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STRUCTURAL AND THERMAL BEHAVIOUR OF INSULATED
FRP-STRENGTHENED REINFORCED CONCRETE BEAMS AND
SLABS IN FIRE
by
Masoud Adelzadeh
A thesis submitted to the Department of Civil Engineering
in conformity with the requirements for
the degree of Doctor of Philosophy
Queen’s University
Kingston, Ontario, Canada
(September, 2013)
Copyright ©Masoud Adelzadeh, 2013
ii
Abstract
Despite the superior properties of Fibre Reinforced Polymer (FRP) materials, the use of
FRPs in buildings is limited. A key cause of concern for their use in buildings arises from
their poor performance in fire occurrences. This thesis presents the results of fire
performance of Reinforced Concrete (RC) beams and slabs strengthened with externally
bonded FRP sheets. The performance and effectiveness of insulation materials and
techniques are also investigated in this thesis. Two full-scale reinforced concrete T-beams
and two intermediate-scale slabs were strengthened in flexure with carbon and glass fibre
reinforced polymer sheets and insulated with a layer of spray-on material. The T-beams
and slabs were then exposed to a standard fire. Fire test results show that fire endurances of
more than 4 h can be achieved using an appropriate insulation system. Tests were
performed in order to understand the behaviour of FRP concrete bond at high
temperatures. An empirical model was then formulated to describe the bond strength
deterioration due to temperature rise. Innovative measurement techniques were employed
throughout the experiments to measure important observables like strain and temperature.
Meanwhile, the effectiveness and practicality of techniques such as Fibre Optic Sensing
(FOS) and Particle Image Velocimetry (PIV) for high temperature applications were
investigated.
A numerical finite-volume heat transfer model was developed to simulate the heat
transfer phenomenon. The validity of the numerical model was verified by comparing the
results with the results from the fire tests. By using this model, parametric analyses were
performed to investigate the effect of different fire scenarios on the performance of the
insulated beams. To simulate the structural performance of the T-beams a numerical model
which was capable of predicting stresses and strains and deflections of a heated beam was
developed. The model is capable of incorporating the effects of axial forces in the response
of a restrained beam. This model was verified and used in combination with the thermal
model to simulate the deflections of T-beams in fire.
iii
Acknowledgements
Numerous people contributed to the completion of this thesis. First I would like to
express my gratitude to Dr. Mark Green. I would also like to thank the industrial
partners who provided financial and technical support during the experiments. Thanks
go to Sika and Sika Canada and Richard Sherping. Most of the tests have been
conducted at Fire Risk Management testing facility at the National Research Council of
Canada. I would like to Thank Dr. Noureddine Bénichou of the National Research
Council of Canada, also the technical officers and staff at the National Research Council
of Canada. I would also like to thank the faculty and staff at the Civil Engineering
Department of Queen’s University, among them Dr. Andy Take, Dr Duncan Cree,
Maxine Wilson, Fiona Froats, Dave Tyron, Lloyd Rhymer, Jamie Escobar, Paul Thrasher
and Neil Porter. Also my friends and colleagues, Dr. Ershad Chowdhury and Tarek
Khalifa. And Finally I would like to thank Minoo, Reza And Sattar Adelzadeh, Parvin
Navadeye Razi and Shadi Ghazimoradi for their support and encouragement.
iv
Statement of Originality
I hereby certify that all of the work described within this thesis is the original work of
the author. Any published (or unpublished) ideas and/or techniques from the work of
others are fully acknowledged in accordance with the standard referencing practices.
Masoud Adelzadeh
July, 2013
v
Table of Contents
Abstract ...................................................................................................................................... ii
Acknowledgements .................................................................................................................iii
Statement of Originality .......................................................................................................... iv
Table of Contents ...................................................................................................................... v
List of Tables ............................................................................................................................ xii
List of Figures .........................................................................................................................xiv
Chapter 1 : Introduction ............................................................................................................... 1
1.1 Concrete structures and need for rehabilitation ............................................................. 2
1.2 FRP materials ....................................................................................................................... 3
1.3 Research objectives ............................................................................................................. 4
1.4 Contributions ....................................................................................................................... 6
1.5 Thesis outline ....................................................................................................................... 7
Chapter 2 : Literature review .................................................................................................... 10
2.1 Effects of fire on structures and fire test procedures ................................................... 10
2.2 Material behaviour at high temperatures ...................................................................... 12
2.2.1 Concrete ....................................................................................................................... 12
2.2.2 Steel .............................................................................................................................. 14
2.2.3 FRP ............................................................................................................................... 17
2.3 Fire performance of strengthened beams and slabs ..................................................... 19
2.4 Bond behaviour at high temperature for externally bonded FRP sheets .................. 20
vi
2.5 Insulation techniques........................................................................................................ 21
2.5.1 Concrete ....................................................................................................................... 22
2.5.2 Sprayed insulation ..................................................................................................... 22
2.5.3 Board insulation systems .......................................................................................... 23
2.5.4 Intumescent coating ................................................................................................... 23
2.6 Fire safety and sensing at high temperatures ............................................................... 24
2.6.1 Stimulated Brillouin scattering for fibre optic sensors ......................................... 25
Chapter 3: Experimental program ............................................................................................ 28
3.1 General.......................................................................................................................... 28
3.2 Fire Tests, T-beams and Slabs .................................................................................... 28
3.2.1 Test specimens ..................................................................................................... 28
3.2.1.1 Dimensions ...................................................................................................... 28
3.2.2 Materials ............................................................................................................... 31
3.2.2.1 Concrete ............................................................................................................ 31
3.2.2.2 Steel ................................................................................................................... 31
3.2.3 Fabrication ............................................................................................................ 32
3.2.3.1 Reinforcing bars .............................................................................................. 32
3.2.3.2 Instrumentation ............................................................................................... 35
3.2.3.3 Curing ............................................................................................................... 38
3.2.4 FRP strengthening ............................................................................................... 39
3.2.4.1 Slab-A ................................................................................................................ 39
3.2.4.2 Slab-B ................................................................................................................ 40
vii
3.2.4.3 Beam-A ............................................................................................................. 44
3.2.4.4 Beam-B .............................................................................................................. 45
3.2.5 Fire proofing ........................................................................................................ 49
3.2.6 Test apparatus ..................................................................................................... 50
3.2.7 Test conditions and procedures ........................................................................ 53
3.2.7.1 End conditions ................................................................................................. 53
3.2.7.2 Loading ............................................................................................................. 53
3.2.7.3 Failure criteria .................................................................................................. 55
3.3 Fire test results and discussion ................................................................................. 56
3.3.1 Temperatures ....................................................................................................... 58
3.3.2 Performance of the insulation system .............................................................. 65
3.3.3 Deflections ............................................................................................................ 68
3.3.4 Summary .............................................................................................................. 71
3.4 FRP-concrete bond tests ............................................................................................. 71
3.4.1 Bond tests results and discussion ..................................................................... 74
3.4.2 Proposed analytical model ................................................................................ 77
3.4.3 Discussion ............................................................................................................ 81
3.4.4 Summary bond tests ........................................................................................... 82
3.5 FRP coupon tests and FOS results ............................................................................ 83
3.5.1 Instrumentation ................................................................................................... 84
3.5.1.1 Results ............................................................................................................... 87
Chapter 4 : Numerical heat transfer simulation ..................................................................... 95
viii
4.1 Finite volume formulation ............................................................................................... 96
4.1.1 Stability criterion ...................................................................................................... 100
4.1.2 Free convection ......................................................................................................... 101
4.1.3 Moisture effect .......................................................................................................... 102
4.1.4 Verification ................................................................................................................ 107
4.2 Model results for slabs and T-beams ............................................................................ 108
4.3 Finite element simulation using ABAQUS .................................................................. 113
4.4 Different fire scenarios ................................................................................................... 116
4.5 Sample design charts ...................................................................................................... 122
4.6 Summary .......................................................................................................................... 131
Chapter 5 : Structural modelling ............................................................................................ 133
5.1 General.............................................................................................................................. 133
5.2 Generating moment-curvature curves ......................................................................... 136
5.3 Beam analysis .................................................................................................................. 137
5.4 Verification ....................................................................................................................... 138
5.4.1 RC Beam 1 (typical RC beam) ................................................................................ 138
5.4.2 RC Beam 2 ................................................................................................................. 141
5.4.3 FRP-RC Beam 1......................................................................................................... 144
5.4.4 FRP-RC Beam 2......................................................................................................... 149
5.5 Deflections simulation in fire exposed T-beams ......................................................... 153
5.5.1 T-Beam C ................................................................................................................... 153
5.5.2 T-Beam A and B ........................................................................................................ 156
ix
5.6 Different fire scenarios ................................................................................................... 160
5.7 Summary .......................................................................................................................... 162
Chapter 6 : Conclusions and Future Research ...................................................................... 165
6.1 General.............................................................................................................................. 165
6.2 Key findings ..................................................................................................................... 166
6.3 Detailed conclusions ....................................................................................................... 167
6.3.1 Fire tests ..................................................................................................................... 167
6.3.2 Bond tests .................................................................................................................. 168
6.3.3 Material testing and Fibre Optic Sensors .............................................................. 169
6.3.4 Numerical models .................................................................................................... 169
6.3.4.1 Heat transfer models ........................................................................................ 169
6.3.4.2 Strength model .................................................................................................. 170
6.4 Recommendations for future work .............................................................................. 171
References .............................................................................................................................. 174
A. Appendix A: Detailed experimental results .............................................................. 180
A.1 Temperature readings for Slabs .............................................................................. 180
A.2 Temperatures and deflections of T-beams ............................................................ 184
A.2.1 Beam-A temperature data ................................................................................ 184
A.2.2 Beam-B temperature data ................................................................................ 190
A.2.3 Deflection Results .............................................................................................. 196
B. APPENDIX-B: T-beam Load Calculation and Design ................................................. 202
B.1 Assumptions, Dimensions and Material properties ............................................ 202
x
B.1.1 Material properties............................................................................................ 203
B.2 Design Flexural Strength of Reinforced Concrete Beam ..................................... 205
B.2.1 Design Flexural Strength according to CSA A23.3-04 ................................. 206
B.2.2 Design Flexural Strength according to ACI 318/318R-05 ............................ 208
B.3 Flexural Capacity of FRP-Strengthened Reinforced Concrete Beam ................. 210
B.3.1 Beam-A FRP-Strengthened load calculation ................................................. 210
B.3.1.1 Flexural Capacity according to CSA S806-02 ............................................ 210
B.3.1.2 Flexural Capacity according to ACI 440.2R-08 ......................................... 212
B.3.1.3 Beam-A design summary ............................................................................. 217
B.3.2 Beam-B FRP-Strengthened load calculation .................................................. 219
B.3.2.1 Flexural Capacity according to CSA S806-02 ............................................ 219
B.3.2.2 Flexural Capacity according to ACI 440.2R-08 ......................................... 221
B.3.2.3 Beam-B design summary ............................................................................. 225
B.4 Superimposed Fire Test Loads ................................................................................ 228
B.4.1 Required Jack Stress during Fire Test ............................................................ 230
C. Appendix C: Material properties at high temperature ................................................ 232
C.1 Concrete ...................................................................................................................... 232
C.1.1 Thermal properties ........................................................................................... 232
C.1.1.1 Thermal conductivity ................................................................................... 232
C.1.1.2 Specific heat ................................................................................................... 234
C.1.2 Mechanical properties ...................................................................................... 237
C.1.2.1 Stress strain relation ...................................................................................... 237
xi
C.1.2.2 Thermal expansion ........................................................................................ 242
C.1.2.3 Creep and Transient strain .......................................................................... 243
C.2 Reinforcing steel ........................................................................................................ 244
C.2.1.1 Stress strain relation ...................................................................................... 244
C.2.1.2 Thermal elongation of reinforcing steel ..................................................... 246
C.3 FRP .............................................................................................................................. 247
C.3.1.1 Thermal properties ....................................................................................... 247
C.3.1.2 Mechanical properties .................................................................................. 248
C.4 Insulation .................................................................................................................... 248
C.4.1.1 Sikacrete 213F ................................................................................................ 248
C.4.1.2 Other Insulation materials ........................................................................... 249
C.4.1.3 Tyfo® Vermiculite-Gypsum (VG) Insulation ............................................ 249
C.4.1.4 Promat-H and Promatect-L ......................................................................... 251
xii
List of Tables
Table 3-1 FRP and insulation details for intermediate-scale slabs. ...................................... 42
Table 3-2 Summary of FRP-Insulation system used for T-beams. ....................................... 44
Table 3-3 Summary of test results ............................................................................................. 57
Table 3-4 General observation during test of T-beams. ......................................................... 57
Table 3-5 Strength results for steady state tests. ..................................................................... 75
Table 3-6 Failure temperatures for transient tests at different sustained load levels. ....... 78
Table 3-7 Specimen information and test regime. .................................................................. 83
Table 3-8 Modulus calculation results for room temperature test at different load levels;
strain is calculated using PIV analysis. .................................................................................... 88
Table 3-9 Steady-state tension test results for FRP at high temperature. ............................ 89
Table 4-1 Coefficients for laminar and turbulent free convection (Bayazıtoğlu, Özışık
1988). ........................................................................................................................................... 102
Table 4-2 Parameters used to produce fire curves. .............................................................. 117
Table 5-1: Properties of the typical RC beam used in the verfication (RC Beam1). ......... 139
Table 5-2: Description of the typical RC beam used in the verification (RC Beam2). ..... 142
Table 5-3. Summary of Properties for FRP-RC Beam1 ........................................................ 147
Table 5-4: Summary of Properties for FRP-RC Beam 2. ...................................................... 151
Table B-1 load factor calculation. ............................................................................................ 229
Table C-1 Values for the main parameters of the stress-strain relationships of normal
weight concrete with siliceous or calcareous aggregates concrete at elevated
temperatures, from Eurocode2. .............................................................................................. 241
xiii
Table C-2 values for the parameters of the stress-strain relationship of hot rolled and
cold worked reinforcing steel at elevated temperatures ..................................................... 245
Table C-3: Coefficient of thermal expansion for FRPs, Ahmad (2010). ............................. 248
xiv
List of Figures
Figure 1-1 FRP consumption share per industry,(Berreur, de Maillard et al. 2002). ........... 4
Figure 2-1 Stress-strain relationship for normal concrete derived in strain-rate controlled
tests (Schneider 1988). ................................................................................................................ 13
Figure 2-2 Stress-strain curves for steel at different temperatures (fy=300 MPa), (Lie
1992) .............................................................................................................................................. 15
Figure 2-3 Variation of strength of (a) reinforcing and (b) pre-stressing steels with
temperature (Holmes, Anchor et al. 1982). .............................................................................. 16
Figure 3-1 Dimensions and reinforcement details of SLAB-A and SLAB-B (dimensions in
mm) ............................................................................................................................................... 29
Figure 3-2 Dimensions and reinforcement details of BEAM-A and BEAM-B (All steel
bars are 10M) ............................................................................................................................... 30
Figure 3-3 Formwork and reinforcement layout for slabs (Williams, 2004). ...................... 33
Figure 3-4 Steel reinforcement for T-beams ............................................................................ 34
Figure 3-5 Formwork and reinforcement layout for T-beams .............................................. 34
Figure 3-6 Location of thermocouples in slab specimens (all dimensions in mm) ............ 36
Figure 3-7 Location of thermocouples in T-beams (all dimensions in mm) ....................... 37
Figure 3-8 Location of displacement gauges (all dimensions in mm). ................................ 38
Figure 3-9: CFRP strips on Slab A. ............................................................................................ 42
Figure 3-10: CFRP Wraps on Slab B.......................................................................................... 43
Figure 3-11 Surface thermocouples and surface preperation T-beams. .............................. 46
Figure 3-12 CFRP plate installation Beam-A. .......................................................................... 47
xv
Figure 3-13 CFRP plate installation Beam-B. .......................................................................... 47
Figure 3-14U-wrap installation Beam-B................................................................................... 48
Figure 3-15 U-wrap installation Beam-A. ................................................................................ 48
Figure 3-16 Thermocouples at FRP-insulation interfce and insulation surface (before
spraying insulation). ................................................................................................................... 49
Figure 3-17 Spraying insulation layer. ..................................................................................... 50
Figure 3-18 Measuring insulation thickness T-Beams. .......................................................... 50
Figure 3-19 ASTM E119 standard time temperture curve. ................................................... 51
Figure 3-20 Intermediate-scale furnace for slabs. .................................................................. 52
Figure 3-21 Full-scale floor furnace for beams. ....................................................................... 52
Figure 3-22 Test setup and instrumentation for slabs. ........................................................... 54
Figure 3-23 Instrumentation at unexposed surface T-beams. ............................................... 55
Figure 3-24 Temperatures vs. exposure time for slab A. ...................................................... 58
Figure 3-25 Temperatures vs. exposure time for slab B. ........................................................ 59
Figure 3-26 Temperatures vs. exposure time comparison for slabs A and B at FRP-
concrete bond line and steel reinforcement locations. ........................................................... 59
Figure 3-27 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A. .... 61
Figure 3-28 Steel reinforcement temperatures (web) Beam-A. ............................................. 62
Figure 3-29 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B. .... 63
Figure 3-30 Steel reinforcement temperatures (web) Beam-B. ............................................. 64
Figure 3-31 Shrinkage cracks in insulation, T-beams before fire test. ................................. 65
xvi
Figure 3-32 Spalling of un-insulated concrete (flange). Note, insulation layer was
removed manually after fire test. .............................................................................................. 66
Figure 3-33 Flames are visible at cracks in the U-wrap location, Beam-B after 1 hour and
53 minutes of fire exposure........................................................................................................ 66
Figure 3-34 Cracks at insulation surface after fire test Beam-B. .......................................... 67
Figure 3-35 Slab-B after test. ...................................................................................................... 67
Figure 3-36 T-beams after fire test in the loading frame. ...................................................... 68
Figure 3-37 Comparison of mid span deflection of Beam-A and Beam-B. ........................ 70
Figure 3-38 Bond test setup. ...................................................................................................... 73
Figure 3-39 Sample preparation. ............................................................................................... 73
Figure 3-40 Strength vs. temperature for steady-state tests. ................................................. 75
Figure 3-41, Room temperature steady state specimen before and after failure.
Debonding happens inside concrete very close to the interface. ......................................... 76
Figure 3-42 Steady state specimen, T=105C, before and after failure. Debonding happens
inside epoxy layer. ...................................................................................................................... 77
Figure 3-44 Transient test results failure temp. vs load level. .............................................. 79
Figure 3-45 Transient test specimens before and after failure and debonded surface for
20% (top) and 80% load level (bottom). ................................................................................... 80
Figure 3-46: CFRP coupon dimensions and fibre optic sensor location (all dimensions in
mm). .............................................................................................................................................. 84
Figure 3-47 Square pixel patches on FRP sheet used in PIV analysis (yellow squares). ... 85
xvii
Figure 3-48 Damage progress during test for specimen 2.1. Temperatures are 28, 77, 183,
200, 210 and 256 ˚C from left to right. ...................................................................................... 86
Figure 3-49 Fibre optic sensor and protective cover installation details. ............................ 87
Figure 3-50 OTDR style curve shows the reflectivity along the fibre length and the right
side curve is a 3-D (top view) of the fibre section under stress. These curves are obtained
from specimen 1.1. ...................................................................................................................... 87
Figure 3-51 CFRP specimen 2.1, transient test, before and after the test. ........................... 89
Figure 3-52 Secant modulus for specimen 2.1 vs. temperature. ........................................... 89
Figure 3-53 Comparison of strain reading using PIV method (dotted line) and FOS (solid
lines) specimen 1.1 at room temperature. ................................................................................ 91
Figure 3-54 Comparison of strain reading using PIV method (dotted line) and FOS (solid
lines) specimen 1.3 at 90°C. ........................................................................................................ 91
Figure 3-55 Comparison of strain reading using PIV method (dotted line) and FOS (solid
lines) specimen 1.2 at 110°C. ...................................................................................................... 92
Figure 3-56 Comparison of strain reading using PIV method (dotted line) and FOS (solid
lines) specimen 1.4 at 130°C. ...................................................................................................... 93
Figure 4-1 Spatial discretization. ............................................................................................... 97
Figure 4-2 Descritization and effective length for different finite volumes ........................ 99
Figure 4-3 Predicted and measured temperatures as a function of exposure time for
different depths within the concrete specimen (experimental data obtained from (Lie,
Woollerton 1988). ...................................................................................................................... 108
xviii
Figure 4-4 Predicted and measured temperatures as a function of exposure time for slabs
at, (a) unexposed surface slab-A (40 mm insulation thickness), (b) FRP-concrete interface
slab-A, (c) unexposed surface slab-B and (d) FRP-concrete interface slab-B.................... 110
Figure 4-5 Predicted and measured temperatures vs. exposure time for T-beams at (a)
unexposed surface, (b) on the centreline with concrete cover of 155 mm, (c) longitudinal
steel, and (d) FRP-concrete interface. ..................................................................................... 111
Figure 4-6 Measured steel temperature (mean ±1 standard deviation) compared to
predicted temperature. ............................................................................................................. 112
Figure 4-7 Steel simulation temperature erorr compared to standard deviation of
measured temperature. ............................................................................................................ 112
Figure 4-8 Temperature contour from FE simulation at the cross section of the recangular
column after 180 min of standard fire exposure (temperatures in °C ). ............................ 113
Figure 4-9 Predicted temperatures for different depths within the concrete specimen
using FV and FE simulations (experimental data obtained from (Lie, Woollerton 1988).
..................................................................................................................................................... 114
Figure 4-10 FE results vs. FV and experimantal results. Temperature is measured at the
bottom longitudinal bar of T-beam A. ................................................................................... 115
Figure 4-11 3D temperature isotherm surfaces from FE simulation at the cross section of
T-Beam-A after 240 min of standard fire exposure (temperatures in °C ). ....................... 116
Figure 4-12 Time temperature curves for four different fire scenarios. ............................ 118
xix
Figure 4-13 Time-Temperature curve in Dalmarnock real compartment fire (mean ± 1
standard deviation) in comparison with ASTM standard fire curve and “fireIV” curve
used here(Stratford, Gillie et al. 2009). ................................................................................... 118
Figure 4-14 Longitudinal steel temperature in beams subjected to Fires I to IV. ............ 119
Figure 4-15 FRP-concrete interface temperature in beams subjected to Fires I to IV. ..... 119
Figure 4-16 Predicted moment capacity of T-beams exposed to different fire curves and
applied maximum moment during the fire test. .................................................................. 121
Figure 4-17: Temperature vs. exposure time at FRP-concrete interface for different
insulation thicknesses (Depth is insulation thickness in mm). ........................................... 123
Figure 4-18: Temperature vs. exposure time with 20 mm concrete cover for different
insulation thicknesses. .............................................................................................................. 124
Figure 4-19: Temperature vs. exposure time with 30 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm). ........................................... 125
Figure 4-20: Temperature vs. exposure time with 40 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm). ........................................... 126
Figure 4-21: Temperature vs. exposure time with 50 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm). ........................................... 127
Figure 4-22: Temperature vs. exposure time with 60 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm). ........................................... 128
Figure 4-23: Temperature vs. exposure time with 70 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm). ........................................... 129
xx
Figure 4-24: Temperature vs. exposure at unexposed surface of concrete slab (thickness
150 mm) for different insulation thicknesses (Depth is insulation thickness in mm). .... 130
Figure 5-1 Free thermal strain vs temperature for various concretes from EuroCode 2. 135
Figure 5-2 Strain compatibility and load equilibrium at a typical section of the T-beam.
..................................................................................................................................................... 137
Figure 5-3 Time temperature curves data points are from Dwaikat and Kodur 2008 and
lines are results of the current model. .................................................................................... 140
Figure 5-4 Mid-span deflection vs. time, dotted line is from Dwaikat and Kodur 2008
and the solid line is current model. ........................................................................................ 140
Figure 5-5 Details of the cross section and loading for RC Beam 2, Dotreppe (1985). .... 141
Figure 5-6: Tension steel temperature vs. time, dotted line is model prediction and solid
line is the test result. ................................................................................................................. 143
Figure 5-7 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result. ............................................................................................................................. 144
Figure 5-8 Details of the cross section and loading for FRP-RC Beam 1, Blontrock (2003).
..................................................................................................................................................... 146
Figure 5-9 Tension steel temperature vs. time, dotted line is model prediction and solid
line is the test result. ................................................................................................................. 148
Figure 5-10 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result. ............................................................................................................................. 149
Figure 5-11 details of the cross section and loading for FRP-RC Beam 2, Blontrock (2003).
..................................................................................................................................................... 150
xxi
Figure 5-12 Tension steel temperature vs. time, dotted line is model prediction and solid
line is the test result. ................................................................................................................. 151
Figure 5-13 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result. ............................................................................................................................. 152
Figure 5-14 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result. ............................................................................................................................. 156
Figure 5-15 Assumed axial load time curves for the T-beams used in the simulation. .. 157
Figure 5-16 Mid-span deflection vs. time for T-beam A, dotted lines are model
predictions for deflection assuming different axial loads, solid line is the test result. ... 158
Figure 5-17 Mid-span deflection vs. time for T-beam B, dotted lines are model
predictions for deflection assuming different axial loads, solid line is the test result. ... 160
Figure 5-18 Longitudinal steel temperatures for Beam-C under different fires. ............. 161
Figure 5-19 Mid-span deflections for Beam-C exposed to different fires, beam fails under
Fire-IV in less than four hours. ............................................................................................... 162
Figure A-1 Temperatures vs. exposure time for slab A. ..................................................... 180
Figure A-2 Temperatures vs. exposure time for slab B. ...................................................... 181
Figure A-3 Interior concrete temperatures Slab-A. .............................................................. 181
Figure A-4 Interior concrete temperatures Slab-B. ............................................................... 182
Figure A-5 Temperatures vs. exposure time comparison for slabs A and B at FRP-
concrete bond line and steel reinforcement locations. ......................................................... 182
Figure A-6 Steel rebar temperatures Slab-A.......................................................................... 183
Figure A-7 Steel rebar temperatures Slab-B. ......................................................................... 183
xxii
Figure A-8 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A. ... 184
Figure A-9 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-A.
..................................................................................................................................................... 185
Figure A-10 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-A.
..................................................................................................................................................... 186
Figure A-11 Steel reinforcement temperatures (web) Beam-A........................................... 187
Figure A-12 Unexposed surface temperature (centerline) Beam-A. .................................. 188
Figure A-13 Unexposed surface temperature (flange) Beam-A. ........................................ 189
Figure A-14 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B. . 190
Figure A-15 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-B.
..................................................................................................................................................... 191
Figure A-16 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-B.
..................................................................................................................................................... 192
Figure A-17 Steel reinforcement temperatures (web) Beam-B. .......................................... 193
Figure A-18 Unexposed surface temperature (centerline) Beam-B. .................................. 194
Figure A-19 Unexposed surface temperature (flange) Beam-B. ......................................... 195
Figure A-20 Deflection at midspan and quatre points for Beam-A. .................................. 196
Figure A-21 Deflection at midspan and quatre points for Beam-B. ................................... 197
Figure A-22 Comparison of mid span deflection of Beam-A and Beam-B. ..................... 198
Figure A-23 load deflection curve Beam-A. .......................................................................... 199
Figure A-24 load deflection curve Beam-B. ........................................................................... 200
Figure A-25 Load deflection comparison for Beam-A and B. ............................................. 201
xxiii
Figure B-1 T-beam cross section. ............................................................................................. 206
Figure C-1 Thermal conductivity of normal weight concrete based on Eurocode 2 (EN
2004) and (Lie 1992). ................................................................................................................. 234
Figure C-2 Eurocode2 compressive stress strain curve for concrete. ................................ 239
Figure C-3 model for stress-strain relationships of reinforcing steel at elevated
temperatures .............................................................................................................................. 244
1
Chapter 1: Introduction
Composites in civil engineering have been used increasingly in past decades. Early
applications of fibre reinforced polymer (FRP) composites go back to the 1970’s (Parkyn
1970). Although early application results were not satisfactory, the FRP application
techniques have been vastly improved. FRPs are used in the construction of new
structures as well as in the rehabilitation and strengthening of existing structures.
