STRATEGIES FOR ENHANCING THE FIRE RESISTANCE OF STEEL FRAMED
STRUCTURES THROUGH COMPOSITE CONSTRUCTION
By
Rustin Fike

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Civil Engineering
2010

ABSTRACT
STRATEGIES FOR ENHANCING THE FIRE RESISTANCE OF STEEL FRAMED
STRUCTURES THROUGH COMPOSITE CONSTRUCTION
BY
Rustin Fike
Steel framed structures often utilize concrete due to several advantages composite construction
offers over other types of construction. The composite action that develops between steel and
concrete significantly enhances structural performance under ambient and fire conditions.
However, the beneficial effects of composite action are not often taken into consideration in
evaluating the fire response of structures due to poor understanding on the behavior of composite
structural systems, and lack of design methodologies for evaluating fire resistance. With the aim
of developing an understanding on the behavior of composite structural systems under fire
exposure, both experimental and numerical studies were carried out as part of this study.
The experimental studies consisted of analyzing the response of four composite beam slab
assemblies under fire exposure. The assemblies consisted of a network of five steel beams, atop
which was cast various types of concrete slabs. The assemblies were tested under design fire
exposure and realistic load levels. In the fire tests, special attention was given to monitor the
development of composite action and tensile membrane behavior under realistic loading and fire
conditions.
Data from the fire resistance tests and the literature were utilized to validate the response of
composite column, beam slab assembly, and full-scale steel framed structural models created in
SAFIR finite element based computer program. The validity of the program is established by
comparing measured temperatures, deflections, and failure modes observed in testing with those

predicted by SAFIR. These validated models were then applied to study the influence that
critical factors have on the fire response of composite structural systems at the element,
assembly, and system levels. In total, more than 2000 numerical simulations were conducted to
quantify the effect of critical parameters on the fire response of steel framed structures. In each
of the simulations, the failure times were evaluated based on strength limit states.
Data generated from the parametric studies was applied to develop design methodologies for
evaluating the fire resistance of concrete filled HSS columns, and composite beam slab
assemblies. The design methodology for concrete filled HSS columns is based on equivalent fire
severity principals, and utilizes the equal area concept to establish equivalency between severity
of a design fire, and that of ASTM E-119 fire exposure for predicting failure of concrete filled
HSS columns under design fire exposure. For beam-slab assemblies, a relationship between
maximum design fire temperature and fire response is utilized to establish a correlation between
fire resistance under standard ASTM E-119 fire exposure and under design fire exposure. The
validity of the proposed methods is established by comparing the predictions from these methods
with results from SAFIR analysis.
To further demonstrate the validity of the proposed methodologies, fire resistance calculations
have been carried out for a typical eight story steel framed office building, and compared with
SAFIR predictions. The building was analyzed under various fire scenarios and structural
configurations to illustrate the improvements in fire resistance achieved through composite
construction. Initially, with unprotected steel members, failure occurred in less than 20 minutes
in the structure, after incorporating concrete filled HSS columns and SFRC beam-slab
assemblies, fire resistance was enhanced to such an extent that fire protection can be eliminated
from columns and secondary beams while still providing the required level of fire resistance.

ACKNOWLEDGMENT

I would like to express my gratitude to my advisor, Prof. Venkatesh Kodur for his continued
support and guidance during the course of my studies. I would also like to thank Prof. Ronald
Harichandran, Prof. Rigoberto Burgueño, and Prof. Indrek Wichman for joining my Ph.D.
committee, and for their valuable advice throughout my education at MSU.
For his support, not just in graduate school, but in my life as well, I am thankful to my father Dr.
Randall Fike. I am also thankful for the friends who have accompanied me on this journey,
especially: Dr. Alicia Findora, Dr. Gilbert Baladi, Nick Brake, and Tyler Dawson.
For her continued support, love, and encouragement, I am thankful to my fiancée Ashleigh
Brewer.
I would like to thank the lab manager, Mr. Siavosh Ravanbakhsh for his support and help during
the experimental program in this research.
Obviously, I would like to extend my thanks to Laura Taylor, Mary Mroz, and Margaret Conner
for all the help they provided.
I would like to thank Aqeel Ahmad, Megan Vivian, Nickolas Hatinger, Nikhil Raut,
Purushutham Pakala, Wasim Khaliq, Mahmud Dwaikat, Monther Dwaikat, Jim Stein, and Emily
Wellman for their support, particularly in the experimental part of this study.
Additionally, I would like to thank all the faculty members and students at the Civil and
Environmental Engineering department at Michigan State University for their help and support
during my Ph.D. study.
Finally, I would like to thank my Lord for the abilities, opportunities, and people he has given
me to accomplish all that I have in life, and for life itself.

iv

TABLE OF CONTENTS
List of Tables ................................................................................................................................. ix
List of Figures ................................................................................................................................ xi
Chapter 1......................................................................................................................................... 1
1
Introduction............................................................................................................................. 1
1.1
General............................................................................................................................ 1
1.2
Behavior of Steel Structures Under Fire Conditions ...................................................... 3
1.3
Methods of Achieving Fire Resistance ........................................................................... 6
1.4
Fire Resistance Evaluation.............................................................................................. 8
1.5
Research Objectives...................................................................................................... 12
1.6
Scope............................................................................................................................. 13
Chapter 2....................................................................................................................................... 14
2
State-of-the-Art Review........................................................................................................ 14
2.1
General.......................................................................................................................... 14
2.2
Fire Incidents ................................................................................................................ 14
2.3
Previous Experimental and Numerical Studies............................................................. 17
2.3.1
Composite Construction........................................................................................ 17
2.3.2
System-Level Structural Response ....................................................................... 28
2.4
Realistic Design Parameters ......................................................................................... 33
2.5
Fire Resistance Evaluation Methods............................................................................. 35
2.5.1
Equal Area Concept .............................................................................................. 35
2.5.2
Maximum Temperature Concept .......................................................................... 37
2.5.3
Minimum Load Capacity Concept........................................................................ 38
2.5.4
Time-Equivalent Formula..................................................................................... 39
2.5.5
Summary............................................................................................................... 39
2.6
High-Temperature Material Properties ......................................................................... 39
2.6.1
Thermal Properties – Steel.................................................................................... 40
2.6.2
Thermal Properties – Concrete ............................................................................. 42
2.6.3
Mechanical Properties – Steel............................................................................... 43
2.6.4
Mechanical Properties – Concrete ........................................................................ 50
2.6.5
Deformation Properties – Steel............................................................................. 52
2.6.6
Deformation Properties – Concrete ...................................................................... 53
2.6.7
High Temperature Properties of Insulation........................................................... 54
2.7
Knowledge Gaps........................................................................................................... 55
Chapter 3....................................................................................................................................... 57
3
Experimental Studies ............................................................................................................ 57
3.1
General.......................................................................................................................... 57
3.2
Element Level – CFHSS Columns ............................................................................... 57
3.2.1
Dimensions ........................................................................................................... 58
3.2.2
Materials ............................................................................................................... 59
v

3.2.3
Fabrication ............................................................................................................ 60
3.2.4
Instrumentation ..................................................................................................... 61
3.2.5
Test Conditions ..................................................................................................... 62
3.2.6
Measured Data ...................................................................................................... 62
3.2.7
Data for Model Calibration................................................................................... 64
3.3
Assembly Level – Composite Floor System................................................................. 65
3.3.1
Test Specimens ..................................................................................................... 65
3.3.2
Instrumentation ..................................................................................................... 69
3.3.3
Test Equipment ..................................................................................................... 72
3.3.4
Test Specimen Installation.................................................................................... 75
3.3.5
Test Conditions ..................................................................................................... 76
3.3.6
Test Results........................................................................................................... 78
3.3.7
Summary............................................................................................................. 111
3.4
System Level – Full-Scale Building ........................................................................... 112
3.5
Summary..................................................................................................................... 116
Chapter 4..................................................................................................................................... 118
4
Numerical Model ................................................................................................................ 118
4.1
General........................................................................................................................ 118
4.2
Analysis Procedure ..................................................................................................... 118
4.2.1
Development of Fire Scenarios........................................................................... 119
4.2.2
Thermal Analysis ................................................................................................ 120
4.2.3
Structural Analysis.............................................................................................. 123
4.3
Program Features ........................................................................................................ 124
4.3.1
General................................................................................................................ 125
4.3.2
Thermal Input...................................................................................................... 126
4.3.3
Structural Input ................................................................................................... 127
4.3.4
Material Models in SAFIR.................................................................................. 128
4.3.5
Modifications to SAFIR...................................................................................... 128
4.4
Validation of SAFIR Computer Program ................................................................... 133
4.4.1
Element Level – CFHSS Columns ..................................................................... 133
4.4.2
Assembly Level – SFRC Floor Slab................................................................... 140
4.4.3
System Level-Steel Framed Building ................................................................. 146
4.5
Summary..................................................................................................................... 152
Chapter 5..................................................................................................................................... 153
5
Parametric Studies .............................................................................................................. 153
5.1
General........................................................................................................................ 153
5.2
Element Level – CFHSS Columns ............................................................................. 153
5.2.1
Column Characteristics....................................................................................... 154
5.2.2
Critical Factors.................................................................................................... 156
5.2.3
Analysis Procedure ............................................................................................. 158
5.2.4
Results and Discussion ....................................................................................... 158
5.2.5
Summary............................................................................................................. 167
5.3
Assembly Level – Composite Floor Assemblies ........................................................ 168
5.3.1
Assembly Characteristics.................................................................................... 168
vi

5.3.2
Critical Factors.................................................................................................... 170
5.3.3
Analysis Procedure ............................................................................................. 172
5.3.4
Results and Discussion ....................................................................................... 172
5.3.5
Summary............................................................................................................. 179
5.4
System Level – Steel Framed Structural Systems ...................................................... 180
5.4.1
System Characteristics ........................................................................................ 180
5.4.2
Critical Factors.................................................................................................... 182
5.4.3
Analysis Procedure ............................................................................................. 183
5.4.4
Results and Discussion ....................................................................................... 183
5.4.5
Summary............................................................................................................. 185
5.5
Summary..................................................................................................................... 185
Chapter 6..................................................................................................................................... 187
6
Development of Design Approach...................................................................................... 187
6.1
General........................................................................................................................ 187
6.2
Design Methodology for CFHSS Columns ................................................................ 187
6.2.1
Factors Governing Fire Resistance of CFHSS Columns .................................... 188
6.2.2
Development of an Approach for Evaluating Fire Resistance............................ 189
6.2.3
Validation of the Proposed Approach................................................................. 193
6.2.4
Illustration of the proposed approach ................................................................. 197
6.2.5
Application and Limitations ............................................................................... 199
6.3
Design Methodology for Composite Beam-Slab Assemblies .................................... 200
6.3.1
Factors Affecting the Fire Resistance of Composite Floor Assemblies ............. 201
6.3.2
Development of Tensile Membrane Action in SFRC Slabs ............................... 201
6.3.3
Development of an Approach for Evaluating Fire Resistance............................ 206
6.3.4
Development of Design Methodology................................................................ 212
6.3.5
Illustration of the Proposed Approach ................................................................ 218
6.3.6
Application and Limitations ............................................................................... 220
6.4
Methodology for System Level Evaluation of Fire Resistance .................................. 221
6.5
Summary..................................................................................................................... 222
Chapter 7..................................................................................................................................... 223
7
Implementation of Design Methodologies.......................................................................... 223
7.1
General........................................................................................................................ 223
7.2
Performance-Based Fire Resistance Design ............................................................... 223
7.2.1
Development of Fire Scenario ............................................................................ 224
7.2.2
Development of Design Parameters and Loading .............................................. 225
7.2.3
Conducting Thermal and Structural Analysis..................................................... 225
7.2.4
Development of Practical Alternatives ............................................................... 226
7.2.5
Use of Performance-Based Design Methodology............................................... 226
7.3
System Level Fire Resistance Evaluation................................................................... 227
7.3.1
Building Description........................................................................................... 228
7.3.2
Numerical Model ................................................................................................ 230
7.3.3
Discretization ...................................................................................................... 230
7.3.4
Model Validation ................................................................................................ 235
7.3.5
ParametricSstudy ................................................................................................ 236
vii

7.4

Summary..................................................................................................................... 246

Chapter 8..................................................................................................................................... 248
8
Conclusions and Recommendations ................................................................................... 248
8.1
General........................................................................................................................ 248
8.2
Key Findings............................................................................................................... 249
8.3
Recommendations for Future Research ...................................................................... 251
8.4
Research Impact.......................................................................................................... 253
Appendix A................................................................................................................................. 256
E-mail Permission for Use of Copyrighted Cardington Figures............................................. 256
Appendix B ................................................................................................................................. 257
High Temperature Material Relationships.............................................................................. 257
Appendix C ................................................................................................................................. 270
SAFIR Thermal Input File ...................................................................................................... 270
Appendix D................................................................................................................................. 272
SAFIR Structural Input File.................................................................................................... 272
Appendix E ................................................................................................................................. 274
CFHSS Column Design Example........................................................................................... 274
Appendix F.................................................................................................................................. 277
SFRC Floor Design Example.................................................................................................. 277
References................................................................................................................................... 282

viii

LIST OF TABLES
Table 3.1: Sample mix proportions for concrete used in CFHSS columns (Lie and Chabot 1992,
Lie and Kodur 1994)...................................................................................................... 59
Table 3.1 (Continued): Sample mix proportions for concrete used in CFHSS columns (Lie and
Chabot 1992, Lie and Kodur 1994) ............................................................................... 60
Table 3.2: Summary of test parameters and fire resistance values for selected CFHSS columns
tested at NRCC .............................................................................................................. 64
Table 3.3: Details of tested beam slab assemblies........................................................................ 66
Table 3.4: Properties of fire insulation ......................................................................................... 68
Table 3.5: Mix proportions used in the tested composite beam-slab assembly............................ 68
Table 4.1: Characteristics of CFHSS columns used for validation of SAFIR............................ 136
Table 4.2: Assumed thermal and mechanical properties ............................................................ 136
Table 4.3: Mechanical properties utilized in steel beam-SFRC slab analysis simulations......... 144
Table 4.4: Thermal and mechanical properties assumed in simulations .................................... 149
Table 5.1: Thermal and mechanical properties assumed in simulations .................................... 155
Table 5.2: Mechanical properties utilized in analysis simulations ............................................. 169
Table 5.3: Thermal and mechanical properties assumed in simulations .................................... 182
Table 6.1: Fire resistance equivalency as predicted by SAFIR and the proposed approach ...... 196
Table 6.2: Load capacity of strip floors considered in numerical simulations ........................... 212
Table 7.1: Various structural configurations and fire scenarios simulated in the building ........ 235
Table B.1: High temperature constitutive relationships for concrete ......................................... 257
Table B.1 (Continued): High temperature constitutive relationships for concrete ..................... 258

ix

Table B.1 (Continued): High temperature constitutive relationships for concrete ..................... 258
Table B.1 (Continued): High temperature constitutive relationships for concrete ..................... 259
Table B.1 (Continued): High temperature constitutive relationships for concrete ..................... 260
Table B.1 (Continued): High temperature constitutive relationships for concrete ..................... 261
Table B.2. Values for the main parameters of the stress-strain relationships for concrete at
elevated temperatures (Eurocode 2004) ...................................................................... 262
Table B.3. Strength reduction factors for SFRC as a function of temperature........................... 263
Table B.4: High temperature constitutive relationships of structural steel................................. 264
Table B.4 (Continued): High temperature constitutive relationships of structural steel ............ 265
Table B.4 (Continued): High temperature constitutive relationships of structural steel ............ 266
Table B.4 (Continued): High temperature constitutive relationships of structural steel ............ 267
Table B.4 (Continued): High temperature constitutive relationships of structural steel ............ 268
Table B.4 (Continued): High temperature constitutive relationships of structural steel ............ 269

x

LIST OF FIGURES
Fig. 1.1: Variation of strength and elastic modulus of steel with temperature ............................... 4
Fig. 1.2: Progression of failure in a steel beam under conventional and fire loading scenarios..... 5
Fig. 1.3: Time-temperature relationships for different fire scenarios ........................................... 10
Fig. 1.4: Conventional and improved structural configuration for evaluating fire resistance ...... 11
Fig. 2.1: Illustration of construction and fire behaviour of CFHSS columns under standard fire
exposure ......................................................................................................................... 19
Fig. 2.1 (Continued): Illustration of construction and fire behaviour of CFHSS columns under
standard fire exposure .................................................................................................... 20
Fig. 2.2: Illustration of construction and tensile membrane action in a composite beam slab
assembly......................................................................................................................... 24
Fig. 2.2 (Continued): Illustration of construction and tensile membrane action in a composite
beam slab assembly........................................................................................................ 25
Fig. 2.3: Post fire pictures from the Cardington tests ................................................................... 31
Fig. 2.4: Illustration of equal area concept for equivalent fire severity........................................ 36
Fig. 2.5: Illustration of maximum temperature concept for equivalent fire severity.................... 37
Fig. 2.6: Illustration of minimum load capacity concept for equivalent fire severity .................. 38
Fig. 2.7: Thermal conductivity of steel as predicted by different models and as measured in
different test programs ................................................................................................... 41
Fig. 2.8: Specific heat of steel as predicted by different models and as measured in different tests
........................................................................................................................................ 41
Fig. 2.9: Thermal conductivity of concrete as a function of temperature..................................... 42
Fig. 2.10: Specific heat of concrete as a function of temperature................................................. 44

xi

Fig. 2.11: Yield strength of steel as predicted by different models and as measured in different
tests ................................................................................................................................ 46
Fig. 2.12: Elastic modulus of steel as predicted by different models and as measured in different
tests ................................................................................................................................ 46
Figs. 2.13a and 2.13b: Temperature-stress-strain relationships for structural steel as per ASCE,
Eurocode and Poh models.............................................................................................. 48
Fig. 2.14: Definition of yield point and proportionality limit in ASCE, EC3, and Poh 2001 ...... 50
Fig. 2.15 Compressive strength of concrete as a function of temperature.................................... 51
Fig. 2.16: Strain at peak stress reduction factor as a function of temperature for concrete.......... 52
Fig. 2.17: Thermal strain of steel as predicted by different models and as measured in different
tests ................................................................................................................................ 53
Fig. 2.18: Coefficient of thermal expansion for concrete as a function of temperature ............... 54
Fig. 3.1: Illustration of RC, FC, and PC square and round column cross-sections tested at NRCC
........................................................................................................................................ 58
Fig. 3.2: Schematic of thermocouple tree used in testing at NRCC ............................................. 61
Fig. 3.3: Thermal response recorded during fire test at NRCC for CFHSS column RP-168 ....... 63
Fig. 3.4: Axial deformation recorded during fire test at NRCC for CFHSS column RP-168 ...... 63
Fig. 3.5: Configuration of beams in the tested assembly.............................................................. 66
Fig. 3.6: Details of deck and shear studs in beam-slab assembly................................................. 66
Fig. 3.7: Fire protection on the girder just after application ......................................................... 67
Fig. 3.8: Instrumentation scheme used in testing of the beam-slab assembly (mm) .................... 69
Fig. 3.8 (Continued): Instrumentation scheme used in testing of the beam-slab assembly (mm) 70
Fig. 3.8 (Continued): Instrumentation scheme used in testing of the beam-slab assembly (mm) 71

xii

Fig. 3.9: View of MSU structural fire testing facility................................................................... 73
Fig. 3.10: Layout of burners and observation ports in fire test furnace........................................ 73
Fig. 3.11: Actuator locations in the furnace.................................................................................. 74
Fig. 3.12: Procedure used for placing of the beam-slab assembly atop the testing furnace ......... 76
Fig. 3.13: Schematic of loading on the beam slab assembly (mm) .............................................. 77
Fig. 3.14: Time temperature curve used in fire resistance test ..................................................... 78
Fig. 3.15: Steam coming out of longitudinal crack in slab. .......................................................... 79
Fig. 3.16: Failure of load splitter during testing of assembly PC-1.............................................. 80
Fig. 3.17: Longitudinal crack at 90 minutes into fire resistance test ............................................ 80
Fig. 3.18: Punching shear accompanying failure of the central beam in PC-2............................. 81
Fig. 3.19: Punching shear accompanying failure of the central beam in PC-3............................. 81
Fig. 3.20: Post fire deflected shape of the beam-slab assembly ................................................... 82
Fig. 3.21: Cracking pattern on the top of the tested plain concrete assemblies after exposure to
fire .................................................................................................................................. 83
Fig. 3.22: Post fire condition of central beam in PC-2 ................................................................. 84
Fig. 3.23: Post fire condition of connection bolts......................................................................... 85
Fig. 3.24: Temperatures in the one hour protected (W12X16) beam with fire exposure time..... 87
Fig. 3.25: Temperatures in the unprotected beam as a function of fire exposure time................. 88
Fig. 3.26: Temperatures at various depths of the lightweight slab as a function of fire exposure
time ................................................................................................................................ 89
Fig. 3.27: Center point deflections recorded during testing for assemblies made with plain
concrete .......................................................................................................................... 91

xiii

Fig. 3.28: Lifting of unsupported edge from the furnace and separation from the deck .............. 93
Fig. 3.29: Crack formation next to W12X16 section.................................................................... 93
Fig. 3.30: Discontinuous curvature along slab edge ..................................................................... 94
Fig. 3.31: Cracking pattern on the top of the tested SFRC beam slab assembly after exposure to
fire .................................................................................................................................. 95
Fig. 3.32: Post fire condition of central unprotected beam........................................................... 96
Fig. 3.33: Post fire condition of fin plate connection ................................................................... 96
Fig. 3.34: Temperatures in the protected (W12X16) beam with fire exposure time .................... 99
Fig. 3.35: Temperatures in the unprotected beam as a function of fire exposure time............... 100
Fig. 3.36: Temperatures at various depths of the slab as a function of fire exposure time ........ 101
Fig. 3.37: Strains at central strain gages (76 mm offset) as a function of fire exposure time .... 103
Fig. 3.38: Strains observed at the middle of the slab as a function of fire exposure time. ......... 105
Fig. 3.39: Strains recorded at the edge of the slab (305 mm inset) as a function of fire exposure
time .............................................................................................................................. 106
Fig. 3.40: Deflection time history in a beam slab assembly exposed to fire .............................. 108
Fig. 3.41: Fin plate connections used in Cardington building .................................................... 112
Fig. 3.42: Furnace constructed around the composite beam for restrained beam test ................ 113
Fig. 3.43: Time temperature relationship achieved during the Cardington restrained beam test
and ISO 834 fire exposure for comparison .................................................................. 114
Fig. 3.44: Measured mid-span deflections for the restrained beam ............................................ 115
Fig. 3.45: Local buckling of beam ends in restrained beam test................................................. 115
Fig. 3.46: Fractured fin plate connections in restrained beam after cooling phase of fire.......... 115

xiv

Fig. 4.1: Schematic of SAFIR operational procedure (Franssen et. al 2000) ............................. 126
Fig. 4.2: Compressive strength of PC and SFRC as a function of temperature.......................... 130
Fig. 4.3: Stress-strain relationships for plain and SFRC concrete at various temperatures........ 131
Fig. 4.4: Tensile strength of PC and SFRC as a function of temperature................................... 132
Fig. 4.5: CFHSS column cross section and elevation discretization in SAFIR.......................... 134
Fig. 4.6: Typical RC, FC, and PC square and round column cross-sections used for validation of
SAFIR .......................................................................................................................... 135
Fig. 4.7: Comparison of predicted temperatures from SAFIR with test data for Column SP-178
...................................................................................................................................... 138
Fig. 4.8: Comparison of predicted axial deformations from SAFIR with test data for Column SP178................................................................................................................................ 139
Fig. 4.9: Comparison of predicted (SAFIR) and measured fire resistance times ....................... 140
Fig. 4.10: Discretization of the tested steel beam-SFRC slab assembly for SAFIR analysis..... 142
Fig. 4.11: Comparison of predicted and measured deflections at the center of the slab and at the
center of the beam in the fire exposed beam slab assembly ........................................ 145
Fig. 4.12: Model of the steel framed Cardington steel framed building used for numerical studies
...................................................................................................................................... 147
Fig. 4.13: Idealization of substructure modeled from the Cardington steel framed building for fire
resistance analysis........................................................................................................ 148
Fig. 4.14: Comparison of measured and predicted temperatures in the steel beam.................... 150
Fig. 4.15: Comparison of measured and predicted mid-span deflections for the beam.............. 151
Fig. 5.1: Elevation and cross-section of RC, FC, and PC filled HSS columns used in parametric
studies .......................................................................................................................... 154
Fig. 5.2: Discretization of CFHSS columns for SAFIR analysis................................................ 155

xv

Fig. 5.3: Time-temperature relationships for various fire scenarios ........................................... 157
Fig. 5.4: Fire resistance as a function of length for column (RP-273) under different fire
scenarios....................................................................................................................... 160
Fig. 5.5: Steel temperatures for column RP-273 exposed to different fire scenarios ................. 160
Fig. 5.6: Temperatures at the center of concrete core for column RP-273 exposed to different fire
scenarios....................................................................................................................... 161
Fig. 5.7: Axial deformation of column RP-273 under different fire scenarios........................... 162
Fig. 5.8: Effect of length and concrete filling on fire resistance of CFHSS columns ................ 164
Fig. 5.9: Effect of load ratio on fire resistance of CFHSS columns ........................................... 165
Fig. 5.10: Dicretization of the steel beam-SFRC slab assembly used in parametric studies...... 169
Fig. 5.11: Standard and design fire scenarios used in parametric studies on beam-slab assemblies
...................................................................................................................................... 171
Fig. 5.12: Fire resistance of beam-slab assemblies under various fire exposures ...................... 173
Fig. 5.13: Variation of mid-span (beam) deflection as a function of fire exposure time for
different load levels...................................................................................................... 175
Fig. 5.14: Fire resistance of beam-slab assembly as a function of slab thickness ...................... 176
Fig. 5.15: Mid-span deflection in secondary beam as a function of time for PC and SFRC slabs
...................................................................................................................................... 178
Fig. 5.16: Elevation and plan view of the simulated steel framed building (used in Cardington
tests) ............................................................................................................................. 181
Fig. 5.17: Discritazation of the steel framed building (used in Cardington tests) for use in
parametric studies ........................................................................................................ 181
Fig. 5.18: Standard and design fire exposures considered for system ........................................ 182
Fig. 5.19: Mid-span deflection of slab-beam assembly for various fire exposures .................... 185

xvi

Fig. 6.1: Range of fire exposures considered in the development of a design methodology for
CFHSS columns........................................................................................................... 189
Fig. 6.2: Illustration of proposed approach for a CFHSS column .............................................. 192
Fig. 6.3: Graphical illustration of the effectiveness of the proposed approach .......................... 194
Fig. 6.4: Comparison of standard and design fire exposure ....................................................... 198
Fig. 6.5: Illustration of forces developed in a beam-slab assembly under fire exposure............ 202
Fig. 6.5 (Continued): Illustration of forces developed in a beam-slab assembly under fire
exposure ....................................................................................................................... 203
Fig. 6.6: Load carrying capacity and deflection as a function of fire exposure time for a SFRC
floor assembly.............................................................................................................. 208
Fig. 6.7: Discretization of beam elements used in the parametric study for evaluating the
response of composite SFRC floor slabs exposed to fire ............................................ 210
Fig. 6.8: Design (real) fires considered in parametric study on composite beam slab assembly 211
Fig. 6.9: Load capacity of strip floor able to achieve two hour fire resistance rating under ASTM
E-119 fire exposure...................................................................................................... 213
Fig. 6.10: Comparison of failure load of slab as predicted by SAFIR and the proposed equation
(6.14)............................................................................................................................ 216
Fig. 6.11: SAFIR and equation predictions for additional data set............................................. 217
Fig. 6.12: Comparison of standard and design fire exposure ..................................................... 219
Fig. 7.1: Framing plan for the steel framed building used to illustrate application of the
developed methodologies............................................................................................. 229
Fig. 7.2: One story numerical model of selected building.......................................................... 231
Fig. 7.3: Three story numerical model of selected building ....................................................... 232
Fig. 7.4: Possible fire scenarios used in the fire resistance analysis........................................... 234

xvii

Fig. 7.5: Deflected shape under service loads and ambient temperature (125x) ........................ 236
Fig. 7.6: Variation of central column axial deflection with time corresponding to for Case 1
analysis......................................................................................................................... 237
Fig. 7.7: Secondary beam mid-span deflection with time corresponding to Case 2 analysis..... 238
Fig. 7.8: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 3 analysis ................................................................................. 239
Fig. 7.9: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 4 analysis ................................................................................. 241
Fig. 7.10: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 6 analysis ................................................................................. 242
Fig. 7.11: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 8 analysis ................................................................................. 243
Fig. 7.12: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 9 analysis ................................................................................. 244
Fig. 7.13: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 10 analysis ............................................................................... 246
Fig. F.1: Load capacity of strip floor to achieve two hour fire resistance rating under ASTM E119 fire exposure.......................................................................................................... 278
Fig. F.2: Load capacity of strip floor to achieve two hour fire resistance rating under ASTM E119 fire exposure.......................................................................................................... 279

xviii

CHAPTER 1
1
1.1

INTRODUCTION
General

Fire represents one of the most severe environmental conditions to which structures may be
subjected, and hence, the provision of appropriate fire safety measures for structural members is
an important aspect in the design of high-rise buildings. Steel is often used as the primary
structural material in high-rise buildings, and these steel structural members have to satisfy
appropriate fire resistance requirements prescribed in building codes.

Unprotected steel

members exhibit a fire resistance of about 20-25 minutes, and hence, have to be provided with
some level of fire protection to enhance their fire resistance level to 1 to 4 hours as stipulated in
building codes.

This is generally achieved by providing external fire insulation to steel

members. Such fire proofing measures, which are based on prescriptive provisions, add to the
cost of construction and do not permit the feasibility of having exposed steel in buildings. Also,
durability (adhesion and cohesion) of fire insulation is often an unreliable issue, and hence
requires periodic inspection and regular maintenance. This, in turn, incurs additional cost during
the lifetime of the structure (FEMA 2002, NIST 2004).
The amount of fire proofing (insulation) to structural members is usually determined by testing
single structural elements such as beams, columns, etc., under standard fire conditions. This
traditional approach of evaluating fire resistance based on element level tests is overly
conservative and may not be realistic, since a number of factors such as composite action,
moment redistribution, member interactions, restraint conditions, and load intensity cannot be
accounted for in single element behavior. Further, compartment characteristics and location, as

1

well as realistic fire scenarios, which influence the behavior and eventual failure of a structure,
are not taken into consideration.
In recent years, there is a growing recognition that structural performance under fire conditions
should be based on realistic fire, restraint, and loading conditions. It is widely believed that a
structural system performs better under actual design (realistic) scenarios, and this might lead to
reduced (or eliminated) fire protection requirements. In fact, there is significant evidence that
shows steel framed structures in high-rise office buildings have historically survived major fires
extremely well, for example, the First Interstate Bank Building Fire in Los Angeles in 1988
(FEMA 1990), and the One Meridian Plaza fire in Philadelphia in 1991 (FEMA 1994). The
large scale fire tests carried out on a steel framed building (British Steel 1998) further confirm
the fact that the fire performance of a whole structure, under design fire scenarios, is much better
than that of individual members under standard fire scenarios.
In addition, fire statistics have shown that the risk to life in office buildings is very low and
rarely do fires develop into the post flashover stage where the stability of the building is
threatened.

Further, in the event of fire, fire safety measures such as fire detection, fire

suppression, smoke management, occupant evacuation, and brigade fire fighting provide many
levels of defense. However, in the current practice of evaluating fire resistance, based on
standard fire tests, none of the above factors are fully taken into consideration. Thus, the current
prescriptive approaches have not only major drawbacks, but also do not permit an engineering
approach to evaluate realistic fire safety in steel structures. The development of engineering
approaches is critical for undertaking rational fire design in a performance-based environment.

2

1.2

Behavior of Steel Structures Under Fire Conditions

Steel, similar to other building materials, loses its strength and stiffness with an increase in
temperature. The rate of loss of strength is faster in steel as compared to concrete. Further, the
high thermal conductivity of steel results in faster heat transmission through the member crosssection. To overcome this, steel has traditionally been provided with external fire insulation to
limit the temperature rise in the steel section. Fig. 1.1 illustrates the variation of normalized
(with respect to ambient temperature properties) strength and elastic modulus of steel as a
function of temperature (SFPE 2005). Of particular significance in Fig. 1.1, is the observation
that the normalized yield strength and elastic modulus drop to about 50% at 550 °C, this has a
considerable impact on the fire resistance of steel structures.
Under fire conditions, the loading on a structure does not significantly change, but, the capacity
(strength) of the member decreases with time of fire exposure due to increasing temperatures in
steel. This decrease in strength continues until the time at which the capacity of the member is
below the applied load, at which point the member fails. This type of response is contrary to
what happens under other conventional loading conditions wherein failure is due to progressive
increase in loading.
Fig. 1.2 illustrates the development of failure in a simply supported steel beam (protected with
fire insulation) exposed to loading under conventional loading conditions, and under fire
exposure conditions. In the conventional loading case, the simply supported beam is subjected to
increasing load levels as encountered in earthquake or wind loads, while in the second case the
beam is exposed to fire and the load level remains constant. In both cases, the beam initially has
an ultimate moment capacity of 400 kip-ft. Under service loads, the applied moment on the
beam is only 200 kip-ft, which is well below the ultimate moment capacity (400 kip-ft.).

3

However, as the applied load increases, the moment demand on the beam increases until failure
occurs.
1
0.9
Reduction Factor

0.8
0.7
0.6
0.5
0.4
0.3

Yield Strength

0.2

Elastic Modulus

0.1
0
0

200

400

600

800

1000

Temperature

Fig. 1.1: Variation of strength and elastic modulus of steel with temperature
For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation
Likewise, in the case of fire exposure, the load under service conditions, just prior to fire
exposure produces a moment of 200 kip-ft. However, as the time of fire exposure increases, the
load level remains the same (200 kip-ft), but the moment capacity decreases due to softening of
steel with an increase in temperatures (Fig. 1.1). As an illustration, in about 20 minutes the
moment capacity decreases to about 350 kip-ft., while at 40 minutes it goes down to about 300
kip-ft. Finally, at 60 minutes, the capacity reaches 200 kip-ft. and failure occurs in the beam.
In both cases, the deflection increases either with increasing load or under fire exposure until
failure of the beam. In the case of increasing load, failure occurs when the applied load exceeds
the capacity of the beam, however, in the case of fire, failure occurs when the capacity of the

4

beam (at the critical section) drops below the applied load (moment). The duration of time from
the initiation of fire exposure until the capacity of the section drops below the applied load
(moment) is termed as the fire resistance of the member. The decrease in moment capacity and
increase in deflection of a structural member under fire conditions are primarily dependent on the
temperature rise in steel. By limiting the fire induced temperature rise in steel, it is possible to
delay the failure of a structural member.

Ambient conditions

Fire conditions
40 K/ft
30 K/ft
20 K/ft

Beam under ambient conditions
400 k.ft

20 K/ft

Beam under fire conditions

400 K.ft
300 K.ft
200 K.ft

0 min
(400 k.ft)

20 min
(350 k.ft)

40 min
(300 k.ft)
60 min
(200 k.ft)
200 K.ft

Moment (red)-capacity (black)
with load

Moment (red)-capacity (black) with
fire exposure time

200 K.ft

0 min
20 min

300 K.ft

40 min

400 K.ft

60 min

Load deflection profile

Time deflection profile

Fig. 1.2: Progression of failure in a steel beam under conventional and fire loading scenarios
This case of a simply supported beam illustrated the propagation of failure for a very simplistic
case. In actual buildings, the performance of a structural member is quite complex and is
5

dependent on a number of factors such as type of fire exposure, continuity, restraint, composite
action, and system characteristics.
1.3

Methods of Achieving Fire Resistance

Unprotected steel structural members when exposed to fire exhibit a fire resistance on the order
of 20-25 minutes. However, in medium to high-rise office buildings, structural members are
required to have fire resistance on the order of 1-3 hours. Thus, steel structural members are
typically provided with some form of fire protection to achieve the required fire resistance.
There are three methods through which fire resistance requirements can be achieved, namely;
applying external protection, providing capacitive protection, or composite construction.
The principle behind external fire protection is to limit heat transmission from fire to the steel
section. This is accomplished through the application of layers of insulation between steel and
probable fire exposure zones. This is often achieved through spray applied fire protection or
intumescent paints.

Spray applied fire protection consists primarily of vermiculite and

cementations materials. Layers of insulation on the order of 0.5-2 inches thickness are required
to achieve a fire resistance of 1-3 hours for most structural members.

The low thermal

conductivity of these insulating materials limits the temperature rise in steel for the required
length of time.
Intumescent paints can also be applied in much thinner layers, and have the appearance of paint
at ambient temperatures. When exposed to elevated temperatures, intumescent paint undergoes
an endothermic carbonation reaction that results in the production of an inert gas (often CO2)
that does not burn, but is retained in the paint layer causing it to “foam” to a much thicker layer
(FEMA 2003). This expanded foam layer has a low thermal conductivity that serves to insulate

6

the structural member after the endothermic reaction has ended, thus limiting the temperature
rise in the steel.
Both of these methods of protecting the steel sections with external insulation have severe
limitations. They add to construction costs and time, reduce usable space, require inspection
(adding additional operation cost), and have problems with adhesion and cohesion
characteristics. Adhesion of these materials was found to be poor during fire tests, and some
specimens delaminated while they were being placed in the testing frame (Sorathia et al. 2003,
FEMA 2002).
As an alternative to external protection, capacitive protection can be used to enhance the fire
resistance of steel structural members. Capacitive methods that have been employed include
filling hollow structural section (HSS) columns with concrete or water. Capacitive protection
limits the temperature rise in steel by absorbing heat from the steel. Since heat is constantly
transferred from the steel to the capacitive material, the temperature in the steel remains low for
a considerable length of time. Though water has been employed in a few cases, due to the
inherent problems of using liquid to increase heat capacity, concrete is preferred in most
situations. The main advantage of concrete is that it can be utilized to carry a portion of the load
at ambient conditions (as composite construction) thus economizing the design (Kodur and Fike
2009a,b).
In lieu of external insulation or capacitive protection, the inherent fire resistance present in steel
structural systems can effectively be utilized to satisfy the required fire resistance ratings. Such
inherent fire resistance exists in all structures, and can be significant in the case of composite
steel-concrete structural systems. In these systems, inherent fire resistance is facilitated by
structural interactions between various connected structural members, composite action, tensile

7

membrane action, and redistribution of forces from fire weakened members to other cooler parts
of the structure. Composite construction is generally accounted for in the ambient temperature
strength design of the members, but is often neglected in evaluating fire response. When
composite action between steel and concrete is accounted for with realistic fire exposures (with a
decay phase to limit the temperature rise in structural members), application of realistic failure
limit states, and load level, it may be possible to achieve the required fire resistance in some
situations without the need for additional fire protection measures (Kodur and Fike 2008, Ponto
2006, Lamont and Lane 2006).
Elimination of external fire protection measures decreases construction time, reduces
construction cost, increases usable space, and provides a more reliable fire resistance
mechanism. While detailed fire resistance analysis may be required to demonstrate inherent fire
resistance, the benefits on the construction side more than offset the additional design effort.
1.4

Fire Resistance Evaluation

The fire resistance of structural members is currently evaluated through standard fire resistance
tests. In these tests, a structural member is exposed to a standard fire in a specially built fire
furnace for a specified fire duration. The fire conditions and procedures used in the fire test are
governed by specifications in applicable standards such as ASTM E-119 (ASTM 2007), and
internationally ISO 834 (ISO 1975). There are a number of limitations that result from these
standard fire tests. The most restrictive limitations are:


The use of a one-size fits all prescriptive standard fire exposure that is often more severe
than commonly experienced by structural members in buildings. In the standard fire
exposure, the fire temperature increases throughout the duration of the fire exposure and

8

there is no decay phase, despite the fact that most building fires die down after a certain
length of time due to a lack of either fuel or air.


Structural elements are tested as individual components (columns or beams) and the
beneficial effects such as redistribution of moments, and composite action, which occur
through interconnected structural members are neglected.



Failure is often defined by a limiting critical temperature in steel, and thus does not
capture the actual failure under strength or deflection limit states.

