polymer reinforced concrete beams under elevated temperatures.”
ACI Structural Journal, 105(6), 701-710.

123.

Raghavan, J. and Meshii, M. (1997) “Creep of polymer composites.” Composites
Science and Technology, 57(12), 1673-1688.

124.

Raman, A.H., Taylor, D.A., and Kingsley, C.Y. (1993) “Evaluation of FRP as
reinforcement for concrete bridges.” Symposium on Fiber-reinforced plastic
reinforcement for concrete structures (FRPRCS), American Concrete Institute,
Detroit, MI, 71-86.

125.

Rasheed, H.A., Harrison, R.R., Peterman, R.J. and Alkhrdaji, T. (2010) “Ductile
strengthening using externally bonded and near surface mounted composite
systems.” Composite Structures, 92(10), 2379-2390.

126.

Rashid, R., Oehlers, D.J. and Seracino, R. (2008) “IC debonding of FRP NSM
and EB retrofitted concrete: plate and cover interaction tests.” Journal of
Composites for Construction, 12(2), 160-167.

127.

Raut, N. and Kodur, V.K.R. (2011) “Response of Reinforced Concrete Columns
under Fire-Induced Biaxial Bending.” ACI Structural Journal, 108(5), 610-619.
366

128.

Rein, G., Abecassis, E.C. and Carvel, R. (2007) “The Dalmarnock Fire Tests:
Experiments and Modeling.” School of Engineering and Electronics, University
of Edinburgh.

129.

Saafi, M. (2002) “Effect of fire on FRP reinforced concrete members.” Composite
Structures, 58(1), 11–20.

130.

Sakashita, M., Masuda, Y., Nakamura, K. and Tanano, H. (1997) “Deflection of
continuous fiber reinforced concrete beams subject to loaded heating.”
Proceedings of 3th International Symposium on Non-Metallic (FRP)
Reinforcement for Concrete Structures, Vol. 2, Sapporo, Japan, 51-58.

131.

Sauder, C., Lamon, J. and Pailler, R. (2004) The Tensile Behavior of Carbon
Fibers at High Temperatures up to 2400°C, Carbon, 42(4), 715-725.

132.

Savva, A., Manita, P. and Sideris, K.K. (2005) “Influence of elevated temperature
on the mechanical properties of blended cement concretes prepared with
limestone and siliceous aggregates.” Cement and Concrete Composites, 27(2),
239-248.

133.

Schapery, R.A. (1968) “Thermal expansion coefficients of composite materials.”
Journal of Composite Materials, 2(3), 380-404.

134.

Schneider, U. (1988) “Concrete at high temperatures – A general Review.” Fire
Safety Journal, 13(1), 55-68.

135.

Sena Cruz, J.M. and Barros, J.A.O. (2002) “Bond behavior of carbon laminate
strips into concrete by pull-out bending tests.” Proceedings of the International
Symposium - Bond in Concrete - from Research to Standards, Budapest, Hungary,
614-621.

136.

Sena-Cruz, J.M. and Barros, J.A.O. (2004) “Bond between near-surface mounted
carbon-fiber- reinforced polymer laminate strips and concrete.” Journal of
Composites for Construction, 8(6), 519-527.

137.

Shokralla, S. A. and Al-Muaikel, N. S. (2010) “Thermal properties of epoxy
(DGEBA)/phenolic resin (Novolac) blends.” Arabian Journal for Science and
Engineering, 35(1), 7-14.

138.

Society of Fire Protection Engineers (2008) “SFPE Handbook of Fire Protection
Engineering.” National Fire Protection Agency, Quincy, MA.

139.

Swamy, R.N., Jones, R. and Bloxham, J.W. (1987) “Structural behavior of
reinforced concrete beams strengthened by epoxy-bonded steel plates.” Structural
Engineer, 65(2), 59-68.
367

140.

TA Instruments (2011) Help document - Thermal Mechanical Analyzer. New
Castle, DE.

141.

Taljsten B., Carolin A. and Nordin H. (2003) “Concrete structures strengthened
with near surface mounted reinforcement of CFRP.” Advances in Structural
Engineering, 6(3), 201-213.

142.

Teng, J.G., Chen, J.F., Smith, S.T. and Lam, L. (2002) FRP-strengthened RC
structures, John Wiley & Sons Inc. Chichester, UK.

143.

Teng, J.G., De Lorenzis, L., Wang, B., Rong, L., Wong, T.N. and Lam, L. (2006)
“Debonding failures of RC beams strengthened with near-surface mounted CFRP
strips.” Journal of Composite for Constructions, ASCE, 10(2), 92-105.

144.

Teng, J.G., Smith, S.T., Yao, J., and Chen, J.F. (2003) “Intermediate crackinduced debonding in RC beams and slabs.” Construction and Building Materials,
17(6), 447-462.

145.

Thomas, F.G. and Webster, C.T. (1953) “Fire resistance of reinforced concrete
columns.” National Building Studies Research Paper No 18, HMSO, London, UK.

146.

Wang, Y.C., Wong, P.M.H., and Kodur, V. (2007) “An experimental study of the
mechanical properties of fibre reinforced polymer (FRP) and steel reinforcing
bars at elevated temperatures.” Composite Structures, 80(1), 131-140.

147.

Wickstrom, U. (1986) “A very simple method for estimating temperatures.” Fire
Exposed Structures, in New Technology to Reduced Fire Losses and Costs.
Elsevier Applied Science, London, UK, 186-194.

148.

William, B. and Richard, D. (1990) A first course in the finite element method,
Irwin,Inc., Boston, MA.

149.

Williams, B. K. (2004). “Fire performance of FRP-strengthened reinforced
concreteflexural members.” Doctoral Thesis, Queen’s University, Kingston,
Canada.

150.

Williams, B. Kodur, V., Green, M.F. and Bisby, L.A. (2008) “Fire endurance of
fiber-reinforced polymer strengthened concrete T-beams.” ACI Structural Journal,
105(1), 60-67.

151.

Wu, Z. S., Iwashita, K., Yagashiro, S., Ishikawa, T., and Hamaguchi, Y. (2004).
“Temperature effect on bonding and debonding behaviour between FRP sheets
and concrete.” FRP Composites in Civil Engineering (CICE), 905-912.
368

Yu, B. and Kodur, V.K.R. (2013) “Factors governing the fire response of concrete beams
reinforced with FRP rebars.” Composite Structures, Vol.100, 257-269.

369