Deteriorating infrastructure is also in need of retrofit and rehabilitation. FRPs have been
adapted to address these problems. High strength, light weight, resistance to
electrochemical corrosion, and ease of installation are advantages that make FRPs
attractive for engineering applications.
While FRPs have superior thermal and mechanical properties in comparison to
conventional construction materials, they are susceptible to degradation in high
temperatures. This makes their application in residential buildings to a certain extent
problematic. The National Fire Protection Association reported that there were over
500,000 structural fires annually in the United States (Karter 2009). While conventional
construction materials are also susceptible to degradation due to fire exposure, their
behaviour has been adequately investigated and researched during the past decades.
The results of these efforts are reflected in several fire safety codes and building codes.
2
The behaviour of FRP materials, on the other hand, has not been thoroughly
investigated and their behaviour at elevated temperatures is rather unknown.
1.1 Concrete structures and need for rehabilitation
Reinforced concrete has been widely used as a construction material during the last
century. The superior characteristics of reinforced concrete and the increasing need for
construction has led to the mass consumption of concrete in infrastructure; however the
continuation of this trend of production and consumption of concrete needs to be
considered attentively. The production of 1.6 billion tons of cement each year is
responsible for about 7% of the global carbon dioxide emission into the atmosphere,
(Mehta 2001). In order to produce one tonne of Portland cement an amount of energy
approximately equal to 4 GJ is needed, (Malhotra 1999). Addressing these concerns,
Freyermuth (2001) has suggested a service life of 100 to 150 years should be
implemented for the design of structures. Keeping in mind the necessity of extending
the service life of existing structures for sustainability, the need for strengthening is
further emphasized considering the economic and environmental aspects of the
problem.
Other than the need for the extension of service life, structures experience
deterioration throughout their designed service life. For example, the American Society
of Civil Engineers (ASCE 2005) estimated the total investment needed to upgrade
3
existing infrastructure to be about $1.6 trillion. Canada’s infrastructure needs $49 billion
for rehabilitation, (Mufti 2003). Further, the Bureau of Transportation reports that there
are approximately 150,000 deficient bridges in the United States, (National
Transportation Statistics 2005). In Canada, it is estimated that about 30,000 bridges are
structurally or functionally deficient (Mufti 2003). Clearly, the existing engineering
technology in construction and materials is not sufficient to address this infrastructure
crisis. Use of FRP strengthening techniques could help alleviate this problem, especially
considering the use of green composites, natural fibres and recycling. A quick overview
of FRP Materials which are the subject of this research will be presented in the following
section.
1.2 FRP materials
It is hard to accurately evaluate global composite production; it was estimated to be 7
million tonnes in year 2000 and 10 million tonnes in year 2006, with over 10% of
production being consumed in Civil engineering and construction industry (Berreur, de
Maillard et al. 2002), Figure 2-1.
4
Figure 1-1 FRP consumption share per industry,(Berreur, de Maillard et al. 2002).
Fibre reinforced polymers have a large share in the composite industry and they have
been commonly used in the aerospace and, automotive industries. FRP is a composite
material made of a polymer matrix which is reinforced by fibres. The fibres are usually
carbon, glass, aramid or basalt (Patnaik et al.2010 ) and the polymer is usually an epoxy,
a vinylester, or a polyester thermosetting plastic. In order to fulfill the design
requirement there is a need to know the behaviour of material at elevated temperatures.
1.3 Research objectives
The objectives of the research presented in this thesis could be summarized in three
main sections:
1. To investigate the behaviour of reinforced concrete beams strengthened
externally with FRP in fire. Specifically,
5
o To evaluate the behaviour of insulated FRP-strengthened intermediate-
scale reinforced concrete slabs exposed to standard fire through fire test
experiments.
o To evaluate the behaviour of insulated FRP-strengthened full-scale
reinforced concrete T-beam exposed to standard fire through fire test
experiments.
o To develop and validate numerical models to predict heat transfer and
thermally-induced strength degradation in FRP-strengthened flexural
members exposed to fire.
2. To investigate material behaviour and load transfer mechanism at bond between
FRP and concrete, specifically,
o To experimentally evaluate the bond behaviour between FRP and
concrete at elevated temperatures.
o To experimentally evaluate the behaviour of FRP materials at elevated
temperatures.
o To develop an empirical FRP-concrete bond behaviour model based on
experiment results.
3. To study the feasibility and effectiveness of instrumentation and sensing at
elevated temperatures, specifically,
6
o To experimentally evaluate the effectiveness of fibre optic sensor (FOS) at
elevated temperatures.
o To investigates the effectiveness and feasibility of particle image
velocimetry imaging (PIV) techniques at measuring strain during high
temperature testing.
1.4 Contributions
This thesis makes several important and original contributions to the understanding of
the performance of FRP strengthened concrete flexural members in fire. The full-scale
fire tests examine FRP materials and insulation systems that have not been previously
studied. The FRP-concrete bond study is particularly novel because no other researchers
have studied this performance at high temperature. Since the bond of FRP to concrete is
critically susceptible to high temperature, this information is vital in understanding the
performance of FRP strengthened concrete structures in fire. Additional innovation was
achieved through the study of FOS at high temperature because such sensors have not
previously been used at such high temperatures. In terms of numerical modelling,
original contributions include the incorporation of transient creep and axial thrust into
the flexural structural modelling, and the investigation of the performance of FRP
strengthened concrete beams when subjected to several different fire scenarios.
7
1.5 Thesis outline
This thesis has 6 chapters. Chapter 2 covers the background information on fire safety
and FRP materials. It also reviews the existing literature on the fire behaviour of FRP-
strengthened reinforced concrete structures, sensing technologies, and other relevant
information. Chapter 3 describes the experimental program and testing procedures
conducted for this thesis. It includes the details of the testing instrumentation and the
equipment used during the tests, and information on intermediate scale and full scale
fire tests. Chapter 3 also presents the experimental procedure, material properties,
testing schemes, and results for FRP concrete bond tests. Chapter 4 gives the details of
the numerical heat transfer model developed for simulation of the experiments. It
includes theoretical details of the model as well as the results of the developed model.
Model verification information is also included in this chapter. Parametric analysis is
also performed to demonstrate the capabilities of the developed model. Chapter 5
presents the numerical simulation results for strength simulation. It includes the details
of the model verification procedure. The effect of axial restraint is also studied in this
chapter. Chapter 6 summarizes the research and presents the conclusions derived from
this thesis and gives recommendations for future work. Detailed temperature and
deflection readings from the fire tests are presented in Appendix A, while load
calculations and design of the beams based on CSA and ACI are presented in Appendix
B, and finally Appendix C summarizes material properties at elevated temperatures.
8
9
10
Chapter 2: Literature review
2.1 Effects of fire on structures and fire test procedures
When considering structural fire safety it is assumed that the fire happens in a room or
an enclosed section of the building. These fires are called compartment fires. When a fire
in a compartment starts, it will grow burning the fuel available in the room. Assuming
sufficient combustible materials exist; temperatures will rise especially in the upper air
layers in the room. If the temperature is high enough, the ambient heat flux reaches a
critical level where all combustible items in the compartment will begin to burn. This
leads to a sharp rise in both heat release rate and temperature. This transition is called
“flashover” and the fire is called “post flashover fire” or a “fully developed fire”
(Feasey, Buchanan 2002).
The rate of fire spread and growth depends on many factors (Gewain, Iwankiw et al.
2003),
• Ventilation of the compartment
• Type of combustible materials and their availability
• Geometry of the compartment and its configuration
• Fire detection systems and subsequent fire suppression systems
• Efficiency of fire barriers
11
The behaviour of the fire will be less predictable in rooms which have large floor areas,
high ceilings or irregular arrangement of fuel or openings. Maximum temperature of a
post-flashover fire will rarely exceed 1000ºC (Alfawakhiri, Hewitt et al. 2002), while in
the case of not fully developed fires the temperature will not exceed 550 °C.
The elevated temperature during the fire is the major factor affecting the safety and
performance of the structure.
Simulation of temperatures in a realistic fire is very complicated due to the multiplicity
of variables involved. Design codes and standards, however, use standard fire tests to
measure the performance of the structural members in fire. Although they may not
represent a real fire incident, standard fire tests could be used to assess and compare the
level of performance of structural members in fire. An actual fire will have a slower
growth phase and will experience temperature fluctuations, thus the standard
temperature-time curve is somewhat conservative because it corresponds to a severe
fire, but not the severest possible fire event (Khoury 2000).
Once the standard temperature-time curves have been established to simulate fire
behaviour, the fire endurance of a member could be measured in a standard fire test.
Fire endurance is typically determined by exposing a structural element to fire in a
specially constructed furnace. The purpose of the fire test is to define a structure’s
ability to withstand fire exposure without losing its function as a load-bearing element
or a barrier to the spread of fire. In North America ASTM E119 describes the standard
12
fire test procedure and standard fire time-temperature curve. A very similar document
“Standard Methods of Fire Endurance Tests of Building Construction and Materials” is
used in Canada. In Europe, ISO 834, Fire Resistance Tests-Elements of Building
Construction defines the standard fire test.
Test specimens for a fire test should be constructed in a similar manner to the building
elements they represent. During the fire test, the temperature in the specimen must be
measured at exposed and unexposed faces. Fire endurance is determined once the
specimen reaches one of the failure criteria. Fire endurance is the duration of fire
exposure until this failure point.
2.2 Material behaviour at high temperatures
Fairly adequate information is available about the behaviour of concrete and steel at
high temperatures; while there is limited data on behaviour of FRP, insulation and
adhesive. Appendix C covers the material models in detail.
2.2.1 Concrete
Rise in temperature affects the stress strain behaviour of concrete. Experimental results
reported by Schneider (1988) for concrete in uniaxial compression at different
temperatures are plotted in Figure 2-1. It could be observed from the diagram that a rise
in temperature results in a degradation of compressive strength and stiffness of the
concrete. Meanwhile the increase in temperature affects the ductility of the concrete.
13
Figure 2-1 Stress-strain relationship for normal concrete derived in strain-rate controlled
tests (Schneider 1988).
Concrete response to uniaxial loading at high temperature is dependent on many factors
like aggregate type, water content etc. and concrete response is also dependant on the
applied compressive stress during heating (Schneider, Kassel 1985) or in other words the
loading history has an effect in behaviour of the concrete. To account for this
phenomenon, an additional strain component is defined in heated concrete. This strain
is called “transient creep strain” or “transient strain” or “load induced thermal strain
(LITS)”.
20 °C 150 °C
350 °C
450 °C
750 °C
550 °C
0
0.2
0.4
0.6
0.8
1
1.2
0 0.0005 0.001
Nor
mal
ized
stre
ss, σ
/f'c
(20)
Strain
14
2.2.2 Steel
A glance at literature suggests that models for yield and ultimate strength of steel vary
considerably because these properties depend on steel composition and the definition of
yield strength (Buchanan 2002). Curves for the stress-strain relation of mild steel at
various temperatures are shown in Figure 2-2. It can be seen that the yield strength
decreases with temperature and there is a yield plateau at lower temperatures which
disappears at higher temperatures. Considering the residual strength of the reinforcing
steel, the reinforcing steel recovers most of its original yield strength after cooling when
the maximum strength experienced by it remains below 500°C (Neves, Rodrigues et al.
1996). The percentage of strength and modulus recovery depends on the highest
temperature experienced by reinforcing steel. When steel is subjected to temperatures
above 500°C a gradual decrease in residual strength is observed.
Extensive research has been performed to evaluate the performance of structural steel at
fire. In general, at approximately 1000 °F (538 °C), steel loses approximately 50 % of its
room-temperature strength and modulus of elasticity (ASCE-78, 1992), see Figure 2-3.
15
Figure 2-2 Stress-strain curves for steel at different temperatures (fy=300 MPa), (Lie
1992)
16
Figure 2-3 Variation of strength of (a) reinforcing and (b) pre-stressing steels with
temperature (Holmes, Anchor et al. 1982).
17
2.2.3 FRP
Thermal and mechanical properties of FRPs are dependent on the properties of their
constituents i.e. fibre and matrix. Volume fraction of fibres and matrix also influences
the behaviour of the FRPs (Sorathia, Rollhauser et al. 1992). Glass and carbon FRPs
generally produce less smoke than aramid fibre. Fibre type also considerably influences
thermal conductivity of FRPs. Carbon FRPs have higher thermal conductivity than glass
and aramid FRPs.
Studies show that carbon fibres experience little to no change in their tensile strength up
1000 °C (Rostasy, Hankers et al. 1992), and they have better performance at high
temperatures than steel. Glass fibres lose almost 50% of their original tensile strength at
550°C (Dimitrienko 1999) and (Sen, Mariscal et al. 1993), which is similar to steel
behaviour at high temperatures. According to Sumida (2001) aramid fibres experience a
linear decline in strength at temperatures above 50°C with 50% loss of strength at 300°C.
FRP on the other hand loses most of its strength when the temperature reaches the glass
transition temperature (Tg) of its adhesive/matrix. At this temperature, the resin softens
and the resin will no longer be as effective in transferring stresses between fibres. As far
as fire behaviour of FRP is concerned, glass transition temperature is the most important
property of any FRP.
There are a couple of techniques for determining Tg of a composite. Among them two
are more popular:
18
• DSC, differential scanning calorimetry (ASTM-E1356) and,
• DMA, Dynamic mechanical analysis (ASTM-D7028).
DSC determines the glass transition temperature based on changes in heat capacity of
the material while DMA does so by measuring changes in the dynamic stress-strain
behaviour. Since DMA measures Tg based on mechanical behaviour of the material
rather than thermal properties, it is more accurate in predicting mechanical behaviour of
FRP in fire.
Another method that determines charring temperature or the temperature at which
thermal decomposition of the constituent materials occurs is TGA or thermogravimetic
analysis (ASTM-E1131). TGA determines Tg by monitoring mass loss with increasing
temperature.
Manufacturers sometimes report Heat Deflection Temperature (HDT) instead of Tg.
Although Tg and HDT are highly correlated they are not the same. Tg is the temperature
at which a polymer structure shifts from a “glassy state” to a “rubbery state”. According
to ASTM-D648, HDT is a temperature at which a polymer sample deflects a certain
amount under heat and load. Measuring HDT is a time consuming procedure. In
addition, HDT is a function of the temperature, stress and strain rate. Due to
inconsistencies in results, methods and interpretation, HDT is not used as commonly as
Tg.
19
2.3 Fire performance of strengthened beams and slabs
There are very few studies in literature concerning the fire behaviour of externally FRP-
strengthened beams. (Deuring 1994) tested six beams (300mm by 400mm by 5m) where
four of them were strengthened with CFRP sheets and were subjected to sustained
loading. Insulated beams showed satisfactory fire endurance in the tests. The un-
insulated beams had a fire endurance of 81minutes while the insulated beams gave an
endurance of 146 minutes. Interestingly the endurance of insulated CFRP plated beam
was larger than that of the un-strengthened RC beam. Blontrock, Taerwe et al. (2000)
tested CFRP plated beams using multiple insulation schemes. During the experiments
once the temperature of FRP reached Tg, the load bearing contribution of FRP was
significantly reduced. Overall the fire endurance observed in the tests was not sufficient.
Williams (2004) and Chowdhury (2005) tested full scale insulated T-beams and
intermediate scale slabs. Beams were subjected to sustained load but slabs were tested
without loading (Williams, Kodur et al. 2008). Length of the beams was 3.81m and the
web and flange width were 1220 and 300 mm respectively. Beam depth was 400mm.
Dimensions of the intermediate slabs were 954 by 1331mm. They concluded that beams
and slabs with sufficient insulation could achieve fire endurances of more than 4 hours.
Stratford, Gillie et al. (2009), studied the performance of bonded FRP strengthening in
real compartment fire (the Dalmarnock Fire Tests). They applied near surface mounted
and externally bonded FRPs. They also used intumescent coating and gypsum boards as
20
insulation materials. They concluded that FRP reinforcements are vulnerable during a
real compartment fire. Palmieri, Matthys et al. (2011) performed fire tests on six near
surface mounted FRP strengthened concrete beams with different insulation systems.
They achieved 2-hour fire endurance in their experiments.
2.4 Bond behaviour at high temperature for externally bonded FRP sheets
The effectiveness of FRP strengthening methods in reinforced concrete (RC) applications
is usually dependant on the effectiveness of the FRP-Concrete Bond (FCB). However
FRP-Concrete bond is susceptible to fracture and environmental factors like
temperature, corrosive materials and humidity (Tuakta, Büyüköztürk 2011, Leone 2009).
Thermosetting epoxies are usually used for attaching FRP plates to the concrete surface.
Structural characteristics of epoxies degrade very rapidly with increase of temperature
beyond the glass transition temperature (Tg) which is in the range of 60°C to 82°C for
most civil engineering applications (ACI-440-2R-08). High temperatures could occur
because of fire or service condition of the bond. There a few studies characterizing FRP
bar concrete bond behaviour at elevated temperatures. Katz, Berman (2000) performed
pull-out tests on FRP bars. They concluded that bond loses about 90% of strength when
temperature reaches 150-200°C. There are limited studies addressing the behaviour of
externally bonded FRP-Concrete behaviour at elevated temperatures in the literature.
Masmoudi et al.( 2011) studied the long-term bond performance of GFRP bars in
21
concrete at temperature ranging from 20 °C to 80 °C . They performed pull-out tests on
heat treated specimens subjected to high temperatures up to 80 °C for a duration of 4 -8
months. They reported 14% reduction of bond strength for the specimen subjected to
80°C (above Tg). Chowdhury (2011) tested lap splice tests on FRP sheets at temperatures
ranging from 20 to 200°C and proposed an analytical model for FRP-FRP bond strength
degradation. Tadeu, Branco (2000) studied the steel concrete bond behaviour at high
temperature. Leone (2009) analysed the behaviour of FRP–concrete interface at elevated
service temperatures ranging from 20°C to 80 °C. They performed double face shear
tests on CFRP and GFRP strengthened specimen. Specimen dimensions were 150 by 150
by 800mm. They observed a decrease of 25% to 75% in bond strength and an increase of
2.5 to 3 times in bond transfer length in temperatures beyond Tg of the
resin. They also derived experimental bond-slip curves. Ahmed, Kodur (2011)
established a numerical model to study the bond behaviour on fire resistance of FRP-
strengthened reinforced concrete beams using a bond-slip model.
2.5 Insulation techniques
Fire proofing is essential for structural elements with low fire resistance. This could be
done by applying a coating of fire suppressing materials or materials with low thermal
conductivity. The insulation materials could be applied as pre-made boards or they
could be sprayed on the structural member. Different types of fire proofing are
22
available. Performance of a number of common insulating materials will be discussed
below.
2.5.1 Concrete
Concrete among construction material is a good insulator however the use of concrete as
insulation has been reduced recently while lighter and more cost effective insulation
techniques are prevalent. Concrete encasing is time consuming and adds considerable
weight to the member. Another problem could be the possibility of explosive spalling.
Despite disadvantages concrete is durable and resistant to impact, abrasions, and
weather exposure.
2.5.2 Sprayed insulation
There are two major types of spray applied insulation materials, cementitious and
mineral fibre. The mineral-fibre mixture combines fibres, mineral binders, air and water.
In its final cured form, the mineral-fibre coating is lightweight, non-combustible,
chemically inert and a poor conductor of heat. Cementitious coating usually
incorporates lightweight aggregates, like vermiculite, in a heat-absorbing matrix of
gypsum or Portland cement. Some formulations also use magnesium oxysulfate,
magnesium oxychloride or calcium aluminate (Gewain, Iwankiw et al. 2003). The
sprayed insulation is cost effective compared to most other systems.
23
2.5.3 Board insulation systems
Gypsum boards are considered the most common type of fire protection boards. Their
fire resistance greatly relies on the chemically-combined water, which is approximately
one fifth of the weight of the boards. When the board system is exposed to fire, the water
gradually evaporates in a process that consumes heat, and thus keeps the temperature of
the protected structural element relatively low. When all the water evaporates, the
temperature of the structural element starts to increase slowly based on the thermal
conductivity of the dry gypsum boards. Less common types of boards include
vermiculite boards. Vermiculite boards are made by pressing vermiculite particles into
board form. These boards can withstand thermal shocks and temperatures up to 1100
°C.
2.5.4 Intumescent coating
Intumescent coating is a paint-like material. When exposed to high temperature (200 to
250 ºC) it swells and produces a charred layer with very low conductivity. Despite its
low conductivity intumescent coating usually provides limited fire resistance of 1 hour
or less. In the charring process a series of decomposition reactions happens. Initially the
inorganic salt in the presence of an amide is decomposed. Following this, the carbonific
agent is decomposed which produces a large amount of char. Eventually the char
24
expands due to temperature as the blowing agent starts to expand. The final result of
these reactions is a solidified material with a very low thermal conductivity.
2.6 Fire safety and sensing at high temperatures
In 2008, the National Fire Protection Association reported that there were over 500,000
structural fires annually in the United States causing 2,900 civilian deaths and $12.4
billion in property damage (Karter 2009). In addition to the direct costs of fires, recent
collapses such as the World Trade Center disaster and other tall buildings in Madrid
and Delft due to fire have emphasized the importance of fire safety. Although fire safety
design of buildings has improved the behaviour of structures in fire, it has not
eliminated the hazards of building fires. Current approaches to reducing fire losses
employ a more holistic view to fire safety by combining and integrating different
technologies. This integration provides early forecasts of the chain of events after the
start of a fire. In the forefront of these technologies is sensing. Sensing technology can
help emergency responders make critical decisions by detecting fire location and
severity, extent of fire spread, and structural integrity.
In addition to fires, structures are prone to other types of damage. Earthquake, aging
and fatigue, and vandalism can all cause problems for structures. To detect these types
of damage and preserve the health of structures, there is a need for sensors.
Conventionally used sensors such as smoke detectors, thermocouples, and electrical
25
resistance strain gauges are among these sensors. However, having multiple types of
sensors in structures is costly and difficult to incorporate. As a result, sensors with the
capacity to sense multiple variables simultaneously are gaining popularity. Fibre optic
sensors (FOS) are capable of sensing many useful variables such as temperature, strain,
displacement, pressure, acceleration, integrity, and cracking extent (Ravet, Briffod et al.
2009, Kersey, Dandridge 1990).
2.6.1 Stimulated Brillouin scattering for fibre optic sensors
Stimulated Brillouin Scattering (SBS)-based sensor systems are distributed sensors that
can measure temperature and strain along the entire length of the fibre. Unlike other
sensors the fibre used to transfer the light to the sensing point is also the sensing
medium. Thus, continuous temperature and strain distributions can be obtained. SBS is
a nonlinear process and the Brillouin frequency shift (BFS) is linearly related to the
temperature and strain in the fibre allowing the measurement of strain and temperature
simultaneously. Recently, most of the strain sensing using Brillouin scattering has been
based on a standard single mode fibre (SMF28) with an acrylate coating, which can only
sustain temperatures of 80°C. Obviously, this limitation is insufficient for sensing in fire
situations, but sensing fibres with a carbon/polyimide coating have been used to
overcome this shortcoming. The temperature limitations are in the range 400~500°C for
this type of fibre.
26
Zeng, Bao et al. (2002) successfully used (SBS)-based sensors to function as a distributed
strain sensor in a reinforced concrete beam with a spatial resolution of 500 mm along a
1650 mm long beam. Additionally, Zou, Bao et al. (2004) have reported temperature and
strain measurement accuracy of 1.3 ±˚C and15 με using (SBS)-based sensors. They
reached a spatial resolution of 150 mm.
27
28
Chapter 3: Experimental program
3.1 General
The experimental program presented here consisted of two parts, the first part
consisting of full-scale fire tests and the second part consisting of material tests on FRP
material and FRP-concrete bond tests at high temperatures. Alongside these tests, fibre
optic sensors (FOS) were used in both full-scale tests and material tests in order to
measure strain and temperature.
3.2 Fire Tests, T-beams and Slabs
3.2.1 Test specimens
The experimental program consisted of fire tests on two intermediate-scale reinforced
concrete slabs and two full-scale reinforced concrete T-beams, all of which were
strengthened with Sika FRP materials applied externally to the specimens. The slabs
were designated as Slab-A and Slab-B and the T-beams were designated as Beam-A and
Beam-B. Details of the reinforced concrete slabs and reinforced concrete T-beams are
shown in Figure 3-1 and Figure 3-2, respectively.
3.2.1.1 Dimensions
The slabs dimensions were 1331 mm by 954 mm and 152 mm. The reinforcement details
are shown in Figure 3-1.
29
Figure 3-1 Dimensions and reinforcement details of SLAB-A and SLAB-B (dimensions in
mm)
305
305
305
305 305
25152
208
208
1331
172 172
954
SECTION A-A:
A A
NTS
15M steel rebar 10M steel rebar
30
The T- beams had a span of 3.9 m (12.7 ft.) and overall height of 400 mm (15.7 in.). The
flange was 1220 mm (48 in.) wide and 150 mm (5.9 in.) thick. The web was 300 mm
(11.8 in.) wide. The reinforcement details are shown in Figure 3-2.
Figure 3-2 Dimensions and reinforcement details of BEAM-A and BEAM-B (All steel
bars are 10M)
31
3.2.2 Materials
3.2.2.1 Concrete
Portland cement Type I was used for fabricating the reinforced concrete slabs and T-
beams. The aggregate type for all specimens was carbonated aggregate. The maximum
aggregate size used in the slabs and T-beams was 13 mm. The concrete for slabs and
beams was supplied by Lafarge, Kingston, Canada. The concrete for the slabs was
designed to have a specified compressive strength of 28 MPa. The concrete for the beams
was designed to have a specified compressive strength of 30 MPa. The 28-day
compressive strength of the slab concrete was 27 ±3 MPa and the compressive strength
on the day of fire test was 26±4 MPa. The average 28-day compressive strength of the T-
beam concrete was 32±2 MPa and the test day strength was 28.5±3 MPa.
3.2.2.2 Steel
Deformed bars were used for reinforcing both the slabs and T-beams (Figures 3-1 and
3-2). In the slabs, four 10M steel bars were along the direction of the 954 mm edge and
three 15M steel bars were placed along the direction of the 1331 mm edge. The clear
cover for 15M steel bars was 25 mm from the bottom. All reinforcements in the slabs had
specified yield strengths of 400MPa. The longitudinal reinforcement in the T-beams
consisted of six 10M steel bars in the flange and two 15M steel bars in the web. For
lateral reinforcement, twenty-six 10M steel ties placed every150mm. Additional lateral
32
bars were placed in the flange. The tested yield strengths of the steel bars were 470 MPa
for the 10M and 15M bars.
3.2.3 Fabrication
The slabs and T-beams were fabricated and cured in the Structures Testing Laboratory at
Queen’s University, Kingston, Canada and then shipped to the Fire Testing Facility of
the National Research Council, Ottawa, Canada. Both slabs and beam-slabs were cast in
plywood formwork.
3.2.3.1 Reinforcing bars
The 15M longitudinal reinforcing bars were placed into holes drilled into the plywood to
maintain a consistent concrete clear cover of 25 mm (1.0 in.). The longitudinal
reinforcements were subsequently tied together using steel ties. Figure 3-3 shows the
formwork and reinforcement layout during fabrication of the slabs.