Hindered by these limitations, the current practice of evaluating fire resistance through
prescriptive based approaches does not lead to rational assessment of structural performance
under realistic fire, loading, and restraint conditions.

To overcome these limitations, it is

necessary to implement a performance-based methodology for evaluating fire resistance.
Performance-based fire resistance evaluation takes into account realistic (probable) fire scenario,
loading, restraint, and boundary conditions of the structural system. Determination of realistic
fire exposure is accomplished by taking into account the compartment fuel load and ventilation
characteristics, as well as other details, such as the presence of sprinklers, on the fire growth and
development. Several methods can be employed to determine the probabilistic (design) fire
exposure.

Eurocode and SFPE provide simplified approaches for determining the time

temperature relationship under design fire exposure (Eurocode 2005a, SFPE 2005). Fig. 1.3
shows time-temperature plots for a mild and severe design fire determined according to SFPE,
and the current ASTM E-119 standard fire. The temperatures in the standard fire exposure
increase throughout the fire duration as seen in Fig. 1.3. Both of the design fires however have
temperatures that initially increase, which subsequently start to decay. This is because initially
the fire is fueled by the contents of the compartment, and is supported by the ventilation (air)

9

present in the compartment. As fire progresses, either the contents of the compartment are fully
consumed, or the ventilation is insufficient to support combustion, and the fire dies down (often
referred to as burnout). As such, while the temperatures in the initial part of a design fire may be
more severe than the standard fire (as seen in Fig. 1.3), the decay phase of fire allows the
structural elements to cool down and enhance the fire resistance. Under design fires, it is
possible for structural elements to survive complete compartment burnout.
1200

Temperature (°C)

1000
800
600
400
Standard

200

Mild
Severe

0
0

40

80

120

160

200

240

Time (min)

Fig. 1.3: Time-temperature relationships for different fire scenarios
In recent years, most high-rise buildings have been equipped with automatic fire suppression
systems (sprinklers). The current method of assessing fire resistance through standard fire
exposures makes no provision for the contribution of these suppression systems. The effect of
sprinklers can be accounted for through modified time-temperature relationships. Given the
ability of design fires to account for automatic suppression systems, and the actual characteristics
of the compartment in which the structural member is located, it is necessary to consider design
fires for realistic assessment of fire resistance.
10

In addition to fire exposure, a number of other factors also influence the fire performance of
structural systems. These include restraint effects, redistribution of forces, member interactions,
and steel-concrete composite action. Many of these effects can be accounted for in the fire
resistance analysis by applying a system-level approach (rather than an element-level approach).
Fig. 1.4 illustrates the conventional method of assessing fire resistance based on the response of
single elements. Note that no consideration is given to the effect of the members surrounding the
fire exposed element or the presence of composite construction. Also shown in Fig. 1.4 is the
system-level approach wherein the effect of connectivity between members, composite action,
realistic loads, realistic fires, and realistic failure criterion can be taken into consideration.

Conventional element approach

Improved system-level approach

Fig. 1.4: Conventional and improved structural configuration for evaluating fire
resistance

By applying a system based approach, composite construction and member interactions in the
structural system can be utilized, and in some cases, it may be possible to achieve the required
fire resistance without the need for additional external fire insulation.

11

1.5

Research Objectives

Recently there is a growing recognition that fire resistance assessment should be based on overall structural behavior under realistic fire and loading scenarios. A number of studies have been
undertaken in this direction. There is, however, no framework for fully utilizing the inherent fire
resistance exhibited by steel structural systems. Specifically, the beneficial effects of composite
action in beam-slab assemblies and in columns are overlooked. This research is aimed at
developing a better understanding of the inherent fire resistance present in steel framed
structures. The main objective is to develop methodologies for utilizing inherent fire resistance
in steel structural systems. To accomplish this, the following specific research objectives were
developed.


Conduct a detailed state-of-the-art review on the fire response of steel and composite
structures. This review will cover experimental and numerical work that has been done,
high temperature material properties, and code provisions pertaining to the fire response
of steel and composite structures.



Conduct an experimental investigation to assess the beneficial effects of composite action
in steel beam-concrete slab assemblies. For this, four test assemblies will be constructed,
three with traditional lightweight concrete and one with SFRC concrete. The objective is
to assess the relative response of the assemblies under fire exposure and to maximize the
effect of tensile membrane action.



Develop numerical models and conduct parametric studies to investigate the effect a
variety of parameters have on the fire resistance of steel framed structures.



Develop simplified design methodologies for evaluating the fire response of concretefilled HSS columns and composite floor assemblies.

12



Conduct a series of case studies to verify the feasibility of unprotected steel in framed
buildings under realistic fire, restraint, composite action, and failure criterion.

1.6

Scope

This dissertation is organized into 8 chapters as follows:


Chapter 1: Provides an introduction to fire resistance, fire performance, and fire design as
it applies to steel and composite structures.



Chapter 2: Reviews the state-of-the-art on the fire response of steel and composite
structures at the element, assembly, and system level. Additionally, high temperature
material properties and fire provisions in current codes and standards are also reviewed.



Chapter 3: Presents the fire resistance experiment on four beam slab assemblies and the
previous work on concrete filled HSS columns.



Chapter 4: Addresses the need for a comprehensive computational program for
parametric studies, and provides an overview of the computational program SAFIR.
Following the overview of SAFIR, element, assembly, and system level models are
validated against test data.



Chapter 5: Presents the results (factors affecting fire resistance) from a series of
parametric studies at the element, assembly, and system levels.



Chapter 6: Overviews the development of simplified design methodologies based on the
factors influencing fire resistance, and shows the methodologies to be effective through a
series of numerical examples.



Chapter 7: Presents an overview of performance-based design followed by a system-level
case study to illustrate the use of the developed methodologies.



Chapter 8: Summarizes conclusions and recommendations for future work.
13

CHAPTER 2
2

STATE-OF-THE-ART REVIEW

2.1

General

Since the 1990’s there has been a growing recognition that the current approach of evaluating
fire resistance based on standard fire tests has a number of drawbacks. Further, observations
from a number of accidental fires pointed to the fact that steel structural systems possess higher
inherent fire resistance under realistic fire, loading, and restraint scenarios.

A number of

experimental and numerical studies have been undertaken to demonstrate the inherent fire
resistance present in steel structural systems. Many of these studies focused on illustrating
enhanced fire resistance through system-level analysis of steel framed structural systems. A
critical review of these studies is presented in this section. Based on the review, the knowledge
gaps in the area relating to fire performance of composite steel framed structures are identified.
2.2

Fire Incidents

A review of accidental fire incidents in Europe, Australia, and North America, clearly indicate
that steel framed structures exhibit higher fire resistance than typically observed in standard fire
tests on singe structural elements. This section presents a summary of the most notable fire
incidents. A comprehensive review of these fires is presented elsewhere (Wang and Kodur 2000,
Nwosu and Kodur 1999)


th

A fire broke out on the 12

story of the First Interstate Bank building in Los Angeles,
th

California, late in the evening on May 4 1988 and burned for over three hours. By the
time it was extinguished, the fire had burned out almost five stories of the building. Over

14

half a million gallons of water were used to extinguish the blaze (FEMA 1990).
However, the building withstood complete compartment burnout of almost five stories
without structural collapse, thus indicating that buildings in actual (real) fire incidents
exhibit higher fire resistance than that based on standard fire tests on single elements. It
should be noted that the structural elements in the building were designed to have a fire
resistance between 1 and 3 hours.


On the evening of June 3

rd

1990, a major fire broke out in a construction contractors hut

located on the first floor of the partly completed 14-story Broadgate building in London,
UK. The building was equipped with sprinklers, but since the building was still under
construction, the sprinklers were not operational after workers left for the day.
Additionally, much of the structural fire protection was not yet applied to the building,
thus, the unprotected steel framing was directly exposed to fire. The fire burned for a
total of 4.5 hours with temperatures estimated to be in excess of 1000 °C for two of those
hours. There was some contraction in columns and large deflections were observed in
the beams, however, the structure did not collapse, thus reinforcing the hypothesis that
steel framed structural systems possess higher fire resistance than individual elements
tested in a furnace. The total damage to the building was ₤25 million, that associated
with the repairs to the structural frame were approximately ₤2 million, and repairs took
only 30 days to complete (Newman et al. 2006).


In another incident, a major accidental fire started on the 22

nd

floor of the 38 story steel
rd

framed One Meridian Plaza building (Philadelphia, Pa) on the evening of Feb. 23 ,
1991. The structural elements were designed to have fire resistance ratings on the order

15

of 1-3 hours depending on the element. When fire fighters arrived, the fire was
completely developed on the 22

nd

st

floor and was spreading to the 21 floor. Due to early

loss of electrical power and failure of emergency generators, fire fighting efforts were
seriously hindered. By the end, the fire had burned for 19 hours consuming 8 stories of
the building. Again, despite the severity and duration of the fire, no structural collapse
was observed, reinforcing that steel framed buildings possess higher fire resistance under
realistic conditions (loading, fire, and restraint) than that exhibited by a single element
tested in a standard test furnace. The total direct cost of fire was $100 million, litigation
related to the reusability of the structure continued for years and cost more than the
damage to the actual building (FEMA 1994).
The above real fire incidents clearly demonstrate that steel framed structural systems exhibit
higher inherent fire resistance than that observed in standard fire resistance tests. The fire
resistance of the overall structural frame can be much greater that that of individual structural
members and depends on a number of parameters. Characteristics inherent to the structure such
as composite construction and member interactions appreciably enhance fire resistance when
considered under realistic fire exposure, loading and failure criterion. However, these beneficial
effects are seldom considered in current design approaches due to the complexity of the analyses,
and the lack of a well defined framework for fire resistance assessment.
In order to define this framework for fire resistance assessment, the following section presents
the previous experimental and numerical studies on the response of steel composite structures
under fire exposure.

Subsequent sections present realistic factors to be considered in fire

resistance assessment, fire correlation methodologies, and material properties for steel, concrete,
and insulation respectively.

16

2.3

Previous Experimental and Numerical Studies

The above real fire incidents have stimulated researchers to develop an understanding of the
overall response of steel framed structures exposed to fire. The objective of most of the studies
was to illustrate the enhanced fire resistance achieved through two categories, namely, steelconcrete composite action and system-level structural response. A review of the research studies
on composite construction (namely CFHSS columns and beam slab assemblies) under fire
exposure is presented first, followed by the state-of-the-art with respect to system-level structural
response of composite steel frames under fire exposure.
2.3.1

Composite Construction

As illustrated in Chapter 1, composite construction consisting of steel and concrete can
significantly enhance the fire resistance of structural systems. This higher fire resistance is
mainly derived from the good fire resistance properties of concrete as well as the high mass of
concrete. The beneficial concrete properties include lower thermal conductivity, higher heat
capacity, and slower degradation of strength and stiffness with temperature. Generally, the
composite construction in steel framed buildings is in the form of composite columns or steel
beam-concrete slab assemblies. Of these, concrete filled HSS columns offer numerous benefits
(construction speed and economy) over other forms of composite columns and thus are widely
used in low-rise buildings. Steel beam-concrete slab assemblies are commonly used due their
efficiency as floor systems in steel framed buildings. These floor systems also have the added
benefit of significantly enhancing fire resistance. A review of previous studies on the fire
performance of composite construction (CFHSS columns and composite beam assemblies) is
presented in the following sections.

17

CFHSS Columns
Alternate approaches for achieving fire resistance in columns have been studied for the last three
decades. Methods such as filling HSS columns with water and concrete are among the most
popular approaches studied by researchers (Kodur and Lie, 1995a, Bond, 1975, Klingsch and
Wittnecker, 1988). However, the use of concrete-filling is the most attractive and feasible
proposition developed thus far.
Fire resistance tests on CFHSS columns were predominantly carried out at the National Research
Council of Canada (NRCC), a few organizations in Europe, and more recently in China. The
experimental program at NRCC consisted of fire tests on about 80 full-scale CFHSS columns
(Kodur and Lie, 1995a,b, Lie and Chabot 1992, Lie and Caron, 1988, Lie and Irwin, 1991). Both
square and circular HSS columns were tested with three types of concrete filling, namely, plain
(PC), bar reinforced (RC), and steel fiber reinforced (FC). The influence of various factors
including type of concrete filling, concrete strength, type and intensity of loading, and column
size were investigated under the ASTM E-119 (2007) standard fire exposure. The tests reported
by European and Chinese studies (Klingsch and Wittbecker 1988, and Grandjean et al., 1981) are
similar to NRCC tests, but the fire exposure was that of the ISO 834 (1975) standard fire; which
has a time-temperature curve similar to that of ASTM E-119 (2007).
Data reported from NRCC tests and numerical studies can be used to illustrate the typical
behavior, as well as beneficial effects, of concrete-filled HSS columns under standard fire
conditions. Fig. 2.1a shows a schematic of a typical CFHSS columns, while Fig. 2.1b shows the
axial deformation as a function of fire exposure time for three typical HSS columns filled with
plain concrete (PC), steel fiber reinforced concrete (FC) and bar reinforced concrete (RC)
respectively (Kodur and Lie, 1995b). The three columns were of similar size and were subjected

18

to similar load levels, hence, the results presented in Fig. 2.1b can be used to illustrate the
comparative behavior of the three types of concrete filling.
At ambient conditions, the applied load on a composite (CFHSS) column is carried by both the
concrete and the steel. When the CFHSS column is exposed to fire, steel carries most of the load
during the early stages of fire since the steel section expands more rapidly than the concrete core.
As time progresses and temperatures increase, the steel section gradually yields due to loss of
strength at elevated temperatures, and the expansion phase gives way to a contraction phase in
about 20 minutes into fire exposure. At this stage, concrete starts to carry an increased portion of
the load. As fire progresses, the strength of concrete also deteriorates to a level where the
column strength is less than the applied load, and at this point failure of the column occurs. The
elapsed time from ignition to failure is termed the fire resistance of the column.

Concrete

Slab

Steel Pipe

(a): Schematic of a typical CFHSS column
Fig. 2.1: Illustration of construction and fire behaviour of CFHSS columns under standard fire
exposure

19

30
FC-Filling

Axial Deformation (mm)

20
10
0
-10
-20

PC-Filling

-30
-40
-50

RC-Filling
0

50

100

150

200

Time (min)
(b): Behaviour of a typical HSS column with different types of concrete filling
Fig. 2.1 (Continued): Illustration of construction and fire behaviour of CFHSS columns under
standard fire exposure
Based on the experimental and numerical studies reported in literature (Kodur and Lie 1996,
Kodur and Lie 1997, Lie and Stringer 1994), it was found that the parameters with the most
influence on fire resistance of CFHSS columns are: type of concrete filling (plain, barreinforced, and fiber-reinforced), outside diameter or width of the column, applied load, effective
length of the column, concrete strength, and type of aggregate. Using these influencing factors
as the basis, the following unified design equation was developed to calculate the fire resistance
of circular and square HSS columns filled with any of the three types of concrete (Lie and
Stringer 1994, Kodur 1999, Kodur and MacKinnon 2000).
'
(fC  20)
D
Rf
D2
(KL  1000)
C

20

[2.1]

where: R = fire resistance in minutes, f’c= specified 28-day concrete strength in MPa, D =
outside diameter or width of the column in mm, C = applied load in kN, K = effective length
factor, L = unsupported length of the column in mm, f = a parameter to account for the type of
concrete filling (PC, RC, and FC), the type of aggregate used (carbonate or siliceous) in
concrete, the percentage of reinforcement, the thickness of concrete cover, and the crosssectional shape of the HSS column (circular or square), values of which can be found in
reference (Kodur and Lie 1996).
The design equation and research presented above, though representing a significant
advancement in the understanding of CFHSS columns exposed to fire, have a number of
limitations. The most restrictive of these limitations are:


No consideration was given to design (realistic) fire exposure



Full range of length and cross sections, as encountered in real applications, were not
investigated due to limitations in furnace dimensions



System-level response of structural systems including 2

nd

order effects was not

considered due to complexities in the analysis
These limitations do not facilitate the use of CFHSS columns in applications such as airports,
schools, atriums, and hotels, where exposed steel is highly desired. Thus, in order to utilize
inherent fire resistance of steel framed structures (and realize unprotected steel), it is necessary to
study the response of full-scale CFHSS columns exposed to realistic design scenarios in a
system-level environment.
The fire test data, numerical models, and resulting design equation available in literature
represent a considerable contribution to the understanding of the performance of CFHSS
columns under fire exposure. While forming a good basis for comparison of column fire
21

resistance, the exclusive use of standard fire exposure in the fire resistance assessment precludes
determination of the actual failure time of a CFHSS column exposed to real fires. Standard fire
exposure does not take into account the compartment characteristics such as ventilation or fuel
supply, and thus presents a monotonically increasing time temperature relationship without a
decay phase, thus representing an unrealistic and overly conservative fire condition.

It is

therefore necessary to develop an understanding on the response of CFHSS columns to design
fire exposure, and to develop a simplified fire resistance design methodology for CFHSS
columns.
Composite Beam-Slab Assemblies
Composite construction in the form of CFHSS columns has been shown to clearly enhance fire
resistance over that of unprotected steel columns. In a similar fashion, composite floor systems
have been shown to have a higher fire resistance than steel beams considered individually. The
beneficial effect of composite floor systems was clearly seen in the Cardington tests (as
discussed in the next section), as well as in the performance of various buildings under fire
accidents. Following the Cardington tests, a number of researches have attempted to develop
models to account for composite action in steel framed structures. Finite element packages that
have been employed include ABAQUS (Gillie, et al. 2001a,b Gillie et al. 2002), VULCAN
(Huang et al. 2000, Huang et al. 2001, Huang et al. 2003a,b), SAFIR (Moss and Clifton 2004)
and ADAPTIC (Elghazouli and Izzuddin 2000, Elghazouli and Izzuddin 2001). In an effort to
focus on the beneficial effects of composite floors, researchers have also conducted small-scale
tests to simulate the behavior of concrete slabs under fire (Lim et al. 2004, Bailey et al. 2000).
Data from the reported tests can be used to illustrate the behavior of beam-slab assemblies
exposed to fire (Kodur and Fike 2009). A typical detail of a composite steel beam-concrete slab

22

assembly is show in Fig. 2.2a. The tensile membrane action observed in such an assembly under
fire conditions is illustrated in Fig. 2.2b, where the response of the assembly is pictorially shown
at various fire exposure times. Prior to fire exposure, the beam slab assembly resists bending
wherein the steel beam takes predominantly tensile forces and the concrete takes compressive
forces, (see the case of “T = 1” in Fig. 2.2b). Under fire exposure, the temperature of the steel
beam gradually increases leading to loss of strength and stiffness. As the steel gets progressively
weaker, the composite assembly begins to undergo large deflections (case of “T = 30” in Fig.
2.2b). This deterioration of strength/stiffness properties of steel and concrete continues with
time and at about 64 minutes the slab has undergone large deflections and the steel beam is
providing very little strength to the composite assembly. Due to the large deflections at this
stage, the reinforcement within the concrete (shrinkage steel) if properly anchored, acts as a
cable and transfers load through a mechanism called tensile membrane action (TMA). This
serves to transfer the load from the fire weakened portion of a structure to the cooler surrounding
parts as illustrated in Fig. 2.2b in the “T=64” row. The perimeter of the slab is in compression
while tensile forces develop in the central heated region as illustrated in Fig. 2.2c. This load
transfer mechanism delays the failure of the assembly and thus enhances the fire resistance of a
composite beam slab assembly. Under design (realistic) fire conditions TMA can be quite
beneficial, and might lead to the beam slab assembly surviving burnout conditions.
Following the Cardington test program, many researchers explored developing a full
understanding of TMA under fire conditions. Bailey (Bailey et al. 2000) postulated that under
fire exposure, the ribbed steel deck on the bottom of a concrete slab offered no structural
contribution. This postulate was based on the observation that the ribbed steel deck rapidly
achieved temperatures exceeding 900 °C in fire, thus causing the ribbed steel deck to have

23

Shear
Stud

Concrete
Slab

Welded Wire
Fabric

Steel
Deck
Embossments
Steel
Beam
(a): Schematic of composite steel beam-concrete slab assembly
Deflected Shape

Membrane Forces

T = 1 min.

T = 30 min.

T = 64 min.
(end)

(b): Deflected shape and force distribution in the slab resulting from TMA
Fig. 2.2: Illustration of construction and tensile membrane action in a composite beam slab
assembly

24

(c): Compressive and tensile zones in TMA
Fig. 2.2 (Continued): Illustration of construction and tensile membrane action in a composite
beam slab assembly
minimal strength (Bailey et al. 2000). To further investigate the failure mechanism of the slab
without the ribbed steel deck, Bailey et al. (2000) cast a concrete slab on a ribbed steel deck, then
removed the deck from the bottom of the slab. This slab was then loaded to failure at ambient
temperature to determine the probable failure patterns that might result under fire conditions.
Based on these experimental studies, Bailey extended the work of Hayes (1968) and developed a
simplified numerical approach to determine the load (moment) capacity of the slab under fire
loading. Utilizing the results from Bailey’s studies, the Building Research Establishment (BRE)
in U.K. has developed guidelines and a simple calculation method to determine the load carrying
capacity of slabs experiencing TMA during fire exposure. Implicit assumptions to the method
developed by BRE are that the reinforcing mesh in the concrete floor slab is fractured over
protected steel members, and that membrane action is based on a lower bound yield line pattern.
Specifics of the methodology are given in references (Bailey and Moore 2000a,b).
Recently Zhang and Li (2008) proposed a calculation method based on first principles for
estimating the load carrying capacity of slabs under fire conditions. In this approach, the slab
was considered to consist of 5 zones: an elliptical center, and four rigid parts around the edge.

25

Through the use of moment equilibrium, a series of equations were developed to determine the
ultimate load carrying capacity of the slab exposed to fire. The explicit assumptions in the
method are that the slab is rectangular with an aspect ratio less than 2, the supporting beams
below the slab are protected with insulation and are strong enough to support the load from the
slab under fire conditions, the slab is vertically restrained around the perimeter with no
horizontal restraint, and that the reinforcement in the slab is continuous and arranged in two
orthogonal directions.

Validation of this numerical method showed that there was good

agreement between the predictions from this method and test data. (Zhang and Li 2008)
An experimental study on the ultimate failure of reinforced concrete slabs in fire was conducted
by Cashell et al. (2008). In this study, the failure of a slab via rupture of the reinforcement was
investigated. The tests were based on the assumption that the concrete floor slab behaves as a
lightly reinforced beam under fire conditions. This is mainly due to the high temperatures
attained in the ribbed metal deck under fire exposure. The quick rise in temperature is believed
to eliminate the structural contribution of the ribbed metal deck, thus the concrete floor slab is
postulated to act as a lightly reinforced concrete beam supported by the reinforcing steel in the
slab. Preliminary analysis and modeling of the tested slabs has been used to show the correlation
between specific parameters used in modeling and the ultimate deflection of the slab at failure.
Based on these studies, and subsequent numerical simulations, the authors concluded that the
stress-strain curves of steel, and bond slip characteristics between steel and concrete assumed in
modeling, have a significant influence on fire resistance of concrete slabs as determined by
computational models.
Lim et al. (2004) studied the response of slabs to fire through experimental and numerical
studies. The fire experiments consisted of three reinforced concrete slabs of 3.3 by 4.3 meters

26

and 90, 100, and 130 mm in thickness respectively. Data from these tests was then utilized to
validate the shell element subroutine recently introduced in SAFIR (Talamona 2005). The
validation process indicated that SAFIR is able to track the deflections and predict the locations
of the tensile and compressive zones in the slab with good accuracy. The results from fire tests
and the SAFIR analysis showed that the simply supported concrete slab contributes to the overall
fire resistance of steel structures.
While the above studies offer considerable insight into the behavior and response of steel framed
structures under fire exposure, there are still a considerable number of limitations to the state of
the art. In Bailey’s studies, the assumed ultimate defections (at failure) in this method are
notably less than those observed in the Cardington tests, and do not take into account the
beneficial beam-slab interactions. The method developed by Zhang and Li (2008) assumed that
the perimeter beams were sufficiently large to support the increased loads from the deflecting
slab, but additionally assumed that the slab had no horizontal restraint. This is unlikely to occur
in reality that a beam will have high vertical restraint with little lateral restraint. In addition, this
study only considered the standard fire exposure and omitted the effects of the beam-slab
interactions.

Tests conducted by Cashell et al. (2008) have two primary limitations, the

assumption that two-way bending in a slab can be characterized as two orthogonal strips with a
shared deflection point in the middle, and the fire exposure used in the fire test and numerical
studies was the standard fire exposure.
The tests conducted by Wellman et al. (2010) offer considerable insight into the response of
composite construction made with lightweight concrete under fire exposure. From these tests, it
is observed that there is a benefit to composite construction, though lightweight concrete with
shrinkage reinforcing does not provide sufficient strength to enhance the fire resistance of the

27

assembly to the levels required in codes and standards. As such, from these tests it can be
concluded that there is a clear need for the development of material systems that can enhance fire
resistance though composite construction.
Additional information on the response of composite construction to fire exposure can be gained
from the experimental and numerical studies which have been carried out on composite steel
structures at the system level. A review of this work is presented in the following section.
2.3.2

System-Level Structural Response

Numerous fire resistance tests on isolated members or small assemblies have been conducted in
the past 30 to 40 years, however, there have been only few tests on full-scale steel structures.
There have been a total of eight significant experimental studies on full-scale structures exposed
to fire since 1976 (Wald et. al), of these, three of them were conducted to assess non-structural
aspects, (Pettersson 1976, Latham et al. 1987, and Thomas et al. 1992) while the remaining five
were conducted to assess the structural response of the frame during fire exposure (Witteveen et
al. 1977, Rubert and Schaumann 1986, Cooke and Latham 1987, Genes 1982, and British Steel
1998). Due to the current research interest in specifically the structural response under fire
exposure, no information on the non-structural tests will be presented here, for those details the
interested reader is directed to the literature (Pettersson 1976, Latham et al. 1987, and Thomas et
al. 1992).
The first tests to consider the structural response of structures under fire exposure were
conducted by Witteveen et al. (1977). In these testes, the stability of both braced and un-braced
frames were assessed under fire exposure.

It was found that the temperature distribution

achieved in columns in standard fire tests as stipulated in ASTM E-119 are not realistic. In these
tests, columns are place in a furnace where the ends are not exposed to fire, and hence,

28

experience much cooler temperatures. This adds stability to the column and causes much higher
failure temperatures to be observed than would be if the entire column were exposed to fire. It
was determined that failure temperatures could be over predicted by as much as 100 °C in the
standard fire resistance test.
To assess the failure temperature of steel frames, Rubert and Schaumann (1986) constructed a
series of three quarter scale steel frames, loaded them, and exposed them to elevated
temperatures using electric heaters. One of the primary observations from these tests is that due
to the heating of only the steel frame, it was necessary to provide considerable restraint against
torsional failure. The only appreciable data reported from these test was the failure temperatures,
no information was provided on either strains or displacements. These testes serve as the
benchmark used to check many finite element models.
Cooke and Latham (1987) tested a steel frame consisting of two columns and a steel beam under
fire exposure. The connections between the steel beam and the column were made with shear
tab connections. Atop the steel beam, a concrete slab was cast on a composite steel deck. To
avoid any contribution from composite action, a ceramic blanket was placed between the beam
and the slab to isolate the behavior of the beam. The fire exposure was provided by the
combustion of wood cribs beneath the assembly. Despite the provision of shear connections,
significant hogging moments developed in the beam due to the fire exposure. It was however
observed that the unprotected steel beam withstood the effect of fire for an ASTM E-119
equivalency of 32 minutes, significantly more than observed in single element tests.
To assess the ability of lightly protected steel beams to resist fire exposure without a loss of
stability, Genes (1982) tested two stories of a larger 28 story building under fire exposure. It was
observed that indeed the lightly protected members can provide some level of fire resistance

29

without loss of structural stability though little additional information is available regarding the
tests.
The most notable experimental studies on the fire response of full-scale steel framed buildings
were conducted by the Building Research Establishment in the U.K. in collaboration with British
Steel (British Steel 1998). For these studies, an eight story steel frame building was constructed
within an aircraft hanger located in Cardington, U.K. This building was designed in accordance
with BS 5950 (British Steel 1998) and represented a typical office building as constructed in
London. Eight fire tests were conducted in the building and a detailed description of each of
these tests is provided in the testing report published by British Steel (1998). A brief summary
of the most relevant tests to the current research is presented below.
Four of these fire tests have direct implications to the research here presented, namely the
“restrained beam” test, “plane frame” test, “corner” test, and “demonstration” test. The first two
tests focused on a specific feature of the structure, (a restrained beam and plane frame
respectively) and the behavior of that member when exposed to standard fire as provided by a
furnace. The latter two fire tests simulated realistic fire exposure in a compartment of a steel
famed building fueled by the combustion of compartment contents.
Since the objective of these fire tests was to exploit the inherent fire resistance of a steel framed
building, all of the structural members, with the exception of columns, were left unprotected. In
the plane frame test, the columns were only insulated up to about 300 mm below the connection.
This un-insulated portion of the column became too hot during the fire test and underwent local
failure (buckling with significant deformation), though no global failure occurred as can be seen
in Fig. 2.3a. From this observation, it was concluded that in the rest of the tests, the columns
were to be protected over their entire length.

30

The duration of the fire exposures simulated in the fire tests was dependent on the fuel source.
Fires lasting 2.5 to 3 hours were simulated when furnaces were used. When combustion of
compartment contents fueled the fires, they were allowed to reach burnout conditions in the fire
compartment. In all of the tests, significant deflections in the beams were observed. Despite the
large deflections that occurred in all of the fires, no global failure (full collapse) occurred (British
Steel 1998) as seen in Fig. 2.3, all figures from Cardington tests are reprinted with permission as
indicated in Appendix A.

a) Column contraction in plane frame test

b) End buckling of beam in corner test

c) Large beam deflection observed during

d) Connection deformation resulting from

demonstration test

restrained beam test

Fig. 2.3: Post fire pictures from the Cardington tests
The primary observation from these tests was that the composite steel beam concrete slab
assemblies demonstrated considerable fire resistance though none of the beams were protected.
It was postulated that this was in large part due to the contribution of the steel beam-concrete

31

slab interactions and the development of tensile membrane action (TMA) (Bailey and Moore
2000a,b). Also, due to the local failure observed in unprotected columns in the plane frame test,
the importance of protecting columns for overall structural stability during fire exposure was
highlighted.
Following the experiments conducted at Cardington, several researchers focused their attention
on system-level response of steel structural systems through numerical simulations. Initially, this
research was primarily conducted in Europe, and focused on the response of steel framed
structures representing typical European construction practices (Gillie et al. 2001a,b, Lamont and
Lane 2006, Cameron 2003). While this work has aided in understanding the failure mechanisms
of steel framed buildings exposed to fire, the use of primarily European construction practices
necessitates similar, independent, investigations utilizing North American construction practices.
Following the collapse of the World Trade Center buildings, researches have accelerated efforts
to develop an understanding on the fire resistance of steel framed structures. Several research
programs have been undertaken to better understand the response of steel framed structures
exposed to fire (Lew et al. 2005, Usmani 2005, Usmani et al. 2003, Flint et al. 2006, Duthinh
2004, and Flint et al 2007). Though providing considerable insight to the behavior of steel
framed buildings exposed to fire, these studies do not fully account for all of the factors that
contribute to inherent fire resistance making it necessary to conduct additional studies. The
significant findings from these research programs are highlighted below:


Full-scale structures demonstrate higher fire resistance than indicated in standard
(element-level) fire tests



Structural systems perform better under real fires than standard fires, and survive burnout
conditions under most design (real) fires situations

32



Composite construction, specifically steel beam-concrete slab assemblies, significantly
enhances the fire resistance of the entire assembly



Steel columns are critical to structural stability of the building and must be provided with
fire protection to maintain structural integrity during fire exposure.

In addition to the explicit findings from the experiential studies presented in this and the previous
section, these studies can be used to identify the realistic factors that need to be taken into
consideration for a holistic fire resistance assessment.

These factors are discussed in the

following section.
2.4

Realistic Design Parameters

In addition to composite action, a few other factors influence the fire resistance of steel framed
structural systems. The prominent factors include fire scenario, load level, and the limit state
used to evaluate failure.

These parameters, as elaborated upon below, are to be properly

accounted for when evaluating the inherent fire resistance in steel framed structures.


The current practice of evaluating fire resistance of structural members is based mainly
on standard fire tests or empirical calculation methods, in which the member is exposed
to a standard fire as specified in standards such as ASTM E-119 (ASTM 2007) or ISO
834 (ISO 1975). In the standard fire exposure, the fire size is the same (irrespective of
compartment characteristics), and fire temperatures increases with time throughout the
fire duration with no decay phase. However, in realistic fire exposure, the resulting fire
size is a function of compartment characteristics, such as ventilation, fuel load,
compartment size, and lining materials, and there is always a decay phase following the
initial growth phase. As the temperatures in the structural member decrease in the decay
phase of the fire, the materials recover part of their strength and stiffness. This recovery

33

of material strength and stiffness helps to withstand the applied loads on the member and
might be sufficient to overcome the destructive effect of fire.


Load level has a significant influence on the fire resistance of structures. The lower the
load, higher is the fire resistance of a structural member.

In prescriptive based

methodologies, fire resistance is often evaluated based on the maximum design load on a
structural member. In recent years there is a growing recognition that the level of
loading in a building under fire conditions is less than the full service loads. A load level
of 1.2DL + 0.5LL is the recommendation of ASCE 7 (ASCE 2005) while Eurocode
recommends using 1.2DL + 0.4LL (Eurocode 2002). Adoption of realistic load levels
will enable realization of inherent fire resistance in structural members.


In fire resistance evaluation, the limit state applied to determine failure has a significant
influence on the resulting fire resistance of the structural member.

The different

criterion that can be applied to define failure include thermal (barrier), strength
(stability), and integrity limit states. In the current prescriptive based approaches, fire
resistance is often evaluated based on critical temperature attained in the steel. Failure is
said to occur when the critical temperature reaches 538 °C in columns and 593 °C in
beams. The rational for this criterion is that steel looses 50% of its room temperature
strength at about 550 °C, thus, the structural member has 50% of its load capacity
remaining. Since service load levels under fire conditions correspond to about 50% of
the ultimate load, failure is assumed to occur when the steel member reaches 538 °C in
columns and 593 °C in beams (ASTM 2007). While this definition of failure based on
critical temperature is simple and convenient in application since only temperature
measurements (predictions) are required in tests (or analysis), it does not represent

34

realistic failure of a structural member which is a function of load level, restraint, and
other factors.

While this aspect has been partially recognized in Eurocode (Eurocode

2005b), fire resistance in North American standards continue to be based on critical
temperature in the steel.

For realistic assessment of failure, actual strength and

deflection limit states are to be used. This aspect is especially critical in the case of
composite construction (beam-slab assemblies and composite columns) where the
concrete can continue to carry the load well after the steel reaches a predefined critical
temperature. Thus, realistic failure limit states such as strength or deflection criterion
should be applied to realize the inherent fire resistance of a structural member.


Other factors that have a minor to moderate effect on the fire resistance of composite
structural systems include concrete strength, aggregate type in concrete, concrete cover
thickness (to reinforcement), restraint etc. Giving due consideration to these factors will
enable realization of inherent fire resistance in composite structural systems.

2.5

Fire Resistance Evaluation Methods

Fire exposure has been clearly shown to have an influence on the fire resistance of a structure,
there are however an infinite number of fire exposures possible in a given compartment. To
avoid conducting fire resistance experiments under a wide range of fire exposures, several
simplified approaches for establishing equivalent fire resistance based on the ASTM E-119 fire
exposure have been developed. A review of these methods and their applicability to composite
construction is presented in the following sections.
2.5.1

Equal Area Concept

The equal area concept, as the name implies, establishes fire resistance equivalency using the
principle of equivalent fire exposure wherein the area under the standard (ASTM E-119 or ISO
35

834) time temperature curve is compared to the area under the design fire time temperature
curve. In this method, the area under the design fire time temperature curve at the time the
structural member fails is determined (area A1 in Fig. 2.4) (Buchanan 2005). Then, the area
under the standard fire curve is estimated at different time steps. The time at which the area
under the standard fire curve is equal to that under the design fire curve (at the time of structural
member failure) is the equivalent fire resistance of the member under standard fire exposure
(area A2 in Fig. 2.4). This approach has been validated for steel structural members and
reasonable agreement between predicted and measured values has been observed (Buchanan
2005). However, the main limitation of the method is that it is not applicable for design fires that
are either very hot and short, or cold and long as compared to the standard fire (Buchanan 2005).
Thus, the method does not accurately correlate the fire resistance time due to the reliance on the
area under the time-temperature curve. Additionally, the equal area concept has not been
validated for use on composite structural members.
Area under
standard fire
curve A2

Point where A1 = A2

Temperature

Standard fire
exposure

Design fire
exposure

Time

Equivalent
fire severity

Area under
design fire
curve A1

Fig. 2.4: Illustration of equal area concept for equivalent fire severity

36

2.5.2

Maximum Temperature Concept

This method was developed based on the assumption that steel structural members fail when
steel reaches a critical temperature. For steel members the critical temperature is often taken as
550 °C. To use this method, the maximum steel temperature achieved under a given design fire
is determined as shown in Fig. 2.5. The time it takes under standard fire exposure to reach the
maximum temperature observed under the design fire is the equivalent ASTM E-119 fire
severity as illustrated in Fig. 2.5. The limitation to this method is that when the temperatures
reached in the design fire are well above or below those that would cause failure in the section,
the method is not as accurate. Also, this method cannot be directly applied to composite
members, since a limiting temperature in steel does not necessarily indicate failure of the
member due to the composite action between the steel and the concrete.

Standard fire
exposure

Max temperature under
design fire exposure

Steel temperature

Steel
temperature
under standard
fire exposure
Design fire
exposure

Time

Equivalent fire
severity

Steel
temperature
under design
fire exposure

Fig. 2.5: Illustration of maximum temperature concept for equivalent fire severity

37

2.5.3

Minimum Load Capacity Concept

This approach utilizes a strength failure limit state to establish equivalency between a standard
and a design fire exposure. Similar to the maximum temperature concept, the minimum load
capacity concept compares the time that it takes to reach a certain load capacity of the section
under the two fires.

The minimum load capacity of the section under the design fire is

determined as shown in Fig. 2.6. The load capacity under the standard fire exposure is then
determined as shown in Fig. 2.6. The point where the load capacity of the member under the
standard fire is the same as that under design fire exposure is the equivalent fire severity as
illustrated in Fig. 2.6. The limitation to this method is the assumption that load level is about
50% of the room temperature capacity of the member, and it does not take into account the actual
load level on the structural member. Further, the method cannot fully account for the effect of
composite action.

Load Capacity

Standard fire
exposure
Load capacity
under design
fire exposure
Load capacity
under standard
fire exposure

Minimum load capacity
under design fire
exposure

Time

Design fire
exposure
Equivalent
fire severity

Fig. 2.6: Illustration of minimum load capacity concept for equivalent fire severity

38

2.5.4

Time-Equivalent Formula

In addition to the above approaches, several empirical relationships such as the CIB and Law
formulae have been proposed to establish equivalency between standard and design fire
exposures (Buchanan 2005).

Globally, these methods were developed for protected steel

sections. As such, these empirical formulae available in literature are incapable of capturing the
effect of composite construction.
2.5.5

Summary

Due to the need to assess fire resistance under a wide range of fire exposures, several methods to
do so based on standard fire resistance have been developed as presented in the previous
sections. These methods were developed based on single element tests and do not take into
consideration the effect of composite construction.

The insulating functionality, capacitive

protection, and load carry capacity of the concrete in composite construction are not taken into
consideration in these approaches.