33
Figure 3-3 Formwork and reinforcement layout for slabs (Williams, 2004).
The stirrups for the T-beams were arc-welded together to form the steel cage (minimal
welding was performed just to keep the cage strong enough for concrete pouring). The
cage was placed on small concrete blocks to maintain a consistent concrete clear of 40
mm to the steel ties. Figure 3-4 and Figure 3-5 show the steel cage for the beam-slabs
during fabrication.
34
Figure 3-4 Steel reinforcement for T-beams
Figure 3-5 Formwork and reinforcement layout for T-beams
35
3.2.3.2 Instrumentation
Chromel-alumel (Type K) thermocouples were used in order to record the temperatures
during the fire endurance tests. Figure 3-6 shows the locations of the thermocouples
within the slabs. Figure 3-7 shows the location of the internal and surface thermocouples
within the T-beams and on the unexposed surfaces of the T-beams. Displacement gauges
were also used during the fire tests to monitor beam deflection, as shown in Figure 3-8.
36
Figure 3-6 Location of thermocouples in slab specimens (all dimensions in mm)
51
51
A
B
LOCATION A
18
1716
CL
Insulation
EpoxyFRPEpoxy
125
100
75
5030
22 15
45
2423
44
43
19
20
21
LOCATION B
LC
CL
LCNTS NTS
37
Figure 3-7 Location of thermocouples in T-beams (all dimensions in mm)
TCs
5,2
9,
37
,44
an
d 4
7 a
re a
t th
e FR
P-I
nsu
lati
on in
terf
ace
TCs
6,3
0,3
8,4
5 a
nd
48
are
on
th
e In
sula
tion
su
rfac
e
A
B
C
DE
FG
26
28
29 30
27
21
20
16
12
91
0
14
18
13
17
11
15
19 25
8
2 (
A) 4
(A
)5
(A
)6
(A
)3 (
A)
34
(C
)
36
(C
)3
7 (
C)
38
(C
)35
(C
)
1 (
D)
7 (
E)
32
(F)
31
(F)
33
(F)
39
(G
)
22
23
24
AB
CE
DG
F47
545
049
955
140
149
945
047
5
925
1050
900
925
50
50150
250
400
6 (
A)
Nu
mb
erS
ecti
on
LEG
END
42
41
B
153
293
147
184
5720
7
40
77
35 35 35
400
150
607
460
40
U-W
rap 46
4748
434445
End
Jcl
ose
to
sect
ion
G
End
Icl
ose
to
sec
tion
D
38
Figure 3-8 Location of displacement gauges (all dimensions in mm).
3.2.3.3 Curing
The slabs and T-beams were cured under wet burlap and plastic sheets at room
temperature and 100% humidity for seven days, after which the formwork was removed
11681168
500123
4
678
5
Location of displacement gauge
39
and the samples were cured in the Structures Testing Laboratory at Queen’s University
at room temperature for at least six months before they were transported to the National
Research Council of Canada, Ottawa.
3.2.4 FRP strengthening
Three strips of Sika® CarboDur S512 CFRP plates were installed side by side to cover a
width of approximately 150 mm on Slab A, Figure 3-9. The FRP on Slab B consisted of
two layers of SikaWrap Hex 103C unidirectional carbon/epoxy FRP strengthening
system Figure 3-10. The FRP was bonded to the tension face of both slabs in the
longitudinal direction. A summary of the strengthening system for the slabs is presented
in Table 3-1.
Installation steps for the installation of FRP sheets or plates for the intermediate-scale
slabs were as follows:
3.2.4.1 Slab-A
1. The concrete surface was prepared using hand grinders to roughen the surface
and create the desired texture.
2. The dust removed by vacuuming the surface.
3. An even layer of SikaDur®-30 epoxy was applied to the prepared concrete
surface where the Sika CarboDur® S512 plates were going to be applied.
40
4. A layer of SikaDur®-30 epoxy was placed on one side of CarboDur plates.
5. The plates were placed on the prepared concrete surface.
6. Even pressure applied to the plated using a roller to assure proper adhesion and
to control the adhesive thickness.
7. Excess epoxy was removed from the specimen
8. Another layer of SikaDur®-30 epoxy was applied on top of the installed plates.
9. Another layer of SikaDur®-300 epoxy was applied to the final surface and special
sand was sprinkled to the saturated surface to increase the bond of insulation to
the FRP surface.
3.2.4.2 Slab-B
1. The concrete surface was prepared using hand grinders to roughen the surface
and create the desired texture.
2. The dust removed by vacuuming the surface.
3. SikaWrap® Hex 103C sheet was cut to the desired length and impregnated using
SikaDur®-300 epoxy.
4. An even layer of SikaDur®-300 epoxy was applied using a nap roller to the
prepared concrete surface where the FRP wrap were going to be applied.
5. The resin-saturated sheet of FRP was placed on the prepared concrete surface.
6. The plates were placed on the prepared concrete surface.
41
7. Even pressure applied to the sheet using a roller to remove air bubbles beneath
the wrap.
8. Another layer of SikaDur®-300 epoxy was applied to the final surface and special
sand was sprinkled to the saturated surface to increase the bond of insulation to
the FRP surface.
42
Table 3-1 FRP and insulation details for intermediate-scale slabs.
Slab A Slab B
FRP Type Sika CarboDur® S512 SikaWrap® Hex 103C
No. Layers/strips 3 side by side 2
FRP Width (mm) 3×50 635
Epoxy SikaDur®-30 SikaDur®-300
Insulation Type Sikacrete®-213F Sikacrete®-213F
Insulation Thickness 40 mm 60 mm
Figure 3-9: CFRP strips on Slab A.
43
Figure 3-10: CFRP Wraps on Slab B.
Beam-A was strengthened by CFRP Sika® CarboDur S812 in flexure and Beam-B was
strengthened by one layer of CFRP SikaWrap® Hex 103C on the bottom of the beam
web. Two different CFRP U-wraps are selected for Beam-A. The U-wrap at one end
consisted of two 635 mm wide layers of SikaWrap® Hex 103C and the other U-wrap had
four 600 mm wide layers of SikaWrap® Hex 230C. In the case of Beam-B, U-wrap at one
end consisted of two 610 mm wide layers of SikaWrap® Hex 100G and the other U-wrap
has four 610 mm wide layers of SikaWrap® Hex 430G. A summary of the strengthening
systems for the T-beams is presented in Table 3-2. Installation specialists from Sika®
installed the strengthening system at the National Research Council of Canada.
44
Table 3-2 Summary of FRP-Insulation system used for T-beams.
Beam A Beam B
Flexural FRP Type Sika CarboDur® S812 SikaWrap® Hex 103C
No. Layers/strips 1 1 FRP Width (mm) 80 200
Insulation Type Sikacrete®-213F
Insulation Thickness 36.0 mm 36.0 mm U-wrap END I Type SikaWrap® Hex 103C SikaWrap® Hex 100G
No. Layers 2 2 Wrap Width (mm) 635 610
U-wrap ENDJ Type SikaWrap® Hex 230C SikaWrap® Hex 430G No. Layers 4 4 Wrap Width (mm) 600 610
Installation steps for the installation of FRP sheets or plates for the beams were as
follows:
3.2.4.3 Beam-A
• The concrete surface was prepared using hand grinders to roughen the surface and
create the desired texture where the longitudinal FRP and U-wraps were going to be
applied.
• A thin layer of SikaDur®-30 epoxy was applied to the prepared concrete surface
where the Sika CarboDur® S812 plate was going to be applied.
• A layer of SikaDur®-30 epoxy was placed on one side of CarboDur plates
45
• The plates were placed on the prepared concrete surface.
• Even pressure applied to the plated using a roller to assure proper adhesion and to
control the adhesive thickness.
• SikaWrap® Hex 103C and SikaWrap® Hex 230C sheets were cut to the required
length for U-wraps and impregnated in SikaDur®-300 epoxy.
• Concrete surface was saturated by a layer of SikaDur®-330 epoxy for U-wraps.
• U-wraps were applied in layers.
• Another layer of SikaDur®-300 epoxy was applied to the final surface and special
sand was sprinkled to the saturated surface to increase the bond of insulation to the
FRP surface.
3.2.4.4 Beam-B
• The concrete surface was prepared using hand grinders to create the desired
texture. And dust removed by vacuuming the surface.
• An even layer of SikaDur®-330 epoxy was applied using a nap roller to the
prepared concrete surface where the FRP wraps were going to be applied.
• SikaWrap® Hex 103C sheet was cut to the desired length and impregnated using
SikaDur®-300 epoxy.
• The resin-saturated sheet of SikaWrap® Hex 103C was placed on the prepared
concrete surface on the bottom of the beam.
46
• Even pressure applied to the sheet using a roller to remove air bubbles beneath the
wrap.
• SikaWrap® Hex 100G and SikaWrap® Hex 430G sheets were cut to the required
length for U-wraps and impregnated in SikaDur®-300 epoxy.
• U-wraps were applied in layers.
• Another layer of SikaDur®-330 epoxy was applied to the final surface and special
sand was sprinkled to the saturated surface to increase the bond of insulation to the
FRP surface.
Figure 3-11 Surface thermocouples and surface preperation T-beams.
47
Figure 3-12 CFRP plate installation Beam-A.
Figure 3-13 CFRP plate installation Beam-B.
48
Figure 3-14U-wrap installation Beam-B.
Figure 3-15 U-wrap installation Beam-A.
49
Figure 3-16 Thermocouples at FRP-insulation interfce and insulation surface (before
spraying insulation).
3.2.5 Fire proofing
In order to provide supplemental fire insulation over the FRP on beams and slabs
Sikacrete®-213F was used as insulation. Sikacrete®-213F is a cement-based, dry mix fire
protection mortar for wet sprayed application. It contains phyllosilicate aggregates,
which are highly effective in resisting the heat of hydrocarbon fires. A 40 mm layer of
Sikacrete®-213F was spray-applied to Slab-A, Beam-A and Beam-B. The insulation
thickness for Slab-B was 60 mm. A steel mesh was installed on the FRP strengthened
surface in the slabs in order to reinforce the bond of the insulation to the slabs. The
sprayed insulation was allowed to cure in the Fire Testing Laboratory at the National
Research Council of Canada (NRC) until the date of the test.
50
Figure 3-17 Spraying insulation layer.
Figure 3-18 Measuring insulation thickness T-Beams.
3.2.6 Test apparatus
During the fire endurance tests, the specimens were exposed to elevated temperatures
on their soffits. The two slabs were tested in the intermediate-scale furnace at NRC, and
the two beam-slabs were tested in the full-scale floor furnace, also at NRC. These
51
furnaces were designed to produce temperature and loading conditions as prescribed in
ASTM E119 and CAN/ULC S101 (Figure 3-19).
Figure 3-19 ASTM E119 standard time temperture curve.
The Intermediate-Scale Furnace can tests specimens up to a maximum size of 1.35m by
1.98m (Figure 3-20). While it is possible to apply load during the fire test, no load was
applied to the slabs in this study. The full-scale floor furnace can test samples to a
maximum size of 4.9 m by 4.0 m. (Figure 3-21).
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (minutes)
ASTM E119
52
Figure 3-20 Intermediate-scale furnace for slabs.
Figure 3-21 Full-scale floor furnace for beams.
The T-beams were subjected to a load from above using 30 distributed hydraulic jacks.
Each jack had a maximum load capacity of 13 kN (refer to Figure 3-21 and Figure 3-23).
Layers of insulation were provided between the two slabs and two beam specimens to
make sure they are thermally independent as shown in Figure 3-22 and Figure 3-36.
The temperatures in the furnaces were measured using Type K thermocouples.
53
3.2.7 Test conditions and procedures
Both the intermediate-scale and full-scale furnaces can produce the conditions described
in ASTM E119, which are similar to those prescribed by CAN/ULC S101.
The two slabs were tested side by side in furnace. Each slab was supported on three
sides. As mentioned earlier, no load was applied to the slabs during the fire exposure
Figure 3-22. The beams were placed in a movable frame and fixed to the frame by steel
mounts at both ends. Then the frame was placed on the furnace and all openings were
filled with ceramic-insulated panels. The relative humidity of each specimen at the time
of testing is given in Table 3-3.
3.2.7.1 End conditions
The intermediate-scale slabs were not subjected to applied load during fire exposure and
therefore their end conditions are not discussed here. The slabs of the T-beams were
axially restrained during the fire test by placing steel shims at their ends prior to testing.
The support conditions were selected to meet the conditions described in ASTM E119
and CAN/ULC S101 corresponding to an axially-restrained flexural assembly.
3.2.7.2 Loading
The purpose of fire testing the intermediate-scale slabs was to evaluate the thermal
performance of the two insulation thicknesses. Thus, the slab experienced no load other
than its self-weight during the fire endurance test.
54
During the full-scale T-beam fire tests, the assemblies were tested under a sustained
uniformly distributed load. The sustained applied load was 25.7 kN/m, which
represented 71% of the ultimate strengthened capacity according to ACI 440.2R-08, and
73% according to CSA S806-02. Details of the load calculations are presented in
Appendix A. The preloading of the T-beam specimens began 45 minutes prior to the
start of the fire exposure. Upon reaching the required load level, the heating in the
furnace was started. The required load level was maintained at a constant value
throughout the fire test.
Figure 3-22 Test setup and instrumentation for slabs.
55
Figure 3-23 Instrumentation at unexposed surface T-beams.
3.2.7.3 Failure criteria
In a fire test, the structural member must not fail under applied load for the required
duration. Because there was no load applied to the slabs, no load-bearing failure criteria
was applicable. Since the purpose of the slab tests was to investigate the performance of
the thermal insulation, the temperatures during the slab fire endurance were compared
with the thermal criteria stated in ASTM E119 and ULC S101. Thus, the slab specimens
were assumed to have failed if any of the following limits were reached:
Slab Criterion 1: Steel temperature reaches 593°C,
Slab Criterion 2: Unexposed surface temperature reaches 140°C,
Slab Criterion 3: Any individual point at unexposed face reaches 180°C.
T-beams were subjected to their service load during fire testing. The beams were
assumed to have failed if any of the following criteria were reached:
56
T-beam Criterion 1: Steel temperature 593°C
T-beam Criterion 2: Average unexposed face temperature reaches 140°C,
T-beam Criterion 3: Any individual point at unexposed face reaches 180°C.
T-beam Criterion 4: Load-bearing capacity of the beam reaches the applied service load
Both T-beams successfully resisted the sustained applied load of 27.7 kN/m for more
than four hours of fire exposure without structural failure. Close the end of the fire
endurance test, the applied load was increased to 39 kN/m but the beams did not fail
even at that load level. After 4.5 hrs the fire test was stopped to prevent any damage to
the floor furnace. Since the T-beams were restrained axially, they were not required to
satisfy the specified temperature limits stated in ASTM E119 to achieve a fire endurance
rating. Thus, the beams achieved a 4-hour fire endurance rating.
3.3 Fire test results and discussion
A summary of results of the fire endurance tests is given in Table 3-3. General
observations recorded during the beams fire tests are presented in Table 3-4. The
temperatures of the furnace, concrete, steel, FRP and insulation, and the vertical
deflections were recorded during the fire endurance tests. The recorded temperatures
for the slabs and beams are given in Appendix-A.
57
Table 3-3 Summary of test results
Relative Humidity (%)
Ambient Temp. (° C)
Ultimate Load Capacity (kN/m)
Applied Load (kN/m)
Failure Load (kN)
Fire Endurance (min.)
Failure Mode
Slab-A 63 23 - - - > 240 N/A Slab-B 63 23 - - - > 240 N/A Beam-A 61 22 38.6 25.7 N/A > 255 N/A Beam-B 61 22 40.4 25.7 N/A >255 N/A
Table 3-4 General observation during test of T-beams.
Time (hr:min) Observations /Actions
Before test Small cracks was observed on the Insulation surface
0:45 earlier Beam was loaded to 25.7 kN/m
0:00 Furnace turned on
0:14 Moisture and emission of steam noted at unexposed surface
0:36 Flaming observed at the at U-warps both beams
0:45 Flaming observed at mid-span, cracks start to widen
4:02 Load increase from 25.7 kN/m to 39 kN/m
4:15 No failure observed, loading stopped
58
3.3.1 Temperatures
Results of thermocouple temperature readings for slabs are given in detail in Appendix
A. These graphs show temperatures at the FRP-concrete bond line and steel
reinforcement during the fire tests. These data indicate that it will be difficult to
maintain the FRP temperature below the glass transition temperature (Tg) of the matrix
for prolonged periods of time during fire. Temperatures in Slab-B are lower compared to
Slab-A temperatures, because of the thicker layer of insulation, but the FRP is still not
fully protected for the full duration of the fire. In both cases, the FRP-concrete
temperature exceeds glass transition temperature in less than 30 minutes. The average
unexposed surface temperature after 4 hours of fire exposure reached 88˚C and 62˚C in
slab A and B, respectively (Figure 3-24, Figure 3-25 and Figure 3-26).
Figure 3-24 Temperatures vs. exposure time for slab A.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Furnace avg.
TC-45 Insulation Surface
TC-44 FRP-Insulation
TC-43 FRP-Concrete
Avg. Unexposed Face
59
Figure 3-25 Temperatures vs. exposure time for slab B.
Figure 3-26 Temperatures vs. exposure time comparison for slabs A and B at FRP-
concrete bond line and steel reinforcement locations.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Furnace avg.
TC-45 Insulation Surface
TC-44 FRP-Insulation
TC-43 FRP-Concrete
Avg. Unexposed Face
0
100
200
300
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
FRP-Concrete Slab-AFRP-Concrete Slab-BRebar Bottom Slab-ARebar Bottom Slab-B
60
Detailed temperature readings for T-beams are given in Appendix A. Similar to the
slabs; FRP-concrete bond temperature exceeds glass transition temperature in less than
30 minutes. Steel temperatures in all tests are below 250 ˚C . Figures 3-27 to Figure 3-30
illustrates temperature recordings in various sections of the T-beams A and B.
61
Figure 3-27 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation sec-B TC-28
Insulation Surface sec-B TC-30
FRP-Insulation sec-B TC-29
62
Figure 3-28 Steel reinforcement temperatures (web) Beam-A.
0
50
100
150
200
250
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Longitudinal Steel sec-A TC-2
Longitudinal Steel sec-A TC-3
Longitudinal Steel sec-B TC-25
Longitudinal Steel sec-B TC-27
63
Results for Beam-B are as follows.
Figure 3-29 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation sec-B TC-28
FRP-Insulation sec-B TC-29
FRP-Insulation sec-B TC-30
64
Figure 3-30 Steel reinforcement temperatures (web) Beam-B.
0
50
100
150
200
250
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Longitudinal Steel sec-A TC-2
Longitudinal Steel sec-A TC-3
Longitudinal Steel sec-B TC-25
Longitudinal Steel sec-B TC-27
65
3.3.2 Performance of the insulation system
There were minor shrinkage cracks in all samples which contributed to further cracking
later during the fire test (Figure 3-31). These cracks gradually widened as the test
progressed, likely due to thermally-induced shrinkage of the insulation material. Wider
cracks accelerated heating of resin impregnated FRP layer to heat up faster at the
location of the cracks. Subsequently stable flames were created at crack locations, see
Figure 3-33. Theses cracks and residual charring are visible for Beam-B in Figure 3-34
and Slab-B in Figure 3-31. The insulation layer protected the concrete from spalling. As
depicted in Figure 3-32, spalling of concrete is visible where there was no fire protection.
There was no separation or spalling of the insulation layer during either of the fire tests,
see Figure 3-35 and Figure 3-36.
Figure 3-31 Shrinkage cracks in insulation, T-beams before fire test.
66
Figure 3-32 Spalling of un-insulated concrete (flange). Note, insulation layer was
removed manually after fire test.
Figure 3-33 Flames are visible at cracks in the U-wrap location, Beam-B after 1 hour and
53 minutes of fire exposure.
67
Figure 3-34 Cracks at insulation surface after fire test Beam-B.
Figure 3-35 Slab-B after test.
68
Figure 3-36 T-beams after fire test in the loading frame.
3.3.3 Deflections
Figure 3-37 illustrates the mid span deflection of Beam-A and Beam-B; it also gives the
magnitude of the superimposed load vs. time. While preloading the distributed load on
the beams increases linearly until it reaches the predefined superimposed load of 25.6
kN/m. The load was then kept constant for approximately 30min before heating started.
The deflections in the preloading sections increased nearly linearly with time. The
subsequent increase in deflection is the result of fire exposure since the load is kept
constant for the first 4 hours of fire exposure. The large jump in the deflections in the
69
first hour of the fire exposure is most likely due to the differential temperature
distribution in the height of the beams. This differential temperature distribution creates
larger thermal strains at the soffit of the beams and results in increase of curvature and
deflection of the beams. Since the dimensions and material used in the beams are similar
(except FRP), it is expected that the final deflections of the beams to be similar in
magnitude to each other. Of course the effect of FRP would be diminished in the first
hour of fire exposure. Nevertheless, as it is apparent from Figure 3-37, Beam-B has a
larger deflection compared to Beam-A. This could be the result of measuring error
during the tests. It is also possible that the loading frame against which the
displacements are measured is deformed unevenly or the load distribution was uneven.
Detailed results of beam deflections are presented in Appendix A.
70
Figure 3-37 Comparison of mid span deflection of Beam-A and Beam-B.
71
3.3.4 Summary
Fire endurance tests were conducted on two intermediate-scale slabs and two full-scale
T-beams. Both T-beams and slabs were strengthened with externally-bonded FRP in
flexure and both were protected using a layer of supplemental fire insulation materials.
From the experimental program, the following conclusions can be drawn:
• Reinforced concrete T-beams strengthened with externally-bonded FRP achieved
fire endurance ratings of more than 4-hours.
• Slabs and T-beams with 40mm and 60mm thickness of the insulation material
satisfied the thermal criteria stated in the ASTM E119 and ULC-S101 standards
for more than 4-hours.
• Insulation material protected concrete and internal steel from adverse effects of
fire, thus preventing the failure of T-beam sand slabs.
3.4 FRP-concrete bond tests
The configuration of the pull-off test for the study of FRP-concrete behaviour at elevated
temperatures is shown in Figure 3-38. An FRP sheet or plate is attached to a concrete
block and the concrete block is clamped by two steel plates at top and bottom. During
the test, FRP and the bottom rod are pulled apart causing a shearing force exactly at the
interface. For high temperature tests the whole setup is placed in an environmental
chamber which controls the testing temperature to the desired testing condition. Internal
72
dimensions of the chamber are 250 mm in width, 250 mm in depth and 300 mm in height
and the machine has a maximum load capacity of 600 kN. Concrete block dimensions
were 6 inches/152 mm in height, 4 inches/102 mm in width and 3 inches/76 mm in depth;
see Figure 3-39. The 28-day compressive strength of the concrete was 30MPa. Concrete
blocks had aged for at least 6 months before the test. Concrete bond surfaces were sand
blasted prior to application of FRP plates. The CFRP plates were Sika® CarboDur S512
but they were cut in half lengthwise to make the width of the FRP plates equal to 25±1
mm. The adhesive used for attaching the plate to the concrete surface was Sikadur30
with a Tg value of 60°C. Glass beads were placed between concrete surface and FRP
sheets to achieve a uniform 1.5 mm adhesive thickness along the bond. Sikadur30 will
reach its design strength after 7 days based on manufacturer’s data sheet. All samples
were aged at room temperature for at least 60 days after application of the FRP.
73
Figure 3-38 Bond test setup.
Figure 3-39 Sample preparation.
There are numerous variables that affect the bond behaviour such as bond length, FRP
width, type of FRP, etc. In this study most variables were kept constant and the main
74
variable was the exposure temperature. For example bond length and adhesive
thickness and material type were identical for all tests.
Two types of thermal tests have been performed: steady state and transient. In steady-
state thermal tests, samples were heated up to the determined temperatures. Tests were
performed at room temperature, 60, 80, 105, 150 and 200°C. The rate of heating was
10°C/min. Four samples were tested in each temperature group. Samples were kept at
the target temperature for 60 minutes to achieve a uniform temperature distribution.
Heated specimens were then exposed to tensile loading while the temperature was kept
constant. The tensile force was increased until failure or debonding at the interface. In
transient temperature testing, samples were loaded to a determined tensile loading that
was maintained throughout the test. Then, the temperature was increased until the
sample failed. Loading levels during the transient tests were 20%, 40%, 60% and 80% of
the room temperature strength determined during the tests. Three samples were tested
for each load level. Temperature was measured on the FRP surface by standard type K
thermocouples inside the environmental chamber.
3.4.1 Bond tests results and discussion
The steady -state test results are presented in Table 3-5. Figure 3-40 depicts the
degradation of bond at higher temperatures; the solid line presents the average value.
As could be seen the bond loses about 50 percent of its strength at approximately 100 °C,
75
which is approximately 40 °C higher than Tg for the adhesive. For the case where the
temperature was 200°C failure happened during the heating process approximately 30
minutes through steady-state heating. The strength value of zero is entered for them.
Table 3-5 Strength results for steady state tests.
Test Temperature, T (°C)
Reduced Strength at Temp. T (kN)
Average Strength (kN)
STD (kN) Strength loss %
Residual strength %
23 (room temp.) 13.6 14.1 13.7 14.6 14.0 0.4 0% 100% 60 (Tg) 12.9 12.9 12.3 16.0 12.7 1.7 9% 91% 80 8.9 8.5 9.7 9.1 9.0 0.5 36% 64% 105 6.5 5.0 6.2 5.7 5.8 0.7 58% 42% 150 2.2 2.7 2.9 3.0 2.7 0.3 81% 19% 200 0.0 0.0 0.0 0.0 0.0 0 100% 0%
Figure 3-40 Strength vs. temperature for steady-state tests.
0.02.04.06.08.0
10.012.014.016.018.0
0 50 100 150 200 250
Stre
ngth
(kN
)
Temperature (°C)
Average
76
In design practices the FRP contribution to load carrying capacity of the structure is
assumed to be zero once its temperature reaches Tg of the adhesive. Based on these
results, this assumption is conservative because the FRP-concrete has retained 90% of its
maximum capacity at Tg. A notable observation is that in high temperature tests, unlike
room temperature tests, failure does not happen in concrete substrate but the failure
surface occurs within the epoxy adhesive layer; Figure 3-41 and Figure 3-42 . The room
temperature failure mode can be described as cohesive concrete failure while the failures
at higher temperatures are adhesive failures. As the failure temperature rises the failure
is less abrupt. It seems that the adhesive material behaves in a brittle manner at lower
temperatures but a more elasto-plastic manner at elevated temperatures.
Figure 3-41, Room temperature steady state specimen before and after failure. Debonding happens inside concrete very close to the interface.
77
Figure 3-42 Steady state specimen, T=105C, before and after failure. Debonding happens inside epoxy layer.
3.4.2 Proposed analytical model
An analytical model of the form,
𝑆(𝑇) = 𝑆𝑟2
+ 𝑆𝑟2�𝑡𝑎𝑛ℎ�−𝑤(𝑇 − 𝑇𝑐)�� (3-2)
could be used to model the mechanical properties of the FRP-concrete bond where S(T)
is the remaining strength at temperature T, Sr is the room temperature strength, Tc is the
central temperature and w is an empirical constant. For current tests Tc is taken as Tg +34
and w is 0.018. Fitted curve and experimental data are shown in Figure 3-43.
78
Figure 3-43 Analytical model vs experimental results dotted lines are 95% confidance interval of the curve. Transient test results are given in Table 3-5 and Figure 3-44. The FRP-concrete bond
could survive higher temperatures at lower sustained load level. At 20% of maximum
capacity the bond could be functional up to approximately 250 °C in a transient thermal
loading as described above. This temperature is significantly higher than Tg for the
adhesive. However the critical temperature is lower for the case of a much higher load
level of 80% (150°C at 80% load level compared to 250°C in the 20% load level case).