As such, these methods are not suitable for use with

composite construction, thus, there is a considerable need for development of methods that can
be used to assess the fire resistance of composite members under realistic fire conditions.
2.6

High-Temperature Material Properties

The response of steel and composite structures is highly dependent on the material models used
for the constituent materials. There are three basic categories of high temperature material
properties that contribute to the response of composite structures, they are: (a) thermal (b)
mechanical and (c) deformation properties. Thermal properties determine the temperature profile
in the steel and concrete sections resulting from fire exposure, while the mechanical properties

39

govern the loss of strength and stiffness as a function of temperature. Deformation properties
determine the extent of deformations of the structural member under fire conditions.
For evaluating realistic fire performance of steel or composite structures, due consideration
should be given to thermal, mechanical, and deformation properties. These properties vary with
temperature and are influenced by the phase changes that occur in steel or concrete at elevated
temperatures. A review of the available constitutive models for high temperature properties of
steel and concrete are presented in the following sections, and the equations presented in both
Eurocode (2004, 2005a) and ASCE (1992) provided in Appendix B.
2.6.1

Thermal Properties – Steel

The main thermal properties that influence the temperature rise in steel are thermal conductivity
and specific heat (often expressed in terms of heat capacity). There is limited test data on the
specific heat and thermal conductivity of steel. Figs. 2.7 and 2.8 show plots of the available data
on thermal conductivity and specific heat of steel as a function of temperature respectively.
Relationships from codes and standards (Eurocode (EC3) 2005a, ASCE 1992), as well as
published test data, were used to compile Figs. 2.7 and 2.8 (Rempe and Knudson 2008, Dale et.
al 2007, Touloukian 1972, Powel and Tye 1960, and Yawata 1969).
It can be seen from Fig. 2.7 that thermal conductivity decrease with temperature in an almost
linear fashion, and there is little variation between the models presented in ASCE manual and
Eurocode. On the contrary, published specific heat models vary considerably above 700 °C, as is
seen in Fig. 2.8. In general, the specific heat of steel increases with an increase in temperature
with a large spike occurring around 750 °C. The increase in specific heat with temperature is due
to individual atoms in steel moving farther apart, thus achieving a higher energy state. The spike
in the specific heat at around 750 °C is due to the phase change that occurs in steel in which the

40

Thermal Conductivity, W/m.˚C

60
50
40
30

Rempe & Knudson 2008
Dale & Prasad 2007
Touloukain 1972
Yawata 1969
Powel 1956
EC3 model
ASCE model

20
10
0
0

200

400
600
Temperature, ˚C

800

1000

Fig. 2.7: Thermal conductivity of steel as predicted by different models and as measured in
different test programs

5000
Rem pe & Knudson 2008
Rem pe & Knudson 2008

Specific Heat, J/kg.˚C

4000

Bentz & Prasad 2007
Touloukian 1972

3000

EC3 m odel
ASCE m odel

2000

1000

0
0

200

400
600
Tem perature, ˚C

800

1000

Fig. 2.8: Specific heat of steel as predicted by different models and as measured in different tests
atoms transition from a face centered cubic “FCC” to a body centered cubic “BCC” structure.
This process absorbs considerable energy (heat), thus accounting for the spike around 750 °C
seen in Fig. 2.8. The variation between the test data and the models shown in Fig. 2.8 is partly
due to the fact that the majority of the existing data on specific heat originates from studies
41

carried out on iron and non-structural steel alloys. Additionally, the maximum temperature
reached in these studies of iron and non-structural steel was below 750 °C, thus not capturing the
full range of temperatures observed in fire conditions.
2.6.2

Thermal Properties – Concrete

As is the case with steel, the thermal properties that have a significant effect on the response of
concrete to fire exposure are thermal conductivity and specific heat. Thermal conductivity of
concrete as a function of temperature is shown in Fig. 2.9 below. Due to the natural variability
of concrete resulting from the use of unprocessed naturally occurring materials, the thermal
conductivity of concrete is given as a range rather than a specific value. This range is applicable
to both siliceous and carbonate based concrete. From Fig. 2.9, it can be seen that the thermal
conductivity of concrete is between 1.4 and 2 W/mK at 20 °C and decreases to 0.75 W/mK at
800 °C.

Thermal Conductivity (W/mK)

2.5
2

Upper Limit
Lower Limit

1.5
1
0.5
0
0

300

600

900

1200

Temperature (°C)

Fig. 2.9: Thermal conductivity of concrete as a function of temperature

42

Specific heat of concrete as a function of temperature is plotted in Fig. 2.10 according to both
ASCE (1992) and Eurocode (2004) procedures. Of note is the large spike in specific heat for
carbonate aggregate concrete as specified in ASCE (1992). This is attributed to the endothermic
dissociation of dolomite within the carbonate aggregate, not present for siliceous aggregate. This
spike is however neglected in the Eurocode (2004) (Fig. 2.10) and the same specific heat model
employed for both siliceous and carbonate aggregate concrete.
2.6.3

Mechanical Properties – Steel

A review of the literature indicates that there have been more studies on the high-temperature
mechanical properties of steel than on thermal properties.

Tests on the high temperatures

strength properties are conducted in two main ways: transient- and steady-state tests. In transientstate tests, the test specimen is subjected to a constant load and then exposed to uniformly
increasing temperature. Temperature and strain are recorded continuously under constant stress.
Thermal strain (evaluated from a separate test) is subtracted from the total measured strain
(Outinen 2007). In the transient-state tests, the heating rate has a great influence on the strain
rate, and thus different heating rates produce different strain rates. Heating rate of steel under fire
conditions depends on the nature of the fire as well as on insulation and steel section properties.
Generally, for a typical beam with 2 hour fire rated protection, the heating rate of steel can vary
between 3-7 °C/min. However, for unprotected steel sections, the heating rate can vary between
25-40 °C/min. In the literature, (Outinen 2007) the reported transient mechanical property tests
were conducted at heating rates ranging between 10 to 50 °C/min. This heating rate can be
suitable for unprotected steel members, but not for protected members with slow heating rates.

43

8000

Specific heat (J/kgK)

7000

ASCE Sil.
ASCE Carb
Eurocode

6000
5000
4000
3000
2000
1000
0
0

300

600

900

1200

Temperature (°C)

Fig. 2.10: Specific heat of concrete as a function of temperature
On the other hand, the steady-state tests are generally faster and easier to conduct than the
transient-state tests. In the steady-state tests, the test specimen is heated to a specific temperature
and after that a tensile test is carried out. Stress and strain values are recorded continuously under
constant temperature. The test can be either load-controlled (loading rate is constant) or straincontrolled (strain rate is constant) (Outinen 2007, Anderberg 1988). Despite the fact that strain
rate has a significant effect on the test results, a large amount of test data on conventional steel is
published without the information on strain rates. Therefore, test standards are still concerned
with defining limits for strain rates in tests (Outinen 2007, Anderberg 1988, and Cooke 1988).
These variations in test methods resulted in variations in the reported mechanical properties,
which in turn resulted in variations in the constitutive models specified in codes and standards.
The following sections present comparative study of these variations.
As mentioned earlier, different test regimes were used to obtain yield strength and elastic
modulus of steel at elevated temperatures. The variations in test parameters resulted in different
44

test measurements, thereby leading to differences in constitutive relationships presented in
different codes and standards. Generally, tensile strength tests are conducted to obtain elastic
modulus and yield strength of steel. There is lack of experiments on the modulus of steel under
compression. This is because in tensile strength tests, complications that may arise due to
geometric instabilities and confinement of specimen are eliminated. However, it is generally
assumed that the modulus of elasticity for steel, derived based on tensile strength tests, is the
same for compression state.
Figs. 2.11 and 2.12 show the yield strength and modulus of elasticity of steel as a function of
temperature respectively. The test data plotted in the figures are compiled from various high
temperature property tests as shown on the figures. Both the yield strength and elastic modulus
decrease as temperature increases. This decrease can be attributed to the nucleus of the iron
atoms in steel moving farther apart due to rising temperature in steel, leading to decreased bond
strength, which in turn reduces the yield strength and elastic modulus.
It can be seen in the figures that there is significant variation in test data on yield strength and
modulus of elasticity at temperatures above 300˚C. This variation can be attributed to many
factors, primarily variable heating and strain/load rates during the test. For example, when the
heating rate of the stressed specimen is small, the specimen will be subjected to stress at elevated
temperatures for longer time duration, therefore, other factors, such as high-temperature creep
(time-dependent plastic strain under constant stress and temperature), can influence the resulting
temperature-stress-strain curves of the tested specimen. The yield strength and elastic modulus
constitutive relationships from ASCE manual, Eurocode, and those proposed by Poh (2001) are
also shown in Figs. 2.11 and 2.12 respectively.

45

Outinen & Mäkeläinen 2004
Outinen et al. 1997
Mäkeläinen et al.1998
Chen et al. 2006
Li et al. 2003
EC3 m odel
ASCE m odel
Poh m odel

1.2

F ,T Fy
F yy,T// F y

1
0.8
0.6
0.4
Yield point "EC3"
0.2
Proportionality limit "EC3"
0
0

200

400
600
Temperature, ˚C

800

1000

Fig. 2.11: Yield strength of steel as predicted by different models and as measured in different
tests

1.2

1

E / S
E sS,T/EE s
,T

0.8

0.6
Chen & Young 2008
Outinen & Mäkeläinen 2004
Outinen et al. 1997
Cooke 1988
Dever 1972
Clark 1953
EC3 model
ASCE model
Poh model

0.4

0.2

0
0

200

400
600
Temperature, ˚C

800

1000

Fig. 2.12: Elastic modulus of steel as predicted by different models and as measured in different
tests

46

As is the case with test data, there is also a considerable variation in the constitutive models for
yield strength and modulus of elasticity. These variations in constitutive models are due to the
large variation in the test data used to compile the respective constitutive models. A review of
the models shows that the Eurocode model predicts less reduction in yield strength of steel with
temperature as compared to the ASCE or Poh models (Kodur et al. 2010). However, the
Eurocode model provides a higher reduction in elastic modulus of steel with temperature as
compared to the ASCE and Poh models as shown in Fig. 2.12. Also, the Eurocode model
assumes no reduction in steel yield strength up to 400˚C, while ASCE and Poh models assume a
loss of 30% and 40%, respectively, at 400˚C, as shown in Fig. 2.11.
Fig. 2.11 also shows that the Eurocode distinguishes between two limits: the proportionality
limit, and the yield limit. The proportionality limit in the Eurocode is the end of the linear
portion of the stress-strain curve, after which point the stress-strain relation remains elastic but
becomes nonlinear. The yield limit in Eurocode is the point after which the stress-strain becomes
both nonlinear and inelastic. This feature of the stress-strain does not exist in either ASCE or Poh
models which both assume a sharp point as a limit between linear-elastic and inelastic material
response. The theory behind introducing proportionality limit in the Eurocode stress-strain
curves (at high temperatures) is to capture visco-elastic behavior that is partly due to creep effect.
The nonlinearity after the proportionality limit indicates that stress causes further strain after this
point than in the linear elastic range. This simplification enables the stress-strain curves of the
Eurocode to partly account for high temperature creep strain at elevated temperature.
Figs. 2.13a and 2.13b show the temperature-stress-strain curves from Eurocode 3, ASCE manual,
and as proposed by Poh (2001) at room temperature and at 600˚C, respectively. The y-axis
represents normalized stress and the x-axis represents normalized strain.

47

1.5
1.25
1

Fs ,T

0.75

Fy

0.5

Steel tem perature= 20 ˚C
ASCE m odel
EC3 m odel
Poh m odel

0.25
0
0

5

10

.

15

20

 s ,T
( Fy / E s )

25

30

a) 20°C stress-strain relationship
0.6
0.5
0.4

Fs ,T
Fy

Steel tem perature= 600 ˚C

0.3
0.2

ASCE m odel
EC3 m odel

0.1

Poh m odel

0
0

5

10

15

 s ,T
( Fy / E s )

20

25

30

b) 600°C stress-strain relationship
Figs. 2.13a and 2.13b: Temperature-stress-strain relationships for structural steel as per ASCE,
Eurocode and Poh models

48

Originally, the Eurocode temperature-stress-strain curves were derived based on transient-tests
under slow heating rates (Twilt 1991 and Anderberg 1988). Therefore, when used in the fire
resistance analysis, the Eurocode constitutive relationships generally produce slightly more
flexible responses as compared to ASCE or Poh constitutive models. This is attributed to the fact
that in the transient-state tests, adopted by the Eurocode, part of high temperature creep is
included in the resulting temperature-stress-strain curves (Buchanan 2005). However, less
information is known about the test data that were used to derive ASCE temperature-stress-strain
curves of steel. On the other hand, Poh (2001) developed generalized temperature-stress-strain
relations for structural steel based on a large set of experimental data. These relations account for
specific features, such as the yield plateau and the effect of strain hardening. These temperaturestress-strain relations have been validated against the specified relationships in codes and
standards, and they have been shown to give more realistic predictions of fire resistance when
used in conjunction with high temperature creep model.
Another difference between the three constitutive models is the assumed limits for the elastic
phase. ASCE manual and Poh models consider a sharp yield point as an end of the linear-elastic
phase, while Eurocode considers another point, called the “proportionality limit” as an end of the
linear phase, as shown in Fig. 2.14. However, the end of elasticity in the Eurocode is the yield
point, and is defined as the offset stress (also known as proof stress) corresponding to 0.2%
strain, as shown in Fig. 2.14.

49

Stress

ASCE m odel
EC3 m odel
Poh model

Yield Point "EC3"
Yield Points "ASCE & Poh"
Proportionality limit"EC3"

Strain

0.2% strain offset

Fig. 2.14: Definition of yield point and proportionality limit in ASCE, EC3, and Poh 2001
2.6.4

Mechanical Properties – Concrete

The mechanical properties that influence the response of concrete to fire exposure differ slightly
from those for steel. Of particular interest in concrete are the compressive strength, and the
stress strain relationships.
Fig. 2.15 presents the compressive strength reduction factor of concrete as a function of
temperature for the full range of temperatures practically achieved under fire exposure. From
Fig. 2.15 it can be seen that the compressive strength reduction factor for carbonate and siliceous
aggregate based concrete are significantly similar over the entire temperature range plotted in
Fig. 2.15.

In both instances, the reduction factor decreases monotonically with increasing

temperatures.
At every temperature above 100 °C concrete has a unique stress strain relationship, for ease of
presentation, the stress strain curves for only five temperatures are shown in Fig. 2.16. From
Fig. 2.16 it can be seen that both the strain at peak stress and the ultimate strain increases for

50

concrete as a function of temperature. This has a considerable effect on the response of a
structure under fire exposure, as the temperatures increase, the deflections in the member will
increase. In the case of floor systems, these increasing deflections allow the concrete to transfer
a portion of the load via tensile membrane action, and hence, enhance the fire resistance of the
structure.

Compressive strength f'c,t/f' c,20

1.2
1

Sil.
Carb

0.8
0.6
0.4
0.2
0
0

300

600

900

1200

Temperature (°C)

Fig. 2.15 Compressive strength of concrete as a function of temperature
Finally, with reference to the mechanical properties of concrete at elevated temperature, the
Eurocode presents a series of equations to define the stress strain relationships as shown in
Appendix B. These equations, as was the case for steel at elevated temperatures, encompass an
infinite number of data points, as such, no graphical representation is presented here, rather, the
interested user is directed to the Eurocode or Appendix B.

51

1
0.9

20°C

0.8

Stress

0.7

200°C
400°C

0.6

600°C

0.5

800°C

0.4
0.3
0.2
0.1
0
0

0.01

0.02

0.03

0.04

Strain

Fig. 2.16: Strain at peak stress reduction factor as a function of temperature for concrete
2.6.5

Deformation Properties – Steel

The deformation properties that influence the fire response of steel structures are thermal strain
and high-temperature creep. The following sections discuss the variations in deformation
properties of steel at elevated temperatures.
There have been many tests to characterize thermal strain of steel at elevated temperatures,
results from some of which are compiled in Fig. 2.17 (Outinen 2004, Cooke 1988, Anderberg
1988, and Stirland 1980,). As seen in Fig. 2.17, thermal strain of steel increases with temperature
up to nearly 750˚C, at which point a phase change takes place (as discussed previously) and the
thermal strain becomes nearly constant up to 800 °C, after which point thermal strain starts to
increase again.
Variation of thermal strain models as specified in ASCE and EC3 are also plotted in Fig. 2.17.
Minimal differences exist between the Eurocode and ASCE models for thermal strain of steel up
to 700 °C. However, in the temperature range of 700-850 °C the ASCE model assumes a
52

continuously increasing thermal strain while the Eurocode model accounts for the phase change
that occurs in steel in this temperature range by assuming a constant thermal strain from 750 °C
to 850 °C, followed by an increasing thermal strain up to 1000 °C (See Fig. 2.8).

1.5

Outinen et al. 2004
Anderberg 1988
Cooke 1988
Stirland 1980
EC3 m odel
ASCE m odel

Thermal Strain, %

1.25
1
0.75
0.5
0.25
0
0

200

400
600
Tem perature, ˚C

800

1000

Fig. 2.17: Thermal strain of steel as predicted by different models and as measured in different
tests
2.6.6

Deformation Properties – Concrete

As was the case with steel, the deformation property of concrete that has the largest influence on
the fire resistance of composite steel-concrete construction is thermal expansion. Fig. 2.18
presents a plot of the thermal expansion of concrete as a function of temperature for both
siliceous and carbonate aggregate based concrete.

It is observed from Fig. 2.18 that the

coefficient of thermal expansion for carbonate aggregate is lower than that of siliceous aggregate
concrete at all temperatures practically achieved under fire exposure. While for both concrete
types, the coefficient of thermal expansion is nearly zero at ambient temperatures, it increases to

53

0.014 by 700 °C for siliceous aggregate concrete, and 0.012 by 805 °C for carbonate aggregate
concrete.
0.016

Thermal expansion

0.014
Sil.

0.012

Carb.

0.01
0.008
0.006
0.004
0.002
0
0

300

600

900

1200

Temperature (°C)

Fig. 2.18: Coefficient of thermal expansion for concrete as a function of temperature
2.6.7

High Temperature Properties of Insulation

Steel and concrete have as their primary function in any structure to resist the applied loads on
the structure. Insulation on the other hand has as its primary objective to prevent heat transfer,
specifically, it is to offer no structural contribution.

As such, the properties of insulation

materials that are of interest to the current research are all thermal in nature. These properties
include thermal conductivity, specific heat, density, and moisture content (SFPE 2005). Given
the wide range of insulations available in the market, and the proprietary nature of many of them,
only the desirable thermal properties of insulation will be discusses. It is desired that insulation
have a low thermal conductivity, high specific heat, low density, and high moisture content to
optimize the protection offered to a structural member.

It is base on these criterion, and

supporting fire resistance experiments, that insulation is selected for use in a specific application.
54

2.7

Knowledge Gaps

The current state-of-the-art presents a large amount of information on the behavior and
mechanics of composite steel structures under fire exposure. The previous research presented in
this chapter focuses on the experimental and numerical studies conducted on the fire resistance
of CFHSS columns and composite floor systems.
Studies on the fire resistance of CFHSS columns have clearly shown that composite construction
in the form of CFHSS columns is capable of providing fire protection to meet the levels required
in codes and standards in most practical applications. While a major contribution to structural
fire engineering, the previous work on CFHSS columns does not provide a rational approach for
fire resistance design. There is a critical need for a simplified design methodology to assess the
fire resistance of CFHSS columns under design fire exposure. The methodology should take into
consideration realistic load levels, failure criterion, and expand the range of columns considered
by increasing the cross-sectional and length limitations associated with the use of Eq. 2.1.
Composite beam slab assemblies have been shown in previous experimental and numerical
investigations to enhance the fire resistance of steel framed structures.

Much of this

enhancement is due to the development of tensile membrane action as the slab deflects due to the
heat from fire reducing the mechanical properties of the constituent material. The benefit that is
achieved through composite construction is however still insufficient to meet the levels required
in codes and standards. To provide an improved fire resistance from composite beam-slab
assemblies, it is necessary in investigate the use of alternate materials in the concrete slab to
enhance the tensile strength of the concrete. Enhancing tensile strength of the concrete will
allow additional load to be transferred through tensile membrane action, and thus, higher fire
resistance to be achieved. In addition, after development of the material system, a simplified

55

approach for fire resistance design using the novel material system needs to be developed. The
simplified approach should permit the use of composite floor slabs for achieving fire resistance
in any fire exposure, under realistic loading and failure criterion, and over a wide range of sizes.
Lastly, the previous work as presented in this chapter highlights the need for fire resistance
evaluation to be considered on the system level, rather than just the element or assembly levels.
This need is based on the observation that the presence of multiple connected members and
composite construction at the system level enhance the fire resistance of composite structural
systems. As such, to provide a holistic approach to fire resistance evaluation, any methodologies
or material systems developed for CFHSS columns or composite beam slab assemblies should be
modeled at the syste--m level for verification of the develop innovations.
The current research as presented in the following chapters is aimed at overcoming these
knowledge gaps. The first step in accomplishing this is to conduct an experimental investigation
on the response of a composite beam slab assembly incorporating steel fiber reinforced concrete
to fire exposure. Details on the experimental program are presented in the following chapter.

56

CHAPTER 3
3
3.1

EXPERIMENTAL STUDIES
General

To develop a methodology for exploiting the beneficial effects of composite construction on the
fire resistance of steel framed structures, it is necessary to undertake detailed analysis at the
element, assembly and system levels. The numerical models to be used for conducting this
detailed analysis require validation at the element, assembly, and system levels. It is therefore
necessary to have experimental data at the element, assembly, and system levels for CFHSS
columns, composite floor assemblies, and a full-scale building respectively. As seen in Chapter
2, comprehensive fire resistance experiments have been conducted on concrete-filled HSS
columns, and on the steel framed structure at Cardington. However, only limited studies have
been conducted on steel beam-concrete slab assemblies, and these do not fully take into
consideration composite action, and specifically, the contribution of tensile membrane action to
fire resistance. To overcome this limitation, four novel fire resistance experiments were carried
out on steel beam-concrete slab assemblies. In this chapter, the details of these novel fire tests
are presented, and the available fire test data at the element and system level reviewed.
3.2

Element Level – CFHSS Columns

A review of the literature, as presented in Chapter 2, indicates that there have been a number of
studies on the fire resistance of CFHSS columns exposed to fire conditions.

The most

comprehensive of the research programs for which test data is available, is that conducted at the
National Research Council of Canada (NRCC).

In this research program, fire resistance

experiments on 85 CFHSS columns were conducted (Kodur and Lie, 1996, Lie and Kodur, 1996,

57

Lie and Chabot, 1992, Lie and Irwin, 1995, Chabot and Lie, 1992). The columns tested at
NRCC were both round and square HSS columns with three different types of concrete filling,
bar reinforced (RC), steel fiber reinforced (FC) and plain concrete (PC). A figure illustrating the
three different types of fillings and the two different HSS cross sections is presented as Fig. 3.1.
The rebar used in RC filled HSS columns was standard deformed rebar ranging in size
depending on the size of the columns. Steel fibers were 50 mm long crimped fibers with yield
strength of 620 MPa as commonly used in construction.

Specific details and response

parameters needed for validation of the SAFIR computer model are summarized below.
D

P

D

D

P

t
P

Fig. 3.1: Illustration of RC, FC, and PC square and round column cross-sections tested at NRCC
3.2.1

Dimensions

All of the tested columns were 3810 mm long from one end plate to the other. Both circular and
square cross-sections were considered in the research program. The circular cross-sections had
wall thicknesses ranging from 1.78 to 12.70 mm, and outside diameters ranging from 141.3 to

58

406.4 mm. The square cross-sections ranged from 152.4 to 304.8 mm in outside width, with a
wall thickness of 6.35 mm.
3.2.2

Materials

Steel strength was not taken as a primary variable in this research program, the steel was
specified as either 300 or 350 MPa in accordance with CSA standard G40.21-M (Kodur and Lie,
1996, Lie and Kodur, 1996, Lie and Chabot, 1992, Lie and Irwin, 1995, Chabot and Lie, 1992).
The concrete used as infill was normal weight aggregate concrete with a 28-day compressive
strength of concrete ranging from 23 to 85 MPa for the different CFHSS columns. Two primary
types of concrete were considered, that made with carbonate aggregate, and that made with
siliceous aggregate. In the majority of cases, the cement used was typical (No. 10) cement,
however, some minor consideration was given to the use of high early strength cement. For all
of the pours done in the research program, the full mix design is provided in the respective
internal test reports (Kodur and Lie, 1996, Lie and Kodur, 1996, Lie and Chabot, 1992, Lie and
Irwin, 1995, Chabot and Lie, 1992). Typical mix proportions for selected concrete mixes (Lie
and Chabot 1992) are reproduced in Table 3.1 to illustrate the detailed information available in
the test reports.
Table 3.1: Sample mix proportions for concrete used in CFHSS columns (Lie and Chabot 1992,
Lie and Kodur 1994)
PC
Cement
(Kg/cu.m)
Course Agg.
(Kg/cu.m)
19 mm
9.5 mm
Total
Fine agg.

FC

RC

355

439

439

1014
1014
855

788
340
1128
621

788
340
1128
621

59

Table 3.1 (Continued): Sample mix proportions for concrete used in CFHSS columns (Lie and
Chabot 1992, Lie and Kodur 1994)
PC
Steel fibers
(Kg/cu.m)
Rebar (mm)
Water
(Kg/cu.m)
Water/cement
Ratio
Superplasticizer
Retarding
admixture
28 day comp.
str. (MPa)
3.2.3

FC

RC

-

42

-

-

-

Various

173

161

161

0.49

0.37

0.37

Master
Builders
100XR

Mighty 150
Master
Builders
100XR

-

33.0

43.2

41.3

-

Fabrication

In order to attach the columns to the loading apparatus, and to provide the desired type of end
restraint, all of the columns had a steel end plate welded to the top and bottom. To allow for the
pouring of concrete into the column, the plate on the top was provided with a hole just smaller
than the inside dimension of the column. In addition to the hole in the top plate on the column, a
total of four 13 mm holes were drilled in the columns to act as steam vent holes, two 457 mm
from the top of the column, and two 457 mm from the bottom of the column. Additionally, a 25
mm hole was placed at the top of the column to allow for entry of the thermocouple wires to the
inside of the column.
For concrete filling, the columns were placed in the upright position and concrete was poured
from a mixing truck. After being filled, the columns were allowed to remain in the upright
position for 28 days, after which point they were placed in the horizontal position until testing.

60

3.2.4

Instrumentation

Instrumentation in the columns consisted of thermocouples and axial displacement transducers.
Thermocouples inside the column were attached to a thermocouple tree in all of the columns and
to rebar in the RC columns. The thermocouple tree consisted of a steel rod running down the
length of the column with additional small pieces of rod attached to it allowing temperatures to
be measured at several points across the cross section as seen in Fig. 3.2. Type K chromelallumel thermocouples with a thickness of 0.91 mm were used.

F
A

A

A

E

B
A-A

C
D

= Thermocouple

Fig. 3.2: Schematic of thermocouple tree used in testing at NRCC
Displacement of the columns was monitored by a displacement transducer which measured the
motion of the loading jack on the top of the column. The transducer used in testing had a
tolerance of 0.002 mm.

61

3.2.5

Test Conditions

The columns were tested at NRCC’s fire test furnace by exposing them to fire and loading.
Loading to the columns was provided via a single hydraulic jack with a capacity of 9778 kN
which was located at the top of the column. With one exception, loading on the columns was
applied concentrically. Loading ranged from 9-47% of the total composite column strength or
from 46-165% of the concrete core strength.
Most of the columns were tested in the simulated fixed-fixed end condition. To achieve this
condition, eight 19 mm bolts were passed through the plates on the ends of the columns and
attached to the loading frame of the furnace.
Fire exposure was simulated as specified in ASTM E-119 standard fire exposure. Heat to the
furnace was provided via 32 propane gas burners evenly spatially distributed in the furnace.
Temperatures within the furnace chamber were also measured with Type K chromel-alumel
thermocouples. A total of eight of them were inserted into the combustion chamber. The
average of all eight of these thermocouples was used to monitor the temperatures inside the
furnace.
3.2.6

Measured Data

Data from fire tests was recorded at one minute intervals depending on the stage of the test. This
data has been made available in the raw form through internal reports and several journal
publications. Test data provided in these reports consists of temperatures at various cross section
locations, furnace temperature, and axial deformation.

Sample plots of the temperature at

various locations and axial deformations are presented for column RP-168 (Table 3.2) as Figs.
3.3 and 3.4 below respectively, see Fig. 3.2 for key to labeling used in Fig. 3.3.

62

1000

Temperature (°C)

800
600
A
B
C
D
E
F

400
200
0
0

30

60

90

Time (min)

Fig. 3.3: Thermal response recorded during fire test at NRCC for CFHSS column RP-168

Axial deformation (mm)

30
20
10
0
-10
-20
-30
0

30

60

90

Time (min)

Fig. 3.4: Axial deformation recorded during fire test at NRCC for CFHSS column RP-168

63

3.2.7

Data for Model Calibration

Detailed data on test parameters and column response is available for all of the 85 columns tested
at NRCC. Given that this information is readily available, it is not prudent, considering the high
cost of testing, to duplicate these tests for the purpose of this research. Rather, the data from
NRCC will be used to validate numerical models constructed in SAFIR, such that parametric
studies can be carried out numerically. For this purpose, 14 CFHSS columns were selected as a
representative sample from the 85 tested at NRCC. Pertinent information from these columns is
presented in Table 3.2. In the designation of columns (ex: RP-355), the first letter (R) represents
section shape (round or square), the second letter (P,F,B) denotes filling type (plain, steel fiber
and bar-reinforced concrete), and the number (355) denotes the diameter (for circular) or width
(for square) of the HSS column section in mm.
Table 3.2: Summary of test parameters and fire resistance values for selected CFHSS columns
tested at NRCC
Column
Designat
ion

Dia. or
Width mm
(in.)

RP-168
RP-273
RP-355
SP-152
SP-178
RF-324
RF-356
SF-203
SF-219
RB-273a
RB-273b
SB-203
SB-254a
SB-254b

168.3 (6.63)
273.1 (10.75)
355.6 (14.0)
152.4 (6.0)
177.8 (7.0)
323.9 (12.75)
355.6 (14.0)
203.2 (8.0)
219.1 (8.63)
273.1 (10.75)
273.1 (10.75)
203.2 (8.0)
254 (10.0)
254 (10.0)

AISC
Factored
Load kN
(kip)
1197 (269)
3508 (788)
5120 (1151)
1409 (317)
1976 (444)
4573 (1028)
6616 (1487)
3506 (788)
3793 (852)
3323 (747)
3333 (749)
2345 (527)
3405 (765)
3405 (765)

Load
Ratio

Fire
Resistanc
e (min)

Concret
e Filling

Aggregat
e Type

0.13
0.15
0.18
0.20
0.28
0.35
0.23
0.26
0.16
0.32
0.57
0.21
0.42
0.65

81
143
170
86
80
199
227
128
174
188
96
150
113
70

Plain
Plain
Plain
Plain
Plain
Fiber
Fiber
Fiber
Fiber
Bar
Bar
Bar
Bar
Bar

Sil.
Sil.
Sil.
Carb.
Sil.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.

64

3.3

Assembly Level – Composite Floor System

In the previous chapter, it was observed that composite floor systems demonstrate higher fire
resistance than observed for steel beams in single element tests. This was attributed to the
development of tensile membrane action in the concrete slab supporting a portion of the applied
load. To study this, tests were carried out on four composite beam slab assemblies under various
configurations and loadings. Initially, three plain concrete floor slabs were constructed and
tested under fire exposure, based on the results from these tests, it was decided to test an
additional, similar assembly made with SFRC.
3.3.1

Test Specimens

The test specimens were specifically designed such that the response of the central beam under
fire exposure could be evaluated. The three plain lightweight concrete assemblies are referred to
as PC-1, PC-2, and PC-3, while the SFRC assembly is referred to as SFRC, the different
construction parameters for each assembly are shown in Table 3.3. The assemblies comprised of
a network of five steel beams and a concrete deck cast on the top. The beam networks consisted
of three W10X15 beams connected to a pair of W12X16 girders (Fig. 3.5) via the connections
denoted in Table 3.3. The W12X16 beams were 3.96 m long while the W10X15 beams were
2.13 m in length. The spacing of the connections on the W12X16 beam was 1.98 m, leaving
152.4 mm of the W12X16 beam extending past the connection of the end W10X15 beam. The
detailing of all steel work was done according to AISC (2005) specifications. The steel used in
the beams was A992 with a specified yield strength of 344 MPa, while the steel used in the
connections was of Grade A36 with a specified yield strength of 248 MPa. Bolts used in the
assembly of the specimen were 19 mm Grade A325 with a shear strength of 68.8 kN.

65

W12X16
W10X15
Insulation
W10X15
W12X16

W10X15
Insulation

Fig. 3.5: Configuration of beams in the tested assembly

Shear stud
Concrete slab
Steel
deck

Steel

(a) Cross-section of beam slab assembly

(b) Deck assembly with shear studs

Fig. 3.6: Details of deck and shear studs in beam-slab assembly
Table 3.3: Details of tested beam slab assemblies
PC-1
Concrete type
Slab
thickness
(mm)
Concrete
strength
(MPa)
Connection
type
Girder
protection
Beam
protection

PC-2

PC-3

Lightweight

Lightweight

Lightweight

101.6

101.6

101.6

127

45.3

44.8

43.8

46.6

Fin plate

Fin plate

Double angle

Fin plate

1 hour (14.3
mm)
1 hour (14.3
mm)

1 hour (14.3
mm)

1 hour (14.3
mm)

2 hour (22
mm)

None

None

None

66

SFRC
Normal
weight SFRC

Atop the network of steel beams was attached a ribbed 20 gauge 38 mm galvanized deck.
Through the galvanized deck, shear studs were welded to the top flange of both the W12X16 and
the W10X15 beams. The shear studs used had a shank diameter of 16 mm and a length of 76
mm for slabs PC-1 to PC-3, and a diameter of 19 mm with a length of 101.6 mm for the SFRC
slab. Shear studs were affixed to the W12X16 section every 178 mm and attached to the
W10X15 section in the valley of every rib, giving them a center to center spacing of 154 mm. A
schematic of the shear stud placing is presented as Fig. 3.6a, and a picture of the as constructed
specimen is shown in Fig. 3.6b.
Following completion of the beam network and attachment of the shear studs to the beams, the
two W12X16 girders and W10X15 beams were provided with fire protection sufficient to
achieve the fire resistance ratings shown in Table 3.3. Carboline Type 5GP fire protection was
applied to the beams and was measured at several points to ensure that the thickness was uniform
over the entire surface. Fire protection was terminated approximately 300 mm from the end of
the W12X16 beams (all of which is outside the fire exposed region) to allow the steel beams to
rest directly on the supports during testing. Fig. 3.7 shows the insulation on the W12X16 beams
shortly after application of the fire protection. The properties of the insulation are tabulated in
Table 3.4.

Fig. 3.7: Fire protection on the girder just after application

67

Table 3.4: Properties of fire insulation
3

Density (wet):

832kg/m

Density (dry):

240kg/m
>4255kPa
112kPa

Adhesion:
Comp strength:

3

After application of fire protection, the remaining galvanize deck was placed, formwork installed
around the perimeter of the assembly, and the concrete poured. The deck was 4.57 m by 3.96 m,
with a maximum thickness of 101.6 mm for slabs PC-1 through PC-3, and 127 mm for the SFRC
slab. The specified compressive strength was 28 MPa with the strengths shown in Table 3.3
corresponding to the strength measured on the day of testing for the respective slabs. The course
aggregate was either lightweight or carbonate (limestone) based depending on the concrete type
shown in Table 3.3. Once the normal weight concrete for use in SFRC was placed in the truck,
steel fibers with a length of 63.5 mm (aspect ratio = 67) were added to the concrete, the mix
proportions are shown in Table 3.5.
Table 3.5: Mix proportions used in the tested composite beam-slab assembly
SFRC

3

Type 1 cement

338 kg/m

Course agg. (19 mm)
Lightweight agg. (19 mm)

1023 kg/m
-

Boarl material

-

Fine agg.

965 kg/m

Water

160 kg/m

Steel fibers
Air
W/C

42 kg/m
4.28%
0.47

Unit weight
Slump*

2459 kg/m
90 mm

3

Lightweight
332 kg/m
89 kg/m

3

495 kg/m

3
3

3

60 kg/m

3
3

3

753 kg/m
161 kg/m
-

3
3

5.74%
0.48
3

1762 kg/m
163 mm

3

*Slump is not required for SFRC, this value was however obtained for comparison purposes.

68

After the slabs were cast, they were covered with a vapor barrier and allowed to cure for a
minimum of 90 days at ambient temperature to achieve a relative humidity level below 75%
prior to testing.
3.3.2

Instrumentation

The test specimens were instrumented with thermocouples, strain gauges, and displacement
transducers to monitor thermal and mechanical response of the specimen during fire testing.
Temperatures were measured with 0.91 mm thick type K chromel-alumel thermocouples, which
were placed on the upper and lower flanges, and on the web of the steel beam at the nine cross
sections indicated in Fig. 3.8a.
207

207
860

= Thermocouple

860

1219
1274
500
207

Furnace

500

= Location where steel section
was thermocoupled
(a): Thermocouple layout on beam cross section
Fig. 3.8: Instrumentation scheme used in testing of the beam-slab assembly (mm)
In addition, the temperatures were also monitored at two points in the depth of the concrete at
four cross-sections, and on the exposed surface of the assembly at seven locations as shown in
Figs. 3.8b and c respectively. Since high temperatures are quickly generated in the furnace,
strains and displacements were measured only on the unexposed surface of the slab. Strains

69

were measured using 60 mm long 120 Ω strain gauges located at the 10 locations shown in Fig.
3.8d. Vertical displacements were measured at 9 locations as shown in Fig. 3.8e using linear
varying displacement transducers (LVDT’s) connected to the top surface of the slab.
1270

1270

711

63
207

64
X

= Thermocouple

1041

X = Location where concrete slab
was thermocoupled

X

X
1041
X

Furnace

(b): Thermocouple layout on slab cross section
1066

1066

1219
207
1041
1041
1041
1041

Furnace
= Surface thermocouple
(c): Thermocouple layout on unexposed side of slab
Fig. 3.8 (Continued): Instrumentation scheme used in testing of the beam-slab assembly (mm)
70

4 @ 305 mm inset
2 @ 76 mm
from center
4 @ 610 mm
from center

Furnace
= Surface strain gauge

(d): Strain gauge layout on unexposed side of slab
114
1105

1066

1066

1105
114
1410

457

1867
Furnace
114
= LVDT location
(e): LVDT Layout
Fig. 3.8 (Continued): Instrumentation scheme used in testing of the beam-slab assembly (mm)

71

3.3.3

Test Equipment

The fire resistance tests were conducted at Michigan State University’s Structural Fire Testing
Furnace shown in Fig. 3.9. The test furnace is design to simulate as closely as possible the
thermal and structural loading to which a structure would be exposed in a building fire. Heat is
provided to the furnace by six independent natural gas burners. The gas is fed into the furnace at
approximately 0.02 MPa and is regulated to assure this pressure is maintained. A main control
valve which trips at sensing any irregularities in pressure (such as a rapid shutdown) is
incorporated to assure that in the case of an emergency, the fuel supply is shut off almost
instantly. In addition to this, if left unused for more than 2 minutes, the valve will again shut
itself off requiring a purge cycle before operation can be resumed. The maximum total gas
3

3

consumption of the furnace is approximately 230 m / hr with a consumption of 100 m /hr while
in the maintenance stage of the ASTM E119 time-temperature relationship. Each of the burners
is capable of producing 406 kW. The six burners are located on the furnace as indicated in Fig.
3.10. Each of the burners is located 1.2 m from the top of the furnace, and can be independently
turned off during the course of the test.

Using the integrated UV detectors, the burners

automatically adjust the fuel to air ratio to achieve a clean burn and minimize pollutants.
As seen in Fig. 3.10, there are two observation ports which allow test specimens to be viewed.
These ports are equipped with high temperature resistant glass, and are large enough to
accommodate a video camera or other similar device.
A constant load was applied to the specimen for the entire duration of testing using hydraulic
actuators. The loading frame used in testing the floor assemblies has the configuration shown in
Fig. 3.11. Two independent load zones exist allowing for several configurations to be used
depending on test requirements. The central hydraulic pump can reach a maximum pressure of

72

20.7 MPa and a minimum pressure of 3.44 MPa. The large actuators have a maximum extension
of 152.4 mm while that of the smaller actuators is 305 mm.

Fig. 3.9: View of MSU structural fire testing facility
X

O

X

X

X

X
O

X

X – Burner
O – Observation port
Fig. 3.10: Layout of burners and observation ports in fire test furnace

73

X

X

O
X

X

X
X – 240 kN Actuator

X

X

X

X
O

O – 2750 kN Actuator
X

X

Fig. 3.11: Actuator locations in the furnace
There are separate fans for combustion air and exhaust. Exhaust flow is controlled manually and
can be adjusted such that either positive or negative pressure is present in the furnace at any
given time. Input air however, as indicated above, is governed by the UV detectors to optimize
combustion at each burner. Exhaust air is taken from the top of the furnace to reduce the
combustion products in the furnace at any given time.
The temperature within the combustion chamber is manually controlled allowing for any time
temperature profile to be simulated. The furnace has been calibrated for ASTM E-119 (ASTM
2007) and E-1529 (ASTM 2001) hydrocarbon fires. The manual control facilitates simulating a
design fire scenario with ease. The sensitivity of the controls allows good control to achieve less
than 1% error while following the ASTM E-119 time-temperature relationship.
There are a total of 90 inputs for the data acquisition system. 10 of these positions were used for
strain gages, 10 are for LVDT’s, while the remaining 70 were used for thermocouples. Data was
collected from all of the channels in five second intervals and recorded in Excel (*.CSV) format
for later analysis.

74

3.3.4

Test Specimen Installation

After curing of the concrete, the test specimens were placed into the testing furnace and all of the
instrumentation attached.

For lifting purposes, four of the shear studs were replaced with

threaded rod of equivalent shear strength, and the rods were long enough for them to pass
through the slab and leave approximately 75 mm of threaded rod exposed past the top surface of
the slab. On this protruding threaded rod, a hook eye was attached for use in lifting the specimen
as shown in Fig. 3.12a.
As seen in Fig. 3.8e, the concrete slab extends 1.2 m past the edge of the W12X16 steel sections,
as such, there is considerable bending moment in these edges where they meet the W12X16
beam. While the specimen is designed to support this force under standard loading, it was feared
that shock during the installation process would cause the unsupported edges to fracture. To
remedy this problem, wooden beams were placed on the top of the slab and used to support the
otherwise unsupported edges during placement as seen in Fig. 3.12b.
The beam slab assembly was brought into the proximity of the furnace utilizing an overhead
crane system. Due to the geometric constraints of the furnace and the overhead crane, it was not
possible for the specimen to be placed directly in the furnace. Rather, the specimen had to be
transferred to a four point, cantilevered, overhead roller system. Once transferred onto the roller
system, a forklift was used to push the assembly into the testing furnace as shown in Fig. 3.12c.
The specimen was then lowed onto support points such that the entire assembly was level and
very near the top of the furnace as shown in Fig. 3.12d. Sufficient distance was maintained
between the furnace and the assembly as to eliminate the possibility of the furnace offering any
structural support to the specimen as it defected due to the effects of fire exposure.

75

b) Lifting of test specimen for placement in the

a) Beam-slab lifting mechanism

furnace

c) Placing of specimen on top of the testing

d) Final position of the beam-slab assembly atop the

furnace

testing furnace

Fig. 3.12: Procedure used for placing of the beam-slab assembly atop the testing furnace
3.3.5

Test Conditions

Loading on the beam-slab assemblies was applied via hydraulic actuators at the 5 points
indicated by arrows in Fig. 3.13. Different point load magnitudes were applied to the center of
the different assemblies (PC-1, PC-2, PC-3, and SFRC) while the four perimeter point loads
were held constant at 22.5 kN for all tests. For test PC-1, the loading on the central actuator was
133.4 kN and the load was split to two point loads separated by 304 mm. For assemblies PC-2
and PC-3, the central actuator applied a load of 111.2 kN. For the SFRC slab, the central
actuator applied a load of 90 kN. The loading was calculated as per AISC provisions (2005), and
76

represented a load ratio of 30-45% on the central unprotected beam, 40-55% on the connections
between the central unprotected beam and the girders, and 50-65% on the protected girders for
the various assemblies. This loading was applied 30 minutes prior to the initiation of testing to
ensure that the deflections reached a steady condition before initiating fire exposure. The slab
was supported on steel supports 152 mm from each end of the W12X16 girders. Support
conditions were such that vertical displacement of the specimen was completely restrained,
horizontal translation of the slab was restrained by the friction between the girders and the
supports, and rotation was completely unrestrained.

1066

1066

1143

457
457

1924

Furnace

= Load application point
Fig. 3.13: Schematic of loading on the beam slab assembly (mm)
The non-standard fire exposure chosen was composed of a growth phase for the first 90 minutes,
followed by a decay phase such that the total fire exposure lasted approximately 4 hours to
simulate a realistic yet severe office fire scenario. The growth phase of the fire followed ASTM
E-119 (2007) fire exposure for 90 minutes, while in the decay phase the temperatures decreased

77

at 5.6 °C/min to ambient temperature as shown in Fig. 3.14. This cooling rate, which is 0.5
°C/min less than specified in Eurocode, was selected to achieve conservative test results by
increasing the duration of the fire exposure. During the fire test, temperatures, deflections, and
strains were recorded at five second intervals, and manual visual observations were recorded at
five minute intervals or when significant events such as spalling or cracking occurred.
1000

Temperature (°C)

800
600
400
200
0
0

50

100

150

200

250

300

Time (min)

Fig. 3.14: Time temperature curve used in fire resistance test
3.3.6

Test Results

Initially, the three plain lightweight concrete slabs were tested under fire exposure, based on the
results from these tests it was decided to conduct an additional test on a similar beam-slab
assembly made with SFRC as described above. As such, the following discussion is divided
between the plain concrete assemblies that were initially tested, and the SFRC assembly tested
later.

78

Visual Observations - Plain Concrete
During the fire test, visual observations of the assembly were made every five minutes, or when
a significant event occurred. Where practical, these events were documented via photographs as
well.
For assembly PC-1, popping noises were heard almost immediately upon initiation of the heating
process. Approximately 10 minutes after initial heating, cracks were becoming visible on the
surface of the assembly with steam and boiling water being emitted from these cracks as shown
in Fig. 3.15. At approximately 26 minutes, it was observed that the large deflection in the beams
was causing the fireproofing to de-bond from the surface of the beams. The test continued with
deflections increasing and moderate levels of cracking until the large deflections of the slab were
sufficient to cause instability in the load splitter, at which point, it failed as shown in Fig. 3.16,
this point was taken as failure of the assembly for the purposes of this research.

Crack emitting
steam

Fig. 3.15: Steam coming out of longitudinal crack in slab.

79

Fig. 3.16: Failure of load splitter during testing of assembly PC-1
Similar to the first lightweight concrete assembly, popping was heard early in the fire exposure
for assembly PC-2 with the first sounds being heard at approximately 11 minutes. As the fire
progressed, cracks began to form on the surface of the assembly with steam and boiling water
being emitted from these cracks. After about 15 minutes of fire exposure, cracks were observed
to form and grow parallel to the W12X16 beams. These cracks grew in length and depth
similarly to those shown in Fig. 3.17. Finally at 27 minutes, the central unprotected beam was
observed to fail as it could not longer support the load. Failure of the unprotected beam was
accompanied by a punching failure of the concrete slab as seen in Fig. 3.18.

Crack
Fig. 3.17: Longitudinal crack at 90 minutes into fire resistance test

80

Fig. 3.18: Punching shear accompanying failure of the central beam in PC-2
Visual observations recorded during the testing of assembly PC-3 follow the same trend as those
observed for assembly PC-2. Popping was heard in assembly PC-3 starting at approximately
seven minutes, and was accompanied by the formation of cracks appearing on the surface of the
specimen. It was observed, as was the case in the previous tests, that cracks formed parallel to
the W12X16 beams at approximately 15 minutes. These cracks continued to grow in both length
and depth as the fire exposure time increased. This trend continued until 31 minutes at which
point the beam could no longer support the applied load, and the specimen failed. As was the
case of assembly PC-2, failure of the beam in assembly PC-3 was accompanied by a punching
failure of the slab as shown in Fig. 3.19.

Fig. 3.19: Punching shear accompanying failure of the central beam in PC-3

81

Post Fire Observations – Plain Concrete
Due to the extreme temperatures achieved during fire testing, it was not possible to trace the
development of cracks during the tests. After the tests, observations were made on the fire
exposed specimen regarding the deflected shape, the cracking pattern on the top of the slab, and
the integrity of the beam network and connections.
The primary post fire observation is that the fire resistance achieved though composite beam-slab
assemblies made with plain concrete is insufficient to meet the levels required in codes and
standards. Assembly PC-1 failed at 51 minutes, PC-2 failed at 27 minutes, and assembly PC-3
failed at 31 minutes, all slabs developed a deflection basin similar to that shown in Fig. 3.20.

Fig. 3.20: Post fire deflected shape of the beam-slab assembly
Considerable insight can be gained on the response of the assemblies to fire exposure through
examination of the cracking pattern on the top of the assembly. In all of the plane concrete
assemblies, cracking was observed to follow the traditional yield line pattern until just prior to
failure of the assembly. When the specimens failed due to softening of the heated central beam,
a multitude of radial cracks rapidly formed from the central actuator to the perimeter of the

82

heated region as observed in Figs. 3.21a-c. It should be noted in reference specifically to Fig.
3.21a that failure of this specimen occurred due to instability in the load splitter, as such, the
same extent of cracking was not observed Fig. 3.21a as in the other specimens.

a) PC-1

b) PC-2

c) PC-3
Fig. 3.21: Cracking pattern on the top of the tested plain concrete assemblies after exposure to
fire
Upon cooling of the specimens, they were removed from the furnace and the post fire condition
of the assembly assessed. For assembly PC-1, due to the presence of one hour of fire protection

83

on the surface of the central beam and failure being attributed to instability in the load splitting
system, only minor deflections were observed in the central beam. Assemblies PC-2 and PC-3
however sustained appreciable damage as shown in Fig. 3.22, due however to the similarities
between the post fire conditions of the specimens, only one figure is shown. From Fig. 3.22 it
can be seen that significant yielding occurred in the unprotected W10X15 beam.

This

deformation is attributed to the inability of the slab to carry the entire load from the central
actuator, as such, a high stress state existed in the unprotected beam causing considerable
yielding of the section. Due however to the continual lateral support provided to the top flange
of the section by the composite deck, no local or global instabilities were observed to develop in
the beam.

Fig. 3.22: Post fire condition of central beam in PC-2
Conditions observed in the connections following fire exposure are consistent with the
deformations observed in the central beam. For assembly PC-1, only minor rotations were
observed in the fin plate connections, and the bolts were observed to be fully functional with no
damage to either the bolts or the holes through which the bolts pass. Assemblies PC-2 and PC-3

84

however revealed a different behavior as compared to assembly PC-1. The large deformations
observed in Fig. 3.22 caused significant rotations in the fin plate connections (PC-2) and double
angle connections (PC-3). These rotations were sufficient to cause shear deformations in the top
bolts of the connections as shown in Fig. 3.23. For more detailed information on the response of
the connections in these tests to fire exposure, the reader is directed to the literature (Wellman
2010).

Fig. 3.23: Post fire condition of connection bolts
Shear studs were observed to have no perceivable deformations at any location (on protected or
unprotected beams) following the fire tests. A maximum temperature of 400 °C was observed in
the shear studs. Even at these temperatures, no deformation of the shear studs was observed.
This is of critical importance as it indicates that there was no slip between the steel and the
concrete at any point during the fire exposure.
In all of the assemblies, the protected W12X16 girders sustained large deflections, but were not
observed to fail. There was no indication of local or global failure of the W12X16 sections in

85

any of the tests, though there were rotations observed in the W12X16 sections resulting from the
forces generated through thermal expansion of the heated central beam.
For all of the tested plain concrete assemblies, the composite deck was observed to have almost
completely delaminated from the concrete slab. It is assumed that the excessive pressure caused
by steam escaping from the heated region of the test caused the decking to delaminate. While
the decking was significantly discolored and delaminated from the concrete, there were no points
where the deck ruptured, thus, the deck helped to protect the concrete from direct fire exposure.
Thermal Response – Plain Concrete
The temperature measurements recorded at various points throughout the thermocouple network
can be used to illustrate the thermal response of the beam-slab assemblies. The three main
components for consideration in the thermal analysis are the protected beam, the unprotected
beam, and the slab. These components will be discussed separately in the following subsections.
Protected Beam – Plain Concrete
For all of the lightweight concrete assemblies, the W12X16 beams were provided with one hour
of fire protection, and in assembly PC-1, the central beam was provided with the same
protection. Temperatures were monitored on the top and bottom flanges as well as on the web of
these beams at several cross sections. Due to the ASTM fire exposure being used in all of the PC
cases, and the assemblies failing prior to reaching the prescribed decay phase, the thermal results
from all of these cross sections in all of the tests are appreciably similar, and as such, the
following discussion should be assumed to apply to all of the beams provided with one hour of
fire protection.

86

From Fig. 3.24, it can be seen that the temperatures in the bottom flange of the beam are the
hottest followed by the web then the top flange. When the central protected beam failed in
assembly PC-1, the temperature in the bottom flange of the beam was approximately 600 °C as
indicated in Fig. 3.24. As such, the beam had approximately 55% of its ambient temperature
capacity remaining when the deflection of the slab caused instabilities in the load splitter and it
failed to support the applied load. For assemblies PC-2 and PC-3, the one hour fire protection
applied to the W12X16 girders provided sufficient strength that failure was observed in the
unprotected central beam.
1200

Fire exposure
Bottom

Temperature (°C)

1000

Web
Top

800
600
400
200
0
0

10

20

30

40

50

Time (min)

Fig. 3.24: Temperatures in the one hour protected (W12X16) beam with fire exposure time
Unprotected Beam – Plain Concrete
As was the case with the protected beam, temperatures were monitored in the bottom flange,
web, and top flange of the unprotected beam, these temperatures are plotted in Fig. 3.25. Fig.
3.25 shows temperatures recorded for assembly PC-3 due to the similarities between the thermal

87

response for the unprotected beam in assemblies PC-2 and PC-3 only one figure is provided. It
is observed from Fig. 3.25 that the temperatures in the unprotected beam follow those of the fire
closely (reaching a maximum temperature of 700 °C) due to the high fire exposed surface area to
the weight ratio (W/D) of the section. This W/D ratio causes a slight “lag” in temperature
between the fire exposure and the steel temperatures. At failure of assemblies, PC-2 and PC-3
had approximately 17% of their ambient temperature strength remaining.

1000

Temperature (°C)

800
600
400

Bottom
Web
Top
Fire exposure

200
0
0

10

20

30

Time (min)

Fig. 3.25: Temperatures in the unprotected beam as a function of fire exposure time
Slab Temperatures – Plain Concrete
Temperatures at the bottom, mid-depth, and top of the plain concrete slab as recorded for
assembly PC-1 are shown in Fig. 3.26. Only results for PC-1 are presented since the thermal
results from assemblies PC-2 and PC-3 are similar with the exception of the shorted fire duration
time, as such, this discussion applies to all of the plain concrete assemblies. Of particular note
from Fig. 3.26 is the observation that temperatures on the unexposed surface are sufficiently low

88

that they do not control failure of the specimen. It can also be seen in Fig. 3.26 that the
temperatures at the bottom and mid-depth of the slab experience a rapid increase at about 30
minutes. This is attributed to the extensive cracking of the slab permitting the heat from fire to
penetrate the slab more readily as deflections increase.
1200

Fire exposure
Bottom

Temperature (°C)

1000

Top
Mid-depth

800
600
400
200
0
0

10

20

30
Time (min)

40

50

Fig. 3.26: Temperatures at various depths of the lightweight slab as a function of fire exposure
time
Structural Response – Plain Concrete
Monitored structural responses consisted of strains and deflections on the top surface of the
assemblies at the locations noted previously. Due to the poor response of the plain concrete
assemblies (short fire resistance), it was necessary to test advanced material systems (SFRC) in a
similar assembly to develop practical alternatives for achieving fire resistance. As such, the
structural response of the plain concrete assemblies will be presented only briefly here, for a full
description of the test results, the interested readier is directed to the literature (Wellman 2010).

89

Strains – Plain Concrete
Fire exposure is one of the most severe conditions to be duplicated in a laboratory environment,
as such, accurate measuring of sensitive data such as strains is inherently difficult. To further
complicate the issue, the adhesives used to attach strain gages to the top surface of the assembly
fail to adhere above 80 °C.

In the case of the 101.6 mm lightweight aggregate slabs,

temperatures above 80 °C are achieved in approximately 15 minutes as seen in Fig. 3.26. The
rapid failure of the strain gages in the fire exposure severely limits the information available
from this portion of the data network, and as such, only a brief discussion on strains can be
presented.
During the initial part of the fire exposure, compression resulting from application of the
mechanical loading is observed over the surface of the assembly.

The magnitude of the

compressive strains decreases as fire exposure time increases (presumably due to thermal
expansion of the central beam), however, the strain gages fail prior to transitioning to the tension
regime, thus little information can be gained from further examination of strains.
Deflections – Plain Concrete
A significant deflection rate is observed at the center of the plain concrete assemblies, and all
three of the assemblies fail in less that one hour as shown in Fig. 3.27. Assembly PC-1 was
observed to withstand the fire exposure for the longest time supporting the applied load for 51
minutes with an ultimate deflection of 78 mm at failure. Assemblies PC-2 and PC-3 did not
perform as well due to the absence of fire protection on the central beam in these assemblies.
Failure was observed in assembly PC-2 at 27 minutes with an ultimate deflection of 133 mm.
Assembly PC-3 was observed to fail at 31 minutes with a total deflection of 132 mm as seen in
Fig. 3.27.

90

Upon inception of the fire exposure, the assemblies are all observed to start deflecting as seen in
Fig. 3.27. These deflections are attributed to the thermal expansion of the supporting steel
sections for the initial portion (15 minutes) of the fire exposure. As the temperatures continue to
increase in the case of PC-2 and PC-3, the unprotected beam continues to lose strength, and
significant yielding of the section is observed. This continued until failure of the assembly at the
respective times indicated above.
0

Deflection (mm)

-20

PC-1
PC-2

-40

PC-3

-60
-80
-100
-120
-140
0

10

20

30

40

50

60

Time (min)

Fig. 3.27: Center point deflections recorded during testing for assemblies made with plain
concrete
Failure of specimen PC-1 was observed to differ slightly from that of either PC-2 or PC-3 as
observed from Fig. 3.27. Due to the presence of fire protection on the central beam for assembly
PC-1, the heating rate of the beam was significantly slower than in the other tests. As such, it
takes more time (25-30 minutes) for the supporting steel beam to be sufficiently weakened that
yielding begins to dominate the response of the assembly. For the period from 25 minutes to the
end of the fire exposure, the beam is slowly increasing in temperature and composite action is

91

developed in the assembly as it deflects. This permitted the assembly to withstand fire exposure
for 51 minutes prior to developing an instability in the load splitter which lead to termination of
the test.
Overall, from the fire resistance tests on composite beam slab assemblies made with plain
lightweight concrete, it was observed that composite action with plain concrete enhances fire
resistance over that observed for structural steel elements tested individually. However, it was
further observed that the fire resistance achieved though this composite action is insufficient to
meet the levels required in codes and standards. As such, an alternative material system (SFRC)
was considered in a similar beam slab assembly and exposed to the same fire exposure shown in
Fig. 3.14. The response of the SFRC assembly including visual observations, post fire analysis,
and thermal and structural responses are presented in the following section.
Visual Observations - SFRC
During the heating portion of the fire exposure, significant popping was heard starting at about 5
minutes as the steel deck de-bonded from the concrete. Often times, the deboning and popping
was accompanied by bursts of steam coming out from around the perimeter of the slab between
the deck and the concrete.
After forty minutes of fire exposure, the unsupported edge of the slab was observed to lift
vertically by a significant amount as seen in Fig. 3.28. This is attributed to thermal expansion
and curvature of the supporting steel sections as mentioned previously.
After approximately 50 minutes of fire exposure, as was observed in the plain concrete slabs, a
crack formed through the thickness of the slab next to the W12X16 beam on both edges as
shown in Fig. 3.29.

92

Fig. 3.28: Lifting of unsupported edge from the furnace and separation from the deck

Crack

Fig. 3.29: Crack formation next to W12X16 section
Following formation of the crack shown in Fig. 3.29, the crack began to grow rapidly until
approximately 90 minutes of fire exposure, at which point the crack reached steady state. During
this time, significant amounts of steam (as in Fig. 3.15) was observed to be coming out of the
crack as additional popping occurred in the slab. After the steam had finished coming out of the
crack, it was observed that the crack was significantly larger than when the steam first began
93

Following propagation of the crack over the entire length of the assembly (parallel to the
W12X16 beam) a discontinuity in the curvature of the slab was observed as shown in Fig. 3.30.
This corresponds to the point when the slab fractured, the edge deflections returned to zero, and
the unsupported edge was resting on the furnace.

Fig. 3.30: Discontinuous curvature along slab edge
Post Fire Observations - SFRC
The primary post fire observation is that the assembly was able to support the applied load for
the entire fire exposure, including the decay phase, with no failures or signs of failure. At no
point did deflections increase rapidly (as seen from the recorded deflection data), or the assembly
show signs of eminent failure. The deflected shape of the specimen is shown in Fig. 3.20 from
which it can be seen that the slab deflected downward causing a deflection basin to form in the
center of the assembly. This deflection basin recovered to a total deflection of approximately 95
mm.
Given that the unprotected beam reached temperatures in excess of 900 °C, it can be assumed
that the beam offered relatively little support to the assembly during the peak of the heating

94

phase. This would cause the central portion of the slab to essentially behave as a two way slab.
Under this postulate, it is reasonable to assume that the central portion of the slab would crack
according to the traditional yield line failure pattern as was the case with the plain concrete slabs.
This cracking pattern was however not observed in the post-fire test assessment due to the high
tensile strength of SFRC. The cracking pattern observed on the top of the beam-slab assembly is
shown in Fig. 3.31 (cracks highlighted to enhance visibility).

Fig. 3.31: Cracking pattern on the top of the tested SFRC beam slab assembly after exposure to
fire
Critical in Fig. 3.31 is the observation that the cracks take the form of concentric circles around
the central load actuator. This cracking pattern is consistent with the development of tensile
membrane action. The deflection of the slab, causing a deflection basin, caused cracks to form
in concentric circles as the tensile strains developed in a radial pattern outward from the center of
the slab. These cracks were quickly arrested by the steel fibers that bridged the cracks, allowing
the assembly to survive complete design fire burnout.
After the assembly had cooled sufficiently, one of the unsupported edges was removed to allow
entry to the furnace and subsequent assessment of the steel beam network. It was found during

95

this inspection that the assembly sustained relatively little damage considering the extreme
temperatures and loading to which it was subjected. As seen in Fig. 3.32, the unprotected beam
underwent considerable deflection, but never lost stability as indicated by the absence of local or
global buckling.

Fig. 3.32: Post fire condition of central unprotected beam
In the same manner, only minor damage was observed in the connections between the beams.
While minor rotations were observed in the fin plate connections, the bolts were observed to be
fully functional with no damage to either the bolts or the holes through which the bolts pass. Fig.
3.33 shows the condition of one connection following the fire exposure (both were similar thus
only one is shown).

Fig. 3.33: Post fire condition of fin plate connection

96

As was the case with the unprotected beam and the connection, only minor damage was observed
in the protected beam. The center of the beam had deflected downward and retained some
deflections as residuals from the fire exposure. There was however no indication of imminent
failure in the protected beam in the form of either local or global buckling.
As was the case with the plain concrete assemblies, the composite deck was observed to have
almost completely delaminated from the concrete slab. It is assumed that the excessive pressure
cause by steam escaping from the heated region of the test caused the decking to delaminate.
While the decking was significantly discolored and delaminated from the concrete, there were no
points where the deck ruptured, thus, the deck helped to protect the concrete from direct fire
exposure.
Lastly, as was the case with the plain concrete slabs, the shear studs were observed to have no
perceivable deformations at any location (on protected or unprotected beams) following the fire
tests. This is of critical importance as it indicates that there was no slip between the steel and the
concrete at any point during the fire exposure.
The observation that the assembly withstood the effects of fire and load while sustaining
relatively little damage led to the development of the postulate that the use of SFRC in composite
floor assemblies can significantly enhance their fire resistance. In this experiment, the behavior
of the floor assembly was enhanced to the point where an unprotected steel beam, which is
commonly assumed to have fire resistance on the order of 15-20 minutes, was able to survive
burnout under a design fire exposure.
Thermal Response – SFRC
The temperature measurements recorded at various points throughout the thermocouple network
can be used to illustrate the thermal response of the beam-slab assembly. The three main

97

components for consideration in the thermal analysis are the protected beam, the unprotected
beam, and the slab. These components will be discussed separately in the following subsections.
Protected Beam – SFRC
Temperatures were monitored in the bottom flange, top flange, and the web of the protected
W12X16 beam at a total of 6 locations (see Fig. 3.8a). The temperatures in the respective
components were significantly similar at each of the cross sections monitored. As such, only one
temperature is plotted for each of the protected beam components (bottom flange, top flange, and
web) as well as the furnace temperature in Fig. 3.34.
From Fig. 3.34 it is clear that the temperatures experienced by the top flange are lower than those
in the bottom flange and web of the beam, this is primarily due to the cooling effect of the slab to
the top portion of the beam. In addition to cooling the top flange of the beam, the concrete slab
also limits the fire exposure on the beam to three-sided exposure. This causes the top flange to
experience notably lower temperatures than the rest of the beam. On the contrary, the bottom
flange of the beam being exposed on all sides and not being directly connected to the slab
experiences the highest temperatures observed in the cross section. Lastly, the web temperatures
are between those in the top and bottom flanges. In large part this is due to the heating and
cooling effects of the bottom and top flanges on the web respectively.
It can also be seen from Fig. 3.34 that the temperatures in the protected beam reach their
maximum of 700 °C approximately 30 minutes after the fire enters the decay phase. This is
attributed to the fact that though in the decay phase, the fire is still hotter than the steel section,
thus, the section keeps increasing in temperature until the fire temperature drops below that of
the steel section. As the beam temperatures decrease, it is observed that temperatures in the

98

beam cross-section begin to converge. This is due to the slow rate of cooling allowing sufficient
time for the section to reach relative equilibrium, facilitated by the high thermal conductivity of
steel.
Peak temperatures in the protected beam were sufficient to cause the bottom flange of the beam
to lose approximately 75% of it yield strength, and the web to lose approximately 60% of it yield
strength. Due to the cooling effect of the slab, the top flange of the beam experienced no loss of
strength.

1200
Bottom
W eb
Top
Fire exposure

Temperature (°C)

1000
800
600
400
200
0
0

60

120

180

240

Time (min)

Fig. 3.34: Temperatures in the protected (W12X16) beam with fire exposure time
Unprotected Beam – SFRC
As was the case with the protected beam, temperatures were monitored in the bottom flange,
web, and top flange of the unprotected beam, these temperatures are plotted in Fig. 3.35. This
instrumentation layout was used only in the center of the beam and no duplicate thermal results
were recorded due to the limited availability of data acquisition channels.

99

Temperatures in the unprotected beam follow those of the fire closely (reaching a maximum
temperature of 950 °C) due to the high fire exposed surface area to the weight ratio (W/D) of the
section. This W/D ratio causes a slight “lag” in temperature between the fire exposure and the
steel temperatures. Thermal lag is also responsible for the temperatures in the steel beam in the
cooling phase exceeding the fire temperatures.

Additionally, in the cooling phase, the

temperature in the top flange of the beam exceeds those in the rest of the beam. This is attributed
to the fact that the slab, which keeps the top flange cooler in the heating phase, heats the top
flange of the beam during the cooling phase, keeping it warmer than the fire temperature.
At peak temperature, the entire unprotected cross-section had about 5% of its ambient yield
strength remaining based on the strength-temperature relationships for steel. Yet, as will be seen
in the discussion on structural response, the assembly did not fail despite losing almost all of the
strength in the central (loaded) beam.

1200
Bottom
Web
Top
Fire exposure

Temperature (°C)

1000
800
600
400
200
0
0

60

120

180

240

Time (min)

Fig. 3.35: Temperatures in the unprotected beam as a function of fire exposure time

100

Slab Temperatures – SFRC
Temperatures in the slab were monitored in the thick part of the ribbing as presented in Fig. 3.8b.
Thermocouples were located on the steel decking, the shrinkage steel, and on the top surface of
the slab. While four points in the slab were instrumented in similar fashion, again, the same
trends were observed in all of the locations, and as such, only one location will be presented.
Fig. 3.36 shows the temperatures across the depth of the slab as a function of fire exposure time.
Intuitively, the temperatures decreases with increasing distance from the fire exposed surface.
The temperature at the steel-concrete interface in the deck experienced the highest temperatures,
with a peak temperature of 800 °C that roughly coincided with the peak fire temperature. The
thermocouples located on the shrinkage reinforcing experienced temperatures in excess of 400
°C with a peak temperature occurring approximately 45 minutes after the peak fire temperature,
while the top surface of the slab reached a maximum temperature of 180 °C approximately three
hours after the peak fire temperature. The delay in peak temperatures associated with increasing
depth is due to the low thermal conductivity of concrete.

1200
Bottom
Mid-depth
Top
Fire exposure

Temperature (°C)

1000
800
600
400
200
0
0

60

120

180

240

Time (min)

Fig. 3.36: Temperatures at various depths of the slab as a function of fire exposure time

101

Temperatures at the deck-concrete interface are observed in Fig. 3.36 to lag the fire exposure
temperature with a plateau occurring at approximately 100 °C which lasted approximately 20
minutes. This is attributed to the presence of water in the concrete. When the concrete reaches
100 °C, the temperature stabilizes until all of the free water is driven out of the concrete. This
results in the temperature profile seen in Fig. 3.36.
Structural Response – SFRC
Instrumentation to capture the structural response of the assembly consisted of strain gages and
displacement transducers. The recorded data is utilized to trace the structural response of the
beam slab assembly.
Strains - SFRC
For the same reasons state in regard to the plain concrete slabs, it is difficult to acquire accurate
strain information under fire exposure conditions. As such, the following sections analyze the
strain data from a qualitative stance as the thicker concrete slab permitted the strain gages to
return data for an extended period of time as compared to the plain concrete slabs. The strain
data is divided into three sections, the center point strain gages which were located 76 mm from
the central load application point, the mid-slab strain gages which were located 610 mm from the
center of the slab, and the outside strain gages which were inset 305 mm from the edge of the
slab. The location of these strain gages can be more clearly seen in Fig. 3.8d. In the following
discussion, when a strain gage no longer returned coherent readings, the channel is terminated in
the respective plots.
Due to the need to accommodate a spreading plate for the loading actuator, the strain gages at the
center of the specimen were located 76 mm from the center of the slab, and were oriented at 90°
from each other. Data from these gages is plotted as a function of fire exposure time in Fig. 3.37

102

below, strain gage 135 is oriented parallel to the unprotected steel beam, while strain gage 136 is
perpendicular to the unprotected beam. Both strain gages are slightly under compression at the
beginning of the test due to the mechanical loading. As the test continues, the strain gages
register considerably more compression, then compression starts to decrease and strain gage 136
enters tension before the gage fails. Gage 136 approaches zero strain, but just prior to failure
again goes into compression.

1000
135

Strain (micro-strain)

500

136

0
-500
-1000
-1500
-2000
-2500
0

60

120

180

240

Time (min)

Fig. 3.37: Strains at central strain gages (76 mm offset) as a function of fire exposure time
Initially, the strain gages are in compression due to the mechanical loading being transferred
across the slab via bending. This compression on the top of the slab is observed until the slab is
sufficiently weakened that it can no longer support the slab via bending. At this point, tensile
membrane action begins to carry a portion of the load. As the slab develops tensile membrane
behavior, the compression decreases at both strain monitoring locations with one gage entering
into tension while compression decreases at the other. At the end of the fire exposure, when the

103

entire specimen is cooling, both strain gages show an increase in compressive strain; this can be
attributed to the cooling of the specimen and the relative thermal shrinkage of the assembly.
Of particular interest in Fig. 3.37, is the observation that the strain gages though very close in
proximity, and having similar initial readings, register significantly different results during the
fire test. This is attributed to the orientation of the strain gages relative to the unprotected steel
beam. Strain gage 135, being parallel to the rapidly expanding and contracting steel beam
experiences stresses caused by the relative thermal expansion difference between steel and
concrete. Strain gage 136 is relatively immune from this thermal expansion incompatibility
being oriented perpendicular to the steel beam, and hence, the different strains observed in Fig.
3.37 result.
The second group of strain gages that can be readily separated for discussion purposes are those
located 610 mm from the center of the slab. These strain gages are all oriented radially from the
center of the slab.

Strain gages 132 and 134 are located on top of (and parallel to) the

unprotected W10X15 section, while strain gages 138 and 140 are located away from any steel
members as seen in Fig. 3.8d above. Strain as a function of fire exposure time for these gages is
shown in Fig. 3.38 below.
While all of the gages start at relatively the same point in compression due to the mechanical
loading, the two gages (132 and 134) located over the steel beam respond differently than those
away from the steel beam, this is attributed to the difference in thermal expansion between steel
and concrete as discussed previously. Early in the fire exposure, all of the strain gages begin to
register increasing compressive strains. This trend is continued until approximately 60 minutes
of fire exposure, at which point all of the gages show a rapid decrease in compression strain with
three of the four gages transitioning to the tensile region as seen in Fig. 3.38. At this transition

104

point, there is a disconnect appearing in the data for gage 134, this is due to the strain gage
failing to register strain readings during this time period. After the transition from compression
to tension, the strain gages stay in the tensile region for as long as data is available with the
exception of gage 140 which transitions back into the compression region in the cooling phase of
the fire due to the decrease in thermally induced strains.
2500
132
134
138

Strain (micro-strain)

2000
1500
1000

140

500
0
-500
-1000
-1500
-2000
-2500
0

60

120

180

240

Time (min)

Fig. 3.38: Strains observed at the middle of the slab as a function of fire exposure time.
Considering that the strain gages are located on the top of the slab, the only way for the strain
gages to experience tension in the given loading configuration, is if the entire depth of the slab is
experiencing tension. As such, the existence of tensile forces as indicated by three of the four
strain gages indicates that the slab has developed tensile membrane behavior.
The final group of strain gages to be discussed is those inset 305 mm from the edge of the slab as
shown in Fig. 3.8d. As observed in Fig. 3.8d, these strain gages are oriented parallel to the edge
to which they are closest. Strain gages 131 and 133 are on the unsupported edges of the slab,
while gages 139 and 137 are located almost over the edge W10X15 beams (which were not

105

exposed to fire). Fig. 3.39 shows the strain at the edge of the slab recorded by these strain gages
as a function of fire exposure time.
100

Strain (micro-strain)

0
-100
-200
-300
-400

131
133
137
139

-500
-600
-700
-800
-900
0

60

120

180

240

Time (min)

Fig. 3.39: Strains recorded at the edge of the slab (305 mm inset) as a function of fire exposure
time
Strain gages 137 and 139 being located above the unheated steel beam show relatively little
change during the course of the fire exposure due to the high strength at that location relative to
other locations on the slab (due to the presence of the steel beam below the strain gages). Strain
gages 133 and 131 however show comparatively interesting results. At one hour, strain gage 131
begins to develop compressive forces while strain gage 133 does not develop these forces until
approximately 80 minutes of fire exposure. These times roughly coincide with the times at
which the mid-slab strain gages transition to tension. Compression in the perimeter of the slab
being an indicator of tensile membrane behavior, serves to reinforce the observation that tensile
membrane action was developed and helped to transfer the load to the cooler parts of the
structure at this time.

106

In Fig. 3.39, it is clear that while strain gages 131 and 133 transition into the compression zone,
gage 133 developed far more compressive strain than gage 131. Given the symmetry of the
specimen there should not be such a discrepancy between similarly placed gages. As discussed
in the visual observations section, a large crack formed along the outside edge of the W12X16
next to strain gage 131. This crack occurring over the full depth and length of the specimen, is
believed to have significantly altered the force transfer across that section.

Hence, the

compressive forces could not be transferred across that discontinuity, causing gage 133 to
register significantly higher compressive forces as shown in Fig. 3.39.
Strain data being inherently volatile in fire resistance experiments should be used with
considerable caution. The preceding qualitative assessment of the strains recorded during the
describe fire resistance test indicate that the slab developed tensile membrane action, with tensile
forces in the center of the slab and compressive force around the perimeter. This hypothesis is
further reinforced by the cracking pattern discussed in the post fire exposure assessment
presented in previous sections.
Deflections – SFRC
As discussed in the instrumentation section, vertical displacements were recorded at a total of
nine locations over the unexposed surface of the slab (Fig. 3.8e). Due to the critical nature of
displacements for the validation of computational models, five of the displacement transducers
were redundant, and as such, the results obtained are not unique, and hence, will not be
discussed. The four unique data sets are those corresponding to the supported edge (over the
unheated 10X15), the center of the slab, the connection of the W10X15 to the W12X16, and the
center of the unsupported edge. The deflection time history recorded by these four displacement
transducers is presented in Fig. 3.40 and will be discussed independently below.

107

Center (A)

40

Connection (B)

20

Supported edge (C)

Deflection (mm)

0

Unsupported edge (D)

-20

C

-40
-60

A

-80

B

D

-100
-120
-140
0

60

120

180

240

Time (min)

Fig. 3.40: Deflection time history in a beam slab assembly exposed to fire
Early into the fire exposure, the deflections of the slab over the connection between the beam
and girder are relatively small, and remain essentially constant due to the insulation protecting
the girder from the effects of fire. The deflections at the center of the slab however increase
rapidly during this time. This can be attributed to the thermal expansion of, and loss of stiffness
properties in, the unprotected W10X15 beam. Due to the heat from fire, the unprotected steel
beam undergoes thermal expansion which caused the beam-slab assembly to deflect downward.
In addition to the thermally induced downward deflection, the unprotected steel beam is losing
strength and stiffness due to the increasing temperatures in steel from fire.
Between 20 and 90 minutes of fire exposure, the deflections increase slowly at both the center of
the slab, and above the connection between the beam and the girder. The deflections at the
connection between the beam and the girder are primarily caused by the slow heating of the
protected W12X16 girder weakening the member, and allowing it to deflect under the load. The
deflection at the center of the slab however, is due to further weakening of the unprotected beam

108

and the weakening of the concrete due to the heat from fire. The temperatures reached in the
steel beam by 90 minutes are in excess of 900 °C, thus, the remaining stiffness in the steel beam
is relatively insignificant (about 6.7% of ambient temperature). The loss of stiffness from the
unprotected beam causes the slab to deflect downward more than 100 mm until the majority of
the load from the central actuator (90 kN) is transferred through the slab via TMA.
After 90 minutes of fire exposure, the fire temperatures begin to decrease due to the presence of
a decay phase. At this time, the temperatures in the unprotected steel beam are in excess of 900
°C. As the fire temperatures start to decrease, the temperatures in the unprotected steel beam
decrease at the same rate. The decreasing temperatures allow the steel beam to recover its
strength and stiffness. As the steel beam re-gains its strength, it again begins to contribute to the
strength capacity of the assembly. The strength contribution from the unprotected beam in
combination with the thermal contraction of the unprotected beam causes the deflections in the
assembly to stabilize at 130 mm by 150 minutes of fire exposure.
After 150 minutes of fire exposure, all parts of the assembly are cooling and subsequently
regaining strength. The combination of increasing strength and thermal contraction due to
cooling causes the assembly to rebound through out the duration of the fire exposure.
Supported edge displacement is relatively constant for the entire duration of the fire exposure. A
maximum downward deflection of 2 mm was reached during the fire exposure at this location.
This deflection is due to the downward deflection in the center of the slab causing the perimeter
of the slab to rotate on the supports, resulting in a minor deflection of the supported section.
The unsupported edge however, shows a very unique response compared to the rest of the
assembly. It is observed in Fig. 3.40 that the unsupported edge of the specimen rises vertically
early in the fire exposure. This behavior is confirmed by observations taken during the test, both

109

the direction and magnitude of this deflection was visually confirmed at the time of testing. The
upward translation observed at this location is due to the thermal expansion of the bottom of the
slab, combined with the displacement caused by the mechanical loading. When the slab is
initially heated, the bottom of the slab expands relative to the top. Inside the network of steel
beams, this causes the slab to deflect downward and place the central strain gages in compression
as noted previously. On the unrestrained edges however, the thermal expansion of the concrete
on the bottom of the slab just causes the unsupported edge to curve up and avoid stress
development from thermally induced strains. In addition to the thermal strains, the center of the
assembly deflects downward in the center relative to the connection as discussed in the preceding
section. These deflections cause the assembly to be sloped at the connection between the beams.
This slope, in combination with the thermal expansion on the bottom of the slab outside the steel
beam network, causes the unsupported edge to translate vertically upward as observed in the test.
Between 20 and 90 minutes of fire exposure, the unsupported edge is observed to relax
downward again until reaching its original location, where it remains essentially unmoved for the
remainder of the test. This behavior corresponds to the time at which large cracks began to
develop along the outside edge of the W12X16 sections. These cracks started in the slab at the
ends of the beam then slowly propagated toward the center of the specimen, joining in the center
at approximately 90 minutes. This crack formation caused a discontinuity in the slab, and
resulted in an inability to transfer forces to the unsupported edge, thus allowing it to return to its
original location. For the remainder of the test, the unsupported edge of the slab rested on the
edge of the furnace and offered little support to the remainder of the assembly.