Table 3-6 Failure temperatures for transient tests at different sustained load levels.
Load level %
Sustained load (kN)
Failure Temp. (°C)
Mean Failure Temp. (°C)
STD
80% 11.2 137 146 154 146 6.4 60% 8.4 159 169 159 162 7.1 40% 5.6 209 238 211 219 16.2 20% 2.8 287 256 283 275 16.9
0.0
5.0
10.0
15.0
20.0
0 50 100 150 200
Stre
ngth
(kN
)
Temperature (°C)
ProposedModel
79
Figure 3-434 Transient test results failure temp. vs load level.
As mentioned above the failure at high temperatures happens in the adhesive layer
therefore the debonding mechanism is different and development length assumptions
which are derived from Linear Elastic Fracture Mechanics (LEFM) concepts may no
longer be valid. Further investigation in this regard is needed to establish proper
development length criteria.
120140160180200220240260280300
0% 50% 100%
Failu
re te
mpe
ratu
re (°
C)
Load level
80
Figure 3-445 Transient test specimens before and after failure and debonded surface for
20% (top) and 80% load level (bottom).
81
3.4.3 Discussion
The results of the steady-state tests are particularly important for high temperature
environments such as hot climates or high operating temperatures in industrial
applications. In such cases, the FRP-concrete bond will need to retain its full room
temperature strength since an overload could be expected at any time during prolonged
high temperature exposure. Thus, an operating temperature limit close to Tg (60°C)
would be reasonable for this application. Therefore, this finding supports the ACI
4402R-08 limit of Tg – 15 °C for maximum service (operating) temperature for FRP (Xian,
Karbhari 2007, Luo, Wong 2002). On the other hand, in a fire scenario, temperatures
increase rapidly and thus correspond more closely to the transient temperature test
conditions. Additionally, loads in a fire are not expected to be at ultimate conditions
because the maximum loading condition is not expected to occur at the same time as a
fire. Typically, the expected loads in a fire are at the service load level or lower (ULC
S101-07). For service load levels, the stresses in the FRP would be approximately 20 to
30% of ultimate. At these low stress levels, the FRP-concrete bond may be structurally
effective at temperatures as high as 200 to 250°C.
82
3.4.4 Summary bond tests
• Testing was performed to evaluate the behaviour of FRP concrete bond at
elevated temperatures. Based on the results of these tests, the following
conclusions can be drawn,
• FRP concrete bonds are sensitive to elevated temperatures and there has been a
50% loss of strength at temperature 40°C above glass transition temperature of
the adhesive.
• Widely accepted rule of ignoring the FRP contribution to carrying capacity once
it reaches Tg is safe and conservatively accounts for the bond behaviour.
• In transient heating cases the FCB could withstand much higher temperatures
than Tg, at 80 % of maximum load this temperature was 150 °C at 10°C/min
heating rate.
• Unlike room temperature debonding failure happens in the adhesive layer rather
than concrete substrate.
• The analytical model presented here is able to describe the mechanical property
degradation adequately.
• Additional testing is required to establish a proper development length of FCB at
higher temperatures.
83
3.5 FRP coupon tests and FOS results
To investigate the mechanical behaviour of carbon fibre reinforced polymer CFRP
material at elevated temperatures, two different types of tests were considered. Four
samples were tested under a steady-state regime and one sample was tested in a
transient regime (Table 3-7) as described in section 3.4. The mechanical behaviour of the
FRP at higher temperatures is dependent on the behaviour of both constituents, i.e. resin
and fibre. The mechanical properties of the resin degrade drastically at a temperature
known as the glass transition temperature (Tg) which is usually between 50 to 120˚C.
Since the FRP may experience significant loss in its mechanical properties near Tg,
steady-state tests were conducted at Tg, Tg +20 and Tg -20 °C (Table 3-7).
Table 3-7 Specimen information and test regime.
Specimen ID
Test Regime Temperature (˚C) Load Level (kN)
1.1 Steady-State 20 1.2 Steady-State Resin Tg (110) 1.3 Steady-State Resin Tg – 20 (90) 1.4 Steady-State Resin Tg + 20 (130)
2.1 Transient 60 % of ultimate (54.6)
Samples were exposed to heating in the middle of the sample; the heated length was
approximately 300 mm. The temperature variance in the furnace was less than ±5˚C. The
rate of temperature increase was 10˚C/min for all steady-state tests. The same rate was
84
used in the transient tests, but to achieve more stable reading by the FOS, temperature
was kept constant for approximately 5 minutes at 100 and 200˚C. Load was applied at a
constant rate of 2.5 mm/min in all tests. To prepare more stable reading situations for
FOS in steady-state tests, load was kept constant for approximately 5 minutes at some
load levels of 20, 40, 60, 70, 75 and 80 kN.1
Figure 3-456: CFRP coupon dimensions and fibre optic sensor location (all dimensions in
mm).
3.5.1 Instrumentation
The important variables were axial deformation and strain, load in the CFRP specimen,
and finally temperature of the furnace. Load was captured by the internal load cell of the
Universal Testing Machine (UTM). Temperature was recorded by two type K
1 Not all load levels were used for all the tests.
700
50 25 FOS
Protection
CFRP tabs
85
thermocouples located inside the furnace. The thermocouple readings were in
agreement with furnace’s target temperature.
The axial strain of FRP samples was measured using particle image velocimetry (PIV)
(White et al. 2003). High resolution images were taken during various stages of the test
procedure. PIV is capable of tracking the movement of any pixel patches in a sequence
of images. This allows for measuring the displacement field in the sample during the
test. To measure the axial strain, the displacement of pixel patches similar to those in
Figure 3-46 were tracked. The difference in axial displacement of the patches divided by
their axial distance gives the strain in that direction. Figure 3-48 shows a sequence of
pictures taken during the transient test. Since the PIV analysis tracks the pixel pattern
around a certain point, difficulties arise when the surface texture changes due to thermal
effects.
Figure 3-467 Square pixel patches on FRP sheet used in PIV analysis (yellow squares).
Pixel Patches
86
Figure 3-478 Damage progress during test for specimen 2.1. Temperatures are 28, 77, 183, 200, 210 and 256 ˚C from left to right. SBS-based2 FOSs were installed on the specimen along their longitudinal axis of
symmetry as shown in Figure 3-46. The fibre was attached to the FRP sample at the ends
using epoxy glue. The glued parts were kept outside the furnace. To further protect the
bond between FOS and the coupon, a protective cover was placed on top of the glued
fibre (Figure 3-49).
2 SBS stands for stimulated Brillouin scattering.
87
Figure 3-489 Fibre optic sensor and protective cover installation details.
3.5.1.1 Results
Based on dynamic mechanical analysis (DMA) tests on the FRP material, Tg was
determined to be 110˚C. Figure 3-50 shows a sample FOS reading from specimen 1.1.
Figure 3-49 OTDR style curve shows the reflectivity along the fibre length and the right
side curve is a 3-D (top view) of the fibre section under stress. These curves are obtained
88
from specimen 1.1.
PIV analysis was performed to calculate the strain at several load levels for the test
sample 1.1. Knowing the load level and the sample dimensions, these strain values were
used to calculate the secant elastic modulus as reported in Table 3-8. Table 3-9 shows
the results of the steady-state tests. No significant loss of strength was observed in tests
performed at temperatures below Tg. The elastic modulus as reported by the
manufacturer is 165 GPa which is in good agreement with the obtained results.
Figure 3-52 shows the secant modulus versus temperature during the transient test. The
modulus of the material decreases as the temperature rises. The rate of reduction
increases dramatically just above the glass transition temperature (110 ˚C).
Table 3-8 Modulus calculation results for room temperature test at different load levels;
strain is calculated using PIV analysis.
Load (kN) Strain PIV Stress (MPa) Secant Modulus (GPa) 40 0.92% 1388 151 60 1.32% 2082 158 80 1.70% 2777 163
89
Table 3-9 Steady-state tension test results for FRP at high temperature.
Specimen ID Temperature (˚C)
Width (mm)
Peak load (kN)
Strength (MPa)
Strength Loss %
1.1 27 24.0 81.6 2830 0.0
1.2 110 24.0 73.1 2540 11.6
1.3 90 24.6 82.1 2780 0.7
1.4 130 23.4 55.3 1970 47.5
Figure 3-50 CFRP specimen 2.1, transient test, before and after the test.
Figure 3-51 Secant modulus for specimen 2.1 vs. temperature.
1.65
1.70
1.75
1.80
1.85
0 50 100 150 200
Seca
nt E
last
ic M
odul
us
(GPa
)
Temperature (˚ C)
90
A comparison between strain readings using PIV method and FOS readings are
presented in Figure 3-53 to Figure 3-56. Since the FOS readings were taken only at
constant load levels the strain readings from FOSs are discontinuous. As is evident in
these figures strain readings from FOSs match the PIV results (with a maximum error of
13%) and FOSs could be used as a reliable strain measurement technique at high
temperature testing. Currently, since the FOS is not refined for commercial purposes
strain readings are very labour intensive especially at post processing stage. Having said
that, FOS has advantages over PIV method, where charring happens at the surface of the
specimen (Figure 3-55 ).
02000400060008000
1000012000140001600018000
0 5 10 15 20 25 30
Stra
in
Time (min) strain FOS (με)
strain PIV (με)
91
Figure 3-523 Comparison of strain reading using PIV method (dotted line) and FOS
(solid lines) specimen 1.1 at room temperature.
Figure 3-534 Comparison of strain reading using PIV method (dotted line) and FOS
(solid lines) specimen 1.3 at 90°C.
-5000
0
5000
10000
15000
20000
25000
20 30 40 50 60
Stra
in
Time (min)
strain FOS (με)
strain PIV (με)
92
Figure 3-545 Comparison of strain reading using PIV method (dotted line) and FOS
(solid lines) specimen 1.2 at 110°C.
02000400060008000
1000012000140001600018000
0.0 10.0 20.0 30.0 40.0 50.0 60.0
Stra
in
Time (min) strain FOS (με)
strain PIV (με)
93
Figure 3-556 Comparison of strain reading using PIV method (dotted line) and FOS
(solid lines) specimen 1.4 at 130°C.
0
2000
4000
6000
8000
10000
12000
14000
16000
0 10 20 30 40 50
Stra
in
Time (min) strain FOS (με)
strain PIV (με)
94
95
Chapter 4: Numerical heat transfer simulation
High temperatures cause severe damage to concrete, steel, and FRP. Therefore,
predicting the temperature distribution in a structural member is a crucial step in
understanding the behaviour of the member. A major challenge is the simulation of the
concrete behaviour due to its complicated chemical and structural composition.
Portland cement paste may undergo various changes such as dehydration, porosity
increase, thermal cracking, spalling and many others. Several models have been
proposed for hygrothermo-mechanical simulation of concrete. Some existing models
account for a coupled field heat and mass transfer problem. These models are capable of
predicting temperature and pore pressure during exposure to elevated temperatures
(Gawin, Majorana et al. 1999, Mounajed, Obeid 2004). If only temperatures are required,
several simplifications can be made, which lead to the solution of a de-coupled field
equation. The following assumptions are usually made for decoupling the problem:
- Temperature of the fluid and the solid are the same at each point
- The amount of heat transferred by mass diffusion is negligible
- Evaporation of chemically and physically bound water is negligible (Capua, Mari
2007).
96
Even more simplified methods for predicting temperature distribution in a concrete
section which use a pre-determined temperature variation in the concrete section are
available (Wickstrom 1986, Malhotra 1982). Although these methods provide a
reasonable approximation in some problems, they are not suitable for complex
geometries.
4.1 Finite volume formulation
The model developed here is a finite-volume (FV) code that is capable of predicting
temperature in an insulated concrete section; refer to (Patankar 1980) for further
information on the finite volume method.
The partial differential equation of heat conduction can be expressed as (Arpaci, Arpaci
1966)
𝜌𝑐 𝜕𝑇𝜕𝑡
= ∇. (𝑘∇𝑇) = 𝜕𝜕𝑥�𝑘 𝜕𝑇
𝜕𝑥� + 𝜕
𝜕𝑦�𝑘 𝜕𝑇
𝜕𝑦� (4-1)
where 𝑘 is thermal conductivity, 𝜌 is density, 𝑐 is heat capacity, T is temperature, t is
time, and x and y are spatial coordinates. In general, k and c.ρ are functions of
temperature and spatial variables. Explicit discretization in time domain is
ii
yTk
yxTk
xtTc
∂∂
∂∂
+∂∂
∂∂
=
∂∂ )()(ρ ( 4-2)
[ ]iii
i
yTk
yxTk
xtTTc
∂∂
∂∂
+∂∂
∂∂
=∆−+
)()(1
ρ ( 4-3)
97
Where the spatial discretization and material properties belong to the current time step
i.e. t=ti. In spatial discretization , the integral form of the heat equation is obtained by
using the Gauss theorem:
∫∫ =∇SV
dSdV n.FF. ( 4-4)
dRTkdRtTc
RR∫∫ ∇∇=
∂∂ ).(ρ ( 4-5)
Applying Gauss theorem
∫∫∫∫ ∂∂
=∇=∇=∇∇CCCR
dCnTkdCTkdCTkdRTk )().().().( nn ( 4-6)
∫∫ ∂∂
=∂∂
CR
dCnTkdR
tTc )(ρ (4-7)
Figure 4-1 Spatial discretization.
pl r
d
u
ld rd
rulu
98
For a two-dimensional rectangular grid (Figure 4-1), the discretized field equation is,
∫∫ ∂∂
=∂∂
CR
dCnTkdR
tTc )(ρ ( 4-8)
∫∫∫∫∫−−−− ∂
∂+
∂∂
+∂∂
+∂∂
=∂∂
rulu udurd rluld lrdld dp
dxnTkdx
nTkdx
nTkdx
nTkdxdy
tTcρ ( 4-9)
∫∫∫∫∫−−−− ∂
∂+
∂∂
+∂∂
−∂∂
−=∂∂
rulururdluldrdldp
dxyTkdy
xTkdy
xTkdx
yTkdxdy
tTcρ ( 4-10)
xyTky
xTky
xTkx
yTkyx
tTc
puprplpdp
∆
∂∂
−∆
∂∂
−∆
∂∂
−∆
∂∂
−=∆∆
∂∂ρ ( 4-11)
xyTT
kyxTT
kyxTT
kxyTT
kyxtTc pu
pupr
prlp
pldp
pdp
∆∆
−+∆
∆
−+∆
∆
−−∆
∆
−−=∆∆
∂∂ρ ( 4-12)
+=
dp
dppd kk
kkk
2or
+=
2dp
pd
kkk both for uniform grid (Patankar 1980),
Finally finite volume discretization equations will be
[ ]i
pupu
prpr
plpl
pdpd
ip
ipi
p xyTT
kyxTT
kyxTT
kxyTT
kyxt
TTc
∆
∆
−+∆
∆
−+∆
∆
−+∆
∆
−=∆∆
∆
−+1
ρ (4-13
)
99
Figure 4-2 Descritization and effective length for different finite volumes
Accounting for Convection and Radiation Boundary Conditions explicit discretization
is, Figure 4-2,
[ ]
⋅∆−+∆−+∆∆
−+∆
∆
−
+∆∆
−+∆
∆
−=∆∆
∆
−+
cip
iacr
ip
ifre
ip
iui
pue
ip
iri
pr
e
ip
ili
ple
ip
idi
pdee
ip
ipi
p
LTThLTThxyTT
kyxTT
k
yxTT
kxyTT
kyxt
TTc
)()(
1
ρ ( 4-14)
Where hr and hc are radiation and convection heat transfer coefficients, by
assuming,
−𝑎p0 = [ρc]pi∆xe∆ye∆t
(4-15)
1 2 3
4
100
yx
ka eipdd ∆∆
=0 xy
ka eipll ∆∆
=0 xy
ka eiprr ∆∆
=0 yx
ka eipuu ∆∆
=0 ( 4-16)
We have,
⋅∆−+∆−
+−+−+−+−=−+
cip
ic
icr
ip
if
if
ip
iuu
ip
irr
ip
ill
ip
idd
ip
ipp
LTThLTTh
TTaTTaTTaTTaTTa
)()(
)()()()()( 000010
( 4-17)
assuming
𝑎∗0 = −�−𝑎p0 + 𝑎d0 + 𝑎l0 + 𝑎r0 + 𝑎u0 + ℎfi∆Lr + ℎci ∆Lc� (4-18)
𝑏0 = ℎfi𝑇fi∆Lr + ℎci 𝑇ci∆Lc (4-19)
By rearranging the equation,
⋅+++++=+ 0000000*
10 bTaTaTaTaTaTa iuu
irr
ill
iddp
ipp ( 4-20)
𝑇𝑝𝑖+1 = �𝑎∗0𝑇𝑝𝑖 + 𝑎𝑑0𝑇𝑑𝑖 + 𝑎𝑙0𝑇𝑙𝑖 + 𝑎𝑟0𝑇𝑟𝑖 + 𝑎𝑢0𝑇𝑢𝑖 + 𝑏0� 𝑎𝑝0� ( 4-21)
Where 𝑇𝑝𝑖+1 is the temperature at point p at time step 𝑡 = 𝑡𝑖+1.
4.1.1 Stability criterion
The explicit finite volume method is not unconditionally stable (Patankar 1980); that is, if
the time step is larger than a specific limit then the order of magnitude of errors are
comparable to the magnitude of the variables. Although the method can be
101
mathematically convergent, it presents no physically meaningful results. Therefore, the
largest permissible value of the time step is limited by the stability criteria given by the
equations below. These equations were determined based on the theory described in
(Cengel, Klein et al. 1998) and (Lie 1992). The stability criteria are satisfied if 000* >paa .
The radiation heat flow can be estimated using
)( 44pfcf TTq −= εσε ( 4-22)
where σ is the Stefan-Boltzmann constant, and εf and εc are the emissivities of fire and
concrete respectively, for the ease of iterative programming the following manipulations
could be done.
))()(( 22pfpfpfcf TTTTTTq −++= εσε (4-23)
)( pfr TThq −= (4-24)
))(( 22pfpfcfr TTTTh ++= εσε (4-25)
4.1.2 Free convection
The amount of free convection heat transfer rate from a horizontal plate when the hot
surface is upward is calculated from following equation.
)( pac TThq −= (4-26)
Where the convection heat transfer coefficient is
102
LkNu=hc. (4-27)
𝑁𝑢 = 𝑐(𝐺𝑟.𝑃𝑟)𝑛𝑙 (4-28)
in which Pr is the material property of air. Pr is a temperature dependant property, and
n and c are given in Table 4-1 for laminar and turbulent convection over heated surface.
Gr is readily calculated as
as
ap
+TT)L-Tg(T
Gr=2
3
ν ( 4-29)
in which Ta and Tp are the air and surface temperatures respectively and L is the
representative length of the surface, g is the acceleration of gravity and ν is the dynamic
viscosity of air which is temperature dependent (Bayazıtoğlu, Özışık 1988).
Table 4-1 Coefficients for laminar and turbulent free convection (Bayazıtoğlu, Özışık
1988).
c n laminar 0.54 1/4 Turbulant 0.14 1/3
4.1.3 Moisture effect
This model assumes there is no moisture migration. The effect of moisture in simulation
would be the increase in heat capacity of moist concrete and also the amount of heat
103
absorbed when the temperature reaches the boiling temperature of water. The former
can easily been accounted by changing the heat capacity of moist concrete as follows
( ) ( ) ( )wcmc ccc ρϕρρ += (4-30)
where,
( )mccρ the density and heat capacity of moist concrete
( )ccρ the density and heat capacity of dry concrete
( )wcρ the density and heat capacity of water
𝜑 volume fraction of moisture with respect to concrete
The evaporation of water needs to be treated more carefully, especially because this
approach may be grid/mesh dependent.
Following the notation used before, for a concrete element with the average moisture
content of pϕ the energy balance would be as
[ ]
⋅∆−+∆−+∆∆
−+∆
∆
−
+∆∆
−+∆
∆
−=∆∆
∆
−+
cip
iacr
ip
ifre
ip
iui
pue
ip
iri
pr
e
ip
ili
ple
ip
idi
pdee
ip
ipi
p
LTThLTThxyTT
kyxTT
k
yxTT
kxyTT
kyxt
TTc
)()(
1
ρ (4-31)
In this case [ ]ipcρ is the properties of moist concrete at time t=ti.
The right hand side in above equation is the amount of entering heat/energy rate so
104
⋅∆−+∆−+∆∆
−
+∆∆
−+∆
∆
−+∆
∆
−==
cip
iacr
ip
ifre
ip
iui
pu
e
ip
iri
pre
ip
ili
ple
ip
idi
pdin
LTThLTThxyTT
k
yxTT
kyxTT
kxyTT
kE
)()(
rateenergy Entering
(4-32)
⋅∆−+∆−
+−+−+−+−=
cip
ic
icr
ip
if
if
ip
iuu
ip
irr
ip
ill
ip
iddin
LTThLTTh
TTaTTaTTaTTaE
)()(
)()()()( 0000 ( 4-33)
⋅∆+∆
+∆+∆++++−+++=
ci
cicr
if
if
ipc
icr
ifurld
iuu
irr
ill
iddin
LThLTh
TLhLhaaaaTaTaTaTaE )( 00000000 ( 4-34)
000*
0000 )( bTaaTaTaTaTaE ipp
iuu
irr
ill
iddin ++−+++=
(4-35)
[ ]tyx
ca eeipp ∆
∆∆= ρ0
yx
ka eipdd ∆∆
=0 xy
ka eipll ∆∆
=0 xy
ka eiprr ∆∆
=0 yx
ka eipuu ∆∆
=0 (4-36)
)( 000000* c
icr
ifurldp LhLhaaaaaa ∆+∆++++−= (4-37)
ci
cicr
if
if LThLThb ∆+∆=0 (4-38)
The mass of water in the form of moisture in the element is equal to
)1( ×∆∆== eeipwwww yxVm ϕρρ (4-39)
Introducing Lh latent heat of water vaporization the amount of heat needed to evaporate
all the water will be
105
)1( ×∆∆== eeipwhwhevp yxLmLE ϕρ (4-40)
The amount of the heat needed to increase the element’s temperature to 100° C is
[ ] ( )
><×∆∆−
=CTCTyxTc
E ip
ipee
ip
ip
10001001100
100
ρ. (4-41)
noting that [ ] ipcρ is the property for moist concrete.
If in step i the representative temperature of the element , Tp, 3 is below boiling
temperature of water i.e. 100° C and the amount of entering heat is enough to increase
the elements temperature to 100° C the excess heat will instead cause the moisture to
evaporate and meanwhile this keeps the temperature constant and equal to 100° C.
Based on the preceding scenario one the following cases will happen,
1- 100EtEE inin <∆= ,the element’s temperature is below 100° C and the amount of
entering heat is not enough to increase the temperature to 100° C which is
obviously does not change the previous formulation.
3 This temperature is not necessarily the temperature at point p and it should represent the thermal capacity of the whole element.
106
2- evpin EEEE +<< 100100 , the element’s temperature is below or equal to 100° C and
the amount of entering heat is more than the required energy to increase the
temperature to 100° C. In this case the excess heat will cause the moisture to
evaporate and meanwhile this keeps the temperature constant and equal to
100°C until all the moisture evaporates. The moisture volume fraction at the end
of the current step would be,
ϕϕϕ ∆+=+ i
pip
1 (4-42)
[ ]11
/)(1
/ 100100
×∆∆−∆
−=×∆∆
−−=
×∆∆∆
=∆
=∆eehw
in
ee
whin
ee
ww
e
w
yxLEtE
yxLEE
yxm
VV
ρρρϕ
(4-43)
In a case that the element's temperature is equal to 100° C, 0100 =E and we have,
1×∆∆∆
−=∆eehw
in
yxLtE
ρϕ
. (4-44)
3- evpin EEE +> 100 , the amount of entering heat will evaporate all the moisture, so
01 =+ipϕ , and the temperature will reach a value larger than 100° C.
[ ] evpineei
pi
pip EEEyxTTc −−=×∆∆−+
1001 1)(ρ ( 4-45)
[ ] 11001
×∆∆
−−+=+
eeip
evpinip
ip yxc
EEETT
ρ, (4-46)
107
[ ] 11001
×∆∆
−−∆+=+
eeip
evpinip
ip yxc
EEtETT
ρ
(4-47)
Noting that [ ] ipcρ here is the properties of dry concrete. Similar to case 2 if the
initial temperature is 100°C then
[ ] 11
×∆∆
−∆+=+
eeip
evpinip
ip yxc
EtETT
ρ
(4-48)
4.1.4 Verification
The model developed here is used to simulate a rectangular concrete section similar to
the one tested by (Lie, Woollerton 1988); the column is subjected to the ASTM E119
standard fire from all four sides. The cross-sectional dimensions of the section are 305 by
305 mm. The model prediction is compared with measured temperatures in Figure 4-3.
Three points A, B, and C with concrete covers of 6, 63, and 152 mm, respectively, are
selected for comparison. For point A (near the surface), the model predicts the
experimental results with a maximum deviation of approximately 50 °C up to just over
400 °C. At that point, larger discrepancies are noted, but the predicted temperatures are
higher than those measured in the test. For points B and C, the temperatures are
underestimated at the early stages (below 100 °C) and then slightly overestimated
afterwards. These discrepancies near 100 °C occur because the model does not account
for moisture migration away from the heated surface. Sources of error could be because
108
of concrete spalling, inaccuracy in measuring the thermocouple location, inability to
follow ASTM temperature curve during the test and inaccuracy or incompatibility of the
material models and numerical errors.
Figure 4-3 Predicted and measured temperatures as a function of exposure time for
different depths within the concrete specimen (experimental data obtained from (Lie,
Woollerton 1988).
4.2 Model results for slabs and T-beams
Two different insulation thicknesses were used in slab A and slab B. Figure 4-4
illustrates a comparison between model results and test data. Temperatures from the
unexposed surface and FRP concrete interface are compared. The model predicts the
temperature at the unexposed surface with a maximum discrepancy of 5 °C. For the
temperature at the FRP concrete interface, the model prediction is not quite as close to
109
the measurement. Once again the discrepancy occurs close to 100 °C and is related to the
lack of modelling moisture migration. The maximum deviation between the prediction
and the measured results is approximately 25 °C.
Figure 4-5 shows the temperature calculation from the model compared to temperatures
measured in fire tests for the T-beams. The dotted line is the average of temperatures
obtained from beam-A and beam-B. The model successfully predicts temperatures on
the longitudinal steel and FRP/concrete interface, which are crucial to predicting the
structural behaviour of the strengthened member. The model is conservative in that it
predicts higher temperatures than those measured in the tests. The maximum error in
predicting steel temperature is 13 °C; see Figure 4-6. This error is within the range of
experimental results obtained from 12 thermocouples installed at various locations
along the longitudinal steel. Figure 4-7 compares the model error with standard
deviation of measured data. This figure demonstrates the discrepancy between
modelling and measurement is within the observed experimental error. Thus, the model
is sufficiently accurate.
110
Figure 4-4 Predicted and measured temperatures as a function of exposure time for slabs
at, (a) unexposed surface slab-A (40 mm insulation thickness), (b) FRP-concrete interface
slab-A, (c) unexposed surface slab-B and (d) FRP-concrete interface slab-B.
111
Figure 4-5 Predicted and measured temperatures vs. exposure time for T-beams at (a)
unexposed surface, (b) on the centreline with concrete cover of 155 mm, (c) longitudinal
steel, and (d) FRP-concrete interface.
112
Figure 4-6 Measured steel temperature (mean ±1 standard deviation) compared to
predicted temperature.
Figure 4-7 Steel simulation temperature erorr compared to standard deviation of
measured temperature.
113
4.3 Finite element simulation using ABAQUS
In order to compare finite volume (FV) results with a finite element (FE) simulation, 2D
and 3D models were simulated using the commercially available finite element package
ABAQUS. Experimental data from fire test of a recangular RC column from (Lie,
Woollerton 1988)) is compared against FV and FE simulations in Figure 4-9. Figure 4-8
shows the temperature contour inside the column at t=180 min.
Figure 4-8 Temperature contour from FE simulation at the cross section of the recangular
column after 180 min of standard fire exposure (temperatures in °C ).
114
Figure 4-9 Predicted temperatures for different depths within the concrete specimen
using FV and FE simulations (experimental data obtained from (Lie, Woollerton 1988).
Figure 4-10 compares the 3D FE and 2D FV predictions vs. experimental values for T-
beam-A at bottom steel after 4 hours of standard fire exposure. It is clear that 2D FV
predictions are very close to 3D FE predictions. Figure 4-11 gives the isotherms for T-
Beam-A. Thus, for this problem, 2D simulations appear to be sufficient.
115
Figure 4-10 FE results vs. FV and experimantal results. Temperature is measured at the
bottom longitudinal bar of T-beam A.
0
50
100
150
200
250
0 60 120 180 240
Tem
pera
ture
(˚C
)
Time (min)
FE Abaqus
FV Model
Test Data
116
Figure 4-11 3D temperature isotherm surfaces from FE simulation at the cross section of
T-Beam-A after 240 min of standard fire exposure (temperatures in °C ).
4.4 Different fire scenarios
Although standard fire curves are widely used for determining the fire resistance of
structural members, the intensity and duration of building fires may vary widely.
Several parameters such as amount of combustible material and ventilation affect the
severity and duration of compartment fires. In some cases, standard fire curves have
serious deficiencies in presenting realistic fire situations (Stratford, Gillie et al. 2009,
117
Leone, Matthys et al. 2009). To investigate the effects of different time temperature
curves on the response of T-beams, four different fire scenarios were selected. Fire time
temperature curves were calculated using the following equation, proposed by (Lie
1992).
𝑇𝑓 = 250(10𝐹)0.1
𝐹0.3� 𝑒−𝐹2𝑡[3(1− 𝑒−0.6𝑡)− (1 − 𝑒−3𝑡) + 4(1 − 𝑒−12𝑡)] + C �600𝐹�0.5
(4-49)
where 𝑇𝑓 is fire temperature, t is time in hours and C is a constant related to the
boundary materials. Different fire loads (Q) and opening factors (F) for different fires
scenarios are given in Table 4-2. Figure 4-12 shows the time temperature curves for Fires
I to IV. Figure 4-13 gives a comparison between actual temperature variation captured in
Dalmarnock fire tests and temperature curves used here. The temperature increase
during the flash-over period is sharper than both ASTM and “FIRE IV” curves, but
temperatures remain below both curves.
Table 4-2 Parameters used to produce fire curves.
𝑭 (√𝒎) 𝑸 (𝒌𝒈/𝒎𝟐) 𝑪 Fire I 0.01 30 0.0 Fire II 0.05 30 0.0 Fire III 0.10 30 0.0 Fire IV 0.10 100 1.0
118
Figure 4-12 Time temperature curves for four different fire scenarios.
Figure 4-13 Time-Temperature curve in Dalmarnock real compartment fire (mean ± 1
standard deviation) in comparison with ASTM standard fire curve and “fireIV” curve
used here(Stratford, Gillie et al. 2009).
119
Figure 4-14 Longitudinal steel temperature in beams subjected to Fires I to IV.
Figure 4-15 FRP-concrete interface temperature in beams subjected to Fires I to IV.
120
According to Figure 4-14, after four hours of exposure to fires I to IV, the longitudinal
steel temperature in all scenarios remains below 250 °C. Under these scenarios, the steel
retains most of its tensile strength after fire exposure (approximately 90 percent). Given
the fact that the temperature of the compression concrete (close to unexposed surface) is
lower than the steel temperature, concrete will suffer negligible losses in strength. As a
result, the reduction in the moment capacity of the un-strengthened section will be
minimal. The predicted strength of T-beams exposed to standard fire is given in
Figure 4-16. These calculations are based on based on CSA A23.3-04 and ACI 318/318R-
08 for reinforced concrete section and CSA S806-02 and ACI 440.2R-08 for FRP
strengthened sections. In the calculation of strength, it is assumed that FRP does not
contribute to moment capacity of the section once FRP-concrete temperature reaches Tg.
The predicted capacity of the section even after 4 h is still larger than the applied service
load. While insulation provides limited protection for FRP in fire situations (less than 30
minutes, Figure 4-15), it plays a major role in protecting the reinforcing steel and
concrete.
121
Figure 4-16 Predicted moment capacity of T-beams exposed to different fire curves and
applied maximum moment during the fire test.
122
4.5 Sample design charts
This section presents temperature predictions based on the numerical model developed
to simulate temperature distribution in a composite concrete-insulation system. A slab
with 150 mm thickness is chosen and temperature-time curves at various locations are
given. The slab is made of normal density concrete and it is exposed to ASTM or ULC
standard fire. The insulation material is SikaCrete-213F. Insulation thicknesses of 20, 30,
40 and 60 mm are chosen for simulation. Temperature curves are given below. These
curves could be used as an estimate to predict the steel temperature inside the slab with
equivalent cover. For example if steel cover (from centre of the bar to fire exposed
surface) is 40 mm and insulation thickness is 30 mm, Figure 4-20 should be used. This
temperature can be used to estimate the residual strength of the reinforcing steel.
Figure 4-24 gives the unexposed surface temperatures for various insulation thicknesses.
This value should be compared with requirements of the fire code. Since the unexposed
surface temperature represents the compression concrete temperature, the reduction in
concrete strength could also be estimated.
123
Figure 4-17: Temperature vs. exposure time at FRP-concrete interface for different
insulation thicknesses (Depth is insulation thickness in mm).
20
60
100
140
180
220
260
300
340
380
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
FRP- Con Ins. Depth 60,
FRP- Con Ins. Depth 40,
FRP- Con Ins. Depth 30,
FRP- Con Ins. Depth 20,
124
Figure 4-18: Temperature vs. exposure time with 20 mm concrete cover for different
insulation thicknesses.
20
40
60
80
100
120
140
160
180
200
220
240
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
cover 20, Ins. Depth 60,
cover 20, Ins. Depth 40,
cover 20, Ins. Depth 30,
cover 20, Ins. Depth 20,
125
Figure 4-19: Temperature vs. exposure time with 30 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm).
20
40
60
80
100
120
140
160
180
200
220
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
cover 30, Ins. Depth 60,
cover 30, Ins. Depth 40,
cover 30, Ins. Depth 30,
cover 30, Ins. Depth 20,
126
Figure 4-20: Temperature vs. exposure time with 40 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm).
20
40
60
80
100
120
140
160
180
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
cover 40, Ins. Depth 60,
cover 40, Ins. Depth 40,
cover 40, Ins. Depth 30,
cover 40, Ins. Depth 20,
127
Figure 4-21: Temperature vs. exposure time with 50 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm).
20
40
60
80
100
120
140
160
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
cover 50, Ins. Depth 60,
cover 50, Ins. Depth 40,
cover 50, Ins. Depth 30,
cover 50, Ins. Depth 20,
128
Figure 4-22: Temperature vs. exposure time with 60 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm).
20
40
60
80
100
120
140
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
cover 60, Ins. Depth 60,
cover 60, Ins. Depth 40,
cover 60, Ins. Depth 30,
cover 60, Ins. Depth 20,
129
Figure 4-23: Temperature vs. exposure time with 70 mm concrete cover for different
insulation thicknesses (Depth is insulation thickness in mm).
20
40
60
80
100
120
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
cover 70, Ins. Depth 60,
cover 70, Ins. Depth 40,
cover 70, Ins. Depth 30,
cover 70, Ins. Depth 20,
130
Figure 4-24: Temperature vs. exposure at unexposed surface of concrete slab (thickness
150 mm) for different insulation thicknesses (Depth is insulation thickness in mm).
20
25
30
35
40
45
50
55
60
0.0 30.0 60.0 90.0 120.0
Tem
pera
ture
(˚C
)
Time (min)
Unexposed surface Ins. Depth 60,
Unexposed surface Ins. Depth 40,
Unexposed surface Ins. Depth 30,
Unexposed surface Ins. Depth 20,
131
4.6 Summary
The preceding chapter presented procedures and results of the model developed to
simulate the thermal behaviour of FRP-strengthened concrete beams and slabs exposed
to fire. The heat transfer model was verified against the results of fire endurance tests on
concrete columns and beams available in literature and the results of the fire tests
presented in this thesis. Furthermore the results of the FV model developed here were
compared with the predictions of finite element method. Also the 2D and 3D finite
element simulations were performed using the commercially available FEA package
ABAQUS. The comparison of 2D and 3D simulations proved that 2D models adequately
simulate the thermal behaviour of flexural members. Parametric analyses were
performed using the FV model to understand the behaviour of the insulated beam under
different fire scenarios. These simulations showed the level of effectiveness and
reliability of the insulation system. Structural failure of the beam was investigated using
the temperature predictions of the thermal model to showcase the capability of the
model. And finally sample design charts were developed to be used for the design of
concrete slabs with varying insulation thicknesses.
132
133
Chapter 5: Structural modelling
5.1 General
The object of the mechanical model is to determine the strain and stress distribution at
all the points inside the specimen and to also calculate the deformations under load. In
an uncoupled field problem, the mechanical behaviour of the materials can be
determined using the temperature history at different points of the member. Material
properties parameters at high temperature for concrete, steel and FRP are discussed in
Chapter 2 and Appendix C.
Previously, Bernoulli’s hypothesis has been used in a simplified model for
determination of mechanical behaviour ((Blontrock, Taerwe et al. 2000, Kodur, Dwaikat
2007, Williams 2004, Capua, Mari 2007, Ahmed, Kodur 2011), which satisfactorily
predicts member behaviour. Cai, Burgess et al. (2003) developed a generalized steel/RC
beam column element model for fire conditions, which accounts for large deformation
which produces a better prediction; see also (Bratina, Čas et al. 2005). Pearce, Nielsen et
al. (2004) used a damage model to model thermal and mechanical damage of the
concrete in fire.
Since the final deformations of the beam are small compared to the size of the structure,
using the simplified Euler-Bernoulli beam seems reasonable for the structural
134
simulation. The main assumptions required for defining the relation between forces and
strains in a section are the following:
1. The Bernoulli hypothesis applies (plane sections remain plane during
deformation)
2. The elements have a uniaxial state of stress.
Using these assumptions the ultimate strain at each point inside concrete and steel
element can be determined considering equilibrium of internal and external forces. This
total strain εt can be divided into four components, εσ stress related strain, εthermal
unconstrained thermal strain, εtransient the transient creep strain or load induced thermal
strain and εcreep time dependant creep strain.
εt = εσ +εthermal +εtransient +εcreep (5-1)
Thermal strain can be simulated as, [ ]θε mthermal = , where [ ] ( )Tm 000111α= ,
following Voigt notation. α is the thermal expansion coefficient of concrete; see
Figure 5-1.
135
Figure 5-1 Free thermal strain vs temperature for various concretes from EuroCode 2.
In an unloaded transient test the concrete specimen will expand by increase in
temperature (εthermal). The strain in a loaded case is significantly different (excluding the
elastic deformation). This difference is called “transient creep” or “load induced thermal
strain” and only happens during the first heating of concrete;(Schneider 1988, Khoury,
Grainger et al. 1985, Thelandersson 1987). This irrecoverable strain has a critical effect in
the response of heated member because it may result is severe tensile forces in the
member. The model used by Williams (2004) did not address transient strain in the
structural model. While there are different models proposed to simulate this transient
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
0 200 400 600 800 1000 1200 1400
Free
ther
mal
stra
in
Temperature (°C)
Siliceous
Calcareous
136
effect, Pearce, Nielsen et al. (2004) gives a three dimensional formulation that can be
implemented in finite element simulations.
A similar formulation is used for steel elements except for the fact that there is no
transient creep strain in steel so the stress component for steel would be
εt = εσ +εthermal +εcreep (5-2)
Likewise for FRP elements, the total strain is discretized as thermal mechanical and
creep although the important factor in simulation of a strengthened beam is the
behaviour of bond between FRP and concrete. In the current model experimental results
from bond test performed as a part of this research has been implemented in the model
to account for the behaviour of the FRP- concrete bond.
5.2 Generating moment-curvature curves
Knowing the temperature and external loading on the beam i.e. axial forces and loading
history at any section (residual transient strain components), moment curvature M-κ
diagrams are created at each time step anywhere in the beam as demonstrated in Figure
5-2.
137
Figure 5-2 Strain compatibility and load equilibrium at a typical section of the T-beam.
In order to calculate a point in the M-κ curve, a value for curvature is selected, and an
initial guess for the strain at top fibre of the concrete is chosen. At this point knowing the
curvature and the strain at top concrete fibre, total strain everywhere in the section can
be calculated assuming plain sections remain plain. Once the total strain is found, forces
can be calculated for every element of concrete steel and FRP as discussed previously.
Once the stresses are calculated, forces are summed up in the section. If the equilibrium
criterion is satisfied (i.e., F_ext=Cc+Cs+Ts+Tfrp see Figure 5-2 above), then the assumed
strain at the top fibre is correct. If equilibrium is not satisfied, then an iterative
procedure is employed until convergences is obtained. The resisting moment is then
derived from the forces and stress in the section to determine a point in the M-κ curve.
Similarly, coordinates of different points are calculated using different curvature values.
5.3 Beam analysis
In order to determine the deflection of the beam and stresses during fire exposure, the
beam is discretized into segments longitudinally. After mesh sensitivity analysis number
138
of longitudinal segments were chosen to be 21. For each segment at each time step, the
temperature field is first determined. Using the results of thermal analysis, M-κ curves
are calculated for each segment of the beam at every time step. Knowing the external
load distribution, M-κ curves at each time step are used to calculate the deflection of the
beam.
5.4 Verification
In order to verify the strength model, four different fire exposed beams were chosen.
Two of them were RC beams reinforced with steel bars and the other two were RC
beams strengthened with steel reinforcing bars inside and externally reinforced by FRP.
Subsequently the model results are compared with the experimental results of T-beams
exposed to fire conducted in this study.
5.4.1 RC Beam 1 (typical RC beam)
In this section results from thermal and strength model is compared to the results of
Dwaikat and Kodur’s Model (Dwaikat, Kodur 2008). Material properties and
dimensions of the beam are tabulated in Table 5-1 below. Beam is subjected to ASTM
E119 Standard fire.
139
Table 5-1: Properties of the typical RC beam used in the verfication (RC Beam1).
Description Dwaikat et. al.( 2008) Cross section Dimensions 300mm x 500mm Length (m) 6 Top reinforcements 2ɸ14 mm Bottom reinforcement 3ɸ20 mm f'c (MPa) 30 fy (MPa) 400 Applied total load (kN) 120 Concrete cover thickness (mm) 40 Aggregate type Carbonate
To compare the thermal predictions from the current model to Dwaikat et.al. model,
the temperature variation is plotted as a function of fire exposure time at various
locations of the beam cross section in Figure 5-3 below. Solid lines are the predictions of
Dwaikat and the dots are temperature predictions of the current model. The
temperature results match closely with results from (Dwaikat, Kodur 2008). After
temperature comparison the mid-span deflection is compared in both models in
Figure 5-4. Deflection predictions from the two models match closely. Dwaikat et.al.
model predicts slightly higher deflection than the current model after 150 min fire
exposure, while the deflections are lower before 150 min mark. Overall behaviour of the
beam predicted by both models is very similar. The difference between the deflection
predictions of the models vary from 25% where t<120min to less than 10% for t>120 min.
140
Figure 5-3 Time temperature curves data points are from Dwaikat and Kodur 2008 and
lines are results of the current model.
Figure 5-4 Mid-span deflection vs. time, dotted line is from Dwaikat and Kodur 2008
and the solid line is current model.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(°C)
Time (min)
Corner barMid depth (center)125 mm from bottomCentrl Rebar375 mm from bottom
0100200300400500600700800900
1000
0 60 120 180 240 300
Defle
ctio
n (m
m)
Time (min)
ModelKodur 2008Dwaikat and Kodur (2008)
141
5.4.2 RC Beam 2
For further verification of the model the temperature and deflection prediction of the
model is compared with experimental results of a RC beam tested by(Dotreppe,
Franssen 1985). The dimensions and material properties of the beam are reported in
Figure 5-5 and Table 5-2. The beam is exposed to the ISO 834 fire that is very similar to
the ASTM E119 fire.
Figure 5-5 Details of the cross section and loading for RC Beam 2, Dotreppe (1985).
6500
1625 3250 1625
600
P P
3 12mm
2 12mm
200
600
40
40
27
142
Table 5-2: Description of the typical RC beam used in the verification (RC Beam2).
Description Dotreppe JC, Franssen JM. 1985 Cross section Dimensions 200mm x 600mm Length (m) 6.5 Reinforcements top 2ɸ12 mm Reinforcements bottom 3ɸ22 mm f'c (MPa) 15 fy (MPa) 300 Applied total load (kN) 65 Concrete cover thickness (mm)
40
Aggregate type Siliceous
Temperature prediction of the computer model for the steel rebar located at the bottom
of the beam is compared with the reported temperatures obtained in the experiment
Figure 5-6. The temperature predictions are in good agreement with the test
measurements. The difference in the beginning of the test between predicted and
experimental results are most likely because of moisture migration effect which is not
included in the thermal model. In this section t<40min maximum error is less than 50°C
and for t>40 maximum discrepancy is less than 20°C.
143
Figure 5-6: Tension steel temperature vs. time, dotted line is model prediction and solid
line is the test result.
The predicted and measured mid-span deflections for RC Beam2 are compared in
Figure 5-7. The predicted results are in good agreement with the experimental
measurements (maximum 10 mm deviation).
0
100
200
300
400
500
600
0 20 40 60 80 100 120
Tem
pera
ture
(°C)
Time (min)
Steel temp. Model
Steel temp. test
144
Figure 5-7 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result.
Results of comparison of the model with other model and experimental results at this
stage indicate that the current model is capable of prediction the thermal and
mechanical behaviour of RC concrete beams exposed to fire. This means the material
models used for simulation of steel and concrete are appropriate and the numerical and
simulation techniques properly capture the physics of the problem.
5.4.3 FRP-RC Beam 1
In previous verification cases the model was used to simulate the behaviour of steel
reinforced RC beams. In order to verify the results of the model for an FRP strengthened
0
50
100
150
200
0 50 100 150
Defle
ctio
n (m
m)
Time(min)
Deflection Test
Deflection Model
145
beam, the results of the computer model is compared with the test results for two FRP
strengthened beam tested by (Blontrock, Taerwe et al. 2000). These tests were performed
at the University of Ghent.
The cross-sectional dimensions of the beam were 200 mm by 300 mm and the length was
approximately 3 m. Steel reinforcements were two ɸ10 mm steel bars at top and two ɸ16
mm bars at the bottom. Concrete clear cover of the steel bars was 25mm. There was a
layer of Promat-H insulation over the FRP laminate at the bottom to protect the FRP
from fire. The thickness of the insulation layer was 25mm and it was mechanically
fastened to the beam. One layer of SIKA Carbodur S1012 CFRP plate was attached to the
soffit of the beam for strengthening purpose. The beam was subjected to four-point
bending of 2x38.6kN loads at 1/3 and 2/3 of its span. Aggregate type of the concrete was
siliceous and the 28-day strength was 15MPa. Yield strength of the steel bars was
300MPa. Figure 5-8 and Table 5-3 give an overall description of the dimensions,
reinforcement details, and the loading condition of the beam.
146
Figure 5-8 Details of the cross section and loading for FRP-RC Beam 1, Blontrock (2003).
2850
950 950 950
P P
3150
300
2 10mm
2 16mm
Insulation
200
300
25
30
30
147
Table 5-3. Summary of Properties for FRP-RC Beam1
Description Blontrock 2003 (BV-B-5)
Cross section Dimensions 200mm x 300mm
Length (m) 3150 mm
Reinforcements top 2ɸ10 mm
Reinforcements bottom 2ɸ16 mm
f'c (MPa) 15
FRP SIKA Carbodur S1012
Insulation Promat-H 25mm mechanically attached
fy (MPa) 300
Applied total load (kN) 2x38.6kN at 1/3 and 2/3 of the beam span
Concrete cover thickness
(mm) 25
Aggregate type Siliceous
148
Figure 5-9 Tension steel temperature vs. time, dotted line is model prediction and solid
line is the test result.
During the test of this beam, debonding of the fibre composite laminate happened very
soon after the start of the fire test, as a result of the premature debonding of glued
protection. A sharp increase in deflection can be observed at 7 minutes after fire starts.
After this point, the beam is unprotected against fire. The test is stopped at 76 minutes
due to excessive deformation of 58 mm in the mid-span. Figure 5-10 shows the model
prediction of the mid span deflection against the experimental measurements.
Maximum discrepancy in the deflection is less than 10% except for first 10 minutes.
0
200
400
600
0 20 40 60 80 100
Tem
pera
ture
(°C)
Time (min)
Steel Temp.Test BV-B-5
Model
149
Figure 5-10 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result.
5.4.4 FRP-RC Beam 2
Similar to FRP_RC Beam1 cross section dimensions were 200 mm by 300 mm and the
length of the beam was approximately 3 m. Steel reinforcements were two ɸ10 mm steel
bars at top and two ɸ16 mm bars at the bottom. Concrete clear cover was 25mm. There
was a 25 mm thick glued layer of Promatect-100 insulation over a SIKA Carbodur S1012
CFRP laminate. Beam was subjected to four points bending of 2x38.6kN loads at 1/3 and
2/3 of the beam span. Aggregate type of the concrete was siliceous and the 28-day
strength was 15 MPa. Yield strength of the steel bars was 300 MPa. Figure 5-11 and
Table 5-4 give an overall description of the dimensions, reinforcement details, and the
loading condition of the beam.
0
20
40
60
80
100
0 20 40 60 80 100
Defle
ctio
n (m
m)
Time (min)
Test BV-B-5
Model
150
Figure 5-11 details of the cross section and loading for FRP-RC Beam 2, Blontrock (2003).
3000
925 1000 925
P P
3150
300
2 10mm
2 16mm
Insulation
200
300
25
30
30
151
Table 5-4: Summary of Properties for FRP-RC Beam 2.
Description Blontrock 2003 (BV-B-4) Cross section Dimensions 200mm x 300mm Length (m) 3 Reinforcements top 2ɸ10 mm Reinforcements bottom 2ɸ16 mm f'c (MPa) 15 FRP SIKA Carbodur S1012 Insulation Promatect-100 25mm glued fy (MPa) 300 Applied total load (kN) 2x38.6kN at 1/3 and 2/3 of the beam span Concrete cover thickness (mm)
25
Aggregate type Siliceous
Figure 5-12 Tension steel temperature vs. time, dotted line is model prediction and solid
line is the test result.
0
100
200
300
400
500
0 20 40 60 80 100
Tem
pera
ture
(°C)
Time (min)
Steel temp. testBV-B-4Model
152
Debonding of the insulation happens 19 min after heating starts. The loss of insulation
layer protecting FRP caused subsequent debonding of the FRP laminate and a sharp
increase in the deflection. Figure 5-13 shows the model prediction of the mid span
deflection against the experimental measurements.
Figure 5-13 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result.
Results of temperature and deflection predictions of the model match closely with
experimental results from the literature, which proves the accuracy and validity of the
numerical model developed here. Deflections are predicted within 5 mm of the
experimental results.
0
10
20
30
40
50
0 30 60 90 120
Defle
ctio
n (m
m)
Time (min)
Test BV-B-4
Model
153
5.5 Deflections simulation in fire exposed T-beams
Results of thermal modelling for the T-beam have been presented Chapter 4. The goal in
this section is to simulate the mechanical behaviour of the tested T-beams. Using the
temperature results of the heat transfer model as input for the mechanical model and the
boundary conditions of the T-beam, the model can predict stresses, strains and the
deflection of the beam at any point during fire exposure. Having verified the mechanical
model for various RC and FRP strengthened RC beams this could be easily done by
feeding the material properties and the dimensions of the T-beam to the thermal and
mechanical model. Defining the proper boundary conditions is of critical importance
since the existence of the axial restraints during fire could influence the mechanical
behaviour of the test beams. For a simply supported beam with no axial restraint, the
boundary conditions are very easy to define as will be demonstrated in the case of
Beam-C in the following section. However for beams with partial axial restraint, the
implementation of the end conditions is more complicated.
5.5.1 T-Beam C
To simulate the mechanical behaviour of a T-beam with no axial constraint, results from
a fire test for Beam-C reported by Hollingshead (2012) is used. T-beam dimensions and
steel reinforcement details are the same as the T-beams A and B. Beam-C was chosen to
be 400 mm deep, with flange being 1220 mm wide by 150 mm deep. 6-10M bars were
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placed in the flange and 2-15M bars in the web as tensile reinforcement. A single layer of
(Tyfo SCH-41) CFRP was attached to the soffit of T-beam, the width of the CFRP wrap
was to 100 mm (4”). Both ends of the beam were wrapped with 600 mm (24”) wide
GFRP (Tyfo SEH-51A) U-wraps. The concrete had an average compressive strength of
35.7 MPa measured before the test. WR-AFP insulation (Tyfo-VG) was specified to be
applied over the FRP to a thickness of 13 mm. The insulation covered the entire web and
100 mm (4”) along the bottom of the flange on either side of the web. Limestone course
aggregate with a maximum size of 14 mm and Type I Portland cement were used in the
concrete mix. All 10M bars had yield strength of 460MPa, while the 15M bars had a yield
strength of 406MPa.
During fire test, Beam C suffered only minor insulation loss, occurring after 214 minutes
along the bottom of the web. The beams were subjected to a uniformly distributed
service load of 24.1 kN/m as per CAN/ULC S101-07, which translated into an applied
bending moment of 43.6 kN.m.
Figure 5-14 shows the measured and predicted midspan deflection of Beam-C. The
model results are in good agreement with the experimental results with a maximum
discrepancy of 10 mm. Deformation before t=0 is preheating deflection of the beam due
to applied uniformly distributed load. Heating starts at t=0. The initial sharp increase in
deflection is due to thermal expansion of the heated area of the beam. The discrepancy
between model prediction and the test results at this section (0<t<90min) mostly relates
155
to the unconstrained thermal expansion model used for concrete. The sharp increase in
deflection in the first 30 to 60min slows down once the rate of temperature gradient
increase slows down. The subsequent increase in deflection is mainly due to loss of
strength and decrease in modulus of steel. In less than 60 min FRP-concrete bond
temperature moves far beyond Tg or Tc (refer to section 3.4.2) of the adhesive (epoxy)
and as a result FRP is not carrying any load at this point. This loss in itself translates into
increased deflection of the beam in the first hour of the fire exposure. Of course the
source of this deflection is the differential thermal expansion of the beam, but loss of
FRP-concrete bond allows for this internal force to translate into deflection. In other
word FRP is no longer resisting the thermal expansion. After the first hour, difference
between an FRP strengthened and un-strengthened beam response in terms of
deflections and stresses would be insignificant (provided that they both have the same
insulation layer which is unlikely).
156
Figure 5-14 Mid-span deflection vs. time, dotted line is model prediction and solid line is
the test result.
5.5.2 T-Beam A and B
The exact end forces of the T-beams A and B are not known in terms of the axial
restraint. Also there was no measurement of the axial load during the test due to space
and test apparatus limitations. To simulate these partially restrained T-beams, ,
assumptions must be made for the axial restraining force. To do this, a load-time curve is
determined by trial and error. Figure 5-15 shows the shape of these load-time curves.