110

3.3.7

Summary

Due to the absence of experimental data on the response of composite floor assemblies to fire
exposure, it was necessary to conduct four novel assembly level fire resistance tests to acquire
data for numerical model calibration. In the fire resistance tests discussed in this section, three
lightweight slabs and a SFRC slab were compositely cast atop networks of 5 steel beams, some
of which were unprotected, and exposed to ASTM E-119 fire exposure for 90 minutes followed
by a 5.6 °C/min decay phase. For the full duration of the fire tests, temperatures, strains, and
deflections were recorded at various locations over the specimen. These data indicate that the
SFRC assembly survived the complete fire exposure reaching a maximum deflection of 137 mm
in the center of the specimen, while the lightweight concrete assemblies all failed in less than an
hour. During the post fire assessment, it was observed that the cracking pattern on the top
surface of the SFRC specimen was one of concentric circles around the central actuator while
those observed on the top of the lightweight concrete assemblies initially followed the yield line
pattern transitioning to radial cracks by the end of the fire test. As such, it is believed that tensile
membrane action was developed in the SFRC slab, and contributed to the fire resistance of the
assembly despite the presence of unprotected steel beams, this belief is further validated by the
recorded data as discussed in the preceding sections, and the early failure times observed in the
lightweight concrete assemblies.

Due to the poor response of the lightweight aggregate

assemblies to fire exposure, it was decided that this material system would not be pursued as a
means of achieving fire resistance through composite construction. Rather, the SFRC system
was selected as the primary focus for the current research, and results from the respective test are
utilized in Chapter 4 for validation of numerical models for use in parametric studies.

111

3.4

System Level – Full-Scale Building

A review of the literature, as conducted in Chapter 2, indicates that several system level studies
on fire resistance of steel framed structures have been conducted. The most comprehensive of
these research programs is that conducted by the Large Building Research Establishment in its
large building test facility in Cardington UK (British Steel 1998). In these tests, collectively
known as the Cardington tests, an eight story steel frame building was subjected to a series of
fires.

A total of 8 fire resistance tests were conducted at this facility.

Results from the

Cardington tests are used in this research to calibrate numerical models of a structural system’s
response to fire exposure. Reviewing the different tests that were conducted at the Cardington
facility, it was determined that the most relevant test to the behavior of system level composite
floor assemblies was the restrained beam test as described below.
The restrained beam test consisted of monitoring the fire response in a compartment of the eight
story braced-frame steel structure where an unprotected UB 305x40 (W12x26 equivalent) beam
spanned between two UC 254 columns. The beam spanned 9 m between the two columns and
was designed to be simply supported while acting compositely with the concrete floor slab. The
floor slab was an in place lightweight concrete floor on a ribbed metal deck, with a maximum
thickness of 130 mm and incorporating A142 anti-crack mesh. The connections of the beam to
the column were typical fin plate connections as seen in Fig. 3.41.

Fig. 3.41: Fin plate connections used in Cardington building

112

A furnace 8 m long and 3 m wide was constructed around a composite beam-slab assembly
supporting the seventh floor of the structure (as seen in Fig. 3.42) to simulate fire exposure.
Loading on the seventh floor of the structure (above the heated beam) was accomplished by
placing sand bags over the floor (also seen in Fig. 3.42) such that the applied load during fire
2

exposure was 4.94 kN/m . The central 8 m of the beam was exposed to fire leaving 500 mm on
each end of the beam, including the connections, outside the fire exposure. The objective of
leaving the connections outside the furnace area was to keep the connections as close as possible
to ambient temperature. The furnace was constructed in such a fashion that it offered no
structural support to the assembly as it deflected.

Fig. 3.42: Furnace constructed around the composite beam for restrained beam test
The assembly was exposed to fire for approximately 2.5 hours, though the time temperature
curve as per ISO 834 (ISO 1975) was to be simulated, the curve designated as “Cardington test”
in Fig. 3.43 resulted. The temperatures attained in the steel beam were in excess of 800 °C, thus,
the steel beam lost approximately 90% of its strength. However, the assembly did not collapse in
spite of recorded deflections as high as 231 mm in the center of the span as seen in Fig. 3.44.
Even when the fire was terminated, there was no sign of runaway deflections in the composite

113

beam. Following the test, the deflection of the beam recovered more than 100 mm to a final
deflection of 113 mm. It was observed that during the test (after about 70 minutes of fire
exposure) local buckling occurred at both ends of the beam just inside the edge of the furnace as
shown in Fig. 3.45. Additionally, there was a slight distortion of the beam bottom flange as
thermal expansion caused the beam to push into the web of the column. It was also observed
that during the cooling phase, the fin plate connection on both ends of the beam fractured as
shown in Fig. 3.46. The fracture of the connections was presumably due to the development of
high thermally induced forces in both the heating and cooling phase of the fire. The main reason
for avoidance of collapse was attributed to the contribution of the concrete slab to load transfer
through TMA (Huang et al. 2001, Alkawakhiri et al. 2004) and the beam-slab interactions both
during the fire exposure and during the cooling phase when the connections failed.
1200

Temperature (°C)

1000
800
600
ISO 834
Cardington test

400
200
0
0

0.5

1

1.5

2

2.5

3

Time (hrs)

Fig. 3.43: Time temperature relationship achieved during the Cardington restrained beam test
and ISO 834 fire exposure for comparison

114

Deflection (mm)

0
-50

0

60

120

180

-100
-150
-200
-250
Time (min)
Fig. 3.44: Measured mid-span deflections for the restrained beam

Fig. 3.45: Local buckling of beam ends in restrained beam test

Fig. 3.46: Fractured fin plate connections in restrained beam after cooling phase of fire
115

3.5

Summary

A large number of fire resistance tests on CFHSS columns have been conducted at NRCC in
Canada. A total of 85 CFHSS columns were tested under exposure to ASTM E-119 fire
exposure. Detailed results from these tests are available through NRCC internal reports, and
through journal publications on the test results. Given the level of detail in the results as
discussed in Section 3.2 of this chapter, and full details on the construction of the assemblies,
this data will be used for the calibration of the element level numerical models necessary in this
research program.
Since there is limited information available on the fire response of composite floor assemblies
under fire exposure, fire resistance tests were carried out on four composite floor assemblies,
three made with lightweight concrete, and one made with SFRC. The test assemblies consisted
of three W10X15 beams and 2 W12X16 beams with the concrete deck on top. To assess the
response of the assemblies to fire exposure, various fire resistance schemes were applied to the
steel beams and the assemblies were subjected to loading under a design fire exposure.
Results from the fire resistance test indicated that the steel beam-SFRC slab assembly, which
incorporated an unprotected steel beam, withstood the full duration of the fire exposure with no
signs of failure while the assemblies made with lightweight concrete did not. Data from the
instrumentation network, which included thermocouples, LVDT’s, and strain gages, indicates
that the SFRC assembly developed tensile membrane action in the composite SFRC slab. This
observation is reinforced by the presence of cracking in concentric circles above the unprotected
steel beam not seen in the lightweight concrete slabs.

Results from this test are used in

subsequent chapters for the validation and calibration of numerical models.

116

A comprehensive series of tests were conducted on an eight story steel frame building at the
Cardington test facility in the UK. Data from these tests including temperatures, displacements,
and construction details is available to the research community. Given the ready availability of
these detailed test results, it is not prudent to conduct additional system level tests, as such, data
from the Cardington tests will be utilized for validation of the system level models created and
employed in this research.

117

CHAPTER 4
4
4.1

NUMERICAL MODEL
General

Recent advances in computational ability and numerical modeling codes offer an attractive
alternative to conducting costly fire resistance tests. Numerical modeling allows the user to
economically investigate the effect of altering a single parameter while holding others factors
constant. This allows the generation of a large data pool for use in statistical regression, trend
identification, and methodology development.

Given the need for such data pools in this

research, not just at the element level, but also at the assembly and system levels, it is necessary
to develop and validate a series of numerical models.
There are several computational models that can be applied for simulating structural response
under fire conditions. These models which are based on finite element formulations include,
ABAQUS, ANSYS, VULCAN, and SAFIR. Of these, ABAQUS and ANSYS are general
purpose finite element programs, while VULCAN and SAFIR were specifically developed for
the analysis of structures exposed to fire. Though general purpose finite element codes can be
employed for analysis of structures under fire exposure, SAFIR was selected for this research
study because it has undergone extensive validation, and predictions from SAFIR have been
shown to closely match fire test data and predictions from other more detailed numerical models
(Franssen, 2005, Gilvary and Dexter, 1997, Talamona, 2005).
4.2

Analysis Procedure

The computer program SAFIR, developed at the University of Liege in Belgium, is capable of
accounting for multiple materials in a cross section, both heating and cooling phase of fire

118

exposure, large displacements, different strain components, non-linear material properties
according to Eurocode 3 (Eurocode, 2005), and residual stresses. Additionally, SAFIR allows
the user to input any time-temperature relationship to facilitate the use of design fire scenarios.
For tracing structural response under fire exposure, the basic equation utilized in SAFIR is:

F   K U 

[4.1]

where {F} is the force vector and [K] is the stiffness matrix. In traditional finite element
analysis, the force vector {F} is changing as a function of time, and, if material non-linearity is
taken into consideration the stiffness matrix [K] changes according to a predefine constitutive
model. For the analysis of structures exposed to fire, additional complexity is added in that
thermal expansion and material degradation due to the effect of fire must be taken into account
both in the stiffness matrix [K], and the force vector {F}. However, before the modified force
vector and stiffness matrix can be determined, it is necessary to determine the temperature at
each node in the assembly. The procedure employed by SAFIR to accomplish this is outlined
below, followed by a description of how SAFIR carries out structural analysis.
4.2.1

Development of Fire Scenarios

The design fire scenario for the desired structural analysis can be established either through the
use of parametric fires (time-temperature curves) specified in Eurocode (2005a) or through
design tables (Magnusson and Thelandersson 1970) based on ventilation, fuel load, and surface
lining characteristics. Once the design fire time-temperature profile is identified (an example
using the Eurocode procedure is presented in Section 6.2.4) this relationship is input into SAFIR
though a *.FCT file. This file is read by the thermal analysis routine, and utilized to determine
the temperatures in the member cross-section according to the following procedure.

119

4.2.2

Thermal Analysis

In the thermal analysis, SAFIR utilizes the general form of the three dimensional heat transfer
(conduction) equation which is:
  2T  2T  2T 
  Q  C T  0
k


 2

t
y 2 z 2 
 x

[4.2]

where:
k

= thermal conductivity

T

= temperature

x,y,z = coordinates
Q

= internally generated heat

C

= specific heat

ρ

= Specific mass density

t

= time

The traditional shape functions as shown in Eqs. 4.3 and 4.4 for triangular and square elements
respectively are used. In Eqs 4.3 and 4.4 ξ and η are the coordinates used to define the reference
elements.

N  1     ; ;
N

1 (1   )(1   ); (1   )(1   )
4 (1   )(1   ); (1   )(1   )

[4.3]
[4.4]

Utilizing these shaped functions, the geometry of the element can be described as a function of
the nodal coordinates as:
x  N i xi ; y  N i yi ; z N i zi

120

[4.5]

And the temperatures at any location in the element can be written as a function of the nodal
temperatures as:
T  N iTi

[4.6]

Since Eq. 4.2 is not in differential form, it is necessary to transform it prior to implementation in
the finite element method. SAFIR accomplishes this by first replacing the temperatures in Eq.
4.2 by the approximation given in Eq. 4.6. After this substitution, the shape functions are used to
weight the function according to the Galerkin method, and then it is integrated over the surface.
Following this integration, the first term in this equation is transformed into a definite integral
through the use of Greens equation. Finally, the system is subjected to the boundary condition of
Eq. 4.7, and Eq. 4.8 is obtained.

qn  kT j N j

 kNi  N j

el


dVTi   CN i N j dVTi   QN j dV  
 N j qn dS
el
el
boundary

[4.7]
[4.8]

where:


  
; ;
x y z

qn = heat flux at the boundary of the element
when all of the contributions from the elements are summed the following is obtained:

K T   C T   g
where:
[K] is the thermal conductivity matrix
[C] is the heat capacity matrix

T is a vector of the nodal temperatures
121

[4.9]

{g} is a vector accounting for the heat exchange at the boundaries
The heat flux across the boundary accounts for convection and radiation according to Eurocode 1
(1995) and is given by Eq. 4.10. If no exposure is specified for a given surface it is assumed that
the surface is adiabatic.
4
4
qn  h Tg  Ts )   (Tg  TS 





[4.10]

where
Tg is the gas temperature
Ts is the surface temperature
h is the convection coefficient
ε is the emissivity
σ is the Stefan Boltzmann constant
For generating matrices [K] and [C] in Eq. 4.9, the integration over the volume of the element is
done according to a Gaussian procedure with the number if integration points being specified by
the user. The integration scheme takes into account that the properties of the material are
temperature dependent and can change over the volume of the element.
For thermal analysis, 2D solid elements are used where the fire exposed sides and the exposure
types are specified by the user. The thermal model in SAFIR neglects heat transfer in the
longitudinal direction, and assumes that every longitudinal cross-section has the same
temperature profile unless otherwise specified. The energy consumed for evaporation of water
present in the concrete is included, but that associated with hydraulic migration within the crosssection is neglected.

122

4.2.3

Structural Analysis

For structural analysis, SAFIR utilizes the incremental form of the principal of virtual work.
Assuming a co-rotational configuration, the incremental form of the principal of virtual work can
be written as:

 ( Dijkl dEklEij  SijdEij )dV   (dfiui  fidui )dV

V

[4.11]

V

The presence of a bar indicates that the variable is evaluated from a rotated position obtained
such that the rigid body rotation matches the deformed shape as closely as possible.
Where:
V  V = the un-deformed volume of the element

Sij = tensor of the second Piola-Kirchoff stress
Dijkl  Dijkl = tensor defining the incremental constitutive law of the material (see Eq below)

Eij = Tensor of the green field of virtual displacement, see equation below
f i = Volume forces

ui = virtual field of displacement from the deformed position of the element
Since the temperatures change during the simulation, the constitutive law can be written as:
Th
m
dSij  Dijkl  dEkl  dEkl   Dijkl dEkl




where

dE th = tensor of incremental strain
kl
dE m = tensor of mechanical or stress related strains
kl

123

[4.12]

where the tensor of the virtual displacement field is given as:

Eij 



1
ui, j  u j ,i  u k ,i u k , j  u k ,i u k , j
2



[4.13]

Utilizing a discretized field to represent the displacement field allows the incremental tensor
strains to be derived as a function of nodal displacements, when this is done, Eq. 4.13 can be
rewritten as:

T DBdVdp  S T dedVdp  K  K dp  f ext  f int
u
s

v
v

B

[4.14]

where
Ku is the linear elastic and the geometric stiffness matrices
Ks is the stress generated stiffness matrix
ext

f

int

f

is the nodal forces which are energetically equivalent to the applied force
are the nodal forces resulting form the integration of internal force.

For structural analysis, SAFIR uses a fiber-based approach wherein each of the solid elements in
the thermal model is considered as a fiber in the structural model. A stress and temperature
dependent stiffness matrix is established that incorporates all of the fibers.
4.3

Program Features

The capabilities of SAFIR for thermal analysis include:


Thermal gradients in two and three dimensional structures, including those with internal
voids, can be determined



For determining the thermal gradients in a structural member, SAFIR considers both
radiation and convection from the fire to the member, and conduction within the member

124



Thermal analysis can be conducted on members incorporating multiple materials in the
cross-section



SAFIR can simulate any time temperature profile including those with a cooling phase

Following completion of the thermal analysis, the thermal information is stored in a text file,
which is then utilized by the structural model. Capabilities of the structural model include:


Deformations in two and three dimensional structures can be determined



Members with pre-stressing forces can be considered



Consideration is given to both thermal and mechanical strains the structural analysis



Both static or dynamic structural analysis can be performed in SAFIR



An arc length convergence criterion is utilized by SAFIR to achieve convergence

Lastly, SAFIR uses some common computational features for both thermal and structural
analysis, they are as follows:


Internal numbering of nodes, SAFIR can automatically re-numbers the nodes to optimize
the matrix bandwidth reducing storage and computational time requirements.



Imposing the same temperature or displacement at two different nodes can be
accomplished using master-slave relations



Thermal and mechanical properties of steel and concrete according to Eurocode 2, 3, and
4 are pre-programmed


4.3.1

All post processing applications are completed with the post processor Diamond
General

As mentioned previously, SAFIR conducts calculations in two steps, the first is a thermal
analysis and the second is a structural analysis.

Each of these steps requires the use of

independent input files, which can be written either by the SAFIR Wizard or manually with text
125

editing software. A schematic of the analysis procedure as reproduced from (Franssen et al.
2000) is shown as Fig. 4.1 below. The link between the thermal and the structural analysis is the
use of a *.tem file produced by the thermal analysis.

This file contains all of the nodal

temperatures in the discretized cross-section. These temperatures are used to determine the
temperature dependent material (structural) properties in the structural analysis procedure. Both
the thermal and the structural analysis produce a *.out file which contains the results from the
respective analysis. This file is opened and viewed by the user via the SAFIR post processor
Diamond as indicated in Fig. 4.1 A brief description of the data in the respective input (*.in)
files is presented for the thermal and structural models in the following sections respectively.
T
hermal analysis 1

T
EXTEDIT
OR

COLUMN.IN

BEAM.IN

COLUMN.OUT

SAFIR

SAFIR

DIAMOND

COLUMN.T
EM

T
hermal analysis 2
S
afirWizard

BEAM.OUT

T
EXTEDIT
OR

DIAMOND

BEAM.T
EM

Mec hanical analysis
T
EXTEDIT
OR

FRAME.IN

SAFIR

FRAME.OUT
DIAMOND

Fig. 4.1: Schematic of SAFIR operational procedure (Franssen et. al 2000)
4.3.2

Thermal Input

While the SAFIR Wizard is capable of writing input files for structural steel members with or
without protection, it is unable to write thermal input files for CFHSS columns or concrete
members, and has no capability to write structural input files.

126

The primary information

contained in the thermal input file is the location of the nodes that compose the member crosssection, the ordering of these nodes to define the elements, and the thermal properties of the
constituent materials such as thermal conductivity, specific heat, emissivity, convection
coefficients, and water content (where applicable). Also defined in the thermal input file are the
materials in the cross section, the fire exposure conditions, and any symmetry in the member. A
detailed summary of the specific format used in the thermal input file is provided in Appendix C.
4.3.3

Structural Input

Once the temperatures in the cross-section(s) are determined, the geometry of the simulated
structure is defined in the structural input file. As there is no pre-processor available for the
structural model, all of the nodes must be manually written in the text input file. A sample of the
input file with descriptions of each line is included as Appendix D. The primary information
contained in the structural input file is the location of the nodes, the ordering of these nodes to
define beam shell or truss elements, and the mechanical properties of the constituent materials
such as Poisson’s ratio, yield strength, compressive strength, tensile strength, and elastic
modulus. For each of the elements in the structural model an associated *.tem file is specified by
the user. SAFIR uses the temperatures in the *.tem file to establish the temperature depended
stiffness matrix for the element under consideration.

Composite action between steel and

concrete is accounted for in SAFIR through the use of the “SAMEALL” or “SAME” commands.
These force nodes at the same location to have the same displacements. The output from the
structural analysis includes the stresses in elements, bending and axial forces, (where applicable)
displacements, and reaction forces. There are however several assumptions employed in the
structural model as enumerated by Kodur et al. (1999) they are:


Plane sections are assumed to remain plane under bending

127



Shear energy is not considered in the analysis in accordance with Bernoulli’s hypothesis



Plastic strain energy is assumed to be temperature independent



The non-linear part of the strain is averaged over the length of the element to avoid
numerical locking



In case of strain unloading, material behavior is elastic with the modulus of elasticity
equal to the Young’s modulus at the origin of the curve


4.3.4

Plastification is only considered in the longitudinal direction of the member
Material Models in SAFIR

The high temperature thermal and mechanical relationships for several common materials are
pre-programmed into SAFIR according to the relations specified in Eurocode (2004, 2005). Of
particular interest for this research are the high temperature constitutive models for steel and
concrete.

Appendix B contains the material models for steel and concrete as specified in

Eurocode (2004) and ASCE (1992) for comparison purposes. The pre-programmed thermal
properties in SAFIR included thermal conductivity, specific heat, and thermal expansion for both
steel and concrete. The pre-programmed mechanical properties in SAFIR include yield strength,
elastic modulus, and ductility for steel, compressive strength, strain at peak stress, and ductility
for concrete.
4.3.5

Modifications to SAFIR

SAFIR has several advantages and pre-programmed material properties as discussed previously.
However, SAFIR lacks a material model for steel fiber reinforced concrete which is paramount
to this research. Therefore, a temperature dependent constitutive material model for SFRC was
implemented in the SAFIR source code.

128

Due to the similarities in thermal properties observed between plain and steel fiber reinforced
concrete (Lie and Kodur, 1995b), only high temperature strength relations for SFRC as found in
Appendix B were added to SAFIR as outlined below.

For the thermal analysis, the pre-

programmed high temperature models for either carbonate or siliceous aggregate should be used,
and the mechanical properties of SFRC is to be specified only for the structural analysis.
Compressive strength of concrete, like other properties, deteriorates with fire exposure time due
to increasing temperature. The normalized (with respect to the ambient temperature compressive
strength of plain concrete) compressive strength of plain concrete (PC) and SFRC are shown as a
function of temperature in Fig. 4.2 below (SFPE 2002, Eurocode 2004, Lie and Kodur 1994,
1995).

Plain concrete behaves as expected in that the strength starts to deteriorate at

approximately 100 °C and the strength deterioration continues in a nearly linear fashion from
200 °C to 800 °C at which point the compressive strength is about 10% of the ambient
temperature strength. SFRC on the other hand behaves markedly differently as seen in Fig. 4.2.
The compressive strength of SFRC increases by about 10% at 200 °C, and this trend is continued
to 400 °C due to the effect of the steel fibers as they help to confine the concrete, and allow it to
act as though under tri-axial compression. This advantage is not fully realized until about 200 °C
due to the need for the concrete to become slightly more ductile before the full advantage of the
steel fibers can be realized. Above 400 °C, the compressive strength of SFRC deteriorates
linearly to zero at 850 °C due to the degradation of the mechanical properties of the steel fibers.
Of particular note is the observation that above 800 °C the compressive strength of PC is higher
than that of SFRC. This, however, is not postulated to adversely affect the performance of
structural members due to the relatively small depth of concrete that would be exposed to
temperatures in excess of 800 °C in most realistic (design) fires.

129

1.2
1

SFRC
Plain

f'c/f'co

0.8
0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°C)

Fig. 4.2: Compressive strength of PC and SFRC as a function of temperature
The addition of steel fibers also significantly enhances ductility of SFRC as compared to PC.
Fig. 4.3 shows the normalized stress strain relationships for PC and SFRC in compression for
different temperatures ranging from ambient to 600 °C as specified by Lie and Kodur (1995b).
From Fig. 4.3, it can be seen that SFRC is more ductile than PC as indicated by the higher
ultimate strain of SFRC at all temperatures plotted. The enhancement that can be achieved
through the inclusion of steel fibers is to such and extent that at 400 °C, the ductility of SFRC is
83% higher than that of PC. This trend is continued such that at 600 °C, the ductility of SFRC is
approximately 3.5 times that of PC. Ductility is enhanced through the inclusion of steel fibers,
not just in terms of the ultimate strain that can be reached, but also in the strain at peak stress. At
all temperatures, the strain at peak stress in the SFRC is considerably higher than that in the PC.
The enhanced ductility of SFRC is critical to the development of TMA. As such, SFRC being
more ductile and at the same time having higher tensile strength, should enhance the
development of TMA. This enhancement of TMA should subsequently significantly improve

130

the fire resistance of floor systems when SFRC is used as part of a composite beam slab
assembly.
1.2
20 SFRC
400 SFRC
600 SFRC
20 Plain
400 Plain
600 Plain

1

Stress

0.8
0.6
0.4
0.2
0
0

0.01

0.02

0.03

0.04

0.05

0.06

Strain

Fig. 4.3: Stress-strain relationships for plain and SFRC concrete at various temperatures
An additional benefit of adding steel fibers to concrete is the enhanced the tensile strength of
concrete throughout the full temperature range practically achieved under fire exposure. Fig. 4.4
(SFPE 2002, Eurocode 2004, Lie and Kodur 1994, 1995) shows the normalized (with respect to
ambient temperature tensile strength) tensile strength of PC and SFRC as a function of
temperature.

The increase in tensile strength through the inclusion of steel fibers is

approximately 38% at ambient temperature, and is continued to temperatures in excess of 800 °C
as seen in Fig. 4.4. The increased tensile strength of SFRC is attributed to the steel fibers
arresting cracks as they propagate across the cement matrix. This causes the cracks to have to
take a more tortuous path to cause failure of the concrete. This enhanced tensile strength from
SFRC facilitates the development of tensile membrane action in the concrete slab, thus
enhancing the fire resistance of composite floor slab assemblies.

131

To aid in achieving convergence of the structural models, some modifications were made to the
material models shown in the previous sections, they are as follows. The compressive strength
while zero above 850 °C, was granted nominal (0.1%) strength up to 1200 °C to avoid the
stiffness matrix arbitrarily becoming zero above 850 °C and causing numerical failure of the
structure. Likewise, the tensile strength model due to an absence of data above 800 °C was
assumed to decay linearly to zero at 1200 °C to avoid numerical instability in the model.

1.4
1.2

f't,t/f't,20

1
SFRC

0.8

Plain

0.6
0.4
0.2
0
0

200

400

600

800

Temp (°C)

Fig. 4.4: Tensile strength of PC and SFRC as a function of temperature
Validation of the material model for SFRC was accomplished by comparing deflection
prediction from SAFIR with those recorded during the novel fire tests conducted on an SFRC
floor system at MSU. A description of the validation of the material model for SFRC, as well as
the use of SAFIR for element, assembly, and system level parametric studies is presented below.

132

4.4

Validation of SAFIR Computer Program

The applicability of SAFIR to trace the response of structural members under fire exposure is
well validated in the literature (Franssen, 2005, Gilvary, 1997, Talamona, 2005). However, there
is a lack of validation for the use of SAFIR to capture the effects of composite construction and
tensile membrane action under fire exposure, particularly for SFRC.

As such, for use in

parametric studies, numerical models of the experimental setups described in the respective
sections of Chapter 3 were created in SAFIR and subsequently validated. For the validation of
these models, and to ensure that they account as closely as possible for the conditions present in
the respective fire tests, thermal and structural results from SAFIR were compared with those
from testing. The following sections present these comparisons for the element, assembly, and
system level models independently.
4.4.1

Element Level – CFHSS Columns

The modeling of CFHSS columns differs significantly from the modeling of typical steel
columns (HSS or W-flange sections) due to the development of composite action. Composite
action in CFHSS columns serves to reinforce the wall of the section against crippling, and reduce
the risk of local bucking. As such, it is possible to accurately model the behavior of these
sections under fire utilizing beam elements. Beam elements are capable of accounting for
composite action between the steel and concrete, and capturing both crushing and global column
buckling.
For the thermal analysis in SAFIR, full advantage was taken of the symmetry in both circular
and square CFHSS columns. Only a quarter section of each column was modeled with double
symmetry to reduce computational requirements. The steel section and rebar were modeled as
having perfect thermal and structural contact with the concrete core. The rebar was included as

133

square elements with an area equivalent to that of the rebar designated in the testing details. As
an illustration of a typical CFHSS column model, an image of the material composition
including discretization for a circular bar reinforced CFHSS columns is presented in Fig. 4.5
below.

Fig. 4.5: CFHSS column cross section and elevation discretization in SAFIR
Beam elements with a length of 150 mm were used for discretization along the length of the
column as shown in Fig. 4.5. End nodes of the beam elements were assumed to have six degrees
of freedom (three translations and three rotations) while the center node of the three nodded
beam elements was assumed to have one degree of freedom. End conditions were provided to
simulate as closely as possible those used in testing, pinned-pinned, pinned-fixed, and fixedfixed conditions were all considered in various simulations. For steel and plain concrete, high

134

temperature material models according to Eurocode were utilized, for SFRC, the high
temperature material model presented in section 4.3.4 was used.
To validate SAFIR for use in modeling the fire response of CFHSS columns including PC, FC,
and RC filling, the fourteen columns in Table 3.1 were analyzed under ASTM E-119 (ASTM,
2007) and the SAFIR predicts compared with the test data.

Fig. 4.6 shows a graphical

representation of the columns considered in the validation, while Table 4.1 presents the critical
mechanical properties for the columns as reported, and Table 4.2 shows thermal and mechanical
properties assumed in the simulations. The thermal and structural response, and ultimate failure
times generated by SAFIR were compared with the measured test data for all of the columns.
All of the columns for which test data was available underwent the same level of scrutiny as the
single column used to illustrate the validation below. However, only a sample validation is
presented below.
D

P

D

D

P

t
P

Fig. 4.6: Typical RC, FC, and PC square and round column cross-sections used for validation of
SAFIR

135

Table 4.1: Characteristics of CFHSS columns used for validation of SAFIR
Column
Designation

Dia. or
Width
(mm)

Load (kN)

f’c

Fire
Resistance
(min)

Concrete
Filling

Agg.
Type

RP-168
RP-273
RP-355
SP-152
SP-178
RF-324
RF-356
SF-203
SF-219
RB-273a
RB-273b
SB-203
SB-254a
SB-254b

168.3
273.1
355.6
152.4
177.8
323.9
355.6
203.2
219.1
273.1
273.1
203.2
254
254

150
525
1050
286
549
1600
1500
900
600
1050
1900
500
1440
2200

35.4
27.4
25.4
46.5
57.0
57.0
53.5
90.1
90.1
46.7
47.0
47.0
48.1
48.1

81
143
170
86
80
199
227
128
174
188
96
150
113
70

Plain
Plain
Plain
Plain
Plain
Fiber
Fiber
Fiber
Fiber
Bar
Bar
Bar
Bar
Bar

Sil.
Sil.
Sil.
Carb.
Sil.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.
Carb.

Table 4.2: Assumed thermal and mechanical properties
Steel
Mechanical properties
(HSS/Rebar)
Young’s modulus
210/210
(GPa)

Heat transfer coefficients
Hot convection
coefficient
Cold convection
coefficient
Relative emissivity

25
9
0.5

Heat transfer coefficients
Hot convection
25
coefficient
Cold convection
9
coefficient
Relative emissivity

Poisson’s ratio

0.3/0.3

Yield strength
350/413
(MPa)
Concrete
Mechanical properties
Poisson’s ratio
Compressive
strength (MPa)
Tensile strength
(MPa)

0.5

.25
Variable
Variable

A comparison of the temperatures predicted by SAFIR and those measured in a fire test at the
steel surface (HSS section), and at the center of the concrete core, is shown in Fig. 4.7 for
Column SP-178. Of note from Fig. 4.7 is the observation that it takes almost 30 minutes to reach

136

600 °C in the steel section.

In unprotected HSS columns this temperature is achieved in

approximately 15-20. The delayed heating in the CFHSS columns can be attributed to the mass
of the concrete in the composite column that absorbs heat from the exposed steel section, thus
limiting the temperature rise in steel. The contribution of the concrete to the thermal response of
the column is observed in both the SAFIR analysis and the test data. Good agreement between
predicted and measured temperatures is observed in Fig 4.7 for the concrete core after 100 °C, at
which point free water is driven off.

The steel temperatures initially deviate such that

temperatures observed in the test are hotter than those predicted by SAFIR.

This can be

attributed to the assumption in SAFIR that there is perfect thermal contact between the steel and
the concrete. When however, the steel approaches the critical phase transformation temperature
of 700-750 °C, at which point the bonded water in the concrete is also driven off, SAFIR begins
to over predict the temperature in the steel. This is mainly due to the assumption in SAFIR that
hydraulic migration in concrete can be neglected. Toward the end of the test, the temperatures
compare reasonably well such that there is only a 30 °C temperature difference between the test
data and the SAFIR simulation.

Overall, the temperature predictions from SAFIR are in

reasonable agreement with data measured from tests.
The structural response predicted by SAFIR was validated by comparing the axial deformations
(at the loaded end of the column) for Column SP-178 with those measured during tests (Fig. 4.8).
The column initially expands as a result of the quick rise in steel temperatures. This increased
temperature leads to eventual loss of strength and yielding of steel, at which point the benefits of
composite construction are observed in the column as the concrete starts to take over most of the
load bearing function, causing the column to contract slightly. A peak deflection (expansion) of
18.3 mm was observed in the tests, while the corresponding peak deflection from SAFIR was

137

17.9 mm. These two maximum deflections show good agreement occurring at 20 and 23
minutes respectively. The differences in deflection between SAFIR data and test data are a result
of the temperature discrepancies seen in Fig. 4.7. The initially higher temperatures in the steel
shell produces higher expansion of the column in the fire test than in SAFIR, as seen in Fig. 4.8.
After peak deflections are reached, the temperatures in the steel shell, as predicted by SAFIR, are
hotter than those observed in tests. This results in the steel retaining slightly higher strength in
tests than in the SAFIR simulation, thus, there is a slightly larger contraction of the column in the
SAFIR simulation than observed in the test. Overall, the predicted deformations compare well
with those measured during the fire test.

SAFIR (C oncrete core - center)

SAFIR (Steel surface)

Test Data (Concrete core - center)

Test Data (Steel surface)

Temperature (°C)

1000
800
600
400
200
0
0

30

60

90

Time (min)
Fig. 4.7: Comparison of predicted temperatures from SAFIR with test data for Column SP-178

138

20
SAFIR
Test

Deflection (mm)

15
10
5
0
-5
0

30

60

90

Time (min)

Fig. 4.8: Comparison of predicted axial deformations from SAFIR with test data for Column SP178
All of the columns were simulated with axial loads and support conditions that matched those in
testing as closely as possible with vertical translation (under loading) permitted at the top. The
failure times in fire tests shown in Table 4.1 correspond to the point at which the column could
not sustain the applied load as indicated by SAFIR through a failure to achieve convergence.
The time to reach that point is defined as the fire resistance of the column. A comparison of the
fire resistance values indicates that the SAFIR predictions are in good agreement with measured
fire resistance values and that SAFIR can accurately model composite construction in the
CFHSS columns. In 5 of the 14 columns modeled, SAFIR predicts a higher fire resistance than
observed in testing, thus representing the un-conservative case as illustrated in Fig. 4.9. For the
9 remaining cases, SAFIR predicts a lower fire resistance than observed in testing, this
corresponds to the conservative case as indicated in Fig. 4.9. The maximum error on the
conservative side was 16% with the maximum error on the un-conservative side being 6%. This

139

small (6%) error on the un-conservative side indicates that there is good agreement between test
results and results from the constructed numerical models. Given this good agreement between
the tests and simulation results, the models, (both the thermal and structural) constructed here are
deemed acceptably conservative for use in parametric studies.

Predicted fire fesistance (min)

250

Un-conservative

200
150
100

Conservative
50
0
0

50

100

150

200

250

Measured (test) fire resistance (min)

Fig. 4.9: Comparison of predicted (SAFIR) and measured fire resistance times
4.4.2

Assembly Level – SFRC Floor Slab

SAFIR has been shown to accurately model the response of floor assemblies exposed to fire
(Talamona 2005). However, the validity of SAFIR for modeling the response of SFRC to fire
exposure has not yet been validated. To that end, the steel beam-SFRC slab structural assembly
described in Chapter 3 and tested at the MSU structural fire testing facility was modeled using
SAFIR, and the response of the assembly as predicted by SAFIR compared to data recorded in
the fire resistance test.

The validation of both the material model and the model of the

constructed assembly are presented in the following sections. No consideration is given to the

140

use of lightweight concrete in the development of validated computational models as presented
in this chapter. Plain lightweight concrete as discussed in Chapter 3 does not enhance fire
resistance to the levels required in codes and standards, as such, it is not a practical alternative
and will be given no further consideration.
In order to minimize the computational time required for fire resistance analysis, full advantage
was taken of symmetry conditions of the beam-slab assembly. A quarter-section of the floor slab
and supporting steel beams was modeled in SAFIR as shown in Fig. 4.10, where the fire exposed
zone is indicated in light gray.

In this region, thermal input files consistent with the fire

exposure were used to capture the temperature evolution in both the concrete slab and the steel
beams. Outside this region, the slab and supporting beams were assumed to be at ambient
temperature. This assumption of a distinct line separating the fire exposed and the unexposed
regions of the test assembly generate considerable stress concentrations at the interface. These
stresses could presumably influence the structural response of the assembly. Given that these
stresses will make the structural analysis more conservative, no further attention was given to the
thermal gradients at this interface.
Given the assumption of a doubly symmetric condition, particular attention was given to the
boundary conditions assumed in the model. Along the symmetric edge, the boundary conditions
were implemented such that vertical translation was allowed, and rotation about the symmetric
axis was restrained. The horizontal restraints were implemented at the symmetric edges to
ensure that any deformations, whether thermal or mechanical, generated in the quarter section
impact only the modeled section.
Supports where the assembly rested on the steel bearing plates were equipped with half rounds to
minimize the friction at the support; these supports were modeled as a vertical support with no

141

restriction to horizontal movement in SAFIR. This support condition neglects the contribution of
friction between the steel bearing plate and the bottom of the protected W12X16 beam. This
assumption is conservative since horizontal restraint at the bottom of the W12X16 should
enhance the response of the assembly to fire by decreasing vertical defection.

As such,

neglecting this restraint is conservative.
The concrete slab was modeled as a series of four nodded 150 mm square shell elements (with
minor geometric alterations to accommodate the geometry of the assembly) with each node
having six degrees of freedom. As has been assumed in previous studies (Bailey 2000, Fike and
Kodur 2009a,b) the slab was assumed to be of uniform thickness equal to the maximum
thickness of the composite deck. Additionally, the strength contribution of the conform steel
decking was neglected under fire exposure. The shrinkage reinforcing previously described was
incorporated in the form of a smeared model. This means that the steel and the concrete were
assumed to exist in the same location, and the steel was assumed to be uniformly distributed over
the cross-section of the slab. The supporting beams were modeled as 150 mm long three nodded
beam elements; the two end nodes each had seven degrees of freedom, while the center node had
one degree of freedom.
B

B

A

Furnace

Modeled
A
portion
Fig. 4.10: Discretization of the tested steel beam-SFRC slab assembly for SAFIR analysis
142

The assumed symmetric condition causes one of the lines of symmetry to run down the length of
the unprotected W10X15 beam in the center of the assembly. Two options exist for modeling
this condition, first, only half of the beam could be modeled, or second, the entire beam could be
modeled and the elastic modulus and yield strength reduced to 50% for the duration of the fire
exposure to simulate the response of the partial section in the symmetric condition. The first
option causes instability in the model due to a non-symmetric beam element about its own axis
and SAFIR has a difficult time converging on a solution, as such, the later option was chosen,
and the entire beam was modeled with a yield strength and elastic modulus of 50%. In addition
to this concern, the bending stiffness of the section is proportional to the elastic modulus
multiplied by the moment of inertia, either of these can be reduced and the effect is the same, as
such, the assumption should not influence the response of the structure to fire exposure. To
establish the validity of this approach, parallel simulations were run for the full assembly and the
reduced assembly with the material properties of the central beam reduced by 50%. Deflections
predicted by the two models almost coincided, having less than a 5% discrepancy at any point
during the simulation. As such, this assumption of reduced material properties is deemed a
reasonable, and in light of the computational savings, a necessary assumption.
In SAFIR, the user must specify the node line or line of action for beams, and the plane of action
for shell elements. The plane of action was assumed to be at the bottom surface of the shell
elements, and the line of action was assumed to be at the top of the top flange in the beam
elements. When the composite action between the steel beams and the concrete slab is modeled,
the selection of these lines of action causes SAFIR to model the interaction at the correct location
on both the shell and beam elements. As described previously, the composite action between the

143

steel beam and the concrete slab is modeled through the use of master-slave node relations via
the “SAMEALL” command.
For validation, the actual temperatures measured in the slab and the beams during the fire test
were input directly into the structural model in SAFIR. This was done to eliminate errors that
can accumulate from thermal analysis. The ability of SAFIR to simulate temperatures produced
by real fire exposure is presented in the literature for plain concrete (Alfwakhiri et. al 2004).
Additionally, the similarities between the thermal response of plain and SFRC has been
established in the literature (Lie and Kodur 1995b) thus no further discussion on the thermal
validation will be presented here.
Due to the inherent instability associated with strains recorded during fire testing as discussed
previously, only deflections are used for calibration of the model discussed in this section. The
two most critical points for use in calibration are the center of the slab, and the connection
between the beams in the heated region. As shown in Fig. 3.31 and discussed in the respective
section, deflections over the supported edge are minor in comparison to these two, and hence, of
little use for calibration purposes. While the deflection of the unsupported edge offers a unique
set of data, the presence of extensive cracking next to the W12X16 beam makes this behavior
intrinsically difficult to simulate. As such, only the center point and the connection deflections
will be used for model validation.