Axial load before fire exposure increases from linearly to a value of 100kN as the
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
-90 -60 -30 0 30 60 90 120 150 180 210 240 270
Defle
ctio
n (m
m)
Time(min)
Beam_C_test
Beam_C_Model
157
distributed load increases on the beam. Since the web of the T-beam was restrained in
the test, rotation of the end of the beam under load was prevented and thus an axial load
would be induced. For the next phase (i.e. fire exposure phase), the axial load increase is
set to increase from 0 to 300 kN for different curves. This makes the final axial load 100,
200, 300 and 400 kN for different curves. For simplicity these curves are name using two
numbers for example in “axial-100-200” curve, axial load increases linearly to 100 kN
before fire and the increase after fire is 200 kN which makes the final axial load the sum
of the two numbers i.e. 300 kN. The increases in axial load during the fire are caused by
the restraint of axial expansion due to thermal effects during the fire.
Figure 5-15 Assumed axial load time curves for the T-beams used in the simulation.
0
100
200
300
400
-60 0 60 120 180 240 300
Axia
l Loa
d (k
N)
Time(min)
Axial-100-0
Axial-100-100
Axial-100-200
Axial-100-300
158
Simulation has been performed using the axial load curves shown above. Deflection
results for Beam A and Beam B are shown in Figure 5-16 and Figure 5-17. There are three
phases in this curve. The preloading phase happens at t<0min where there is no thermal
loading and the mechanical load increases from zero to the service load level (super
imposed load). The second phase is the fire exposure phase where the distributed load
on the beam is constant but the beam is subjected to ASTM E119 thermal loading.
Finally, since the beam did not fail under fire loading the service load was increased to
the maximum capacity of the hydraulic jacks to attempt to reach failure during which
ASTM E119 curve was followed for furnace temperature.
Figure 5-16 Mid-span deflection vs. time for T-beam A, dotted lines are model
predictions for deflection assuming different axial loads, solid line is the test result.
0
5
10
15
20
25
30
-60 0 60 120 180 240 300
Defle
ctio
n (m
m)
Time(min)
Model Axial=100-0Model Axial=100-100Model Axial=100-200Model Axial=100-300Beam_A_Test
159
As can be observed in Figure 5-16, the measured deflection for Beam-A from the
experiment (solid line) falls between the “axial-100-100” and “axial-100-200” curves.
Thus, the axial load should follow a curve between “axial-100-100” and “axial-100-200”
curves. In the first phase, there is an increase in deflection due to quasi-static load
increase on the beam. Model predictions match very well with experimental results in
this phase with maximum discrepancies of 2 mm. During the second phase (i.e. fire
exposure) there is a sharp increase in the deflection due to differential thermal
expansion. Both the axial load and unconstrained thermal expansion models used for
concrete have important effects for estimating deflection of the beam in this phase, but
as discussed for Beam C, the effect of the thermal expansion model is likely more
important. In this portion (0<t<60min), the models underestimate deflections by
approximately 2 to 5 mm. As discussed earlier and based on experimental bond test
results presented in Chapter 3 the FRP-concrete bond is completely deteriorated within
the first hour of fire exposure. As could be seen the deflection curve reaches a plateau
after the first hour due to existence of axial load. Similar results could be seen in
Figure 5-17 for T-beam B. In this case choosing “Axial-100-200” for axial load seems
reasonable. As discussed before in Chapter 3 the discrepancy between the displacement
readings for Beam-A and Beam-B is most likely due to measurement errors, otherwise
axial loads for beams A and B should be similar since they have the same dimensions
160
and the materials in both beams are comparable. Again similar to T-beam A, there is a
sharp increase in deflection in the first hour of fire exposure followed by a plateau.
Figure 5-17 Mid-span deflection vs. time for T-beam B, dotted lines are model
predictions for deflection assuming different axial loads, solid line is the test result.
5.6 Different fire scenarios
In order to simulate the behaviour of an insulated T-beam under various fire scenarios,
simulations have been done using different time temperature curves introduced
previously in Chapter 3 i.e. Fire-I to Fire- IV. As a reminder this beam has a layer of WR-
AFP insulation and the thickness of this layer is 13 mm. Temperature predictions for
longitudinal steel are presented in Figure 5-18. In all fire scenarios except for Fire-IV, the
0
5
10
15
20
25
30
-60 0 60 120 180 240 300
Defle
ctio
n (m
m)
Time(min)
Model Axial=100-0Model Axial=100-100Model Axial=100-200Model Axial=100-300Beam_B_Test
161
steel temperature remains below 593°C even after 5 hours of fire exposure. However, the
steel temperature reaches the limiting failure temperature of 593°C in 222 min when the
beam is subjected to Fire-IV. This failure is also evident in Figure 5-19 where the slope of
mid-span deflection becomes very sharp as it approaches t=222 min where the beam
fails. These results suggest that the model could successfully simulate a realistic fire
scenario. Also, the performance of the FRP strengthened concrete beams is adequate for
most fire situations under a range of fire scenarios. Fire IV is very severe and represents
conditions similar to that of a hydrocarbon fire. Even in this severe scenario, the FRP
strengthened beam has a fire endurance of over 3 hours.
Figure 5-18 Longitudinal steel temperatures for Beam-C under different fires.
0
200
400
600
800
0 60 120 180 240 300
Tem
pera
ture
(°C)
Time(min)
Steel Temp. Fire I
Steel Temp. Fire II
Steel Temp. Fire III
Steel Temp. Fire IV
Steel Temp. E119
162
Figure 5-19 Mid-span deflections for Beam-C exposed to different fires, beam fails under
Fire-IV in less than four hours.
5.7 Summary
The preceding chapter presented procedures and results of the model developed to
simulate the structural behaviour of FRP-strengthened concrete beams exposed to fire.
The model is capable of predicting stresses and deflections. The model was verified
against the results of various fire endurance tests from literature. After verifying the
model it was successfully used to simulate the deflections of a simply supported T-
beam. The model then was used to simulate the deflections of the partially restrained T-
beams in fire where the effect of axial restraint was taken into consideration. And finally
parametric analyses were performed using the strength model to understand the
0
50
100
150
200
0 60 120 180 240 300
Defle
ctio
n (m
m)
Time(min)
Deflection Fire I
Deflection Fire II
Deflection Fire III
Deflection Fire IV
Deflection E119
163
behaviour of the insulated beam under different fire scenarios by predicting their
deflections.
164
165
Chapter 6: Conclusions and Future Research
6.1 General
The main objective of this thesis was to investigate the fire performance of FRP
strengthened RC flexural members through experimental and numerical methods. In an
experimental study, intermediate scale slabs were tested to evaluate the thermal
behaviour of the insulation system. Full scale fire tests were later performed on T-beams
under sustained load in order to realistically simulate the T-beams at fire. This thesis has
also helped obtain a better insight in the bond behaviour of externally bonded FRP
strengthening systems at elevated temperatures. A simplified model was proposed for
FRP-concrete bond strength at high temperature. The model determines the bond
strength degradation at high temperatures. Several innovative techniques such as FOS
and PIV methods were used to measure strain and temperature during the experimental
program. Fibre optic sensors were used in full scale and material tests, and their
accuracy and effectiveness were investigated and compared with other methods. FOS
application in material testing successfully predicted strain at high temperature. A
numerical model was developed in order to trace the thermal and mechanical response
of FRP-strengthened RC beams which takes into account fire, loading and axial restraint
conditions. The model consists of two separate modules: a thermal simulation module
and a structural modelling module. The thermal simulation takes into account radiation
166
conduction and convective heat transfer mechanisms. The underlying numerical
approach for the model is the finite volume method. The mechanical model uses time-
dependent moment-curvature relationships to trace the response of the beam under fire
conditions. The model effectively incorporates several factors such as high temperature
material models, different strain components, FRP concrete bond degradation, and axial
restraint forces.
6.2 Key findings
The main conclusions are:
• With sufficient insulation, FRP strengthened beams and slabs can be safely used
in buildings and structures where fire exposure is a concern, and can achieve fire
resistances of up to 4 hours under exposure to a range of practical fire scenarios.
• Both FOS and PIV sensing systems can be applied for measuring strains at
elevated temperatures.
• FRP to concrete bonds are sensitive to elevated temperatures. There has been a
50% loss of strength at temperature 40 °C above glass transition temperature of
the adhesive.
• New numerical models have been developed that incorporate transient creep
and axial thrust, and have been validated against experimental results.
167
6.3 Detailed conclusions
6.3.1 Fire tests
• Based on the experimental results, none of the slabs or beams failed during the
fire tests, which suggests that with sufficient insulation, FRP strengthened beams
and slabs could be safely used in buildings and structures where fire exposure is
a concern.
• All specimens achieved 4-hour fire endurance according to ASTM E119
specifications.
• The results confirm the vulnerability of the FRP/Concrete bond during a fire.
Results confirm that FRP reached its glass transition temperature in all
specimens in less than 30 min., which means FRP does not contribute to the load
carrying capacity of the beam beyond this point.
• Despite the fact that FRP-concrete bond degrades rapidly even in an insulated
beam, the insulation system used in all cases effectively protected T-beams and
slabs mainly by keeping internal steel temperatures below 250 ˚C.
• Despite initial shrinkage cracks in the insulation, there was no spalling or
debonding of the insulation material in the fire tests. Localized cracking was
observed during the fire tests, which likely caused localized areas to be
susceptible to rapid heat ingress.
168
6.3.2 Bond tests
Based on FRP-concrete bond test results at elevated temperature, the following
conclusions can be drawn.
• FRP to concrete bonds are sensitive to elevated temperatures and there has been
a 50% loss of strength at temperature 40 °C above glass transition temperature of
the adhesive.
• The widely accepted rule of ignoring the FRP contribution to load carrying
capacity once it reaches Tg is safe, and conservatively accounts for the bond
behaviour.
• In transient heating cases the FRP-concrete bond could withstand much higher
temperatures than Tg. For example, at 80 % of room temperature strength, the
failure temperature was 150 °C at a 10C/min heating rate. This was higher than
the Tg=60°C of the adhesive.
• Unlike the room temperature debonding mechanism where failure happens in
concrete substrate, at higher temperatures the debonding face is within the
adhesive layer.
• Bond failure at high temperatures is ductile compared to brittle fracture in
concrete at room temperature.
• The analytical model presented is able to describe the mechanical bond strength
degradation adequately.
169
6.3.3 Material testing and Fibre Optic Sensors
• For FRP coupon testing for tensile strength, no significant loss of strength
occurred at temperatures below Tg, and the CFRP coupons preserved slightly
more than half of their room temperature strength even at temperatures above
their Tg. This residual strength exceeds the strength requirements in most
flexural strengthening applications, provided that adequate bond can be
maintained between the FRP and concrete.
• Results showed that PIV analysis is a convenient and accurate method of strain
measurement, but the analysis will not be suitable where the surface texture of
the material is damaged.
• Fibre optic sensors used in the experiments successfully predicted the strain at
high temperatures and matched the PIV strain measurements. Thus, FOSs are
suitable for high-temperature strain measurements.
• The computational cost of PIV strain measurement (where applicable) is
considerably lower than FOS method.
6.3.4 Numerical models
6.3.4.1 Heat transfer models
• The two-dimensional FV thermal model, developed in this thesis, is capable of
predicting internal temperature in insulated concrete beams with adequate
170
precision. Model predictions were verified using existing test data from the
literature for RC and insulated members. The crucial steel temperature was
predicted with a maximum error of ±13˚C.
• A similar numerical model was developed to allow prediction of temperatures in
FRP-strengthened and insulated reinforced concrete slabs. The model was
validated against test data, and was found to adequately predict temperatures
within the member.
• Using the numerical models, parametric studies were performed on the effect of
different realistic fire scenarios on the response of insulated T-beams.
6.3.4.2 Strength model
• The numerical model developed here could predict the stress strain fields and
subsequently calculate the deflection of insulated/un-insulated RC beams. The
model uses time-dependent moment-curvature relationships to trace the
response of the beam under fire conditions.
• The model considers multiple strain components such as thermal, transient, and
creep components to achieve a realistic prediction.
• The model was successfully verified by comparing the results of several fire test
results from the literature. The model is capable of predicting the structural
behaviour of un-strengthened and FRP-strengthened beams.
171
• The model is capable of incorporating the axial restraint forces in the response of
the beam. A trial and error method was used to predict the response of the
beams with partial axial restraint.
6.4 Recommendations for future work
While this research has made many contributions in the experimental and numerical
characterization of FRP-strengthened members, more research is needed to further
investigate the behaviour of FRP materials and FRP-strengthened structures at elevated
temperatures. The following are some recommendations for further research:
• Accurate measurement of the end restraints during the fire tests are needed in
order to further investigate the effect of end conditions where partial or full
restraints are present.
• Full-scale fire testing of insulation systems other than the one studied in this
program should be performed in order to achieve an optimum insulation
thickness at critical locations. One such scenario could be the use of more
insulation materials at U-wraps or corners.
• Improving the thermal model to include moisture migration and evaporation in
concrete and insulation could result in better temperature predictions. The effects
of moisture migration were apparent in the recorded temperature data.
172
• Numerical models developed here could be used to simulate a frame including
beams and columns to achieve realistic loading and end-conditions.
• More tests are needed to further understand the FRP-concrete bond behaviour in
order to address the effect of additional variables such as material type, bond
length, loading rate, and moisture.
173
174
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180
A. Appendix A: Detailed experimental results
In this chapter the temperature and deflection readings from the fire tests are reported in
detail.
A.1 Temperature readings for Slabs
Figure A-1 Temperatures vs. exposure time for slab A.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Furnace avg.
TC-45 Insulation Surface
TC-44 FRP-Insulation
TC-43 FRP-Concrete
Avg. Unexposed Face
181
Figure A-2 Temperatures vs. exposure time for slab B.
Figure A-3 Interior concrete temperatures Slab-A.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Furnace avg.
TC-45 Insulation Surface
TC-44 FRP-Insulation
TC-43 FRP-Concrete
Avg. Unexposed Face
0
50
100
150
200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
TC-34 Cover 15 mm
TC-33 Cover 30 mm
TC-32 Cover 50 mm
TC-31 Cover 75 mm
TC-30 Cover 100 mm
TC-29 Cover 125 mm
Avg. Unexposed Face
182
Figure A-4 Interior concrete temperatures Slab-B.
Figure A-5 Temperatures vs. exposure time comparison for slabs A and B at FRP-
concrete bond line and steel reinforcement locations.
0
50
100
150
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
TC-34 Cover 15 mm
TC-33 Cover 30 mm
TC-32 Cover 50 mm
TC-31 Cover 75 mm
TC-30 Cover 100 mm
TC-29 Cover 125 mm
Avg. Unexposed Face
0
100
200
300
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
FRP-Concrete Slab-AFRP-Concrete Slab-BRebar Bottom Slab-ARebar Bottom Slab-B
183
Figure A-6 Steel rebar temperatures Slab-A.
Figure A-7 Steel rebar temperatures Slab-B.
0
50
100
150
200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
TC-26 Top of Rebar
TC-28 Base of Rebar
TC-27 Middle of Rebar
0
50
100
150
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
TC-26 Top of Rebar
TC-28 Base of Rebar
TC-27 Middle of Rebar
184
A.2 Temperatures and deflections of T-beams
A.2.1 Beam-A temperature data
Results for Beam-A are as follows.
Figure A-8 Insulation and FRP temperatures at mid-section (Section-B) for Beam-A.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation sec-B TC-28
FRP-Insulation sec-B TC-29
Insulation Surface sec-B TC-30
185
Figure A-9 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-A.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation U-wrap End J (secG) TC-43
FRP-Insulation U-wrap End J (secG) TC-44
Insulation Surface U-wrap End J (secG) TC-45
186
Figure A-10 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-A.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation U-wrap End I (secD) TC-46
FRP-Insulation U-wrap End I (secD) TC-47
Insulation Surface U-wrap End I (secD) TC-48
187
Figure A-11 Steel reinforcement temperatures (web) Beam-A.
0
50
100
150
200
250
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Longitudinal Steel sec-A TC-2
Longitudinal Steel sec-A TC-3
Longitudinal Steel sec-B TC-25
Longitudinal Steel sec-B TC-27
188
Figure A-12 Unexposed surface temperature (centerline) Beam-A.
15
20
25
30
35
40
45
50
55
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Un-exposed Surface sec-D TC-1
Un-exposed Surface sec-E TC-7
Un-exposed Surface sec-B TC-9
Un-exposed Surface sec-F TC-32
Un-exposed Surface sec-G TC-39
189
Figure A-13 Unexposed surface temperature (flange) Beam-A.
0
20
40
60
80
100
120
140
160
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Un-exposed Surface sec-B TC-8
Un-exposed Surface sec-B TC-10
Un-exposed Surface sec-F TC-31
Un-exposed Surface sec-F TC-33
190
A.2.2 Beam-B temperature data
Results for Beam-B are as follows.
Figure A-14 Insulation and FRP temperatures at mid-section (Section-B) for Beam-B.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation sec-B TC-28
FRP-Insulation sec-B TC-29
FRP-Insulation sec-B TC-30
191
Figure A-15 Insulation and FRP temperatures at U-Wrap End-J (Section-G) for Beam-B.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation U-wrap End J (secG) TC-43
FRP-Insulation U-wrap End J (secG) TC-44
Insulation Surface U-wrap End J (secG) TC-45
192
Figure A-16 Insulation and FRP temperatures at U-Wrap End-I (Section-D) for Beam-B.
0
200
400
600
800
1000
1200
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
ASTM E119
Ave. furnace temp.
Concrete-Insulation U-wrap End I (secD) TC-46
FRP-Insulation U-wrap End I (secD) TC-47
Insulation Surface U-wrap End I (secD) TC-48
193
Figure A-17 Steel reinforcement temperatures (web) Beam-B.
0
50
100
150
200
250
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Longitudinal Steel sec-A TC-2
Longitudinal Steel sec-A TC-3
Longitudinal Steel sec-B TC-25
Longitudinal Steel sec-B TC-27
194
Figure A-18 Unexposed surface temperature (centerline) Beam-B.
15
20
25
30
35
40
45
50
55
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Un-exposed Surface sec-D TC-1
Un-exposed Surface sec-E TC-7
Un-exposed Surface sec-B TC-9
Un-exposed Surface sec-F TC-32
Un-exposed Surface sec-G TC-39
195
Figure A-19 Unexposed surface temperature (flange) Beam-B.
0
20
40
60
80
100
120
140
0 60 120 180 240
Tem
pera
ture
(˚C)
Time (min)
Un-exposed Surface sec-B TC-8
Un-exposed Surface sec-B TC-10
Un-exposed Surface sec-F TC-31
Un-exposed Surface sec-F TC-33
196
A.2.3 Deflection Results
Figure A-20 Deflection at midspan and quatre points for Beam-A.
197
Figure A-21 Deflection at midspan and quatre points for Beam-B.
198
Figure A-22 Comparison of mid span deflection of Beam-A and Beam-B.
199
Figure A-23 load deflection curve Beam-A.
200
Figure A-24 load deflection curve Beam-B.
201
Figure A-25 Load deflection comparison for Beam-A and B.
202
B. APPENDIX-B: T-beam Load Calculation and Design
This chapter presents detailed load calculations for T-beams tested at the National
Research Council, Ottawa, Canada. Load calculations are based on CSA A23.3-04 and
ACI 318-02/318R-05 for un-strengthened beams. ACI 440.2R-08 design guide and CSA
S806-02 are used in addition for strengthened load calculations. And finally test
superimposed load calculators are performed in accordance with ULC-S101-07.
B.1 Assumptions, Dimensions and Material properties
T-beams are 3900mm in length, and their height is 400mm, web and flange width are 300
and 1220mm respectively.
The initial live load for the design of un-strengthened beam is assumed to be 2.4kPa, and
the dead load is the self-weight plus an additional 1kPa for partition load. An increase in
live load is assumed as a practical strengthening scenario. Beams are subjected to an
increased live load of 4.8kPa. After initial design the maximum capacity of the beam is
the basis for the calculation of superimposed test load (it is assumed that in the worst
case the beam is subjected to maximum allowable load which can be larger than the
initial design loads).
One of the T-beams is strengthened by CFRP Sika® CarboDur S812 in flexure and the
other one is strengthened by 1 layer of CFRP SikaWrap® Hex 103C on the bottom of the
203
beam web. A summary of strengthening system for T-beams are presented earlier in
Chapter 3.
B.1.1 Material properties
Material properties of steel, concrete and FRP is as listed below,
Longitudinal Steel Elastic Modulus, Es= 200000 MPa Yield Strength of Longitudinal Reinforcing Steel, 𝑓𝑦 =400 MPa
Concrete 28-day Concrete Compressive Strength, 𝑓𝑐′ =30 MPa Desity, γc= 2400 Kg/m3 Elastic Modulus, Ec= 26621 MPa
CFRP SikaWrap® Hex 103C Cured Laminate Properties with Sikadur® Hex 300 Epoxy [21° - 24°C (70° - 75°F)/5 days and 48 hrs post cure at 60°C (140°F)]
Elastic Modulus, Ef= 70552 MPa Ultimate Strain, 𝜀𝑓𝑢∗ = 1.12% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ =849 MPa Thickness of the FRP, 𝑡𝑓 = 1.016 mm
CFRP Sika® CarboDur S812 Cross section area flexural FRP, Afrp=96 mm2 Elastic Modulus, Ef= 165000 MPa Ultimate Strain, 𝜀𝑓𝑢∗ = 0.017 Ultimate Tensile Strength, 𝑓𝑓𝑢∗ = 2800 MPa Thickness of the FRP, 𝑡𝑓 =1.2 mm
204
SikaWrap® Hex 100G Cured Laminate Properties with Sikadur® Hex 300 Epoxy [21° - 24°C (70° - 75°F)/5 days and 48 hrs post cure at 60°C (140°F)]
Elastic Modulus, Ef= 26119 MPa Ultimate Strain, 𝜀𝑓𝑢∗ =2.34% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ =612 MPa Thickness of the FRP, 𝑡𝑓 =1.016 mm
CFRP, SikaWrap® Hex 230C Cured Laminate Properties with Sikadur® 330 Epoxy Properties after standard cure at 21° - 24°C (70° - 75°F)/5 days
Elastic Modulus, Ef = 65402 MPa Ultimate Strain, 𝜀𝑓𝑢∗ =1.37% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ = 894 MPa Thickness of the FRP, 𝑡𝑓 = 0.381 mm
GFRP, SikaWrap® Hex 430G Cured Laminate Properties with Sikadur® 330 Epoxy Properties after standard cure [21° - 24°C (70° - 75°F)/5 days and 48 hrs post-cure at 4°C (39°F)]
Elastic Modulus, 𝐸𝑓 = 26493 MPa Ultimate Strain, 𝜀𝑓𝑢∗ = 2.03% Ultimate Tensile Strength, 𝑓𝑓𝑢∗ = 537 MPa Thickness of the FRP, 𝑡𝑓 = 0.508 mm
205
B.2 Design Flexural Strength of Reinforced Concrete Beam
The reinforced concrete specimens had two layers of flexural reinforcements: 6 No. 10M
bars in the flange on top and 2 No. 15M bars as tension steel in the bottom of the web,
see Figure 1. Flexural strength contribution of steel in the flange is neglected; therefore
design is based on flexural strength contribution from the two 15M reinforcing bars in
tension and two 10M reinforcing bars on the top of the web.
Area of primary tension steel is (two 15M bars) 𝐴𝑠 = 2(200) = 400 𝑚𝑚2 and the distance
from extreme compression fibre to the centroid of the primary longitudinal tension steel,
𝑑, is:
𝑑 = ℎ − 𝑐𝑜𝑣𝑒𝑟 − 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑡𝑖𝑟𝑟𝑢𝑝 − 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑠𝑡𝑒𝑒𝑙 (15𝑀)
= 400− 40 − 11 − 162� ≅ 341 𝑚𝑚
Area of top steel4 (two 10M bars), 𝐴𝑠′ = 2(100) = 200 𝑚𝑚2 and the distance from
extreme compression fibre, 𝑑′, is:
𝑑′ = 𝑐𝑜𝑣𝑒𝑟 + 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑡𝑖𝑟𝑟𝑢𝑝 + 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑠𝑡𝑒𝑒𝑙 (10𝑀) = 40 + 11 + 112�
≅ 56.5 𝑚𝑚
4 This steel will be in tension see calculation results below.
206
Figure B-1 T-beam cross section.
B.2.1 Design Flexural Strength according to CSA A23.3-04
According to Clause 10.3.3, the overhanging flange width on each side is the lesser of:
a) One fifth the span length = 38065� = 761.2 𝑚𝑚
b) 12 times the flange thickness= 12 × 150 = 1440 𝑚𝑚
c) One-half of the clear distance to the next web= (1220 − 300) 2⁄ = 460
Therefore the effective flange width, 𝑏𝑓 = 2[min (761, 1440, 460)] + 300 = 1220 𝑚𝑚 .
Assuming,
• strain distribution in linear in the section depth,
• Neural axis is within the flange
• Primary tension steel has yielded
• Section will fail by concrete crushing in compression
We have:
150
400
300
15M bars
56.5
341
207
Strain at the extreme compression concrete fibre 𝜀𝑐 is equal to ultimate concrete
strain 𝜀𝑐𝑢 = 0.0035 (Clause 10.1.3).
By trial and error depth of neutral axis, 𝑐 = 11.90 𝑚𝑚 , will satisfy the equilibrium of
forces in the section.
Strain at the bottom steel 𝜀𝑠 and strain at the top steel 𝜀𝑠′ will be:
𝜀𝑠 = 𝜀𝑐𝑢 �𝑑 − 𝑐𝑐
� = 0.0035 �341− 11.9
11.9� = 0.09678
𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐𝑐 � = 0.0035 �
56.5− 11.911.9
� = 0.01311
And the stresses at steel reinforcement will be
𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 0000(0.09678)� = 400 MPa
𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 0000(0.09678)� = 400 MPa
The forces in steels will be
𝑇𝑠 = 𝜙𝑠𝐴𝑠𝜎𝑠 = 0.85(400)(400) = 136000 𝑁
𝑇′𝑠 = 𝜙𝑠𝐴′𝑠𝜎𝑠 = 0.85(200)(400) = 68000 𝑁
𝜙𝑠, the resistance factor for steel is equal to 0.85 according to Clause 8.4.3.
Compression force in concrete can be calculated using the Whitney's equivalent stress
block,
𝐶𝑐 = −(𝛼1𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝑎);
𝑎 = 𝛽1𝑐
According to clause 10.1.7,
208
𝛼1 = max�(0.85− 0.0015𝑓𝑐′), 0.67� = max�(0.85 − 0.0015 × 30), 0.67� = 0.81
𝛽1 = max�(0.97− 0.0025𝑓𝑐′), 0.67� = max�(0.97− 0.0025 × 30), 0.67� = 0.90
𝐶𝑐 = −(𝛼1𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.81(. 65)(30)] ∙ (1220) ∙ [0.90(11.90)] = −204000 𝑁
𝜙𝑐, the resistance factor for concrete is equal to 0.65 according to Clause 8.4.2.
Sum of the forces is equal to zero,
𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 = −204000 + 68000 + 136000 = 0
The sectional moment resistance is:
𝑀𝑟 = 𝐶𝑐𝛽1𝑐
2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ = −204000
0.90(11.9)2
+ 341(136000) + 56.5(68000)
= 49.1 𝑘𝑁.𝑚
B.2.2 Design Flexural Strength according to ACI 318/318R-05
According to Clause 8.10.2, the width of slab effective as a T-beam flange on each side is
the lesser of:
a) One-quarter of the span length = 38064� = 951 𝑚𝑚
b) 8 times the slab thickness= 8 × 150 = 1200 𝑚𝑚
c) One-half of the clear distance to the next web= (1220 − 300) 2⁄ = 460
Therefore the effective flange width, 𝑏𝑓 = 2[min (951, 1200, 460)] + 300 = 1220 𝑚𝑚 .
Strain at the extreme compression concrete fibre 𝜀𝑐 is assumed to be equal to ultimate
concrete strain 𝜀𝑐𝑢 = 0.003 (Clause 10.2.3).
Taking neutral axis, 𝑐 = 9.076 𝑚𝑚 , will satisfy the equilibrium of forces in the section.
209
Strain at the bottom steel 𝜀𝑠 and strain at the top steel 𝜀𝑠′ will be:
𝜀𝑠 = 𝜀𝑐𝑢 �𝑑 − 𝑐𝑐
� = 0.003 �341 − 9.08
9.08� = 0.10972
𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐𝑐 � = 0.003 �
56.5− 9.089.08
� = 0.01568
And the stresses at steel reinforcement will be
𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.10972)� = 400 MPa
𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.01568)� = 400 MPa
The forces in steels will be
𝑇𝑠 = 𝐴𝑠𝜎𝑠 = (400)(400) = 160000 𝑁
𝑇′𝑠 = 𝐴′𝑠𝜎𝑠 = (200)(400) = 80000 𝑁
Compression force in concrete can be calculated using the Whitney's equivalent stress
block,
𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝑎);
𝑎 = 𝛽1𝑐
According to clause 10.2.7.3,
𝛽1 = max��0.85− 0.05�𝑓𝑐′ − 30
7 �� , 0.65� = max�(0.85− 0.05 × 0), 0.65� = 0.85
𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.85(30)] ∙ (1220) ∙ [0.85(9.08)] = −240000 𝑁
Sum of the forces is equal to zero,
𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 = −240000 + 80000 + 160000 = 0
The sectional moment resistance is:
210
𝑀𝑟 = 𝜙 𝑀𝑛
According to Clause 9.3.2.1 𝜙 in a tension-controlled section is equal to 0.90.
𝑀𝑟 = 𝜙 � 𝐶𝑐𝛽1𝑐
2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′�
= 0.90 �−2400000.85(9.08)
2+ 341(160000) + 56.5(80000)� = 52.3 𝑘𝑁.𝑚
B.3 Flexural Capacity of FRP-Strengthened Reinforced Concrete Beam
Detailed calculation for FRP strengthened will be presented in this section. Calculations
for Beam-A and Beam-B will be presented separately.
B.3.1 Beam-A FRP-Strengthened load calculation
Beam-A is strengthened with one strip of Sika CarboDur® S812 bonded to the soffit of
the beam.
B.3.1.1 Flexural Capacity according to CSA S806-02
According to Clause 7.1.6.2, FRP resistance factor is 𝜙𝐹 = 0.75. Also CSA-S806 limits the
strain in the FRP to 0.007 (Cl. 11.3.1.1). Similar to un-strengthened section a linear strain
distribution is assumed.
By trial and error taking neutral axis, 𝑐 = 35.3 𝑚𝑚 , will satisfy the equilibrium of forces
in the section.
Assuming strain in FRP, 𝜀𝑓, reaches 0.007 before crushing happens in concrete, strain
values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:
211
𝜀𝑓 = 0.007, 𝜀𝑐 < 𝜀𝑐𝑢
𝜀𝑠 = 𝜀𝑓 �𝑑 − 𝑐ℎ − 𝑐
� = 0.007 �341 − 35.3400 − 35.3
� = 0.00587
𝜀𝑠′ = 𝜀𝑓 �𝑑′ − 𝑐ℎ − 𝑐 �
= 0.007 �56.5− 35.3400 − 35.3
� = 0.00041
And the stresses at steel and FRP reinforcement will be
𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00587)� = 400 MPa
𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00041)� = 81.55 MPa
𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.007(165000) = 1155 MPa < fFu = 2800 MPa
The forces in steels will be
𝑇𝑠 = 𝜙𝑠𝐴𝑠𝜎𝑠 = 0.85(400)(400) = 136000 𝑁
𝑇′𝑠 = 𝜙𝑠𝐴′𝑠𝜎𝑠 = 0.85(200)(81.55) = 13863 𝑁
𝑇𝑓 = 𝜙𝑓𝐴𝑓𝜎𝑓 = 0.75(96)(1155) = 83160 𝑁
Compression force in concrete can be calculated by direct integration of concrete stress-
strain curve or by using the Whitney's equivalent stress block. Here since strain at top
fibre of concrete does not reach concrete’s ultimate strain, stress block coefficients
should be adjusted accordingly. In the modified stress block the height of stress block is
assumed to be 𝑎 = 𝛽𝑐 and the stress is 𝛼𝑓𝑐′.
Knowing the strain distribution and stress-strain distribution of concrete then stress can
be determined by knowing the position of the fibre in the section ∴ 𝜎𝑐 = 𝜎𝑐(𝑦).
𝛼𝛽 = � �𝜎𝑐(𝑦)𝑓𝑐′
�𝑑𝑦1
0
212
𝛼𝛽2 = 2� �𝜎𝑐(𝑦)𝑓𝑐′
� (1 − 𝑦)𝑑𝑦1
0
By evaluating the two integrals 𝛼 and 𝛽 can be determined.
𝜀𝑐 = 𝜀𝑓 �𝑐
ℎ − 𝑐� = 0.007 �
35.3400− 35.3
� = 0.000677
𝛼 = 0.4134
𝛽 = 0.6721
𝐶𝑐 = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝑎) = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝛽𝑐);
𝐶𝑐 = −[0.41(0.65)(30)](1220)[0.67(35.3)] = −233023 𝑁
Sum of the forces is equal to zero,
𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −233023 + 13863 + 136000 + 83160 = 0
The sectional moment resistance is:
𝑀𝑟 = 𝐶𝑐𝛽𝑐2
+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝑇𝑓ℎ
= −2330230.67(35.3)
2+ 341(136000) + 56.5(13863) + 400(83160)
= 77.7 𝑘𝑁.𝑚
B.3.1.2 Flexural Capacity according to ACI 440.2R-08
The effective ultimate strength of the FRP wrap is taken as the product of the ultimate
strength and an environmental reduction coefficient 𝐶𝐸 as follows, (CL. 9.4):
𝑓𝑓𝑢 = 𝐶𝐸 ∙ 𝑓𝑓𝑢∗
𝑓𝑓𝑢 = 0.95 ∙ 2800 = 2660 𝑀𝑃𝑎
Similarly, the design rupture strain is:
213
𝜀𝑓𝑢 = 𝐶𝐸 ∙ 𝜀𝑓𝑢∗
𝜀𝑓𝑢 = 0.95 ∙ 1.7% = 1.62%.
In order to prevent intermediate crack-induced debonding failure, ACI 440.2R-08 Clause
10.1.1 limits the stress in FRP to 𝜀𝑓𝑑. 𝜀𝑓𝑑, the effective strain in FRP reinforcement is the
strain level at which debonding may occur
𝜀𝑓𝑑 = 0.41�𝑓𝑐′
𝑛𝐸𝑓𝑡𝑓≤ 0.9𝜀𝑓𝑢 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠
Where,
𝐸𝑓 = tensile modulus of elasticity of FRP (MPa)
𝑛 = number of plies of FRP reinforcement
𝑡𝑓 = nominal thickness of one ply of FRP reinforcement (mm)
𝜀𝑓𝑑 = 0.41�30
1(165000)(1.2) = 0.00505 ≤ 0.9(0.01615) = 0.015
Taking neutral axis, 𝑐 = 9.9842 𝑚𝑚 , will satisfy the equilibrium of forces in the section.
Strain values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:
𝜀𝑓 = 𝜀𝑓𝑑 = 0.00505, 𝜀𝑐 < 𝜀𝑐𝑢
𝜀𝑠 = 𝜀𝑓 �𝑑 − 𝑐ℎ − 𝑐
� = 0.00505 �341− 9.98400− 9.98
� = 0.004283
𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐ℎ − 𝑐�
= 0.00505 �56.5− 9.98400 − 9.98
� = 0.000602
And the stresses at steel and FRP reinforcement will be
𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.004283)� = 400 MPa
214
𝜎𝑠′ = min�𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.000602)� = 120.4 MPa
𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.00505(165000) = 832.7 MPa
The forces in steels will be
𝑇𝑠 = 𝐴𝑠𝜎𝑠 = (400)(400) = 160000 𝑁
𝑇′𝑠 = 𝐴′𝑠𝜎𝑠 = (200)(120.4) = 24076 𝑁
𝑇𝑓 = 𝐴𝑓𝜎𝑓 = �1.2(80)�(832.7) = 79941 𝑁
𝜀𝑐 = 𝜀𝑓 �𝑐
ℎ − 𝑐� = 0.00505 �
9.98400− 9.98
� = 0.000192
Compression force in concrete can be calculated using the Whitney's equivalent stress
block,
𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝑎);
𝑎 = 𝛽1𝑐
According to ACI 318-05 Clause 10.2.7.3,
𝛽1 = max��0.85− 0.05�𝑓𝑐′ − 30
7 �� , 0.65� = max�(0.85− 0.05 × 0), 0.65� = 0.85
𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.85(30)] ∙ (1220) ∙ [0.85(9.98)] = −264017 𝑁
Sum of the forces is equal to zero,
𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −264017 + 24076 + 160000 + 79941 = 0
Clause 10.2.10 reduces the contribution of FRP in the nominal flexural strength by
introducing a reduction factor 𝜓𝑓= 0.85.
215
𝑀𝑛 = 𝐶𝑐𝛽1𝑐
2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝜓𝑓𝑇𝑓ℎ
= −2640170.85(9.98)
2+ 341(160000) + 56.5(24076) + 0.85(400)(79941)
= 82.0 𝑘𝑁.𝑚
The sectional moment resistance is:
𝑀𝑟 = 𝜙 𝑀𝑛
According to Clause 10.2.7, 𝜙 in defined as:
𝜙 =
⎩⎪⎨
⎪⎧ 0.9 𝜀𝑡 ≥ 0.005
0.65 +0.25�𝜀𝑡 − 𝜀𝑠𝑦�
0.005− 𝜀𝑠𝑦 𝜀𝑠𝑦 < 𝜀𝑡 < 0.005
0. 65 𝜀𝑡 ≤ 𝜀𝑠𝑦
𝜀𝑡 is the net tensile strain in extreme tension steel. Here 𝜀𝑡 = 𝜀𝑠 = 0.004283 therefore,
𝜙 = 0.65 +0.25(0.004283− 0.002)
0.005− 0.002= 0.852
And finally,
𝑀𝑟 = 𝜙 𝑀𝑛 = 0.852(82.0) = 69.9 𝑘𝑁.𝑚
B.3.1.2.1 Serviceability criterion
Clause 10.2.7 requires the following limits,
• The stress in the steel reinforcement under service load should be limited to 80%
of the yield strength
• compressive stress in concrete under service load should be limited to 45% of the
compressive strength
216
Assuming steel 𝜎𝑠 = 0.8𝑓𝑦 strains and stresses and forces in steel FRP and concrete are:
𝑐 = 43.50 𝑚𝑚
𝜀𝑓 = 𝜀𝑠 �ℎ − 𝑐𝑑 − 𝑐
� = 0.0016 �400 − 43.5341 − 43.5
� = 0.0019
𝜀𝑐 = 𝜀𝑐𝑢 �𝑐
𝑑 − 𝑐� = 0.0016 �
43.5341 − 43.5
� = 0.00023
𝜎𝑐 = 5.82 𝑀𝑃𝑎 < 0.45𝑓𝑐′ = 0.45(30) = 13.5 𝑀𝑃𝑎
Corresponding service and factored moments are
𝑀𝑠 = 53.4 𝑘𝑁.𝑚
𝑀𝐹 = 𝑀𝑠(𝛼𝐷 + 𝛼𝐿)
2= 53.4
(1.2 + 1.6)2
= 74.8 𝑘𝑁.𝑚
B.3.1.2.2 Strengthening Limits
The existing strength of the structure should be sufficient to resist a level of load as
described by (Cl. 9.2),
(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ (1.1𝑆𝐷𝐿 + 0.75𝑆𝐿𝐿)𝑛𝑒𝑤
Assuming DL=LL,
(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ �1.85
2(𝑆𝐷𝐿 + 𝑆𝐿𝐿)�
𝑛𝑒𝑤
= 0.925 𝑆𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤
(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 = 52.3 𝑘𝑁.𝑚
𝑀𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤 =(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔
0.925=
52.30.925
= 56.5 𝑀𝑃𝑎
The corresponding factored moment will be,
𝑀𝐹 = 𝑀𝑠(𝛼𝐷 + 𝛼𝐿)
2= 56.5
(1.2 + 1.6)2
= 79.2 𝑘𝑁.𝑚
217
B.3.1.3 Beam-A design summary
Considering the strengthening limit and serviceability limit and section nominal
strength, the maximum strengthening limit according to ACI is:
𝑀𝐹 = 69.9 𝑘𝑁.𝑚
𝑀𝑠 = 49.9 𝑘𝑁.𝑚
This limit according to CSA is:
𝑀𝐹 = 77.7 𝑘𝑁.𝑚
𝑀𝑠 = 56.5 𝑘𝑁.𝑚
B.3.1.3.1 U-wrap design
Two different CFRP U-wraps are selected for this beam. The U-wrap at one end consists
of two 635 mm wide layers of SikaWrap® Hex 103C and the other U-wrap has four 600
mm wide layers of SikaWrap® Hex 230C.
According to ACI 440.2R-08 Clause 13.1.2 when the factored shear force at the
termination point is greater than 2/3 the concrete shear strength (𝑉𝑢 > 0.67𝑉𝑐), the FRP
laminates should be anchored with transverse reinforcement (U-wrap) to prevent FRP
end peeling or cover delamination. The area of the U-wrap reinforcement 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 is:
𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =�𝐴𝑓𝑓𝑓𝑢�𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙�𝐸𝑓𝜅𝜈𝜀𝑓𝑢�𝑎𝑛𝑐ℎ𝑜𝑟
𝜅𝜈 is bond-dependent coefficient for shear and is calculated using:
218
𝜅𝜈 =𝑘1 𝑘2 𝐿𝑒
11900 𝜀𝑓𝑢 ≤ 0.75 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠
The active bond length 𝐿𝑒 and bond reduction factors, 𝑘1 and 𝑘2 are defined as:
𝐿𝑒 =23300
�𝑛𝑓 𝑡𝑓 𝐸𝑓�0.58
𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠 ( 𝐸𝑓in MPa 𝑡𝑓 in mm)
𝑘1 = �𝑓𝑐′
27�
23
(𝑓𝑐′ 𝑖𝑛 𝑀𝑃𝑎)
𝑘2 =𝑑𝑓𝑣 − 𝐿𝑒𝑑𝑓𝑣
𝑓𝑜𝑟 𝑈 − 𝑤𝑟𝑎𝑝𝑠
𝑑𝑓𝑣 is the effective depth of FRP shear reinforcement (mm). Le in mm
B.3.1.3.1.1 SikaWrap® Hex 103C U-wrap
𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚
𝐿𝑒 =23300
�2 (1.016)(70552)�0.58
= 24 𝑚𝑚
𝑘1 = �3027�23
= 1.07
𝑘2 =211 − 24
211= 0.89
𝜅𝜈 =1.07 (0.89)(24)11900(0.0106)
= 0.18 ≤ 0.75
𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =96(2660)
70552(0.17)(0.0106) = 1901 𝑚𝑚2
Area of two layers of SikaWrap® Hex 103C is:
𝐴𝑓𝑟𝑝𝑣 = 2(2)�635(1.016)� = 2581 𝑚𝑚2 > 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟
219
B.3.1.3.1.2 SikaWrap® Hex 230C U-wrap
𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚
𝐿𝑒 =23300
�4 (0.381)(65402)�0.58
= 29 𝑚𝑚
𝑘1 = �3027�23
= 1.07
𝑘2 =211 − 29
211= 0.86
𝜅𝜈 =1.07 (0.86)(29)11900(0.0137)
= 0.17 ≤ 0.75
𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =96(2660)
65402(0.17)(0.0137) = 1712 𝑚𝑚2
Area of two layers of SikaWrap® Hex 230C is: 𝐴𝑓𝑟𝑝𝑣 = 2(2)�610(0.381)� = 1859 𝑚𝑚2 > 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟
B.3.2 Beam-B FRP-Strengthened load calculation
Beam-B is strengthened with one 200 mm wide layer of SikaWrap®Hex-103C bonded to
the soffit of the beam.
B.3.2.1 Flexural Capacity according to CSA S806-02
According to Clause 7.1.6.2, FRP resistance factor is 𝜙𝐹 = 0.75. Also CSA-S806 limits the
strain in the FRP to 0.007 (Cl. 11.3.1.1). Similar to un-strengthened section a linear strain
distribution is assumed.
By trial and error taking neutral axis, 𝑐 = 34.7 𝑚𝑚 , will satisfy the equilibrium of forces
in the section.
Assuming strain in FRP, 𝜀𝑓, reaches 0.007 before crushing happens in concrete, strain
values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:
220
𝜀𝑓 = 0.007, 𝜀𝑐 < 𝜀𝑐𝑢
𝜀𝑠 = 𝜀𝑓 �𝑑 − 𝑐ℎ − 𝑐
� = 0.007 �341 − 34.7400 − 34.7
� = 0.00587
𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐ℎ − 𝑐�
= 0.007 �56.5− 34.7400 − 34.7
� = 0.00042
And the stresses at steel and FRP reinforcement will be
𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00587)� = 400 MPa
𝜎𝑠′ = min�𝐹𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00042)� = 83.58 MPa
𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.007(70552) = 494 MPa < fFu = 849 MPa
The forces in steels will be
𝑇𝑠 = 𝜙𝑠𝐴𝑠𝜎𝑠 = 0.85(400)(400) = 136000 𝑁
𝑇′𝑠 = 𝜙𝑠𝐴′𝑠𝜎𝑠 = 0.85(200)(83.58) = 14209 𝑁
𝑇𝑓 = 𝜙𝑓𝐴𝑓𝜎𝑓 = 0.75�1.016(200)�(494) = 75265 𝑁
𝜀𝑐 = 𝜀𝑓 �𝑐
ℎ − 𝑐� = 0.007 �
34.7400− 34.7
� = 0.000665
𝛼 = 0.4066
𝛽 = 0.6719
𝐶𝑐 = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝑎) = −(𝛼𝜙𝑐𝑓𝑐′)𝑏𝑓 (𝛽𝑐);
𝐶𝑐 = −[0.41(0.65)(30)](1220)[0.67(34.7)] = −225473 𝑁
Sum of the forces is equal to zero,
𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −225474 + 14209 + 136000 + 75265 = 0
The sectional moment resistance is:
221
𝑀𝑟 = 𝐶𝑐𝛽𝑐2
+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝑇𝑓ℎ
= −2254730.67(34.7)
2+ 341(136000) + 56.5(14209) + 400(75265)
= 74.7 𝑘𝑁.𝑚
B.3.2.2 Flexural Capacity according to ACI 440.2R-08
The effective ultimate strength of the FRP wrap is taken as the product of the ultimate
strength and an environmental reduction coefficient 𝐶𝐸 as follows, (CL. 9.4):
𝑓𝑓𝑢 = 𝐶𝐸 ∙ 𝑓𝑓𝑢∗
𝑓𝑓𝑢 = 0.95 ∙ 849 = 806.55 𝑀𝑃𝑎
Similarly, the design rupture strain is:
𝜀𝑓𝑢 = 𝐶𝐸 ∙ 𝜀𝑓𝑢∗
𝑓𝑓𝑢 = 0.95 ∙ 1.12% = 1.06%.
In order to prevent intermediate crack-induced debonding failure, ACI 440.2R-08 Clause
10.1.1 limits the stress in FRP to 𝜀𝑓𝑑. 𝜀𝑓𝑑, the effective strain in FRP reinforcement is the
strain level at which debonding may occur
𝜀𝑓𝑑 = 0.41�𝑓𝑐′
𝑛𝐸𝑓𝑡𝑓≤ 0.9𝜀𝑓𝑢 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠
Where,
𝐸𝑓 = tensile modulus of elasticity of FRP (MPa)
222
𝑛 = number of plies of FRP reinforcement
𝑡𝑓 = nominal thickness of one ply of FRP reinforcement (mm)
𝜀𝑓𝑑 = 0.41�30
1(70552)(1.016) = 0.0084 ≤ 0.9(0.01064) = 0.0095
Taking neutral axis, 𝑐 = 12.052 𝑚𝑚 , will satisfy the equilibrium of forces in the section.
Strain values at bottom steel, 𝜀𝑠, and strain at the top steel fibre 𝜀𝑠′ will be:
𝜀𝑓 = 𝜀𝑓𝑑 = 0.0084, 𝜀𝑐 < 𝜀𝑐𝑢
𝜀𝑠 = 𝜀𝑓 �𝑑 − 𝑐ℎ − 𝑐
� = 0.0084 �341 − 12.05400 − 12.05
� = 0.00711
𝜀𝑠′ = 𝜀𝑐𝑢 �𝑑′ − 𝑐ℎ − 𝑐 �
= 0.0084 �56.5− 12.05400 − 12.05
� = 0.00096
And the stresses at steel and FRP reinforcement will be
𝜎𝑠 = min�𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.0071)� = 400 MPa
𝜎𝑠′ = min�𝜀𝑠𝑦 , 𝐸𝑠 × 𝜀𝑠� = min�400, 200 000(0.00096)� = 192.2 MPa
𝜎𝑓 = 𝐸𝑓 × 𝜀𝑓 = 0.0084(70552) = 592 MPa
The forces in steels will be
𝑇𝑠 = 𝐴𝑠𝜎𝑠 = (400)(400) = 160000 𝑁
𝑇′𝑠 = 𝐴′𝑠𝜎𝑠 = (200)(192.2) = 38440 𝑁
𝑇𝑓 = 𝐴𝑓𝜎𝑓 = �1.016(200)�(592) = 120247 𝑁
𝜀𝑐 = 𝜀𝑓 �𝑐
ℎ − 𝑐� = 0.0084 �
12.05400 − 12.05
� = 0.00026
223
Compression force in concrete can be calculated using the Whitney's equivalent stress
block,
𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝑎);
𝑎 = 𝛽1𝑐
According to ACI 318-05 Clause 10.2.7.3,
𝛽1 = max��0.85− 0.05�𝑓𝑐′ − 30
7 �� , 0.65� = max�(0.85− 0.05 × 0), 0.65� = 0.85
𝐶𝑐 = −(0.85𝑓𝑐′)𝑏𝑓 (𝛽1𝑐) = −[0.85(30)] ∙ (1220) ∙ [0.85(12.05)] = −318688 𝑁
Sum of the forces is equal to zero,
𝐶𝑐 + 𝑇′𝑠 + 𝑇𝑠 + 𝑇𝑓 = −318688 + 38440 + 160000 + 120247 = 0
Clause 10.2.10 reduces the contribution of FRP in the nominal flexural strength by
introducing a reduction factor 𝜓𝑓= 0.85.
𝑀𝑛 = 𝐶𝑐𝛽1𝑐
2+ 𝑇𝑠𝑑 + 𝑇′𝑠𝑑′ + 𝜓𝑓𝑇𝑓ℎ
= −3186880.85(12.05)
2+ 341(160000) + 56.5(38440)
+ 0.85(400)(120247) = 96.0 𝑘𝑁.𝑚
The sectional moment resistance is:
𝑀𝑟 = 𝜙 𝑀𝑛
According to Clause 10.2.7, 𝜙 in defined as:
224
𝜙 =
⎩⎪⎨
⎪⎧ 0.9 𝜀𝑡 ≥ 0.005
0.65 +0.25�𝜀𝑡 − 𝜀𝑠𝑦�
0.005− 𝜀𝑠𝑦 𝜀𝑠𝑦 < 𝜀𝑡 < 0.005
0. 65 𝜀𝑡 ≤ 𝜀𝑠𝑦
𝜀𝑡 is the net tensile strain in extreme tension steel. Here 𝜀𝑡 = 𝜀𝑠 = 0.00711 therefore,
𝜙 = 0.9
And finally,
𝑀𝑟 = 𝜙 𝑀𝑛 = 0.9(96.0 ) = 86.4 𝑘𝑁.𝑚
B.3.2.2.1 Serviceability criterion
Clause 10.2.7 requires the following limits,
• The stress in the steel reinforcement under service load should be limited to 80%
of the yield strength
• compressive stress in concrete under service load should be limited to 45% of the
compressive strength
Assuming steel 𝜎𝑠 = 0.8𝑓𝑦 strains and stresses and forces in steel FRP and concrete are:
𝑐 = 43.10 𝑚𝑚
𝜀𝑓 = 𝜀𝑠 �ℎ − 𝑐𝑑 − 𝑐
� = 0.0016 �400 − 43.1341 − 43.1
� = 0.0019
𝜀𝑐 = 𝜀𝑐𝑢 �𝑐
𝑑 − 𝑐� = 0.0016 �
43.1341 − 43.1
� = 0.00023
𝜎𝑐 = 5.79 𝑀𝑃𝑎 < 0.45𝑓𝑐′ = 0.45(30) = 13.5 𝑀𝑃𝑎
Corresponding service and factored moments are
𝑀𝑠 = 52.3 𝑘𝑁.𝑚
225
𝑀𝐹 = 𝑀𝑠(𝛼𝐷 + 𝛼𝐿)
2= 52.3
(1.2 + 1.6)2
= 73.2 𝑘𝑁.𝑚
B.3.2.2.2 Strengthening Limits
The existing strength of the structure should be sufficient to resist a level of load as
described by (Cl. 9.2),
(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ (1.1𝑆𝐷𝐿 + 0.75𝑆𝐿𝐿)𝑛𝑒𝑤
Assuming DL=LL,
(𝜙𝑅𝑛)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 ≥ �1.85
2(𝑆𝐷𝐿 + 𝑆𝐿𝐿)�
𝑛𝑒𝑤
= 0.925 𝑆𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤
(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 = 52.3 𝑘𝑁.𝑚
𝑀𝑠𝑒𝑟𝑣𝑖𝑐𝑒,𝑛𝑒𝑤 =(𝑀𝑟)𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔
0.925=
52.30.925
= 56.5 𝑀𝑃𝑎
The corresponding factored moment will be,
𝑀𝐹 = 𝑀𝑠(𝛼𝐷 + 𝛼𝐿)
2= 56.5
(1.2 + 1.6)2
= 79.2 𝑘𝑁.𝑚
B.3.2.3 Beam-B design summary
Considering the strengthening limit and serviceability limit and section nominal
strength, the maximum strengthening limit according to ACI is:
𝑀𝐹 = 73.2 𝑘𝑁.𝑚
𝑀𝑠 = 52.3 𝑘𝑁.𝑚
This limit according to CSA is:
𝑀𝐹 = 74.7 𝑘𝑁.𝑚
226
𝑀𝑠 = 54.3 𝑘𝑁.𝑚
B.3.2.3.1 U-wrap design
Two different GFRP U-wraps are selected for this beam. The U-wrap at one end consists
of two 610 mm wide layers of SikaWrap® Hex 100G and the other U-wrap has four 610
mm wide layers of SikaWrap® Hex 430G.