The mechanical properties utilized in the analysis are

summarized in Table 4.3 below.
Table 4.3: Mechanical properties utilized in steel beam-SFRC slab analysis simulations
Steel
Young’s modulus (GPa)

210

Poisson’s ratio

0.3

Yield strength (MPa)

SFRC
Poisson’s ratio
Compressive strength
(MPa)
Tensile strength (MPa)

350

144

0.25
46.6
5.34

Fig. 4.11 shows the comparison of deflections predicted by SAFIR and those measured during
the fire test at the center of the slab, and over the center of the W12X16 beam (see Figs. 3.1 and
3.8 for layout of the test assembly). The predicted and measured deflections at the center of the
W12X16 beam compare well for most of the fire duration. The peak deflections from SAFIR
and test were 61.8 mm at 135 min and 63.8 mm at 145 min respectively, thus showing close
agreement. There is however a slight divergence between measured and predicted data starting
at around 130 minutes. This may be partially attributed to the slight variations between the
actual high temperature stress-strain relationships for SFRC and those used in SAFIR.

0

60

120

180

0

Deflection (mm)

-20

Beam

-40
-60

Slab

-80
-100
-120

Slab (Test)
Beam (T est)
Slab (SAFIR)
Beam (SAFIR)

-140
Time (min)

Fig. 4.11: Comparison of predicted and measured deflections at the center of the slab and at the
center of the beam in the fire exposed beam slab assembly
The predicted deflections from SAFIR are also close to measured deflections at the center of the
slab for the duration of the test as can be seen in Fig. 4.11. However, after about 80 minutes, the
predicted deflections from SAFIR diverge from the measured deflections.

The differences

between the predicted and the actual response are such that the peak defection at the center of the

145

slab predicted by SAFIR is 130 mm at 130 min, and that measured in the fire test was 135 mm at
155 min. At this point of fire exposure, the unprotected steel beam is offering little strength to
the assembly due to the high steel temperatures. Additionally, the deflection at the center of the
W12X16 beam is accurately predicted as seen in Fig. 4.11. Given these observations, the
difference in deformations between the SAFIR simulation and the test results can be attributed to
the discrepancies between assumed and actual properties of the SFRC used in the test.
From the above discussion, it is believed that SAFIR is fully capable of simulating the structural
response of the tested assembly with SFRC under design fire exposure. This validation indicates
that SAFIR is fully capable of simulating the structural response of SFRC at elevated
temperatures. As such, the material model input into SAFIR as discussed previously is assumed
to be accurate and correctly programmed in SAFIR. Secondly, the model of the tested assembly
is sufficiently accurate to warrant its use in parametric studies to identify the factors affecting the
response of a composite floor assembly made with SFRC to fire exposure.
4.4.3

System Level-Steel Framed Building

The validity of SAFIR in predicting the system level response of structural systems under fire
exposure has been established previously (Lim at. al 2004, Lamont and Lane 2006). As such, it
is only necessary to validate SAFIR for use with the specific model constructed for this research.
To that end, the test conditions for the Cardington restrained beam test as described in the
previous chapter were modeled as closely as possible in SAFIR. Following completion of the
numerical model, the deflection time history for select locations as predicted by SAFIR, were
compared to those recorded during the fire resistance test.
Due to the symmetry within the structure, only a portion of the structure was modeled in SAFIR.
Fig. 4.12a and 4.12b (British Steel 1998) show the elevation and plan views of the steel framed

146

building respectively, with the location of the restrained beam highlighted, and the portion of the
building that was modeled in this simulation indicated.

Due to the complexities that are

associated with modeling a ribbed composite floor slab, it was decided to use a slab represented
by shell elements of uniform thickness as has been done in other studies (Zhang et al. 2008,
Cashell et al. 2008). The thickness chosen for the slab was that of the thickest part of the ribbed
flooring system, 130 mm. Fig. 4.13 shows the portion of the structure as modeled in the SAFIR
computer program.
In the numerical model shown in Fig. 4.13, the concrete slab was modeled using four nodded
shell elements with six degrees of freedom at each of the nodes. The beams and columns were
modeled using three nodded beam elements with seven degrees of freedom at the end nodes and
one degree of freedom at the center node. To simulate the composite action between the steel
beam and the floor slab, the “SAMEALL” command was used for the nodes where the beam and
shell elements coincide. This caused all of the translations and rotations at these points to be the
same for the beam and slab, thus simulating the fully composite condition.

Fire Compartment

Modeled

Fire Compartment
Column
a: Elevation view

Modeled
b: Plan view

Fig. 4.12: Model of the steel framed Cardington steel framed building used for numerical studies

147

Fig. 4.13: Idealization of substructure modeled from the Cardington steel framed building for fire
resistance analysis
Particular attention was given to the boundary conditions used in the simulation. It was assumed
that the ends of the columns where they pass though the adjacent floors acted as fixed supports
with all degrees of freedom being fully restrained. It was also assumed that the portion of the
structure which was not modeled, being significantly larger than the modeled potion, was
essentially rigid compared to the modeled portion. As such, the horizontal translation on the
continuous edges was fully restrained in both directions. Due to the continuity of the slab over
these points, the rotation about the length of the edge was assumed to be restrained, thus
simulating the realist defection at the center of an unsupported slab.

Lastly, the vertical

translation was completely unrestrained, thus allowing the continuous edges of the modeled
portion to deflect with realistic restraint. The validity of these assumptions of symmetry will be
discussed in the following section.
For validation of the SAFIR model, the above depicted portion of the steel framed building was
modeled under the time-temperature curve used in the restrained beam test (shown in Fig. 4.14)

148

2

and under the test load of 4.94 kN/m (British Steel 1998). For the analysis, the thermal and
mechanical properties shown in Table 4.4 were utilized in SAFIR.
Table 4.4: Thermal and mechanical properties assumed in simulations
Steel
Heat transfer coefficients
Hot convection
25
coefficient
Cold convection
9
coefficient
Relative emissivity

0.5

Heat transfer coefficients
Moisture content
46
3
(kg/m )
Hot convection
25
coefficient
Cold convection
9
coefficient
Relative emissivity
0.5

Mechanical parameters
Young’s modulus
210
(GPa)
Poisson’s ratio

0.3

Yield strength
350
(MPa)
Concrete
Mechanical parameters
Poisson’s ratio
Compressive
strength (MPa)
Tensile strength
(MPa)
-

.25
35.4
1.78
-

Fig. 4.14 shows a comparison of the temperatures predicted by SAFIR with those observed
during fire tests in the bottom corner of the heated beam. It can be seen that the temperatures
predicted by SAFIR closely match those measured during the test. Toward the end of the
simulation period there is a divergence in the temperatures, this is mainly due to ventilation
issues inside the furnace causing the beam to cool differently, which could not be capture in the
SAFIR analysis. The temperatures at several points in the unprotected steel beam and in the
concrete floor slab were compared with predictions from SAFIR, and similarly good agreement
was found at all locations. Overall, there is good agreement in the temperatures measured during
testing and those predicted by SAFIR.

149

1000

Temperature (°C)

800
600
400

Test
SAFIR

200

Fire exposure

0
0

30

60

90

120

150

180

210

240

Time (min)

Fig. 4.14: Comparison of measured and predicted temperatures in the steel beam
The structural response from SAFIR was validated by comparing the measured mid-span
deflection of the heated beam-slab assembly with that predicted by SAFIR (Fig. 4.15). As seen
in Fig. 4.15, there is good agreement between the test data and the predictions from the SAFIR
model in the heating phase. This indicates that SAFIR is able to accurately capture the effect of
composite construction and the development of tensile membrane action during fire exposure.
Due however to the unavailability of the test data beyond 150 minutes, it is not possible to
validate the response of the model during the cooling phase of the fire. During testing, it was
observed that the center of the heated beam rebounded such that a total deflection of 113 mm
remained after the cooling phase. From Fig. 4.15 it can be seen that the same degree of rebound
is not observed from the SAFIR model as 180 mm of deflection remain after the structure has
completely cooled. This discrepancy is due to the material models used in SAFIR. It is assumed
within SAFIR that both steel and concrete have the same mechanical properties at a specific

150

temperature in both the heating and cooling phase of fire. Thus SAFIR neglects any damage that
occurred to the constitutive materials due to the heat from fire.
The existence of only slight variations in the heating phase indicates that the SAFIR model
accurately accounts for the contribution of composite and tensile membrane action during the
heating phase of fire exposure. Ultimate deflections after fire exposure however cannot be
accurately assessed using the validated model. As such, the following discussion deals with
survival of the structure and maximum deflections, not the residual deflections after the structure
has completely cooled. Any variation between the predicted and observed deflections in the
heating phase can be attributed to assumptions made in the structural model constructed in
SAFIR. These assumptions include the boundary conditions as discussed previously and the
assumption that the steel beam and the slab act in complete composite action.
0

Deflection (mm)

-50
-100

Test
SAFIR

-150
-200
-250
0

60

120

180

240

Time (min)

Fig. 4.15: Comparison of measured and predicted mid-span deflections for the beam
Given the thermal and structural model validations presented above, it was concluded that the
models were sufficiently accurate to be used in parametric studies.

151

4.5

Summary

SAFIR was selected as the computational model of choice for use in the numerical studies
conducted as part of this research program. Use of SAFIR to trace the response of structural
members under fire exposure is well validated in the literature. However, there is a lack of
validation for the use of SAFIR to capture the effects of composite construction and tensile
membrane action under fire exposure, particularly for SFRC.
In order to validate the ability of SAFIR to accurately capture the effect of composite action
under fire exposure, the assemblies tested at the element, assembly, and system levels as
discussed in Chapter 3 were modeled using SAFIR. Results, (both thermal and structural) from
the SAFIR simulations were compared with those recorded in fire tests. It was seen that in all
cases, SAFIR predictions closely match the behavior of the specimen during the heating phase of
fire exposure and not in the cooling phase. Thus, SAFIR is capable of capturing the contribution
of composite construction to fire resistance only during the heating phase of fire exposure.
Additionally, through validation of the tested steel beam-SFRC slab assembly, SAFIR was
shown to accurately predict the behavior of steel fiber reinforced concrete under fire exposure,
thus, the high temperature constitutive model implemented in SAFIR is deemed to be acceptable.

152

CHAPTER 5
5
5.1

PARAMETRIC STUDIES
General

For developing a methodology for fire resistant design of steel frame structures, the influence of
critical factors on fire resistance is to be quantified. To that end, the numerical models discussed
in the previous chapter were applied to conduct a series of parametric studies. These studies
were conducted at the element, assembly, and system levels to quantify the influence of various
factors on fire resistance of steel framed structures incorporating composite construction. At the
element level, the effect of fire scenario, length, concrete filling type, load ratio, cross sectional
size, and failure criterion were considered. For the assembly level, the effect of fire scenario,
load level, slab thickness, and concrete type were studied. Finally, at the system level, the effect
member interactions including composite construction and tensile membrane action were
studied. These parameters were selected based on the previous studies in literature where the
key parameters having an influence on structural fire resistance were identified. Further details
on the range of variables selected and the full results from the parametric studies are provided in
each section for the respective level of analysis.
5.2

Element Level – CFHSS Columns

To study the factors influencing the response of CFHSS columns exposed to fire, the calibrated
SAFIR model discussed in Chapter 4 was applied to conduct a series of parametric studies. Data
from these studies was used to identify trends on the response of CFHSS columns under fire
exposure over a wide range of variables, details of which are presented below.

153

5.2.1

Column Characteristics

For the parametric studies, 20 CFHSS columns were selected. Fourteen of these were columns
tested at NRCC (Table 3.1), while the remaining six are typical CFHSS columns specifically
selected to cover a wider range of sectional sizes. The columns consisted of round and square
sections filled with plain, steel fiber, and bar reinforced concrete as shown in Fig. 5.1.

Fig. 5.1: Elevation and cross-section of RC, FC, and PC filled HSS columns used in parametric
studies
For thermal analysis, the columns were modeled using two dimensional shell elements as shown
in Fig. 5.2. For structural analysis, the columns were discretized along their length using threenode beam elements with an average length of 150 mm. The beam elements were assumed to
have six degrees of freedom (three translations and three rotations) at the end nodes, and one
degree of freedom at the middle nodes. Both the thermal and structural models used material
properties according to Eurocode (2005a,b) for both steel and concrete. The specific material
properties input into SAFIR for the thermal and structural analyses are presented in Table 5.1.

154

Fig. 5.2: Discretization of CFHSS columns for SAFIR analysis
Table 5.1: Thermal and mechanical properties assumed in simulations
Steel
Mechanical parameters
(HSS/Rebar)
Young’s modulus
210/210
(GPa)

Heat transfer coefficients
Hot convection
coefficient
Cold convection
coefficient
Relative emissivity

25
9
0.5

Heat transfer coefficients
Moisture content
46
3
(kg/m )
Hot convection
25
coefficient
Cold convection
9
coefficient
Relative emissivity
0.5

Poisson’s ratio

0.3/0.3

Yield strength
350/413
(MPa)
Concrete
Mechanical parameters
Poisson’s ratio
Compressive
strength (MPa)
Tensile strength
(MPa)
-

155

.25
Variable
Variable
-

5.2.2

Critical Factors

Utilizing the SAFIR computer program, the 20 columns employed in the parametric study were
exposed to a wide range of fire scenarios, lengths, loads, concrete strengths/composition, and
failure criterion. These parameters were selected because their influence on the fire resistance of
CFHSS columns in a performance-based environment has yet to be quantified. As such, a total
of seven fire scenarios, five of which are shown in Fig. 5.3, were considered in the analysis.
These fires were selected to represent the full range of fire exposures that would be practically
experienced in typical medium rise office buildings. Fire exposure was assumed on all four sides
(or around) of the column with the bottom and top 5% of the column unexposed to fire. It should
be noted that the analysis was continued until the column attained failure or 240 minutes of
exposure to fire. As such, if a fire resistance of 240 minutes is reached, it is indicative of the
column withstanding compartment burnout, not that the column failed at 240 minutes unless
specifically noted.
In addition to fire exposure, column length has been identified in the literature as a factor that
can have a significant influence on the fire resistance of CFHSS columns that is yet to be
investigated. To address this factor, columns ranging from 3.81 to 10 meters were considered
under all fire exposures and load ratios to cover the practical range of columns that would be
used in construction. To account for the fact that longer columns typically have lower load
capacities that shorter columns, the load ratio was maintained constant in all analysis regardless
of the length. That is to say, shorter columns had a higher (magnitude) load than longer
columns.

156

1200

Temperature (°C)

1000
800
600
ASTM E-119
Mild
Medium
Severe
ASTM E-1529

400
200
0
0

40

80

120

160

200

240

Time (min)

Fig. 5.3: Time-temperature relationships for various fire scenarios
As alluded to in the previous paragraph, load is also assumed to have a considerable influence on
the fire resistance of CFHSS columns. To that end, the full range of columns was considered
under different load levels to quantify the effect of load on fire resistance. Loads were modified
to maintain a constant load ratio for all of the lengths modeled for a specific cross-section
according to the AISC analysis procedure (AISC 2005). The applied loads on the columns were
also modified to take into account the effect that the type of concrete filling has on fire
resistance, accounting for the fact that steel fiber and bar reinforced concrete-filled HSS columns
have a higher load capacity than columns filled with plain concrete.
Clearly, the type and strength of concrete will also have an influence on the fire resistance of
CFHSS columns. As such, a wide range of concrete compressive strengths, the three primary
filling types (PC, FC, and RC), and two primary types of concrete (siliceous and carbonate) were
considered in the parametric study.

157

Lastly, failure criterion was considered as a factor influencing the fire resistance of CFHSS
columns. In the physical domain, there are two ways in which a column can fail, the column can
crush or buckle, i.e. material or stability failure. Often the provisions in codes and standards
apply simplified criterion such as critical temperature to evaluate failure of a column, and these
criterion do not take into account the beneficial effects of composite action on fire resistance.
The presence of the concrete core serves to cool the steel shell and carry a portion of the load,
and as such needs to be taken into consideration when evaluating the fire resistance of CFHSS
columns. The effect of failure limit states on fire resistance for the full range of columns is
presented in the respective section below.
5.2.3

Analysis Procedure

To study the effect of each variable outlined in the previous section, a series of parametric
studies were carried out using the validated models. For each study, only one variable was
changed at a time so the effect of that variable could be quantified. The primary output used to
establish the effect of each parameter on fire resistance was the failure time of the column under
fire exposure. No consideration was given to deflection in the analysis, only the failure time of
the column as indicated by the inability of SAFIR to converge on a solution was used as a means
for comparison.
5.2.4

Results and Discussion

This parametric study generated a total of 980 numerical simulations. The results (trends)
discussed in the following sections apply to all three types of columns considered (PC, FC, RC)
unless otherwise noted. To reduce redundancy however, only one column type is used to
illustrate each point.

158

Effect of Fire Exposure
The effect of fire severity on fire resistance is illustrated in Fig. 5.4 by plotting the fire resistance
as a function of length for column RP-273 under different fire scenarios. As is intuitive, as the
fire severity decreases, the fire resistance of the column increases. It can be seen in Fig. 5.4 that
fire resistance of four hours or more can be obtained for columns up to 10 m long under mild fire
conditions. However, for other fire exposures, fire resistance decreases with an increase in
length. A closer look at Fig. 5.4 indicates that fire resistance of a 5 m long CFHSS column
ranges from 240 minutes for medium and mild fire exposure, to 68 minutes under severe
exposure, with ASTM exposure yielding 100 minutes.

The reason for this decreased fire

resistance with increased fire severity can be attributed to the higher internal temperatures
attained under severe fire exposure. Consequently, the column loses its strength and stiffness at
a faster rate leading to early failure.

Figs. 5.5 and 5.5 show the difference in internal

temperatures observed in the steel shell and at the center of the concrete core for the fire
exposures shown in Fig. 5.3.
It can be seen in Fig. 5.5 that two of the three design fires produce higher initial temperatures in
steel than the ASTM E-119 (ASTM, 2007) fire.

This effect is continued in concrete

temperatures also, (Fig. 5.6) though to a lesser extent. The presence of the decay phase in the
design fires causes the temperature in all locations of the column to be less (cooler) than that for
the ASTM E-119 (ASTM, 2007) fire at the end of the simulation period. Column stability is
maintained under design fires, despite the more severe initial temperatures, due to the decay
phase of the fire allowing cooling of the steel before significant loss of strength in the concrete
core occurs, as discussed in the following sections.

159

Fire Resistance (min)

240
ASTM E-119
ASTM E-1529 (Hydro)
Severe
Medium
Mild

180

120

60

0
3

4

5

6

7

8

9

10

Length (m)

Fig. 5.4: Fire resistance as a function of length for column (RP-273) under different fire
scenarios

1200

Temperature (°C)

1000
800
600
400

ASTM E-119
ASTM E-1529 (Hydro)
Severe
Medium
Mild

200
0
0

40

80

120

160

200

240

Time (min)

Fig. 5.5: Steel temperatures for column RP-273 exposed to different fire scenarios

160

1200
ASTM E-119
ASTM E-1529 (Hydro)
Severe
Medium
Mild

Temperature (°C)

1000
800
600
400
200
0
0

40

80

120

160

200

240

Time (min)

Fig. 5.6: Temperatures at the center of concrete core for column RP-273 exposed to different fire
scenarios
To illustrate the effect of fire scenario on the structural response, Fig. 5.7 displays the axial
deformation of column RP-273 resulting from ASTM E-119 (ASTM, 2007), severe, medium,
and mild fire exposure. In all simulations, the column initially expanded due to the increasing
steel temperatures. After this initial expansion, the response of the column is significantly
influenced by the type of fire exposure. In the case of severe and medium fire scenarios,
significant contraction occurs though the column does survive compartment burnout.

The

residual shortening of the column is attributed to residual damage from the heating phase of fire.
During the heating phase of the fire, the column sustains damage in the form of steel yielding
and some loss of concrete strength. When the column enters the cooling phase, the HSS section
is in its damaged (shorter) condition. Hence, when the shorter damaged column cools, additional
contraction (thermal shrinkage) is observed and the combined effect of cooling and the
mechanical damage to the column results in the column suffering axial shortening by the end of

161

the fire exposure period. However, under ASTM E-119 (ASTM, 2007) fire exposure, the
column failed in 32 minutes without much contraction due to the absence of a cooling phase.
Under the mild fire exposure, the temperatures achieved in the column are insufficient to cause
failure of the HSS section and the subsequent load transfer to the concrete core. As such, there is
minimal damage to the column and no residual deformation is observed.
30
ASTM E-119
Severe
Medium
Mild

25
Axial Deflection (mm)

20
15
10
5
0
-5
-10
-15
-20
0

60

120

180

240

Time (min)

Fig. 5.7: Axial deformation of column RP-273 under different fire scenarios
Effect of Length
The results presented in Fig. 5.4 can be used to demonstrate the effect of length on the fire
resistance of CFHSS columns. In the analysis, the load on the column was reduced as the length
was increased, such that the load ratio on a single column was kept constant through all of the
simulations. As would be expected, fire resistance for a given fire exposure decreases with an
increase in column length. This is due to the increase in slenderness that accompanies the
increase in length. Fire resistance is drastically reduced when the failure mode switches from

162

crushing to buckling with increased length. This is most pronounced for the “medium” and
“severe” fire exposure as can be seen in Fig. 5.4. Fire resistance under the medium fire drops
from 240 to 45 minutes when length is increased from 5 to 7 m. Under severe fire exposure, the
fire resistance decreases from 240 to 75 minutes for an increase in length from 3.81 to 5 m.
However, under mild fire exposure, fire resistance remains high for all cases, and the length does
not have any influence. The reason for such a drastic reduction in fire resistance with increased
length in PC-filled HSS columns (not observed for RC and FC-filled columns as described in the
next section) for more severe fire exposures is attributed to the weakening of the HSS section
due to the heat from fire. PC-filled columns do not have sufficient strength (mainly tensile) in
the concrete core to resist buckling when the heat from fire reduces the structural contribution of
the HSS section. The composite columns that experience a rapid rise in temperature fail at a
much shorter time when the dominant mode of failure switches from crushing to buckling.
Based on the results and discussion presented here, it is clear that length has a significant
influence on column fire resistance, specifically under severe fire exposures and for PC-filled
HSS column.
Effect of Concrete Filling
The effect of concrete filling type on fire resistance is illustrated by analyzing HSS columns with
different concrete filling types under ASTM E-119 (ASTM, 2007) fire exposure. As was the
case with the effect of length, the applied load was modified according to AISC analysis
procedures (AISC, 2005) to account for the different types of concrete filling in these cases. The
fire resistance is plotted as a function of length for three similar CFHSS columns (Fig. 5.8), each
with a different type (plain, steel fiber reinforced, bar reinforced) of concrete filling, columns
selected for this comparison are RP 355, RF 356, and RB 406 respectively. The fire resistance

163

decreases with an increase in length for all of the filling types. However, columns filled with bar
or steel fiber reinforced concrete demonstrate higher fire resistance than the plain concrete-filled
HSS column for all lengths. This can be attributed to the increased load carrying capacity and
the increased resistance to buckling provided by the inclusion of reinforcement, and also due to
the slower loss of strength in columns filled with RC and FC. These results indicate that it is
possible to significantly enhance the fire resistance of CFHSS columns by changing the type of
concrete filling.

Fire Resistance (min)

240

180

120

PC-filling (RP-355)
FC-filling (RF 356)

60

RC-filling (RB 406)

0
3

4

5

6

7

8

9

10

Length (m)

Fig. 5.8: Effect of length and concrete filling on fire resistance of CFHSS columns
Effect of Load Ratio
The effect of load ratio on fire resistance was investigated by analyzing three columns under
ASTM E-119 (ASTM, 2007) fire, with load ratios ranging from 0.1 to 1.0 (10% to 100%). The
analysis was carried out for three types of concrete filling, namely: plain (RP 273), steel fiber
reinforced (SF 219), and bar reinforced (RB 273) filling. It can be seen in Fig. 5.9 that only the
bar reinforced concrete-filled HSS column withstood the ASTM E-119 (ASTM, 2007) fire for
164

240 minutes with a load ratio of 10% (0.1). Columns SF-219 and RP-273 lasted for 234 and 170
minutes respectively. The fire resistance decreases rapidly with an increase in load ratio up to
0.4. After which point the rate of decrease in fire resistance is slower. This can be attributed to
the fact that concrete filling generally provides a load bearing contribution of about 30%-40% of
the overall composite column capacity. In a fire scenario, the steel shell looses its strength very
quickly, and concrete carries most of the load. Thus, for load ratios higher than 40%, the
concrete filling has to be strengthened either through the use of bar-reinforcement, or through the
use of steel fibers to achieve higher fire resistance. In design fires, the same trend is observed as
in the ASTM E-119 (ASTM, 2007) fire, with the exception that the times to reach failure are
increased depending on the type of design fire considered. Design fires allow the use of load
ratios in the range of 40-50%, while still achieving the required fire resistance

Fire Resistance (min)

240
PC-filling (RP 273)
FC-filling (SF 219)
RC-filling (RC 273)

180

120

60

0
0

0.2

0.4

0.6

0.8

Load Ratio

Fig. 5.9: Effect of load ratio on fire resistance of CFHSS columns

165

1

Effect of Cross-section Size
Results from the analysis indicate that the fire resistance of CFHSS columns increases with an
increase in cross-sectional size. This is due to the increased contribution of the concrete core to
the column strength. When cross-section size is increased, the concrete core comprises a larger
percentage of the load bearing capacity of the section. When a CFHSS column is exposed to
fire, the steel section loses its strength quickly and transfers the load to the concrete core. The
core in turn being larger, is capable of providing longer fire resistance times. The strength loss
in the concrete core is slower than in the HSS section, allowing the column to achieve enhanced
fire resistance. The increased cross-sectional size also enhances stiffness, and thus, resistance to
buckling of the column, allowing higher fire resistances to be achieved in longer columns.
Columns filled with plain concrete however, realize no additional advantage from cross-section
increases beyond 400 mm. This is due to high-temperature instability of the concrete core
causing premature failure for larger cross-sectional sizes when plain concrete is used.
Effect of Aggregate Type
Results from the SAFIR analyses indicate that aggregate type has a moderate influence on the
fire resistance of CFHSS columns.

The two common types of aggregate used in CFHSS

columns are: carbonate (mainly consisting of limestone) and siliceous (mainly consisting of
quartz) aggregate. Carbonate aggregate concrete typically demonstrates higher fire resistance
than siliceous aggregate concrete (Kodur and Lie, 1996, Kodur and Lie, 1997). This is due to an
endothermic reaction occurring in carbonate aggregate at 600-800 °C, in which the dolomite
within the aggregate dissociates.

Consequently, the heat capacity of carbonate aggregate

increases significantly and is approximately 10 times higher than siliceous aggregate in the same
temperature range. As a result, there is a slower increase in temperature in the carbonate

166

aggregate concrete, and thus, a slower loss of strength. Therefore, the fire resistance of CFHSS
columns filled with carbonate aggregate concrete is about 10% higher than siliceous aggregate
concrete-filled HSS columns.
Effect of Failure Criterion
The two limit states considered in codes and standards for defining failure of steel columns under
fire conditions are: limiting temperature, and stability retention. ASTM E-119 (ASTM, 2007)
defines fire resistance as the time it takes to reach a maximum average section temperature of
538 °C, or a maximum single point temperature of 649 °C. On the contrary, stability-based
failure criterion are based on the duration of time during which a column maintains structural
stability (strength) during fire exposure. In the case of CFHSS (composite) columns, using the
limiting temperature criterion for steel does not reflect realistic fire resistance performance due
to the significant structural contribution from concrete through composite action.

As an

illustration, column RP-273 achieved fire resistance of 143 minutes in testing, and 128 minutes
in the SAFIR simulation, thermal failure criterion however would only yield a resistance of 38
minutes for this column. Clearly, thermal failure criteria do not reflect the contribution of the
concrete filling to the fire resistance of CFHSS columns. As such, it is necessary to employ
stability-based failure criterion in the evaluation of the fire resistance of CFHSS columns.
5.2.5

Summary

Based on the above analysis, the following points can be summarized with respect to critical
factors influencing the fire resistance of CFHSS columns:


Type of fire exposure has a significant influence on the fire resistance of CFHSS columns.

The fire resistance of CFHSS columns under most design fire scenarios is higher than that under
ASTM E-119 (ASTM, 2007) standard fire exposure.

167



Apart from fire exposure, the other significant factors that affect the fire resistance of

CFHSS columns are length, type of concrete filling, load ratio, and failure criterion.


It is possible to obtain unprotected CFHSS columns up to 10 m in length capable of

withstanding complete compartment burnout through the use of different types of concrete
filling.


The limiting criterion, used for determining failure, has a significant influence on the fire

resistance of CFHSS columns. The conventional failure criterion, such as limiting steel
temperature can not be applied to CFHSS columns. Strength and deformation failure criteria
should be considered for evaluating fire resistance of CFHSS columns.
In the following Chapter, these factors will be utilized to develop relevant design methodologies
for enhancing the fire resistance of CFHSS columns.
5.3

Assembly Level – Composite Floor Assemblies

To study the factors influencing the response of composite floors incorporating SFRC to fire
exposure, the calibrated assembly level model of the tested steel beam-SFRC slab assembly was
applied to conduct a series of parametric studies. Data from the parametric studies was utilized
to identify trends in the response of composite floors incorporating SFRC under fire exposure
over a wide range of variables, details of which are presented below.
5.3.1

Assembly Characteristics

For all of the simulations, the beam-slab assembly had the same geometric configuration as the
validated model discussed in Chapter 4. A quarter-section of the floor slab and supporting steel
beams was modeled in SAFIR as shown in Fig. 5.10. The concrete slab was modeled as a series
of four nodded 150 mm square shell elements (with minor geometric alterations to accommodate
the geometry of the assembly) with each node having six degrees of freedom. The supporting
168

beams were modeled as 150 mm long three nodded beam elements; the two end nodes each had
seven degrees of freedom, while the center node had one degree of freedom. The mechanical
properties as input in SAFIR for the steel and concrete are summarized in Table 5.2.
B

B

Furnace

A

Modeled
A
portion
Fig. 5.10: Dicretization of the steel beam-SFRC slab assembly used in parametric studies
Table 5.2: Mechanical properties utilized in analysis simulations
Steel

Concrete

Young’s modulus
(GPa)

210

Poisson’s ratio

0.3

Yield strength
(MPa)

350

Poisson’s ratio
Compressive
strength (MPa)
Tensile strength
(MPa)

0.25
46.6
5.34

The assumed symmetric condition causes one of the lines of symmetry to run down the length of
the unprotected W10X15 beam in the center of the assembly. Two options exist for modeling
this condition, first, only half of the beam could be modeled, or second, the entire beam could be
modeled and the elastic modulus and yield strength reduced to 50% for the duration of the fire
exposure to simulate the response of the partial section in the symmetric condition. The first
option causes instability in the model due to a non-symmetric beam element about its own axis
and SAFIR has a difficult time converging on a solution, as such, the later option was chosen,
169

and the entire beam was modeled with a yield strength and elastic modulus of 50%. In addition
to this concern, the bending stiffness of the section is proportional to the elastic modulus
multiplied by the moment of inertia, either of these can be reduced and the effect is the same, as
such, the assumption should not influence the response of the structure to fire exposure. To
establish the validity of this approach, parallel simulations were run for the full assembly and the
reduced assembly with the material properties of the central beam reduced by 50%. Deflections
predicted by the two models almost coincided, having less than a 5% discrepancy at any point
during the simulation. As such, this assumption of reduced material properties is deemed a
reasonable, and in light of the computational savings, a necessary assumption.
5.3.2

Critical Factors

Utilizing the SAFIR computer program the effect of fire exposure, load level, slab thickness, and
concrete type (SFRC) on the fire resistance of composite floor assemblies was studied. These
parameters were selected because their influence on the fire resistance of steel beam-concrete
slab assemblies in a performance-based environment has yet to be quantified. As such, to
investigate the effect of fire exposure, ASTM E-119 fire exposure and four levels of design fires
were considered as shown in Fig. 5.11. The design fires utilized in this study are an extreme fire
representing a large open workspace, a severe case representing a small more compartmentalized
workspace, and a medium fire representing a storage area in which the fuel load is considerable
but ventilation is poor. In addition, the analysis was also carried out under the fire scenario used
in the fire test (Fig. 3.14). A mild fire case was not considered in these simulations since very
few failures occur as a result of mild fire exposure. The effect of each of these parameters is
discussed independently in the following sections.

170

1200

Temp (°C)

1000
800
600
Medium
Severe
Extreme
ASTM E119

400
200
0
0

1

2

3

4

Time (hrs)

Fig. 5.11: Standard and design fire scenarios used in parametric studies on beam-slab assemblies
In addition to fire exposure, load level was considered as a primary factor influencing fire
resistance of the composite floor assemblies. To investigate the influence that load has on the
structure, three load levels were considered, a high, medium, and low load level. It should be
noted that the load was not adjusted for changes in slab thickness or concrete strength, as such,
the load refers to an absolute magnitude value load rather than a load ratio as was the case with
CFHSS columns.
From the literature, it was determined that slab thickness also plays a significant role on fire
resistance of floor systems, as such, slab thickness was investigated as part of this research study.
Slab thicknesses ranging from 110 to 150 mm were considered atop the steel beam network
previously described, and the effect of slab thickness on fire resistance was determined.
Lastly, the effect of concrete type, namely, plain and steel fiber reinforced concrete, on the fire
response of beam-slab assemblies was studied to quantify the influence of SFRC as presented in
the following sections.
171

5.3.3

Analysis Procedure

To study the effect of each variable outlined in the previous section, a series of parametric
studies were carried out using the validated model. For each study, only one variable was
changed at a time so the effect of that variable could be clearly isolated. The primary output
used to establish the effect of each parameter was the failure time of the assembly under fire
exposure. Failure of the assembly was said to occur in the analysis at the time when SAFIR
failed to converge on a solution.
5.3.4

Results and Discussion

The parametric study generated a total of 81 numerical simulations under different parameters.
It should be noted that only the significant trends are discussed, and that the discussion applies to
all of the assembly models unless otherwise noted.
Effect of Fire Exposure
Fig. 5.12 illustrates the effect of different fire exposures on the fire resistance of the beam-slab
assembly. It can be seen in Fig. 5.12 that both beam slab assemblies (with plain concrete and
SFRC) survive complete compartment burnout under the medium fire exposure. This can be
attributed to the relatively low temperatures achieved in the medium fire exposure being
insufficient to substantially reduce the structural capacity and stiffness of the assembly. Under
the test (Fig. 3.14) and severe (Fig. 5.12) fire exposures, only the assembly with the SFRC slab
survives compartment burnout. Though the temperatures in the severe fire case are more severe
than in the medium case, the enhanced tensile strength and ductility properties of SFRC, coupled
with the early onset of the cooling phase in the severe fire exposure, help the steel beam-SFRC
assembly to survive compartment burnout. In the case of the steel beam-PC slab, the structural
contribution of the concrete is insufficient, and the assembly fails in the simulation. This serves

172

to highlight the effect of tensile membrane action on fire resistance under different fire exposure
conditions.

The superior tensile strength of SFRC as compared to PC enhances the fire

resistance of the assembly sufficiently, through the development of TMA, for the assembly to
reach burnout conditions and survive the severe fire exposure.

Fire Resistance (min)

240
SFRC

180

PC

120
60
0
Test

Medium

Severe

Extreme

Fire Exposure

Fig. 5.12: Fire resistance of beam-slab assemblies under various fire exposures
Lastly, under extreme fire exposure, neither the plain concrete nor the SFRC concrete slab
assemblies achieved one hour fire resistance. This can be attributed to very high temperatures
(in excess of 1100 °C) reached in the beam early in the fire exposure.

The high early

temperatures in the beam do not allow sufficient heating of the slab for the benefits of composite
construction to be realized. For the development of TMA, significant deflections need to be
achieved in the slab, under the fire exposure, failure occurs before these defections can develop.
In typical office building compartments however, it is highly unlikely that such extreme
temperatures would be achieved, and the “medium” and “severe” fire exposures (where
temperatures are in the range of 700-1000 °C) are far more representative fire scenarios. Under

173

such fire conditions, the beam-slab assembly made with SFRC (despite reaching large
deflections) can withstand complete compartment burnout. This is attributed to the enhanced
properties of SFRC (tensile strength) allowing the assembly to survive until the cooling phase of
the fire, at which point the assembly begins to regain strength and stiffness. As such, it is
possible under design fire exposure, for beam-slab assemblies made with SFRC and utilizing
unprotected steel beams to provide 1-2 hours of fire resistance.
Effect of Load
The fire response of the beam slab assembly was investigated under three (high, medium, and
low) load levels representing a range of load ratios of 24-36% in the central unprotected beam,
32-48% in the connections of the central beam to the protected girders, and 40 to 60% in the
protected girders. This range of load levels was selected because it represents the realistic
(reduced) load levels that would be on the floor system of a typical office building under fire
exposure when load factors for fire conditions as specified in ASCE-07 (1.2DL + 0.5LL) are
applied. Fig. 5.13 shows SAFIR predictions for the mid-span deflections in the beam under the
high and low load ratios for an assembly with a 130 mm thick SFRC slab exposed to the
“severe” fire. While a total of 81 simulations were conducted under different combinations of
fire exposure, loading, slab thickness, and concrete type, Fig. 5.13 presents only two cases to
illustrate the typical response of the assembly. From Fig. 5.13 it can be seen that under the high
load ratio, the assembly demonstrates approximately 70 minutes of fire resistance, while in the
case of the low load ratio, the assembly survives compartment burnout.
Of particular interest from Fig. 5.13 is the observation that the deflection profiles in both cases
follow a similar trend for the first 20 minutes of fire exposure, with deflections under the high
load ratio being only slightly greater than those under the low load ratio. This can be attributed

174

to the response of the beam-slab assembly being controlled by the strength of the unprotected
steel beam early in fire exposure. As the temperatures in the unprotected beam continue to
increase as a result of fire exposure, the strength contribution of the beam is reduced, and the
benefit of composite action is utilized. Under the low load ratio, the strength contribution
achieved through composite action and SFRC is sufficient to transfer the entire load from the
failing unprotected beam to the protected girders, thus leading to the beam-slab assembly
surviving compartment burnout. Under the high load ratio however the slab is unable to transfer
the full load from the failing unprotected beam through TMA, so the beam fails after
approximately 70 minutes of fire exposure.
0

60

120

180

0
Low load
High load

Deflection (mm)

-20
-40
-60
-80
-100
Time (min)

Fig. 5.13: Variation of mid-span (beam) deflection as a function of fire exposure time for
different load levels
Effect of Slab Thickness
The effect of slab thickness on fire resistance of the assembly was evaluated by simulating three
different thicknesses of slab (110, 130, and 150 mm) under different combinations of loading,
fire exposure, and concrete type (PC and SFRC) previously discussed. The limit state used to
175

determine failure in these analyses is that of structural integrity, though temperatures on the
unexposed surface were monitored, they did not govern. Though a total of 81 simulations were
conducted, two cases are potted in Fig. 5.14 that correspond to an assembly with a SFRC slab of
110 mm and 150 mm (thin and thick respectively) exposed to a severe fire and subjected to a
medium load level to illustrate the typical response observed in the simulations. For the first
fifteen minutes of fire exposure, both slabs produce similar deflection trends and at the same
rate, this can be attributed to the structural contribution of the unprotected steel beam early in the
fire exposure.

As the steel beam weakens later in the fire exposure due to increasing

temperatures, the thin slab due to higher temperatures and the inability of the slab to develop
TMA starts to deflect rapidly until failure of the assembly.

The thicker slab however,

experiences lower temperatures (due to the increased thermal capacity of the thicker slab) and is
able to develop higher TMA (due to the thicker slab). This benefit of composite construction
slows the deflection rate of the slab and allows the thick assembly to survive until the cooling
stage of the fire, and hence, survive compartment burnout.
0

60

120

180

0
Thin
Thick

Deflection (mm)

-20
-40
-60
-80
-100
-120
-140
-160
Time (min)

Fig. 5.14: Fire resistance of beam-slab assembly as a function of slab thickness

176

Effect of Concrete Type
Results presented in Fig. 5.12 can also be used to illustrate the effect of concrete type used in the
slab on the fire response of beam-slab assemblies. Under “test” fire conditions (Fig. 3.14), the
beam-slab assembly with SFRC attained more than four hours of fire resistance, (survived
compartment burnout) while plain concrete slab assembly achieved only about a hour of fire
resistance as seen in Fig. 5.12. The ability of the steel beam-SFRC slab assembly to survive
compartment burnout in this condition can be attributed to several factors, the most significant of
which is the development of TMA. The stress distribution as predicted by SAFIR was markedly
different for assemblies with SFRC and plain concrete slabs. The SFRC specimen had a tensile
field develop in the center of the slab consistent with a tensile membrane action mechanism,
while the plain concrete slab did not develop TMA. The development of this tensile field helped
redistributed loads from the failing unprotected W10X15 beam to the cooler insulated W12X16
beams that supported the specimen (see Fig. 3.13 for the structural layout).

This load

redistribution allowed the assembly to withstand the heating phase of the fire and enter the
cooling regime (decay phase) in which the beam slabs could regain their strength and stiffness
properties.
The structural response of two beam slab assemblies (PC and SFRC) is plotted in Fig. 5.15
which shows that both assemblies behave similarly early in the fire exposure (prior to failure of
the W10X15 beam at about 20 minutes). However, when the unprotected W10X15 beam begins
to fail, due to increasing steel temperatures, the slab starts to carry an increasing portion of the
load in both cases. At this point, the response of the respective slab begins to differ. The rate of
deflection did not significantly change for the plain concrete slab, thus indicating that the plain
concrete slab was unable to support the additional load being transferred to it by the failing

177

W10X15 beam. In the plain concrete slab specimen, the rate of deflection remained relatively
unchanged until a deflection of approximately 80 mm was achieved in the center of the slab. At
this point, the rate of deflection changed because the plain concrete slab failed to develop tensile
membrane action. This contribution increased the fire resistance by about 10 minutes with the
specimen ultimately failing at about an hour.

0

60

120

180

0

Deflection (mm)

-20
-40

SFRC

-60

PC

-80
-100
-120
-140
Time (min)

Fig. 5.15: Mid-span deflection in secondary beam as a function of time for PC and SFRC slabs
The behavior of the SFRC assembly, however, is markedly different as can be seen in Fig. 5.15.
When the unprotected W10X15 beam looses its strength capacity, the SFRC slab due to
enhanced tensile and ductility properties of SFRC was able to transfer the load to the cooler parts
of the assembly through TMA. This load transfer significantly lowered the deflection rate after
approximately 25 minutes. Between 25 and 90 minutes, deflections increased gradually (due to
increasing slab temperatures) until the fire entered the decay phase. During the initial stages of
the decay phase, the deflections were steady and the load was carried by the SFRC slab through

178

TMA.

When the unprotected W10X15 steel beam starts to cool and re-gain strength and

stiffness, the beam starts to carry some portion of the load. This contribution of the W10X15 to
load transfer, combined with the thermal shrinkage of the deck and supporting steel beams
caused the slab to rebound as seen in Fig. 5.15. This markedly different behavior is made
possible by the better tensile and ductility properties of SFRC that enhanced the beneficial
effects of TMA.
5.3.5

Summary

Based on the above analysis, the following points can be summarized with respect to critical
factors influencing the fire resistance of composite floor assemblies:


Composite floor assemblies under fire exposure develop significant tensile forces
through tensile membrane action; this facilitates load transfer from fire weakened steel
beams to other cooler parts of the slab. The extent of load transfer achieved though
tensile membrane action is dependent on the fire exposure, slab thickness, and concrete
type.



Through the utilization of composite action, fire resistance can be significantly enhanced
in steel beam-concrete slab assemblies.

Unprotected steel beams that have fire

resistance of only 20-25 minutes can survive compartment burnout under most low to
moderate fire exposure scenarios when part of a composite beam-slab assembly.


The use of SFRC in slabs, in place of plain concrete, further enhances the fire resistance
of the beam-slab assembly even under medium to high fire scenarios. This is attributed
to the high tensile strength of SFRC facilitating the development of tensile membrane
action. Thus, no consideration is given to the use of plain concrete for achieving fire
resistance in composite beam slab assemblies in the following chapters

179



Through the use of SFRC, in place of plain concrete, in composite beam-slab assemblies,
it is possible to achieve fully unprotected secondary steel beams even under medium to
high fire scenarios.

In the following Chapter, these conclusions will be utilized to develop relevant design
methodologies for enhancing the fire resistance of composite beam slab assemblies.
5.4

System Level – Steel Framed Structural Systems

To study the factors influencing the response of a full-scale composite steel framed structure to
fire exposure, the calibrated model of the Cardington Restrained beam test was applied to
conduct a series of parametric studies. Results from these parametric studies were used to
identify trends in the response of composite steel framed structures under fire exposure over a
range of variables, details of which are presented below.
5.4.1

System Characteristics

For all of the simulations, the validated model of the Cardington restrained beam test as
described in Chapter 4 was utilized. Fig. 5.16a and 5.16b show the elevation and plan views of
the steel framed building respectively, with the location of the restrained beam highlighted, and
the portion of the building that was modeled in these simulations indicated.
In the numerical model shown in Fig. 5.17, the concrete slab was modeled using four nodded
shell elements with six degrees of freedom at each of the nodes. The beams and columns were
modeled using three nodded beam elements with seven degrees of freedom at the end nodes and
one degree of freedom at the center node. To simulate the composite action between the steel
beam and the floor slab, the “SAMEALL” command was used for the nodes where the beam and
shell elements coincide.

180

Fire Compartment

Modeled

Fire Compartment
Column
a: Elevation view

Modeled
b: Plan view

Fig. 5.16: Elevation and plan view of the simulated steel framed building (used in Cardington
tests)

Fig. 5.17: Discritazation of the steel framed building (used in Cardington tests) for use in
parametric studies
To aid in achieving convergence of the numerical model, it was assumed that the steel decking
on the bottom of the slab did not contribute to the strength of the slab at elevated temperature, as
was assumed by Bailey et al. (2000). Therefore, the ribbed steel deck was omitted from the
model used in the parametric studies. High temperate material models as specified in Eurocode
were utilized with the thermal and mechanical input parameters shown in Table 5.3.

181

Table 5.3: Thermal and mechanical properties assumed in simulations
Steel
Heat transfer coefficients
Hot convection coefficient
Cold convection coefficient
Relative emissivity

25
9
0.5

Heat transfer coefficients
3
46
Moisture content (kg/m )
Hot convection coefficient

25

Cold convection coefficient
Relative emissivity

9
0.5

5.4.2

Mechanical properties
(beams/reinforcement.)
Young’s modulus (GPa)
210/210
Poisson’s ratio
0.3/0.3
Yield strength (MPa)
350/413
Concrete
Mechanical properties
Poisson’s ratio
.25
Compressive strength
35.4
(MPa)
Tensile strength (MPa)
1.78
-

Critical Factors

Based on a review of the literature, the primary factor influencing fire resistance that is unique to
system level analysis is the effect of member interactions (including the effect of composite
construction and tensile membrane action). As such, the effect of member interactions on
structural fire resistance at the system level was studied as part of this research.
1200

Temperature (°C)

1000
800
600
Mild
Medium
Severe
ASTM E119

400
200
0
0

1

2

3

4

Time (hrs)

Fig. 5.18: Standard and design fire exposures considered for system

182

5.4.3

Analysis Procedure

To study the effect of member interactions on the fire response of a steel framed structure, the
validated model of the Cardington restrained beam test was applied to conduct parametric
studies. The response of the structure under the design fire exposures shown in Fig. 5.18 was
simulated and evaluated, the results are presented below. It should be noted that the simulations
were run for 180 minutes (as opposed to 240 minutes as was done for the element and assembly
level simulations) to reduce computational time. As such, if an end time of 180 minutes is
observed, that is indicative of the simulation surviving compartment burnout rather than the
simulation failing, unless otherwise noted.
5.4.4

Results and Discussion

The parametric study generated a total of 68 numerical simulations under different parameters.
It should be noted that many of the trends discussed at the element and assembly levels were also
studied at the system level, since these factors have been presented previously, no further
discussion on them will be presented here. The following discussion presents only those results
unique to the system level response. For a discussion on all of the parameters investigated at the
system level utilizing this model, the interested reader is directed to the respective literature
(Fike and Kodur 2009b).
Effect of Member Interactions
Fig. 5.19 plots the deflection time history predicted by SAFIR for the center of the heated beam
for each of the fire exposures shown in Fig. 5.18. As seen in Fig. 5.19, failure is observed in
each of the simulations when the unprotected beam reaches approximately 750 °C (+/- 30 °C).
This can be attributed to the combined strength of the steel beam and the plain concrete slab
dropping below the applied load at this point. Intuitively, since the fire exposures take different

183

lengths of time to reach this temperature in the unprotected steel beam, the failure time of the
system will vary depending on the fire exposure modeled. Of interest however are the different
deflections achieved as shown in Fig. 5.19. The longer the fire resistance, the greater the
deflection achieved, this is in spite of the fact that the steel beam is almost the same temperature
(750 °C) at failure in each of the simulations. While the steel beam is at the same temperature at
failure in each simulation, the average concrete temperature in the mild fire exposure is
approximately 100 °C higher than in either of the other simulations. This results in the combined
strength of the steel beam-plain concrete slab being significantly less in the mild fire scenario
that in the other three fires. Yet, the slab is observed to achieve the highest fire resistance under
the mild fire exposure. This is attributed to the redistribution of forces that is achieved though
member interactions. Though the system is weaker at failure in the mild fire exposure, the
slower heating rate allows sufficient deflections to be developed for the redistribution of the
applied load though member interactions and TMA. Thus, a higher fire resistance time is
achieved.
The beneficial effect of member interactions at the system level has been clearly shown to
enhance fire resistance by permitting larger deflections. However, the current models are not
capable of the detailed analysis that would be required to develop a methodology for enhancing
fire resistance though member interactions.

As such, the knowledge gained though these

simulations will be used to illustrate the use of the design methodologies developed at the
element level for CFHSS columns and at the assembly level for composite SFRC floor
assemblies.

184

Deflection (mm)

0
ASTM
Severe
Medium
Mild

-100
-200
-300
-400
0

30

60

90

120

Time (min)

Fig. 5.19: Mid-span deflection of slab-beam assembly for various fire exposures
5.4.5

Summary

Based on the above analysis, the main factor influencing fire resistance that is unique to the
system level is the effect of member interactions including composite construction and tensile
membrane action. It was observed that member interactions serve to enhance the fire resistance
of composite steel framed structures by redistributing forces from fire weakened members to
other cooler parts of the structure. Given the complex nature of member interactions at the
system level, it is not practical to develop simplified system level evaluation techniques at this
time.

Rather, system level analysis taking into account the beneficial effects of member

interactions will be used in subsequent chapters to illustrate the use of the design methodologies
developed for CFHSS columns and composite beam-slab assemblies.
5.5

Summary

In order to develop design methodologies for evaluating the fire resistance of steel framed
structures, a set of parametric studies were conducted at the element, assembly, and system

185

levels. At the element level, the effect of fire scenario, length, concrete filling type, load ratio,
cross sectional size, and failure criterion on the fire resistance of CFHSS columns was
investigated. For the assembly level, the effect of fire scenario, load level, slab thickness, and
concrete type on the fire resistance of a composite beam slab assembly was studied. Finally, at
the system level, the effect of member interactions on the fire resistance of a full-scale composite
steel framed building was studied. Based on these parametric studies, the following conclusions
can be drawn:


It is possible to achieve unprotected structural members through the use of composite

construction.


Type of fire exposure and failure criterion has a significant influence on the fire resistance

of composite construction.


At the element level, the effect of fire scenario, length, concrete filling type, load ratio,

cross sectional size, and failure criterion were identified as influencing fire resistance.


At the assembly level, the effect of fire scenario, load level, slab thickness, and concrete

type were identified has influencing fire resistance.


At the system level, the effect of member interactions was identified as having a significant

influencing on fire performance of the structure.
In the following chapter, the information gained in the parametric studies of this chapter will be
utilized for the development of simplified design methodologies for achieving fire resistance in
CFHSS columns and composite steel beam-SFRC slab assemblies.

186

CHAPTER 6
6
6.1

DEVELOPMENT OF DESIGN APPROACH
General

Data generated from the experimental and numerical studies is utilized to developed relevant,
simplified design methodologies for evaluating fire resistance.

As noted in the previous

chapters, CFHSS columns offer a practical means for achieving the required fire resistance
without the need for external fire protection. However, at the present there is no simplified
approach for their use under design fire exposures. Based on the data from parametric studies, a
simplified method to determine the fire resistance of CHFSS columns under non-standard fire
exposure is proposed.
Similarly, composite steel beam-SFRC floor systems offer an attractive method of achieving fire
resistance without the need for applied fire protection, and there is no design methodology for
their use in any capacity. Based on the results from the experimental and numerical studies, a
simplified design methodology to determine the load carrying capacity of composite steel beamSFRC slab assemblies under fire exposure is proposed. Finally, an overview of fire resistance
evaluation at the system level is presented.
6.2

Design Methodology for CFHSS Columns

At the present, a design equation exists wherein the fire resistance of a specific column can be
determined under standard fire exposure. It is therefore practical extend this equation to account
for design fire exposures. To accomplish this, all factors affecting fire resistance need to be
taken into account in the analysis used as the basis for development of the correlation

187

methodology. To that end, a brief review of the factor affecting fire resistance of CFHSS
columns is presented in the following section.
6.2.1

Factors Governing Fire Resistance of CFHSS Columns

Based on the parametric studies conducted in the previous chapter, fire exposure was identified
as a primary factor influencing fire resistance. Additionally, column length, concrete filling
type, load ratio and failure criterion influence the fire resistance of CFHSS columns. Given
however the importance of fire exposure on fire resistance, it is necessary to compile additional
information on the effect of fire exposure on fire resistance of CFHSS columns. To that end, the
14 columns presented in Table 3.2 were analyzed by exposing them to 75 design fires. For all
analyses, the factors identified in chapter five as having an influence on fire resistance were
taken into account.

The result was 1050 fire-column combinations being simulated, thus

providing the wide range of data necessary to establish an approach for determining fire
resistance equivalency. The time-temperature curves for each of these design fires were selected
by assessing different compartment characteristics. The selected fire scenarios ranged from
severe fire, representing a library room or records storage area, to a mild fire scenario,
representing an average office room in a typical building. Five of these fires, including the most
severe fire and the most mild fire are shown in Fig. 6.1 along with 2 standard fires (ASTM E-119
and ASTM E-1529). All of the design fires used in this study were taken from Magnusson and
Thelandersson (1970).
Load ratio on the columns was maintained at the same levels noted in Table 3.2. This allowed
the influence of other inherent properties of the column to be investigated without the added
ambiguity of varying loads. All of the loads were applied as a concentric load on the top of the
column (including the self weight). The point load was applied along the longitudinal axis such

188

that no eccentricity resulted from the load application. This was done to simulate the conditions
believed to be present during testing.

In order however to simulate the constructional

imperfections present in any structure, the columns were assumed to have an out of straightness
of H/500 at the center of the column, where H is the height of the column.
Failure was said to occur based in the strength limit state when the column can no longer support
the applied load. In SAFIR, this point generally corresponds to the time at which the stiffness
matrix is no longer positive. Failure of the column can occur due to either local failure within
the beam elements used for the column cross section, or it can be due to global buckling of the
column.
1200

Temperature (°C)

1000
800
600
ASTM E-119
Mild
Medium
Severe
ASTM E-1529

400
200
0
0

40

80

120

160

200

240

Time (min)

Fig. 6.1: Range of fire exposures considered in the development of a design methodology for
CFHSS columns
6.2.2

Development of an Approach for Evaluating Fire Resistance

As pointed out in previous sections, available methods for equivalent fire severity were
developed for traditionally protected steel members, failure of which is based on a limited

189

temperature rise in steel. When these methods (equivalent area, maximum temperature, and
minimum load) discussed above were applied to the CFHSS columns presented in Table 3.2, it
was quickly determined that none of the methods can accurately predict the failure time of
CFHSS columns under design fire exposure based on the ASTM E-119 fire resistance. The main
reason for this is that CFHSS columns derive their fire resistance from the strength contribution
of the concrete core, and thus determining the fire resistance based on critical steel temperature
does not indicate true failure.
In the process of checking each of the equivalent fire severity concepts for CFHSS columns, it
was observed that CFHSS columns either fail in less time in the design fire than the standard fire,
or they survive complete compartment burnout. Further scrutiny revealed that a modification to
the equal area concept produced a method by which failure of a column in a design fire can be
predicted with a high degree of reliability by considering only the initial fire severity. Since a
CFHSS column will either fail in less time in a design fire than in standard fire, or will survive
complete compartment burnout, only the severity of the fire up to the time of column failure
under standard fire exposure needs to be compared. It should however be pointed out that
determining the time of failure for the column in a design fire is not the objective, it is rather to
determine if the column will fail in the design fire or withstand complete compartment burnout.
The proposed approach can be applied to establish equivalency (survival of a column) between a
standard and design fire. As a first step, the fire resistance of the CFHSS column under standard
fire is evaluated using Eq. 2.1.

R f

(f'c 20)
D
D2
(KL  1000)
C

190

[2.1]

To determine the survivability of the column under a design fire exposure, the equivalency can
be established by comparing the area under the standard time temperature curve to that under the
design fire time temperature curve.
To determine if the column will fail in a design fire, the area under both the standard and the
design fire time temperature curves is determined at the time the column fails in the standard
fire. If the area under the standard fire curve is greater than the area under the design fire curve,
the column will not fail in the design fire, that is to say the column will survive complete
compartment burnout. If however, the area under the standard fire curve is less than that under
the design fire curve, the column will fail in the design fire. Most notably, in the latter case, the
column will fail in less time in the design fire than in the standard fire.
The application of this approach is illustrated in Fig. 6.2 which shows the time temperature
curves corresponding to the standard (ASTM E-119) and a design fire exposure. Knowing the
basic details of the column, the fire resistance of the column under standard fire exposure can be
estimated by applying Eq. 2.1. Once both the design fire and the failure time of the column
under standard fire exposure are known, the area under the standard fire time temperature curve
(Area A in Fig. 6.2) and the area under the design fire time temperature curve (Area B in Fig.
6.2) can be determined at the time of column failure under standard fire exposure. The areas A
and B are now compared: if the area under the standard fire curve (Area A) is less than the area
under the design fire curve (Area B) the column is said to have failed in the design fire, and most
notably in less time than in the standard fire. If however, the area under the standard fire curve
(Area A) is greater than that under the design fire curve (Area B) the column is said to not have
failed in the design fire, that is to say the column will survive complete compartment burnout
(Fike and Kodur 2009a).

191

1200

Design Fire

Temperature (°C)

1000

ASTM E-119

Area B

800

Area A

600

Column fails in
ASTM E-119

400
200
0
0

30

60

90

120

150

Time (min)
Fig. 6.2: Illustration of proposed approach for a CFHSS column
The approach proposed here is predicated on the concept that design fires have a similar initial
rate of temperature increase, and most design fires achieve higher initial temperatures than the
standard fire exposure, as seen in Fig. 6.1. It should be noted that the proposed method is not
applicable for design fires that do not have a similar initial temperature rise as that of the ASTM
E-119 fire exposure (up to ten minutes of fire exposure). Since the failure time of the column
under standard (ASTM E-119 or ISO 834) fire exposure is known (using Eq. 2.1), only the fire
severity up to this point needs to be compared with that of the design fire. Given the previous
observation that the initial temperatures in most design fires are higher than in the standard fire,
the only way for the design fire to be less severe than the standard fire over the same time period
is if the design fire enters the cooling phase (in which the column regains strength) prior to the
end of the time period (defined as column fire resistance under standard fire exposure). The area

192

under the respective time-temperature relationships serves as a ready means for comparing the
relative fire severity. Since only the initial portion of the fires is being compared, the problem of
drastically different fire exposures is avoided, and an accurate comparison is possible. Hence the
conclusion that if the area under the standard fire curve (Area A in Fig. 6.2) is greater than the
area under design fire curve (area B in Fig. 6.2), the column will not fail in the design fire. On
the contrary, if the area under the standard fire curve (Area A in Fig. 6.2) is less than that under
the design fire curve (Area B in Fig. 6.2), the column will fail in the design fire.
6.2.3

Validation of the Proposed Approach

The proposed approach was applied to the 1050 column-fire combinations analyzed using
SAFIR to determine if the columns fail or survive complete compartment burnout. In 761 out of
the 1050 column-fire combinations analyzed, both SAFIR and the proposed approach indicated
that no failure occurs in the column. This high percentage of survivability can be attributed to
the fact that the decay phase of the fire allows the column to regain part of its strength, resulting
in a fire exposure that is less severe than the “standard” fire exposure. The agreement in failure
predictions between SAFIR and the proposed approach for a large number of columns illustrates
the strength of the proposed approach.
Of the 289 remaining column-fire combinations, both SAFIR and the proposed approach
predicted failure in 182 of them. The failure of CHFSS column can be attributed to the high
severity of fires encountered in these cases. Again, the agreement between the actual (SAFIR)
failure and that predicted by the proposed approach indicates the validity of the proposed
approach. Further, for another 90 column-fire combinations while failure was not observed in
SAFIR, the proposed approach predicted failure. This can be attributed to fires that are similar to
ASTM E-119 for the considered time period, entering the decay phase possibly only minutes

193

before the column failed under ASTM E-119 fire exposure. This can however be taken as
conservative for design purposes.

For the remaining 17 column-fire combinations, SAFIR

predicted that the columns would fail while the proposed approach does not. This can be
attributed to fires with a low ventilation coefficient and a comparatively large fuel load. The
resulting long duration cool fire imparts more heat to the columns than short duration fires that
are hotter causing them to fail much later in the simulation.
Failure predicted No
failure observed
8.6%
Failure predicted
Failure observed
17.3%
1.6%
72.5%

No failure predicted
Failure observed

No failure predicted No
failure observed
Predicted = Proposed approach
Observed = SAFIR analysis

Fig. 6.3: Graphical illustration of the effectiveness of the proposed approach
To illustrate the effectiveness of the proposed approach, a statistical representation of the 1050
numerical simulations is presented in Fig. 6.3. In 72.5% (761) of the column-fire combinations,
both the SAFIR and proposed approach indicated that the column would not fail. In 17.3% (182)
of the cases both SAFIR and the proposed approach indicate that the column-fire combination
will result in failure of the column. SAFIR predicts that failure will not occur while the proposed

194

approach indicated that failure will occur in 8.6% (90) of the column-fire combinations, thus
being a conservative prediction. In the remaining 1.6% (17) of the column-fire combinations,
SAFIR indicates the column will fail while the proposed method indicated that the column will
not. This low (1.6%) probability of an un-conservative estimation of column failure for the
selected range of fire exposures serves to further reinforce the strength of the proposed method.
A subset of the data is presented in Table 6.1 to illustrate the results from analysis. For each of
the column-fire combinations, Table 6.1 presents the failure time as determined by SAFIR where
applicable, and whether or not the column is determined to fail using the proposed method.
Boxes occupied by a “-“ in the “SAFIR Failure” column indicate that no failure was observed in
SAFIR analysis under that design fire exposure. Of the 252 column-fire combinations in Table
6.1, both SAFIR and the proposed approach indicate that the column will not fail in 131 of them.
Of the 121 remaining column-fire combinations, both SAFIR and the proposed approach
predicted failure in 86 of them. For another 31 column-fire combinations while failure was not
observed in SAFIR, the proposed approach predicted failure. In the remaining 4 column-fire
combinations, SAFIR predicted that the columns would fail while the proposed approach does
not. Reasons for the observed results are the same for this subset as for the entire data set, as
such, the reasons given above will not be reiterated here, though this data subset serves to further
reinforce the validity of the proposed approach.
As an example from Table 6.1, SAFIR analysis of CFHSS column RP 168 under standard fire
exposure yielded a failure time of 82 minutes, while no failure was observed for “FIRE 1”
through “FIRE 5” with failure occurring in “FIRE 6”. The proposed approach also predicts no
failure for “FIRE 1” through “FIRE 4”, predicting failure for “FIRE 5” and “FIRE 6” though
failure is not observed in “FIRE 5”

195

Table 6.1: Fire resistance equivalency as predicted by SAFIR and the proposed approach

ASTM
FIRE 1
FIRE 2
FIRE 3
FIRE 4
FIRE 5
FIRE 6
FIRE 7
FIRE 8
FIRE 9
FIRE 10
FIRE 11
FIRE 12
FIRE 13
FIRE 14
FIRE 15
FIRE 16
FIRE 17
FIRE 18
FIRE 19
FIRE 20
FIRE 21
FIRE 22
FIRE 23
FIRE 24
FIRE 25
FIRE 26
FIRE 27
FIRE 28
FIRE 29
FIRE 30
FIRE 31
FIRE 32
FIRE 33
FIRE 34
FIRE 35
FIRE 36
FIRE 37
FIRE 38
FIRE 39
FIRE 40
FIRE 41
FIRE 42

82
77
49
49
42
42
42
54
54
45
45
45
59
59
44
44
44
39
39
39
178
63
63
45

NA
N
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
N
N
Y
Y
Y
Y
Y
Y
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
Y
Y
Y
Y

74
70
70
47
47
47
40
40
40
52
52
43
43
43
58
58
42
42
42
37
37
37
178
60
60
43

NA
N
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
N
N
Y
Y
Y
Y
Y
Y
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
Y
Y
Y
Y

204
-

NA
N
N
N
N
N
N
N
N
Y
N
N
Y
N
N
N
N
N
N
N
Y
N
N
Y
N
N
N
N
N
N
N
N
Y
N
N
Y
N
N
N
N
N
N
N

196

121
123
85
83
74
73
94
89
77
77
99
76
76
69
69
110
-

NA
N
N
N
N
N
Y
N
Y
Y
N
Y
Y
N
N
N
N
N
N
Y
Y
N
Y
Y
N
N
N
N
Y
Y
N
Y
Y
N
Y
Y
N
N
N
N
Y
Y
N

98
94
67
67
58
58
72
72
62
62
139
82
81
61
61
67
54
54
146
88
85
-

NA
N
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
N
N
N
Y
Y
Y
Y
Y
N
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
N
Y
Y
Y

130
88
77
94
80
80
72
72
-

Predicted
Failure

SB 203

Predicted
Failure
SAFIR
Failure
(min)

RB 273b

Predicted
Failure
SAFIR
Failure
(min)

SF 203

Predicted
Failure
SAFIR
Failure
(min)

RF 324

Predicted
Failure
SAFIR
Failure
(min)

SAFIR
Failure
(min)

Type of
Fire
Exposure
↓

SP 152

Predicted
Failure
SAFIR
Failure
(min)

RP 168

NA
N
N
N
N
N
Y
N
Y
Y
N
Y
Y
N
N
N
N
N
N
Y
Y
N
Y
Y
N
N
N
N
Y
Y
N
Y
Y
N
Y
Y
N
N
N
N
N
Y
N

It should be reiterated that this method does not determine the fire resistance of CFHSS columns
in design fires in a quantified manner, rather, it predicts whether or not the column will survive
the design fire exposure. If it is determined that the column does not survive the fire exposure,
that is all the information available, the duration of survival is not known from this method. As
such, there is a built in factor of safety in that all columns designed according to this method will
have sufficient fire resistance to withstand complete burnout of the probabilistic fires to which
the column would be exposed, rather than satisfying specific fire resistance requirements. It
might be possible to achieve more deterministic results using more sophisticated methods, but
that would increase the complexity of the calculations and make the approach less practical for
use in design. To illustrate the use of the proposed approach, a design example is presented
below followed by the limitations to the proposed approach.
6.2.4

Illustration of the proposed approach

Application of the proposed equivalent area approach for a design situation is illustrated through
a numerical example. Detailed calculations for this example are presented in Appendix E.
A CFHSS column located in a room 3 m high with a 6 m by 4 m floor that has a fuel load of 550
2

MJ/m (of floor area) is to be designed. The room has one window opening 3 m wide by 2 m
high. In this compartment, the architect has proposed a 273 mm diameter circular HSS column
filled with plain concrete made with siliceous aggregate. The height of the column needs to be
3.81 m (to accommodate the drop ceiling and utilities) with fixed connections on both ends. The
building code requires the column to have a 2-hour fire resistance rating. Now it is desired to
know if this column will satisfy the code requirements by withstanding complete burnout of the
fire that would occur within the compartment.

197

The first step is to determine the design fire that is most likely to occur within the compartment.
The fire scenario can be determined using the Eurocode (2005a) method.

The detailed

calculations associated with this example are presented in Appendix E, along with further details
on the compartment characteristics. The ventilation factor for this example is 0.079 m

1/2

and the

burning duration is 0.79 hours. The time temperature curve determined using this method and
the standard (ASTM E-119) time temperature curve are shown in Fig. 6.4.
1200

Temperature (°C)

1000
800
600
Design Fire

400

ASTM E-119

200
0
0

30

60

90

120

150

180

Time (min)

Fig. 6.4: Comparison of standard and design fire exposure
The second step is to determine the fire resistance of the column under standard fire exposure
(ASTM E-119 or ISO 834). Applying Eq. 2.1, the fire resistance of the column is determined to
be 101 minutes. The area under the standard time temperature curve at 101 minutes is 1462
min*°C. The corresponding area under the design fire curve at 101 minutes is 1503 min*°C.
Since the area under the design fire time temperature curve is greater than that under the standard

198

time temperature curve, the column will fail in less time in the design fire than when exposed to
standard fire, as such, practical alternatives need to be developed.
The most practical alternative is to simply change the type of aggregate used in the concrete. By
switching to carbonate aggregate, according to Eq. 2.1 the fire resistance of the column increases
from 101 to 116 minutes under standard fire exposure. At 116 minutes, the area under the
standard (ASTM E-119) time temperature curve is 1701 min*°C, while that under the design fire
time temperature curve is 1626 min*°C. As such, since the area under the design fire curve is
less than that under the standard fire curve, the column will survive complete compartment
burnout, thus, the column is safe for use in this building because it has the highest fire resistance
rating possible, surviving complete compartment burnout when carbonate aggregate is used in
the concrete. Thus, the proposed approach facilitates the use of CFHSS columns in buildings
where traditional prescriptive design would not utilize these columns.
6.2.5

Application and Limitations

The proposed method offers a practical approach for evaluating the fire resistance of CFHSS
columns exposed to design (real) fires. However, the applicability of this method is limited to
the range of parameters that were considered in the numerical study which formed the basis for
developing this approach. The explicit limitations for the proposed methods are as follows:


The initial temperature rise (in the first 5-10 minutes) in the design fire must be similar to
the ASTM E-119 temperature rise



The maximum fire temperature reached must be greater than that of ASTM E-119 during
the first 20 minutes.



This method is not applicable for the ASTM E-1529 hydrocarbon fire exposure due to the
absence of a decay phase

199



The approach is only applicable for unprotected CFHSS columns (i.e. no insulation
provided on the steel



Since the approach makes use of Eq. 2.1, all of the limitations that apply to Eq. 2.1
(length, concrete compressive strength, end conditions, and cross section) also apply to
this method



This method is applicable for bar, steel fiber, and plain concrete filled HSS columns

It should be noted that the above limitations are specified due to a lack of validation for these
conditions. Through further validation, it should be possible to extend this method to overcome
some of these limitations.
6.3

Design Methodology for Composite Beam-Slab Assemblies

The state-of-the-art review presented in Chapter 2 indicated that composite construction, and
considering assemblies rather than single elements in fire resistance tests has a significant
influence on the observed fire resistance. At the present however, the fire resistance that can be
achieved through composite floor systems is insufficient to meet the levels required in codes and
standards, without the application of external fire protection to the supporting steel beams. To
overcome this limitation, a novel material system (SFRC) was tested in composite floor
assemblies under fire exposure as outlined in Chapter 3. Following the experimental program, a
computational model was constructed and the factors influencing fire resistance of the assembly
identified in Chapter 4 and Chapter 5 respectively.

Based on these findings, a design

methodology for determining the fire resistance of composite steel beam SFRC slab floor
assemblies under any fire exposure is presented below. As was the case with CFHSS columns,
all factors identified as influencing the fire resistance of composite steel beam-SFRC floor slabs
were taken into account in all relevant simulations. A review of the factors influencing the fire

200

resistance of composite steel-beam-SFRC floor systems under fire exposure is presented in the
following section.
6.3.1

Factors Affecting the Fire Resistance of Composite Floor Assemblies

The primary factors influencing the development of TMA in composite floor assemblies under
fire exposure are fire scenario, load level, slab thickness, span, and concrete type. Through the
novel experimental program and numerical studies presented in this research, it has been shown
that concrete type, namely the use of SFRC significantly enhances the response of composite
construction to fire exposure under realistic conditions. This is attributed to the enhanced tensile
strength of SFRC as compared to plain concrete facilitating the development of tensile
membrane action. To illustrate the beneficial effects of using SFRC in floor slabs, the following
section presents a derivation of the effect that concrete tensile strength has on the development of
TMA, and consequently enhancing fire resistance. Once having established the beneficial effect
of SFRC in composite floor assemblies, a design methodology for predicting the response of
SFRC floor systems to fire exposure will be presented.
6.3.2

Development of Tensile Membrane Action in SFRC Slabs

The mechanics associated with the contribution of SFRC to fire performance of a beam slab
assembly are derived by expanding Bailey’s (2000) approach.

For a typical concrete slab

experiencing two-way bending, the failure patterns as determined by yield line analysis are
shown in Fig. 6.5a.

The slab is considered to be comprised of four zones.

Equilibrium

principals can be applied to these zones to quantify to define an upper bound for the contribution
of SFRC to overall fire resistance. Due to symmetry, only two zones defined by yield line
failure theory as shown in Fig. 6.5b are considered. Based on the geometry of the elliptical

201

tensile region shown in Fig. 6.5b, Fig. 6.5c gives the location of the forces C and T2 in terms of
the slab lengths L and D. The primary difference between the derivation shown below and that
originally published by Bailey (2000) is that the tensile strength (f’t) contribution of SFRC is
accounted for in this derivation.

Element 1

Element 2

Symm.
Symm.

(a): Failure patterns for a two-way slab based on yield line theory.
L

C

kbβtf’t

nL

C
L

C
A
1

S

S

θ
T2
bβtf’t

T2

T1

2

d

(b): Forces on SFRC slab undergoing yield line failure
Fig. 6.5: Illustration of forces developed in a beam-slab assembly under fire exposure

202

kbβtf’t

C

2

2

(1/(1+k))√((nL) +d /4)
2

d/2

2

(k/(1+k))√((nL) +d /4)
T2
nL

bβtf’t

(c): Dimensions of yield line based on geometry
L/2
nL
C
A
bβtf’td/2

1

S

θ

T2
T1
(d): Fracture equilibrium at failure
Fig. 6.5 (Continued): Illustration of forces developed in a beam-slab assembly under fire
exposure
where k and b are modification factors of the SFRC tensile force, L and d are the length and
width of the slab respectively, f’t is the tensile strength of SFRC, t is the thickness of the slab, β

203

is a correction factor to account for the strain distribution through the thickness of the slab (0<
β<1), and C, T1, T2, and S are the compressive, tensile, and shear forces on the elements
respectively.
by applying force equilibrium (Fig. 6.5b), the relationship between forces C, T1, and T2 can be
shown to be:

T1
sin( )  (C  T2 )
2

[6.1]

from further consideration of Figs. 6.5b and 6.5c the forces T1, T2, and C can be determined to
be the following:

T1  b tf 't ( L  2nL)

[6.2]

2
b tf 't  1 
2d
T2 

 (nd )
2  1 k 
4

[6.3]

2
kb tf 't  k 
2d
C

 (nd )
2 1 k 
4

[6.4]

by substituting Eqs. [6.2-6.4] into Eq. [6.11] k can be expressed as:

2

L
4n   (1  2n)
d
k  
1
2
L

4n 2    1
d 

[6.5]

Lastly, the geometry of element 1 as shown in Fig. 6.5b can be used to define the angle of the
yield lines relative to the long axis of the slab as:

204

nL

sin( ) 

d
( nd )2 

[6.6]

2

4

Assuming that failure occurs due to the formation of a full depth crack along the centerline of
element 1 in the short direction, the force distribution shown in Fig. 6.5d can be assumed. The
primary difference between the equilibrium shown in Fig. 6.5d and that assumed by Bailey
(2000) is that only tensile strength of SFRC is considered to contribute to the fracture resistance
of element 1 whereas Bailey (2000) considered the contribution of the shrinkage steel only.
Taking equilibrium of the fractured element 1 shown in Fig. 6.5d about point A yields the
following:


2
L ( L / 2  nL)  1
1 1 
2 d 
T2  cos  
 

 (nd ) 

2
cos( )  tan( ) 3  1  k 
4 



2
L 1 k 
2 d 
C sin   
 (nd ) 

2 3  1 k 
4 


2
L T1  1  L
   tf ' td
 S cos( )     nd   
2 2 2  2
8


[6.7]

By substitution and re-arranging b can be expressed as:

d2
b
8( A  B  C  D )

[6.8]

where A, B, C, D are given as:

2
1  1   d 2 ( L / 2  nL 
2d
A 

 (nL)


2  1  k   8n
nL
4


205

2
 1  1 
2d
 
 (nL)
 3  1 k  
4








[6.9]

2
1  k 2   nL2
k 
2d
B 


 (nL)
2  1  k   2 3(1  k ) 
4









[6.10]

d2
C
(k  1)
16n

[6.11]

L
 L nL 
D    nL   
2
 4 2 

[6.12]

Taking the moment for element 1 about the support at an arbitrary deflection Δ yields the
following expression for the contribution of SFRC to load bearing capacity of element 1:


n(3k  2)
nk 3 

M   tf 't Lbw  (1  2n) 


3(1  k ) 2 3(1  k ) 2 



[6.13]

where b and k are as derived above, n, t, f’t, and L are based on the geometry of the assembly
and material properties, and β is an assumed value between 0 and 1 based on test results. This
equation being intrinsically positive (assuming downward deflection Δ to be positive) illustrates
that the tensile strength of concrete contributes to the moment capacity of a concrete slab. SFRC
having superior tensile strength properties as compared to normal strength concrete will
maximize this benefit well into fire exposure.
6.3.3

Development of an Approach for Evaluating Fire Resistance

Through the fire test, parametric studies, and derivation presented previously, it has been
demonstrated that the use of SFRC in the floor slab can enhance the fire resistance of composite
beam slab assemblies. The fire resistance enhancement that can be achieved through the use of
composite construction with SFRC is to such an extent, that it may by possible to eliminate the
need for fire protection on secondary steel beams, while still achieving the required fire

206

resistance rating. It is therefore desirable to determine if such a level of fire resistance can be
practically achieved through the inclusion of steel fibers in the slab. If so, it is desirable to
develop a design equation that will allow practitioners to readily use SFRC for achieving fire
resistance in practical design applications.
Fire exposure, thickness, and load were identified in the previous section as factors that have a
significant influence on the fire resistance of SFRC floor assemblies. In addition to these factors,
the secondary beam section and the secondary beam spacing can significantly impact the fire
resistance of the floor assembly. While related to the loading on the floor system, the network of
supporting beams is a relatively independent variable which depends not only on structural
considerations, but on geometric and architectural considerations. This added variability makes
the number of simulations that would be required to evaluate the response of composite floor
assemblies under the full range of variables untenably large.
To reduce the size of the parametric study, and to enhance the applicability of the developed
design methodology, observations made from SAFIR analysis can be utilized to make relevant
simplifying assumptions. The first observation made was that the load capacity of the composite
beam slab assembly under fire exposure longer than 20 minutes is relatively independent of the
supporting secondary steel beam section.