The area of the U-wrap reinforcement 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 is:
𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =�𝐴𝑓𝑓𝑓𝑢�𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙�𝐸𝑓𝜅𝜈𝜀𝑓𝑢�𝑎𝑛𝑐ℎ𝑜𝑟
𝜅𝜈 is bond-dependent coefficient for shear and is calculated using:
𝜅𝜈 =𝑘1 𝑘2 𝐿𝑒
11900 𝜀𝑓𝑢 ≤ 0.75 𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠
The active bond length 𝐿𝑒 and bond reduction factors, 𝑘1 and 𝑘2 are defined as:
𝐿𝑒 =23300
�𝑛𝑓 𝑡𝑓 𝐸𝑓�0.58
𝑖𝑛 𝑆𝐼 𝑢𝑛𝑖𝑡𝑠
𝑘1 = �𝑓𝑐′
27�
23
𝑘2 =𝑑𝑓𝑣 − 𝐿𝑒𝑑𝑓𝑣
𝑓𝑜𝑟 𝑈 − 𝑤𝑟𝑎𝑝𝑠
𝑑𝑓𝑣 is the effective depth of FRP shear reinforcement (mm).
B.3.2.3.1.1 SikaWrap® Hex 100G U-wrap
𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚
227
𝐿𝑒 =23300
�2 (1.016)(26119)�0.58
= 42 𝑚𝑚
𝑘1 = �3027�23
= 1.07
𝑘2 =211 − 42
211= 0.80
𝜅𝜈 =1.07 (0.80)(42)11900(0.0234)
= 0.13 ≤ 0.75
𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =203(807)
26119(0.13)(0.0234) = 2056 𝑚𝑚2
Area of two layers of SikaWrap® Hex 100G is:
𝐴𝑓𝑟𝑝𝑣 = 2(2)�600(1.016)� = 2438 𝑚𝑚2 > 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟
B.3.2.3.1.2 SikaWrap® Hex 430G U-wrap
𝑑𝑓𝑣 = 250 − 11 −162− 20 = 211 𝑚𝑚
𝐿𝑒 =23300
�4 (0.508)(26493)�0.58
= 42 𝑚𝑚
𝑘1 = �3027�23
= 1.07
𝑘2 =211 − 42
211= 0.80
𝜅𝜈 =1.07 (0.80)(42)11900(0.0203)
= 0.15 ≤ 0.75
𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟 =203(807)
26493(0.15)(0.0203) = 2040 𝑚𝑚2
Area of two layers of SikaWrap® Hex 430G is:
228
𝐴𝑓𝑟𝑝𝑣 = 2(2)�610(0.508)� = 2479 𝑚𝑚2 > 𝐴𝑓,𝑎𝑛𝑐ℎ𝑜𝑟
B.4 Superimposed Fire Test Loads
ULC S101-07 requires a superimposed load to be applied to the test specimens during
the fire test. This load is determined to simulate the total specified load (M) on the T-beams.
Following is a brief definition for some of the terms used in this section:
Md dead load during test (weight of the beam)
M total specified load on the beam
MD dead load
ML live load
Ms required superimposed load on column
Mr factored flexural resistance
α load factor on total specified load
αD dead load factor
αL live load factor
r dead-to-live load ratio
The required superimposed load Ms is calculated as,
Ms=M-Md
Knowing the dead-to-live ratio(r), M can be back calculated from factored flexural
resistance (Mr),
229
𝑟 =𝑀𝐷
𝑀𝐿
M= Mr/ α, where α is,
𝛼 =𝑟𝛼𝐷 + 𝛼𝐿𝑟 + 1
As a results Ms= Mr/ α -Md .
Assuming a dead to live ratio of r= MD/ML =15 , Table 1 give a summary of the
calculations.
𝛼 =𝛼𝐷 + 𝛼𝐿
2
Table B-1 load factor calculation.
αD αL 𝒓 =𝑷𝑫𝑷𝑳
𝜶 =𝒓𝜶𝑫 + 𝜶𝑳𝒓 + 𝟏
ACI 318-05 1.2 1.6 1 1.4 CSA S806-02 1.25 1.5 1 1.375
Considering load calculation summary, sections 0 and 0, maximum moment allowable
for both Beams are selected as:
According to ACI 440.2R-08
𝑀𝑟 = 73.2 𝑘𝑁.𝑚
5 As in example 1 clause C 1.3 of ULC S101-07
230
𝑀 = 52.3 𝑘𝑁.𝑚
According to CSA S806-02
𝑀𝑟 = 77.7 𝑘𝑁.𝑚
𝑀 = 56.5 𝑘𝑁.𝑚
Since CSA S806-02 gives a higher load, for that reason superimposed load calculations
are based on CSA S806-02 values.
Existing dead load Md=11.0 kN.m. So the superimposed load on the beam is
Ms=M-Md=56.5-11.0=45.5 kN.m.
B.4.1 Required Jack Stress during Fire Test
The load is delivered to the beam through a set of 6 jacks. The total load required along
the beam is:
𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑝𝑒𝑟𝑖𝑚𝑝𝑜𝑠𝑒𝑑 𝑗𝑎𝑐ℎ𝑖𝑛𝑔 𝑙𝑜𝑎𝑑 =8𝑀𝑠
𝐿=
8 × 45.53.806
= 95.7 𝑘𝑁
There are 6 jacks and each jack head has a diameter of 2.5in, leading to a jack area of:
𝐽𝑎𝑐𝑘 𝐴𝑟𝑒𝑎 = 𝜋𝐷2
4= 3166 𝑚𝑚2 = 4.91 𝑖𝑛2
Hence, the stress required in each jack during loading is:
𝑱𝒂𝒄𝒌 𝑺𝒕𝒓𝒆𝒔𝒔 =𝑻𝒐𝒕𝒂𝒍 𝒍𝒐𝒂𝒅𝑱𝒂𝒄𝒌 𝑨𝒓𝒆𝒂
= 𝟓.𝟎𝟑 𝑴𝑷𝒂 = 𝟕𝟑𝟎 𝒑𝒔𝒊
231
232
C. Appendix C: Material properties at high temperature
The fire performance of FRP-strengthened RC beams under fire exposure is governed by
the thermal and mechanical properties of concrete, steel reinforcement, FRP
reinforcement, adhesive and insulation materials. Thermal properties are necessary to
determine the temperature field inside the structural element at any specific time,
specifically where the member exposed to fire. The thermal properties that affect the
thermal behaviour and temperature distribution in the member are thermal
conductivity, specific heat and density. In these chapter thermal and mechanical
properties of material is presented in detail.
C.1 Concrete
C.1.1 Thermal properties
C.1.1.1 Thermal conductivity
(Lie 1992) suggested the following equations for the thermal conductivity of siliceous
aggregate concrete,
CTforkCTforTk
c
c
8000.1
80005.1000625.0
>=
≤≤+−=( C-1)
The temperature, T, has units of ºC and ck has units of W/m-ºC. And for
Calcareous aggregate
233
CTforTkCTfork
c
c
2937162.1001241.0
293355.1
>+−=
≤= ( C-2)
Eurocode 2 (EN 2004) gives the following equations for lower and upper limit of thermal
conductivity of concrete. The upper limit of thermal conductivity of normal weight
concrete is determined using the following equation
CTCformKWTTkc 120020/
1000107.0
1002451.02
2
≤≤
+
−= ( C-3)
And the following equation could be used for the lower limit
CTCformKWTTkc 120020/
1000057.0
100136.036.1
2
≤≤
+
−= ( C-4)
Following figure compares the two models.
234
Figure C-1 Thermal conductivity of normal weight concrete based on Eurocode 2 (EN
2004) and (Lie 1992).
C.1.1.2 Specific heat
(Lie 1992) suggested the following equations for the volumetric specific heat for siliceous
aggregate concrete,
0.00
0.40
0.80
1.20
1.60
2.00
2.40
0 200 400 600 800 1000 1200
Ther
mal
cond
uctiv
ity W
/mK
Temperature °C
EC2 upper limit
Sillicious Lie, TT
Carbonated Lie, TT
EC2 lower limit
235
CTCforccc 400200107.2 6 ≤≤×=⋅ρ
( ) CTCforTccc 500400105.2013.0 6 ≤≤×−=⋅ρ
( ) CTCforTccc 600500105.10013.0 6 ≤≤×+−=⋅ρ
( C-5)
Density, cρ , has units of kg/m3, specific heat, cc , has units of J/kg-ºC, temperature, T,
has units of ºC, and thermal capacity, cc c⋅ρ , has units of J/m3-ºC.
(Lie 1992) suggests the following for Calcareous aggregate,
CTforccc400010566.2 6 ≤≤×=⋅ρ
( ) CTCforTccc 41040010034.681765.0 6 ≤≤×−=⋅ρ
( ) CTCforTccc 4454101000671.2505043.0 6 ≤≤×+−=⋅ρ
CTCforccc 50044510566.2 6 ≤≤×=⋅ρ
( ) CTCforTccc 6355001044881.501603.0 6 ≤≤×−=⋅ρ
( ) CTCforTccc 7857151007343.17622103.0 6 ≤≤×+−=⋅ρ
( C-6)
( ) CTforTccc2000107.1005.0 6 ≤≤×+=⋅ρ
CTforccc600107.2 6 ≥×=⋅ρ
( ) CTCforTccc 7156351090225.10016635.0 6 ≤≤×−=⋅ρ
CTforccc78510566.2 6 ≥×=⋅ρ
236
Lie’s model does not account for moisture content of the concrete and moisture effect
should be accounted for separately.
Eurocode 2 gives the following equations for the specific heat of dry concrete (no
moisture),
100°C T 20°C K) (J/kg 900 =)( ≤≤Tcc
200°C T < 100°Cfor K) (J/kg 100) - (T + 900 =)( ≤Tcc
400°C T < 200°Cfor K) (J/kg 200)/2 - (T + 1000 =)( ≤Tcc
1200°C T < 400°Cfor K) (J/kg 1100 =)( ≤Tcc
( C-7)
When the moisture content of concrete is not accounted for in the calculation method,
the function given for the specific heat of dry concrete should be adjusted to account for
the moisture. For both siliceous and calcareous aggregates this could be modelled by a
constant value, cc.peak, situated between 100°C and 115°C with linear decrease between
115°C and 200°C.
• cc.peak = 900 J/kg K for moisture content of 0 % of concrete weight
• cc.peak = 1470 J/kg K for moisture content of 1,5 % of concrete weight
• cc.peak = 2020 J/kg K for moisture content of 3,0 % of concrete weight
And linear relationship between (115°C, cc.peak) and (200°C, 1000 J/kg K).
237
The variation of density with temperature is influenced by water loss and is defined as
follows,
115°C 20°Cfor (20°C) =)( c ≤≤TTc ρρ
°C002 115°Cfor 85115 - T0.02 - 1(20°C) =)( c ≤<
⋅⋅ TTc ρρ
°C004 200°Cfor 200
200 - T0.03 - 0.98(20°C) =)( c ≤<
⋅⋅ TTc ρρ
°C0021 400°Cfor 800
400 - T0.07 - 0.95(20°C) =)( c ≤<
⋅⋅ TTc ρρ
( C-8)
C.1.2 Mechanical properties
C.1.2.1 Stress strain relation
(Lie 1992) provides an estimate for the stress-strain relationship of concrete at high
temperature. The stress in the concrete is a function of the strain in the material and its
relation to the strain at maximum stress (εcmax).
238
For ascending branch where :max thencc εε ≤
−−⋅=
2
max
max' 1c
cccc ff
εεε
And for the descending branch where :max thencc εε >
⋅−
−⋅=2
max
max'
31
c
cccc ff
εεε
Where:
≥
−
⋅−⋅
<= CTifTf
CTifff
c
c
c º4501000
20353.2011.2
º450'0
'0
'
( C-9)
Here cε is the strain in concrete, maxcε is the concrete strain at maximum stress, fc is the
stress in concrete (MPa) , f’c is the temperature dependent concrete strength (MPa) and
f’c0 is the concrete strength at room temperature (MPa). The concrete strain at
maximum stress, maxcε , is dependent on the temperature and is defined as below.
Temperature is in ºC.
( ) 62max 1004.00.60025.0 −×⋅+⋅+= TTcε ( C-10)
The strain at crushing failure in the concrete is not strictly defined in Lie’s model.
Williams 2005 assumed that at all temperatures, the crushing strain in the concrete (εcult)
239
is related to the strain at maximum stress ( maxcε ) by the same ratio that applies room
temperature.
Eurocode 2 proposes a stress stain curve for uniaxially stressed concrete at elevated
temperatures as could be seen in the figure below.
Figure C-2 Eurocode2 compressive stress strain curve for concrete.
The stress in concrete σ(𝜃) is related to strain 𝜀 using the following equation,
𝜎(𝜽) = �
𝟑𝜺𝒇𝒄,𝜽
𝜺𝒄𝟏,𝜽�𝟐+�𝜺
𝜺𝒄𝟏,𝜽�𝟑�
𝜺 < 𝜺𝒄𝟏,𝜽
Linear or nonlinear descending branch 𝜺𝒄𝟏,𝜽 < 𝜺 < 𝜺𝒄𝒖𝟏,𝜽
( C-11)
240
The stress-strain relationship in ascending branch is defined by two parameters, the
compressive strength 𝒇𝒄,𝜽 and the strain 𝜺𝒄𝟏,𝜽 corresponding to 𝒇𝒄,𝜽. These two
parameters are temperature dependent and could be determined using the following
table. Where fck is Characteristic cylinder strength (MPa). εcu1,θ the ultimate strain. A
descending branch could be adopted for numerical purposes for strains larger than 𝜺𝒄𝟏,𝜽.
241
Table C-1 Values for the main parameters of the stress-strain relationships of normal
weight concrete with siliceous or calcareous aggregates concrete at elevated
temperatures, from Eurocode2.
Concrete temp.θ
Siliceous aggregates Calcareous aggregates
fc,θ / fck εc1,θ εcu1,θ fc,θ / fck εc1,θ εcu1,θ
[°C] [-] [-] [-] [-] [-] [-]
1 2 3 4 5 6 7
20 1.00 0.0025 0.0200 1.00 0.0025 0.0200
100 1.00 0.0040 0.0225 1.00 0.0040 0.0225
200 0.95 0.0055 0.0250 0.97 0.0055 0.0250
300 0.85 0.0070 0.0275 0.91 0.0070 0.0275
400 0.75 0.0100 0.0300 0.85 0.0100 0.0300
500 0.60 0.0150 0.0325 0.74 0.0150 0.0325
600 0.45 0.0250 0.0350 0.60 0.0250 0.0350
700 0.30 0.0250 0.0375 0.43 0.0250 0.0375
800 0.15 0.0250 0.0400 0.27 0.0250 0.0400
900 0.08 0.0250 0.0425 0.15 0.0250 0.0425
1000 0.04 0.0250 0.0450 0.06 0.0250 0.0450
1100 0.01 0.0250 0.0475 0.02 0.0250 0.0475
1200 0.00 - - 0.00 - -
242
C.1.2.2 Thermal expansion
The coefficient of thermal expansion is a function of temperature; Lie (1992) proposed
the following equation for both carbonated and siliceous aggregate concretes.
610)6008.0( −×+= Tcα ( C-12)
The temperature, T, has units of ºC, and αc has units of ºC-1.
Eurocode 2 suggests the following equations to calculate the thermal strain in concrete,
For siliceous aggregates:
εc(θ) = -1,8 × 10-4 + 9 × 10-6θ + 2,3 × 10-11θ 3 for 20°C ≤ θ ≤ 700°C
εc(θ) = 14 × 10-3 for 700°C < θ ≤ 1200°C ( C-13)
and for calcareous aggregates:
εc(θ) = -1,2 × 10-4 + 6 × 10-6θ + 1,4 × 10-11θ 3 for 20°C ≤ θ ≤ 805°C
εc(θ) = 12 × 10-3 for 805°C < θ ≤ 1200°C ( C-14)
Where θ is the concrete temperature (°C). These strains are calculated with reference to
the length at 20°C.
243
C.1.2.3 Creep and Transient strain
Creep deformation in concrete at room temperature is small but at elevated
temperatures creep could be significant for example where concrete is subjected to an
elevated service temperature for prolonged length of time. (Anderberg, Thelandersson
1976) concluded that creep could be ignored at temperatures below 400°C. In the case of
severe compartment fires where the duration of exposure is relatively short, the effect of
creep is minimal and it is usually ignored.
𝜀𝑐𝑟 = 0.00053 𝜎𝑐𝑓𝑐,𝑇
� 𝑡180
𝑒0.00304(𝑇−20) ( C-15)
where 𝑓𝑐,𝑇 is the strength of concrete at temperature T (°C) and t is time in minutes. 𝜎𝑐 is
the applied stress.
In addition to time dependant creep strains in concrete there is another component of
strain which is called transient strain or load induced thermal strain (LITS). LITS
develops in addition to creep during the first heating under load (Khoury 2000). In
Anderberg’s formulation transient strain is related to unconstrained thermal expansion
of concrete 𝜀𝑡ℎ and the stress history of the element as could be seen in the following
equation.
𝜀𝑡𝑟 = −𝑘2𝜎
𝑓𝑐,20𝜀𝑡ℎ ( C-16)
𝑘2 is an empirical constant between 1.8 to 2.35.
244
C.2 Reinforcing steel
C.2.1.1 Stress strain relation
Lie (1992) provides a set a equations for the stress-strain relationship of reinforcing steel
at high temperature as follows.
( )
( ) ( ) ( )
>−+−+⋅
≤⋅=
pspsp
pss
y
TfTfTf
Tf
fεεεεε
εεε
001.0,001.0,001.0
001.0,001.0
001.0,
( C-17)
Where: ( ) ( )( )[ ] 9.603.030exp104.050),( ⋅⋅+−−⋅⋅−= εε TTTf and 06104 yp fx ⋅= −ε .
The variable T is the temperature (ºC) of the steel rebar, and fy0 is the room temperature
yield strength of the steel (MPa).
Eurocode 2 suggests a different equation for the reinforcing bars, as can be seen in the
figure below.
Figure C-3 model for stress-strain relationships of reinforcing steel at elevated
temperatures
245
The following equations determine the state of stress at any temperature given a specific
strain.
𝜎(𝜃) =
⎩⎪⎪⎨
⎪⎪⎧
𝜀𝐸𝑠,𝜃 𝜀 < 𝜀𝑠𝑝,𝜃
𝑓𝑠𝑝,𝜃 − 𝑐 + �𝑏𝑎� �𝑎2 − �𝜀𝑠𝑦,𝜃 − 𝜀�2�
0.5𝜀𝑠𝑝,𝜃 ≤ 𝜀 ≤ 𝜀𝑠𝑦,𝜃
𝑓𝑠𝑦,𝜃 𝜀𝑠,𝜃 ≤ 𝜀 ≤ 𝜀𝑠𝑡,𝜃
𝑓𝑠𝑦,𝜃�1− �𝜀 − 𝜀𝑠𝑡,𝜃� �𝜀𝑠𝑢,𝜃 − 𝜀𝑠𝑡,𝜃�� � 𝜀𝑠𝑡,𝜃 ≤ 𝜀 ≤ 𝜀𝑠𝑢,𝜃 0.0 𝜀 > 𝜀𝑠𝑢,𝜃
( C-18)
Where a, b and c are determined using the following equations.
𝑎2 = �𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃��𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃 + 𝑐/𝐸𝑠,𝜃�
𝑏2 = 𝑐�𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃�𝐸𝑠,𝜃 + 𝑐2
𝑐 =�𝑓𝑠𝑦,𝜃 − 𝑓𝑠𝑝,𝜃�
2
�𝜀𝑠𝑦,𝜃 − 𝜀𝑠𝑝,𝜃�𝐸𝑠,𝜃 − 2�𝑓𝑠𝑦,𝜃 − 𝑓𝑠𝑝,𝜃�
εsp,θ = fsp,θ / Es,θ , εsy,θ = 0,02, εst,θ = 0,15, εsu,θ = 0,20,
εst,θ = 0,05 and εsu,θ = 0,10
The temperature dependant parameters could be determined using the following table;
fyk is the room temperature yield stress of the reinforcement.
Table C-2 values for the parameters of the stress-strain relationship of hot rolled and
cold worked reinforcing steel at elevated temperatures
246
Steel
Temperature fsyθ / fyk fspθ / fyk Esθ / Es
θ [°C] hot
rolled
cold
worked
hot
rolled
cold
worked
hot
rolled
cold
worked
20.00 1.00 1.00 1.00 1.00 1.00 1.00
100.00 1.00 1.00 1.00 0.96 1.00 1.00
200.00 1.00 1.00 0.81 0.92 0.90 0.87
300.00 1.00 1.00 0.61 0.81 0.80 0.72
400.00 1.00 0.94 0.42 0.63 0.70 0.56
500.00 0.78 0.67 0.36 0.44 0.60 0.40
600.00 0.47 0.40 0.18 0.26 0.31 0.24
700.00 0.23 0.12 0.07 0.08 0.13 0.08
800.00 0.11 0.11 0.05 0.06 0.09 0.06
900.00 0.06 0.08 0.04 0.05 0.07 0.05
1000.00 0.04 0.05 0.02 0.03 0.04 0.03
1100.00 0.02 0.03 0.01 0.02 0.02 0.02
1200.00 0.00 0.00 0.00 0.00 0.00 0.00
C.2.1.2 Thermal elongation of reinforcing steel
Based on Eurocode 2 the thermal strain εs(θ) of steel could be calculated from the
following equation.
247
εs(θ) = -2,416 × 10-4 + 1,2x10-5 θ + 0,4 × 10-8 θ 2 for 20°C ≤ θ ≤ 750°C
εs(θ) = 11 × 10-3 for 750°C < θ ≤ 860°C
εs(θ) = -6,2 × 10-3 + 2 × 10-5 θ for 860°C < θ ≤ 1200°C
( C-19)
where θ is the steel temperature (°C) and strains are measured with reference to state of
deformation at 20°C.
C.3 FRP
C.3.1.1 Thermal properties
Thermal properties of FRP depend on the type of fibres and matrix material used in its
composition and the volume fraction of the constituents. Material used as matrix
generally has lower thermal conductivity compared to the fibres. For example thermal
conductivity of epoxy is 0.346 W/m-°C compared to 50~130 W/m-°C in the case of
Carbon fibres (PK Mallick 1993). This cause directional dependency of thermal
properties in FRPs. Specifically in the case of unidirectional FRPs thermal conductivity is
high in the direction of the fibres which the conductivity in transverse directions is
lower. In transverse directions the defining factor is the thermal conductivity of the
matrix rather than fibres.
248
C.3.1.2 Mechanical properties
Coefficient of thermal expansion of some common FRP composites is reported in
Table C-3 below (Mallik 1988).
Table C-3: Coefficient of thermal expansion for FRPs, Ahmad (2010).
Material Coefficient of Thermal Expansion W/m-°C
Longitudinal Transverse
Glass-Epoxy 6.3 19.8
Aramid-Epoxy -3.6 54
High Modulus Carbon-Epoxy -0.09 27
Ultra-high Modulus Carbon-Epoxy -1.44 30.6
C.4 Insulation
C.4.1.1 Sikacrete 213F
Sikacrete 213F is a cement-based, dry mix fire protection mortar for wet sprayed
application. It contains phyllosilicate aggregates, which could effectively resist the heat
of hydrocarbon fires. The manufacturer reported thermal conductivity for it is
0.23W/mK at 10°C. and the compressive strength of the insulation is approximately 2.0
MPa. In order to determine the specific heat and thermal conductivity of the insulation
the 50 mm by 50mm by 15mm samples of insulation was prepared during the
installation. Later when the moisture content of the samples was stabilized they were
249
tested in Thermal Conductivity Meter (Kyoto Electronics Model TC-31). Using a non-
steady (transient) state measurement technique.
After averaging the results appropriate curves were fitted following equations is the
result of this procedure.
The thermal conductivity of Sikacrete 213F could be approximated using the following
equation.
𝑘𝑐(𝑇) = 0.46 � 𝑇1000
�2− 0.21 � 𝑇
1000�+ 0.32 ( C-20)
And the equation for specific heat of Sikacrete213F is
𝑐𝑐(𝑇) = 14.96 � 𝑇100
�2− 116.4 � 𝑇
100�+ 1611 ( C-21)
Density was calculated to 700kg/m3.
C.4.1.2 Other Insulation materials
C.4.1.3 Tyfo® Vermiculite-Gypsum (VG) Insulation
This insulation product is manufactured by Tyfo®. (Bisby 2003) reported the following
equations for thermal properties based on Thermogravimetric Analysis (TGA) in
addition to material property estimates from litraturte. Tyfo® VG insulation consists of
two components gypsum and vermiculite. Assuming a mixture ratio of 2:1 of
vermiculite and gypsum, Bisby (2003) obtained the following relationships for specific
heat (J/kg-ºC) and temperature (ºC).
250
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
39167.0:690
31663663690
9167.06976.16976.1:690663
31610610663
8509.06976.18509.0:663610
31153153610
8509.00136.10136.1:610153
31137137153
0136.13722.13722.1:153137
31125125137
3722.19066.69066.6:137125
317878125
3058.19066.63058.1:12578
312002078
1763.13058.11763.1:7820
31763.1:200
EcT
ETcT
ETcT
ETcT
ETcT
ETcT
ETcT
ETcT
EcT
VGVG
VGVGVG
VGVGVG
VGVGVG
VGVGVG
VGVGVG
VGVGVG
VGVGVG
VGVG
=≤
⋅
−⋅
−−
−=≤≤
⋅
−⋅
−−
+=≤≤
⋅
−⋅
−−
−=≤≤
⋅
−⋅
−−
−=≤≤
⋅
−⋅
−−
−=≤≤
⋅
−⋅
−−
+=≤≤
⋅
−⋅
−−
+=≤≤
=≤≤
( C-22)
Using a similar method thermal conductivity (W/m-ºC) with temperature was derived
assuming that the thermal conductivity of vermiculite is constant with temperature.
( ) ( )
( ) ( )
( ) ( )8008001000
1224.02087.01224.0:800
400400800
0726.01224.00726.0:800400
0726.0:400101
100100101
0726.01158.01158.0:101100
1158.0:1000
−⋅−−
+=≤
−⋅−−
+=≤≤
=≤≤
−⋅−−
−=≤≤
=≤≤
VGVGVG
VGVGVG
VGVG
VGVGVG
VGVG
TkT
TkT
kT
TkT
kT
( C-23)
And finally for density the following equations could be used.
251
( ) ( )
287:200
100100200287351351:200100
351:1000
=≤
−⋅−−
−=≤≤
=≤≤
VGVG
VGVGVG
VGVG
T
TT
T
ρ
ρ
ρ
( C-24)
C.4.1.4 Promat-H and Promatect-L
Promat H and Promat L are medium and light density calcium silicate boards with a
density at 20 °C of 870 kg/m3 and 500 kg/m3 respectively, (Blontrock, Taerwe et al. 2000).
Thermal conductivity of Promat H as function of temperature (T) is as follows
𝑘𝑝𝑟,𝐻(𝑊/𝑚℃) = 0.196− 0.207 ∙ 10−2 � 𝑇100
�+ 0.131 ∙ 10−2 � 𝑇100
�2 ( C-25)
And for the specific heat this equation could be used.
𝑐𝑝𝑟,𝐻(𝐽/𝑘𝑔℃) = 561 − 101.1 � 𝑇100
�+ 22.4 � 𝑇100
�2
+ 2.5 � 𝑇100
�3( C-26)
Thermal conductivity of Promat L as function of temperature (T) is as follows
𝑘𝑝𝑟,𝐿(𝑊/𝑚℃) = 0.0804− 0.589 ∙ 10−3 � 𝑇100
�+ 1.541 ∙ 10−3 � 𝑇100
�2( C-27)
And for the specific heat this equation could be used.
𝑐𝑝𝑟,𝐿 �𝐽𝑘𝑔℃� = 561 − 101.1 � 𝑇
100� + 22.4 � 𝑇
100�2
+ 2.5 � 𝑇100
�3( C-28)
252
253
Recommended