This trend is attributed to the extreme temperatures

that are rapidly reached in the unprotected steel section reducing its structural contribution to a
nominal value. As such, after 20 minutes of fire exposure the SFRC slab dominates the response
of the section, and there is no need to model the steel section in the structural models, only the
floor slab.
The second observation made, is that the load capacity of the composite floor system does not
monotonically decrease as a function of fire exposure time, rather, it follows the trend shown in

207

Fig. 6.6. This trend is presumably due to the relative heating rates of the constituent materials in
the assembly. At ambient temperatures, the capacity of the composite section is dominated by
the steel section contributing considerable load bearing capacity. As the fire exposure time
increases, the temperatures in the unprotected beam increase, this causes the steel beam to
weaken and much of the load is transferred to the SFRC slab. The SFRC slab being cool and at
relatively low deflections can not develop TMA, as such, a minimum is observed in the load
capacity. As the SFRC slab is slowly heated, the slab becomes more ductile and deflections in
the slab increase. These increasing deflections provide the geometry necessary to develop TMA
in the slab. As the load which can be carried through TMA in the slab increases, the load
capacity of the system is observed to increase as seen in Fig. 6.6. Later in fire exposure, (after
150 minutes for the case shown in Fig. 6.6) the tensile strength of SFRC begins to deteriorate

25
Load capacity
Dis placement

2

Load (KN/m )

20
15
10
5
0
0

60

120

200
180
160
140
120
100
80
60
40
20
0
180

Deflection (mm)

due to increasing concrete temperatures.

Fire Exposure Time (min)

Fig. 6.6: Load carrying capacity and deflection as a function of fire exposure time for a SFRC
floor assembly

208

Ultimately, the tensile strength of the concrete deteriorates to a point where the load which can
be transferred through TMA decreases to a nominal and impractical value, and the assembly
fails. Based on this, if the assembly can survive past the local minimum in load capacity, it is
highly likely that the assembly will reach compartment burnout in most design fires.
Based on the above observations, the two simplifications that can be made to the approach used
for the development of a design methodology for composite SFRC floor system under fire
exposure are as follows


The contribution of the unprotected secondary beam was neglected in the simulations,
and only the SFRC floor slab was simulated under fire exposure. This is justified by the
observation that for fire exposures longer than 20 minutes, the response of the composite
floor system is independent of the steel section utilized.



Rather then trying to determine the load capacity of the floor system exposed to design
fires, the maximum applied load under which the assembly can survive compartment
burnout is desired.

To determine the maximum load that would allow the assembly to survive compartment burnout,
without consideration being given to the supporting secondary beams, beam elements were used
to model a strip of the SFRC floor slab (here unto referred to as a strip slab) exposed to fire. The
beam elements employed were fiber based elements which had been discretized to represent the
SFRC floor slab as shown in Fig. 6.7 below. Beam elements offer several advantages over shell
elements for the type of analysis being conducted. Stability of the simulated strip slab is
considerably easier to achieve, and the need to apply boundary conditions over the length of the
strip slab is eliminated. Lastly, computational time is also reduced through the use of beam
elements as compared to a larger number of shell elements.

209

Fig. 6.7: Discretization of beam elements used in the parametric study for evaluating the
response of composite SFRC floor slabs exposed to fire
Having simplified the models using the information gathered in the parametric studies described
above, an additional data pool is necessary for the development of a practical engineering design
methodology. To that end, numerical models were constructed to simulate a strip of SFRC floor
slab 1.5 m wide with different spans and thicknesses exposed to different design and standard
fires. A slab width of 1.5 m was selected to ensure that the thickness was no more than 10% of
the slab width in any of the simulations, and to avoid lateral torsional buckling of the strip slab.
Simulated spans ranged from 4.6 to 12.2 m, thicknesses from 100 to 150 mm, and the range of
fire exposures considered are shown in Fig. 6.8. It should be noted that the span referred to in
the following discussion is that corresponding to the short direction of the slab, i.e. in the
direction of the secondary beams. The floor strip was assumed to be fully supported at the ends
with all rotations and translations restrained. In all simulations, the compressive strength of the
3

SFRC was assumed to be 28 MPa and the steel fiber content 42 kg/m (1.75% by mass).
In order to evaluate the load carrying capacity of the flooring strips as a function of time,
traditional analysis methods could not be employed. Given the presence of a local minimum in
load capacity of the floor system exposed to fire as seen in Fig. 6.6, were a specified load to be
applied to the system and the analysis run, the system will either fail in a very short period of
time, or survive compartment burnout. As such, alternate methods to evaluate the load capacity
of the system under increasing temperatures had to be employed.

210

1400

Temperature (°C)

1200
1000
800
600
Extreme
Severe
Medium
Mild
Check
ASTM E-119

400
200
0
0

1

2

3

4

Time (h)

Fig. 6.8: Design (real) fires considered in parametric study on composite beam slab assembly
SAFIR was used to determine the thermal profiles in the floor system over the entire duration of
fire. This data was then used to determine the cross-section temperatures in the floor system at
each desired time. This temperature profile was then assumed static at the time of the structural
analysis, and the loads applied to the system were increased. From this structural analysis, the
failure load of the beam-slab assembly could be determined based on the time at which
instability (failure) occurs in the slab.
For the results presented in the following sections, the load capacity of the system was
determined every 10 minutes until the fire was well into the decay phase (compartment burnout).
This approach resulted in more than 1200 simulations being conducted for the six fire exposures
shown in Fig. 6.8. Table 6.2 shows a summary of the load capacity for the different sections
considered under the full range of design fires.

211

Table 6.2: Load capacity of strip floors considered in numerical simulations
Slab
thickness
(mm)

ASTM

Span
(m)

Extreme Severe Medium
1 hour
2 hour (kN/m2) (kN/m2) (kN/m2)
2
2
(kN/m ) (kN/m )

4.57

8.10

5.23

5.23

4.74

5.12

5.63

7.62

4.12

4.12

3.52

4.07

4.34

9.15

3.42

3.42

2.99

3.39

3.53

2.93

2.93

2.03

2.91

2.98

2.57

2.57

1.44

2.24

2.57

4.57

16.48

16.48

14.17

16.06

12.54

6.10

11.18

11.18

10.68

11.22

10.88

7.62

8.39

8.39

6.57

8.34

8.57

9.15

6.72

6.59

4.90

5.68

6.76

10.67

5.54

4.69

2.81

3.73

5.46

12.20

4.44

3.55

1.86

2.77

4.49

4.57

15.45

15.45

13.01

14.82

9.83

6.10

12.38

12.38

10.37

12.00

11.60

7.62

10.24

10.24

9.83

10.91

8.85

9.15

9.29

9.29

8.37

9.29

8.35

10.67

8.71

6.86

5.32

5.73

7.66

12.20

6.3.4

7.05

12.20

150

6.41

10.67

125

7.26

6.10
100

7.26

7.12

5.35

3.51

4.03

5.35

Development of Design Methodology

For development of a design methodology, results from only three of the fires shown in Fig. 6.8
were used. This was done to provide two distinct data sets, one (three cases) to develop the
design methodology, and the second (remaining two cases) for validation of the methodology.
The fire exposures selected were extreme, severe, and medium, the load capacity of the floor
strips under these fire exposures as determined by SAFIR simulations can be seen in Table 6.2.

212

Based on results from the numerical investigations discussed in the previous section, a
correlation was developed between the load capacity of a specific slab able to survive two hours
of ASTM E-119 fire exposure (hereunto referred to as the two hour ASTM load capacity), and
the load capacity of the same slab able to survive burnout of a design fire (hereunto referred to as
burnout load capacity). Given the complex nature of fire design, and the wide range of floor
systems that can be represented with a single figure, a design equation to determine load capacity
under ASTM E-119 fire exposure was not developed. Rather, Fig. 6.9 which shows the load
capacity of a floor that survives two hours of ASTM E-119 fire exposure is referenced to
determine the two hour ASTM load capacity of a specific slab spanning a specific length. Also,
of note, is that the method presented here only determines the load capacity of the slab which
will allow it to reach compartment burnout, not the specific fire resistance duration (time to
failure) of the slab under a given load.

2
Load Capacity (KN/m )

18
15

100 mm
125 mm
150 mm

12
9
6
3
0
4

6

8

10

12

14

Span (m)

Fig. 6.9: Load capacity of strip floor able to achieve two hour fire resistance rating under ASTM
E-119 fire exposure

213

It is assumed at this point that the designer is familiar with the procedure to develop a
probabilistic design fire time-temperature curve based on the compartment characteristics (if this
is not the case, the reader is referred to Eurocode (2002)). Having the design time-temperature
curve based on compartment characteristics, the peak temperature of the design fire is recorded.
Having this value, Eq. 6.14 is used to determine the load capacity of the SFRC slab that will
allow it to reach compartment burnout under the design fire exposure.

Design Load Capacity 

ASTM Two Hour Load Capacity
t

101.6

[6.14]

where the ASTM Two Hour Load Capacity is read from Fig. 6.9, α is equal to the maximum
design fire temperature divided by the ASTM E-119 temperature at two hours (1006 °C) and
must be greater than or equal to 1, and t is the thickness of the slab in mm. Units of load
capacity are unimportant in the equation.
From Fig. 6.9 it can be seen that load capacity of a concrete slab increases with slab thickness,
contrary to this, Eq. 6.14 shows thickness of the slab in the denominator of the equation, thus
indicating that increasing thickness decreases load capacity of the slab. Upon closer inspection,
it is observed that the ASTM load capacity (as seen in Fig. 6.9) increases with increasing
thickness, and this is taken into consideration in the numerator of Eq. 6.14. Therefore, thickness
being in the denominator indicates that the design fire burnout capacity does not increase as
much with thickness as the two-hour ASTM E-119 load capacity. As an example, under ASTM
2

fire, the load capacity for a 100 mm slab spanning 7.62 m is 4.12 kN/m . If this thickness of slab
2

is increased to 125 mm, the load carrying capacity of the section increases to 8.39 kN/m . Using
Eq. 6.14 and the peak fire temperature for the extreme fire case (1224 °C), the load capacity of

214

2

the 100 mm thick slab is 3.38 kN/m and the load capacity of the 125 mm thick slab is 5.52
2

kN/m . In this example, increasing floor thickness from 100 to 125 mm increases the load
capacity under ASTM fire by 100%, and under the design fire by only 73%. As such, despite the
fact that thickness is in the denominator of Eq. 6.14, the load capacity of the slab does increase
with an increase in slab thickness under design fire exposure. This increase is just not as large as
the increase realized when the ASTM E-119 fire is simulated.
The proposed approach was first used to predict the burnout load capacity of the 18 spanthickness combinations shown in Table 6.2 which correspond to the three design fires used in the
development of the approach. The results from this comparison are shown in Fig. 6.10 with
conservative and un-conservative predictions appropriately indicated. A total of 54 simulations
and corresponding predictions are shown in Fig. 6.10.

Of those 54 simulations, an un-

conservative prediction of load capacity of the floor system is returned only once by the
proposed method. This un-conservative prediction corresponds to the 100 mm slab spanning
12.2 m and exposed to the extreme fire condition. Because this configuration is outside the
practical range, the un-conservative prediction is not believed to indicate a fundamental failure of
the developed method. Based on the data set shown in Fig. 6.10 (that which was use in the
development of the equation) the proposed approach accurately predicts the load capacity of the
floor system 98% of the time.
From Fig. 6.10 it can also be seen that the proposed design equation is quite conservative when
2

SAFIR predicts a load capacity greater than 15 kN/m . This does result in some economic
advantage being lost due to the conservative nature of the proposed approach. Considering

215

however the use of reduced loads in fire as per ASCE (2005), and the lack of any other safety

2
Failure load from Eq. 6.14 (kN/m )

factor in the proposed approach, this level of conservatism is not believed to be excessive.
30
25

Un-conservative

20

Conservative

15
10
5
0
0

5

10

15

20

25

30

2
Failure load from SAFIR (kN/m )

Fig. 6.10: Comparison of failure load of slab as predicted by SAFIR and the proposed equation
(6.14)
While the proposed approach predicts the burnout load capacity for the data set used to develop
the approach very accurately (<2% un-conservative predictions), it is necessary to consider an
independent data set to fully check the validity of the approach. To that end, two additional fires
were simulated and the burnout load capacities determined. The two additional fires correspond
to the “mild” and “check” fire shown in Fig. 6.8. A comparison of the burnout load capacity
predictions from SAFIR and those from the proposed design methodology are presented in Fig.
6.11 below. Again in Fig. 6.11, a line indicating safety of the proposed approach is included
with the conservative and un-conservative regions indicated.

216

2
Method Predictions (KN/m )

25
20

Un-conservative
15

Conservative

10
5
0
0

5

10

15

20

25

2
SAFIR Predictions (KN/m )

Fig. 6.11: SAFIR and equation predictions for additional data set
The same trend is observed in Fig. 6.11, as was noticed in Fig. 6.10, in that the proposed method
is conservative in the vast majority of cases. Of the 36 simulations represented in Fig. 6.11, the
proposed method predicts the burnout load capacity of the floor system un-conservatively once,
and conservatively 35 times. The un-conservative data point corresponds to the 100 mm thick
slab spanning 10.67 m and exposed to the “check” fire exposure. As was the case with the
previous data set, the parameters are outside the practical range, and as such, are not believed to
indicate a fundamental weakness in the proposed design methodology. Considering only the data
used for validation, and excluding that in Fig. 6.10 (which was used in the development of the
proposed approach), the proposed approach predicts the burnout load capacity of the floor
conservatively 97% of the time. Considering the entire data set, (represented in Figs. 6.10 and
6.11) the proposed approach predicts the burnout load capacity conservatively 97.8% of the time.
Based on the comparisons of SAFIR predictions and those from the proposed approach, it is
reasonable to conclude that the proposed approach can accurately predict the burnout load

217

capacity of a floor exposed to design fires base on the two hour ASTM E-119 load capacity. To
illustrate the applicability of the proposed approach in design situations, an example is presented
below followed by the limitations to the proposed approach.
6.3.5

Illustration of the Proposed Approach

Applicability of the proposed approach for fire resistance design of a SFRC floor system is
illustrated through a numerical example. Detailed calculations for this problem are presented in
Appendix F.
A room 3 m high with a 6 m by 4 m floor (with secondary beams spanning in the 6 m direction)
2

and a fire load of 5.25 kN/m is to be designed. The room has one window opening 3 m wide by
2 m high. The architect has indicated that the room below the considered compartment has the
2

same dimensions and will have a fuel load of 550 MJ/m (of floor area). Now, it is desired to
know what thickness the floor needs to be to satisfy the code requirements by withstanding
complete burnout of the probabilistic fire that would occur within the compartment.
The first step is to determine the design fire that is most likely to occur within the compartment.
The fire scenario can be determined using the Eurocode (2005a) method.

The detailed

calculations associated with this example are presented in Appendix F, along with further details
on the compartment characteristics. The ventilation factor for this example is 0.079 m

1/2

and the

burning duration is 0.79 hours. The time temperature curve of the possible fire determined using
this method, and the standard (ASTM E-119) time temperature curve are shown in Fig. 6.12.
The second step is to assume a floor thickness and check that thickness using Fig. 6.9 and Eq.
6.14 to determine if the floor will meet the specified fire resistance requirements and support the
applied load until compartment burnout. For this example, the assumed floor slab thickness will

218

be 100 mm, with this information Fig. 6.9 is referenced as done in Appendix F, and the limit load
2

capacity of the floor at 2-hours of standard fire exposure is found to be 5.5 kN/m . The second
step it to determine the maximum design fire temperature which is 1089 °C for the example
given (see Appendix F). Having this information, Eq. 6.14 is applied and the burnout load
capacity of the floor is found to be 5.08 kN/m

2

The burnout load capacity of the floor is found to be less than the applied load on the slab during
a fire event, as such, it is necessary to enhance the fire resistance of the floor slab. The most
practical way to accomplish this is to increase the thickness of the floor system. A second
thickness of 112.5 mm is selected and the process repeated as detailed in Appendix F. The result
2

of the thicker floor slab is a burnout capacity of 6.98 kN/m which is sufficient to withstand the
2

applied load of 5.25 kN/m , thus, the SFRC floor is capable of sustaining burnout conditions,
and there is no need for applied fire protection on the secondary beams.
1200

Temperature (°C)

1000
800
600
Design Fire
AST M E-119

400
200
0
0

30

60

90

120

150

Time (min)

Fig. 6.12: Comparison of standard and design fire exposure
219

180

6.3.6

Application and Limitations

The proposed method offers a practical approach for evaluating the fire resistance of floor
systems exposed to design (real) fires. However, the applicability of this method is limited to the
range of parameters that were considered in the numerical study which formed the basis for
development of the approach. The explicit limitations for the proposed methods are as follows:


This method is applicable for standard fire exposure up to two hours, and design fires that
have a similar temperature rise in the first 20 minutes as ASTM E119 followed by a
cooling phase.



The approach is only applicable for slabs ranging from 100 to 150 mm thick, and
spanning between 4.57 and 12.2 m in the short direction.



Slabs must be supported on the edge by protected beams that provide vertical, horizontal,
and rotational support to the slab during the entirety of the fire exposure.



Slabs must be supported by unprotected secondary beams, the presence of protection on
the secondary beams will significantly alter the load capacities determined in the above
simulations, and hence, Eq. 6.14 may not be valid.



The approach is valid only for SFRC made with carbonate or siliceous aggregate, and
having a specified compressive strength of between 25 and 30 MPa and a steel fiber
content between 1.75 and 2.25% by mass.



One and two-way slabs can be designed using the proposed approach since the
development was conservatively done considering only one-way slabs.

It should be noted that the above limitations are specified due to a lack of validation for these
conditions. Through further validation, it should be possible to extend this method to overcome
some, if not all, of these limitations.

220

6.4

Methodology for System Level Evaluation of Fire Resistance

The contribution of composite construction and tensile membrane action to fire resistance is best
considered at the system level. In order however to account for all relevant design variables, the
complexity associated with analysis is compounded as compared to element or assembly level
analysis and the models are excessively large. It is therefore not practical or feasible to develop
simplified design methodologies that can include all relevant factors as for system level analysis.
Any such approach would have to account for a significant number of variables, and as such,
would cease to be either simplified or rational.
System level fire resistance evaluation is far better suited for specific applications, and to
investigate the effect of specific parameters on fire resistance. The system level simulations
conducted for this research, as presented in Chapter 5, served to identify the factors affecting fire
resistance at the system level. In addition to the factors that influence fire resistance at the
element and assembly level, composite action, the development of tensile membrane action, and
member interactions enhance fire resistance at the system level. These factors enhance fire
resistance by providing alternate load paths to transfer loads from fire weakened members to
other cooler parts of the structure.
Thus far in this research, numerical models have been employed to identify factors that influence
fire resistance, and for the development of rational design methodologies. Due however to the
complexities involved in evaluating system level fire resistance, system level models will
henceforth be utilized to study the applicability of the design methodologies developed for
enhancing fire resistance through composite construction.

In all simulations conducted at the

system level, the factors affecting the fire resistance at the system level, namely, composite
construction, development of tensile membrane action, fire exposure, member interactions, and

221

failure criterion, are taken into account. The detailed procedure for assessing fire resistance at
the system level is outlined in Chapter 7, and as such will not be presented here.
6.5

Summary

Rational design methodologies for the fire resistant design of CFHSS columns and composite
steel beam-SFRC slab assemblies are presented in this chapter. In the development of these
methodologies, the beneficial effects arising from composite construction, realistic fire scenarios,
loading, and restraint conditions are taken into consideration. Through extensive validation,
these design methodologies are deemed conservative for use in practical applications.
For CFHSS columns, the developed methodology allows the survivability of a CFHSS column
under design fire exposure to be determined. The methodology capitalizes on the previous
research on CFHSS column to establish the fire resistance of a column under standard fire
exposure. This fire resistance time evaluated under standard fire exposure is then used with an
equivalent area approach to determine with a high degree of accuracy if the column will fail
under the specified fire exposure, or survive compartment burnout.
Similar to the case of CFHSS columns, based on an equivalent fire severity approach, a
correlation between structural performance under standard fire and design fire exposure is
presented. The design methodology allows the limit load capacity under which an SFRC floor
system can survive complete compartment burnout to be determined based on the load capacity
under standard fire exposure. In this approach, the developed figure is referenced for a specific
slab thickness and span to determine the two hour load capacity of the floor system under
standard fire exposure. The proposed correlation methodology is then applied to the two hour
load capacity of the system, and the load limit for the slab to survive complete burnout of the
specified design fire exposure is obtained.

222

CHAPTER 7
7
7.1

IMPLEMENTATION OF DESIGN METHODOLOGIES
General

Concrete is utilized in almost all steel framed buildings due to the advantages composite
construction offers over other types of construction. For fire resistance evaluation however, the
beneficial effects of composite construction are not taken into consideration. For evaluating fire
resistance, current provisions in codes and standards apply a critical temperature criterion in steel
members to define failure. Thus, the contribution of concrete in enhancing the fire resistance is
steel framed structures is not taken into consideration. This prescriptive approach continues to
be used due to the lack of design methodologies for evaluating fire resistance based on all
significant factors including composite construction.
To overcome these drawbacks, this chapter presents guidance on the two possibilities for
utilizing composite construction to enhance fire resistance, the first is a detailed finite element
analysis procedure, while the second utilizes the design methodologies developed in Chapter 6.
Following the discussion on performance-based design, a case study is presented to illustrate the
implementation of the design methodologies for evaluating the fire resistance of steel frames
incorporating composite construction.
7.2

Performance-Based Fire Resistance Design

In recent years, performance-based approach to fire safety design is becoming popular since
cost-effective and rational fire safety solutions that can be developed using such an approach
(Kodur, 1999). One of the key aspects in any performance-based fire safety design is the fire
resistance design of structural members. Currently, to evaluate the fire resistance of structural

223

members, numerical models that can simulate the response of the member under realistic fire,
loading, and restraint scenarios must be used. The main steps needed to undertake performancebased design of structural members at the present are:
1. Developing proper design (realistic) fire scenarios
2. Developing realistic design parameters such as loading, restraint, and other structural
parameters
3. Carrying out detailed thermal and structural analysis by subjecting the structural member to
specified fire conditions; and
4. Developing relevant practical solutions to achieve the required fire resistance.
Each of these steps will be elaborated upon in the following sections, following this discussion, a
simplified approach utilizing the design methodologies of this research will be presented.
7.2.1

Development of Fire Scenario

When evaluating fire resistance in a performance-based environment, it is paramount that
realistic (design) fires be used. Real fires generally have a cooling phase after the initial growth
and combustion phase. This cooling phase limits the temperature rise in structural members, and
is followed by a reduction in temperatures that allow the members to regain strength and
stiffness. As the materials regain strength and stiffness, they contribute to the load bearing
capacity of the system and serve to enhance the fire resistance of the entire structure. In
addition, the use of design fires permits the beneficial effects of fire suppression systems to be
accounted for in the modelled fire exposure.
The design fire scenarios for any given situation should be established either through the use of
parametric fires (time-temperature curves) specified in Eurocode (2005a) or through design
tables (Magnusson and Thelandersson 1970). These methods take into consideration critical

224

factors influencing fire resistance by accounting for compartment size, ventilation characteristics
(compartment openings), room use (fuel load), and the decay phase is based on the duration of
combustion prior to cooling. An example is provided in Section 6.2.4 in which the Eurocode
procedure is utilized to developed a design fire for a specific compartment, as such, it will not be
reiterated here.
7.2.2

Development of Design Parameters and Loading

For evaluating fire realistic fire resistance, it is necessary to account for the actual conditions the
structural system would experience under fire conditions. These factors include composite
construction, restraint levels (boundary conditions), and load levels. Composite construction and
restraint levels are implicitly taken into consideration when the numerical model is established;
load level on the other hand needs to be explicitly taken into consideration. As discussed in
Chapter 2, during fire exposure, structural members are assumed to experience reduced loading
due to the low probability of a fire event. The reduced load levels to be considered in the
analysis can be evaluated by using the provisions presented in ASCE or Eurocode namely 1.2DL
+ 0.5LL (ASCE 2005) or 1.2DL + 0.4LL (Eurocode 2002) should be used.
7.2.3

Conducting Thermal and Structural Analysis

Once the fire scenarios and structural parameters are established, fire resistance analysis can be
carried out using computer programs that are capable of conducting the thermal and structural
analysis. Computational programs such as SAFIR, ABAQUS, and ANSYS can be used to
undertake fire resistance analysis.

Once the computational program is selected, a detailed

discretized model is to be constructed that takes into consideration the high temperature material
properties of the constituent materials. Given however the large scale of these models, it is
necessary to consider a wide range of practical fire exposures as the entire structure is not
225

necessarily exposed to fire at the same time. This last factor of fire size results in there being
hundreds if not thousands of simulations that need to be conducted. It is critical that in all of
these simulations the effect of composite action, fire scenarios, load levels, restrain, high
temperature properties of constituent materials, and realistic failure limit states.
7.2.4

Development of Practical Alternatives

Results generated by the fire resistance analysis can be utilized to develop alternate strategies for
achieving the required fire resistance levels. This can be accomplished by altering design
parameters such as the thickness of a floor system, the concrete type used in the floor system, or
the type of columns utilized.

The method adopted to achieve the practical alternatives is

dependent on the weak link in the structure as identified by the numerical simulations. This
iterative process should be repeated and additional factors changed until the desired fire
resistance level is achieved. When developing the practical alternatives, the fire resistance
benefits must be considered in light of economics and sound engineering principles. In this
chapter, a case study is presented which illustrates the development and implementation of
practical alternatives for achieving fire resistance through composite construction. Specific
methods implemented in this chapter include optimizing the concrete type utilized in CFHSS
columns, and optimizing the type of concrete used in composite floor systems.
7.2.5

Use of Performance-Based Design Methodology

The process outlined for detailed fire resistance analysis requires significant time, effort,
advanced skills and expensive computational software. As an alternative, simplified design
methodologies can be applied for evaluating fire resistance of CFHSS columns or composite
floor assemblies.

226

For fire resistance analysis utilizing simplified design methodologies, the first two steps in
section 7.2 remain the same, the design time-temperature curve and loading on the respective
member/system must be determined. The design methodologies can then be applied to assess the
fire resistance of the structural member and to develop practical alternatives. For enhancing fire
resistance, practical alternative can include increasing the thickness of floor system, altering the
concrete type, developing alternate design fire exposure, changing the filling in CFHSS columns,
or reducing load levels on the assembly. After implementation of a practical alternative, the
developed methodologies are reapplied to assess the fire resistance. This iterative procedure is
repeated until the desired level of fire resistance is achieved in the structure.
The case study presented in this chapter illustrates use of the simplified design methodologies
developed in this research. To carry out this example, a typical steel framed building is modeled
in SAFIR, and a series of simulations undertaken to illustrate the effectiveness of both the
proposed structural components (CFHSS columns and composite floor slabs made with SFRC)
to achieve fire resistance, and to illustrate the use of the respective design methodologies. In
each of the cases, the structural geometry or the fire exposure is altered to illustrate the effect that
each change has on fire resistance of the structure.
7.3

System Level Fire Resistance Evaluation

To illustrate the effectiveness of the simplified methodologies developed as part of this thesis, it
is necessary to compare fire resistance evaluated through the simplified approach with that
obtained from detailed analysis utilizing finite clement models of a building constructed
according to recent (AISC 2005) U.S. design standards exposed to fire. To that end, a numerical
model of a typical eight story steel framed building is constructed in SAFIR, and the proposed
design methodologies applied in evaluating fire resistance. Utilizing results from the numerical

227

simulations and proposed design methodologies, the feasibility of achieving the required levels
of fire resistance in steel framed structures utilizing composite construction is explored under
different fire scenarios.
7.3.1

Building Description

The building selected for the fire resistance evaluation is the William Beaumont West Bed
Tower in Troy, Michigan. This is an eight story steel framed building constructed in 2008, and
represents typical office and heath care facilities built according to current construction practices
in the United States. Though the building represents typical construction for hospital and office
buildings, the methods developed in this research are only sufficient to satisfy fire resistance
requirements as they pertain to office buildings. This is because typical sprinklered office
buildings generally require less fire resistance (1-2 hours) that health care facilities (3-4 hours),
henceforth, for this reason, the building will be referred to as an office building.
The structural framing details of this building were acquired from Douglas Steel, the design firm
responsible for the design and construction of the structure. A partial structural framing plan for
th

the 5

story is shown as Fig. 7.1. The secondary beams used are W16x26 and the primary

beams spanning on line C and D in the middle of the structure are W21x57 sections, the edge
beams are W30X124. In plan, the building is 56.7 m by 29.3 m, each of the bays is 10 m by 10
m. Emergency evacuation stairs are located in two of the corners with a third set of stairs located
in the center of the building as seen in Fig. 7.1.
Connections used in the structural frame consist of both shear and moment connections.
Moment connections are provided in the exterior frames to provide resistance to lateral (wind)
force. All connections on the interior of the structure, including those on the ends of secondary
beams, are shear connections.
228

The floor slab in the buildings comprised of a composite deck, shear studs, and shrinkage
reinforcement. The deck in each story of the structure was poured in one continuous pour
without shoring to the floor beams.

10 m

10 m

10 m

Modeled
Portion

4m

10 m

10 m

Fig. 7.1: Framing plan for the steel framed building used to illustrate application of the
developed methodologies
The first four stories of the structure are larger in plan to accommodate other service
functionalities. As such, the fifth floor was selected for fire resistance analysis to eliminate the
interaction of multiple functions on the same floor, and to reduce the size of the structure being
modeled.

229

7.3.2

Numerical Model

Having selected a typical building to be used in the fire resistance analysis, it was necessary to
construct a numerical model of the building. While a model of the entire building would be most
desirable in terms of simulation results, this is impractical due to the many simulations (case
scenarios) desired. It was therefore decided that two levels of analysis would be conducted. As
such, a one story model was created to assess the practicality in application of the proposed
design methods, and a three story model was constructed to assess the ability of the proposed
methods to create a design capable of withstanding a multi-story fully developed fire including a
cooling phase. As described in the following section, great care was taken in constructing the
model to accurately reflect the system level behavior of the structure, and to capture the
contribution of composite construction and tensile membrane action to the fire resistance of the
steel framed structure.
7.3.3

Discretization

Due to the complexities that are associated with modeling a ribbed composite floor slab, it was
decided to use a slab represented by a shell element of uniform thickness as has been done in
previous studies (Zhang et al. 2008, Cashell et al. 2008). The thickness chosen for the slab was
that of the thickest part of the ribbed flooring system, 130 mm. This slab was modeled using
four nodded shell elements with six degrees of freedom at each of the nodes. The beams
supporting the slab and the columns were modeled using three nodded beam elements with seven
degrees of freedom at the end nodes, and one degree of freedom at the center node. To simulate
the composite action between the steel beam and the floor slab, the “SAMEALL” command was
used for the nodes where the beam and shell elements coincide.

230

This caused all of the

translations and rotations at these points to be the same for the beam and slab, thus simulating the
fully composite condition.
Due to the large floor plan for the entire structure, and the computational time associated with
such a large model, only the portion of the building indicated in Fig. 7.1 was modeled. This
section was modeled as a single story (5
th

th

th

story) as shown in Fig. 7.2 and a three story model

th

(5 , 6 , 7 stories) as shown in Fig. 7.3. Modeling only the portion of the structure indicated in
Fig. 7.1 requires that particular attention be given to the boundary conditions used in the
simulation. It was assumed that the column ends where they pass though the adjacent floors
acted as fixed connections with all degrees of freedom being fully restrained. It was also
assumed that the portion of the structure that was not modeled, being significantly larger than the
modeled potion, was essentially rigid compared to the modeled portion. As such, the horizontal
translation on the continuous edges was fully restrained perpendicular to the modeled edge. Due
to the continuity of the slab over these points, the rotation about the length of the edge was
assumed to be restrained, thus simulating the realistic support offered by the portion of the
structure which was not modeled.

Fig. 7.2: One story numerical model of selected building

231

Fig. 7.3: Three story numerical model of selected building
It was assumed in the models that the full floor area with the exception of the stair area was
exposed to fire. The stair area was designated in the plans as a fire escape rout, thus, the walls
separating the stairs from the rest of the structure provided a 3-hour fire resistance rating.
2

Loading on the structure was taken to be 4.5 kN/m based on the reduced loads present during
fire exposure, and the loads used in the Cardington test. This is a typical load for office
buildings and is based on 1.2DL + 0.5LL. It was assumed that the fire exposure was the same to
all parts of the fire exposed member. That is to say that the ends of beam that would be
protected from direct fire exposure in a real structure, were modeled as being fully exposed to
the same severity of fire as experienced by the center of the beam span. Beams and columns on
the perimeter of the structure were assumed to be supplied with fire protection. It was assumed
that secondary beams which attach to protected structural members were also supplied with fire
protection for 150 mm past the connection, thus allowing the connection to remain cool enough
that its structural integrity was not compromised. This assumption was invoked to eliminate the
need to consider the complex behavior of the connection at elevated temperatures. Due to the

232

continuity in the concrete slab and the relatively high tensile strength of SFRC, it was assumed
that all of the connections acted as moment connections. This assumption is predicated on the
assumption that the concrete slab will not fracture over the supporting beams, and as such, will
maintain moment restraint throughout the course of fire exposure.
Four design fire scenarios and ASTM E-119 fire exposure were considered in the analyses, these
fires were developed to represent firs that could occur in a typical steel framed office building.
In the development of these fires, structural geometry and typical fuel loads are taken into
consideration. The developed fire exposures are shown in Fig. 7.4. All one story simulations
were run for 3 hours, or until the structure became unstable and the simulation indicated failure
of the structure. For the three story models, it was assumed that it took one hour from ignition of
the first floor until the second floor was exposed to fire, and subsequently it took another hour
for the third floor to be exposed to fire. As such, in all three story cases, the first floor was
experiencing a fully developed fire when the second floor was ignited, when the third floor
ignited, the second floor was fully developed and the first floor was in the cooling phase. The
simulations were continued until the third floor had been exposed to three hours of fire exposure
(for total fire duration of 5 hours) or until SAFIR indicated that the structure was unstable and
failure of the simulation occurred.
The fire resistance analysis was carried out for a total of 11 cases which correspond to different
fire scenarios, column configurations, and floor slab types. The analysis matrix corresponding to
these cases is presented in Table 7.1. The analysis with Case 1 was conducted to assess the
performance of the structural frame without any fire protection on the columns or secondary
beams to determine the “weak link” in the structural system under fire conditions. Case 2
analysis was conducted to assess the beneficial effects of composite construction on the fire

233

performance of the structure if the wide flange columns in Case 1 were replaced with equivalent
CFHSS sections designed as per AISC provisions (AISC 2005). For the remaining cases (Case 9
through Case 11), the columns and floor system were replaced with CFHSS columns and SFRC
floor systems (respectively) designed according AISC provisions. One and three story models of
this modified structural system were exposed to all of the design fires shown in Fig. 7.4 to assess
the applicability of the developed design equations. For each of these cases, fire resistance is
evaluated using the developed finite element analysis and also by applying the simplified
approach proposed in chapter 6. Failure times and location of failure for each case are presented
in Table 7.1, and a more detailed discussion for each case is presented in the following sections.
In each of the simulations, the constitutive models from Eurocode are utilized and the parameters
shown in Table 5.3 were input into SAFIR.
1400

Temperature (°C)

1200
1000
800
600
Extreme
Severe
Medium
Mild
ASTM E-119

400
200
0
0

1

2

3

Time (Hour)

Fig. 7.4: Possible fire scenarios used in the fire resistance analysis

234

4

Table 7.1: Various structural configurations and fire scenarios simulated in the building
Fire exposure
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Case 8
Case 9
Case 10
Case 11

7.3.4

ASTM E-119
ASTM E-119
ASTM E-119
Extreme
Extreme
Severe
Severe
Medium
Mild
Medium
Mild

# of stories
under fire
1
1
1
1
3
1
3
1
1
3
3

Column
configuration
W
CFHSS
CFHSS
CFHSS
CFHSS
CFHSS
CFHSS
CFHSS
CFHSS
CFHSS
CFHSS

Floor slab
configuration
Plain
Plain
SFRC
SFRC
SFRC
SFRC
SFRC
SFRC
SFRC
SFRC
SFRC

Fire resistance
(min)
16.5
58
118
12.5
13
37
39
No failure
No failure
No failure
No failure

Failure
zone/member
W-column
Floor slab
Floor slab
Floor slab
Floor slab
Floor slab
Floor slab
None
None
None
None

Model Validation

For validation of the numerical model, due to the lack of information on the response of the
considered structure to fire exposure, it is necessary to consider the structural response of the
building at ambient temperatures. To accomplish this, structural analysis on the 8-story building
2

under ambient temperature was conducted utilizing SAFIR with a design load of 9.8 kN/m to
represent a typical ambient temperature design load on the structure. Deflection predictions from
SAFIR were then compared with deflection limits specified in codes and standards. A maximum
deflection of 19.9 mm was observed in the center of the secondary W16x26 beams.

By

considering the deflection limit to be L/480 for a structural element supporting a structural
element that could be damage by deflections, the allowable deflection of the beam is 20.8 mm,
thus, the deflection limit is satisfied. Additionally, the deflected shape of the structure returned
from the simulation as shown in Fig. 7.5 is intuitively correct based on elementary structural
principals.
Given that the deflection limit is satisfied by predictions from the numerical model, and that the
deflected shape of the structure is intuitively correct, it is concluded that the structural model of
the eight story steel framed building is realistically constructed in SAFIR. While full validation
235

cannot be completed for the structure due to a lack of fire response data, it should be noted that
the same model will be used in all of the simulations. As such, any error in model construction
would be applied to all of the models. Thus, any error resulting from the numerical idealization
of the structure will exist in all cases, and thus be self-canceling.

A
B

Fig. 7.5: Deflected shape under service loads and ambient temperature (125x)
7.3.5

ParametricSstudy

Using the models described and validated above, the simulations corresponding to the 11 cases
shown in Table 7.1 were conducted. Each of these simulations is addressed separately in the
following sections.
Case 1
To form a baseline for the study, the structural frame was simulated under ASTM E-119 fire
exposure assuming that the primary and exterior beams, and the exterior columns had 2-hour fire
protection, while the interior columns and secondary beams had no protection. Failure occurred
in this simulation at 16.5 minutes due to failure of the central unprotected W14x61 column,

236

which is marked with an “A” in Fig. 7.5. Failure is achieved early in the fire exposure due to the
elevated temperature rapidly achieved in the unprotected steel section. Axial deflection at the
top of the column is plotted as a function of fire exposure time in Fig. 7.6. From Fig. 7.6, it can
be seen that the column failed suddenly at 16.5 minutes. Results from this simulation indicate
that failure of the column which was loaded to approximately 40% of its design strength
occurred at an average section temperature of 625 °C due to global buckling of the section.
0

Deflection (mm)

-10
-20
-30
-40
-50
-60
-70
-80
0

5

10

15

20

Time (min)

Fig. 7.6: Variation of central column axial deflection with time corresponding to for Case 1
analysis
Case 2
Results from Case 1 indicate that the weak link in the simulated building was the W-shape
column. To explore the possibility of improving fire resistance through the use of composite
construction, an equivalent CFHSS column was selected to replace the W14x61 section used in
Case 1.

Design of the column was conducted according to AISC (AISC 2005) ambient

temperature trength design, and the fire resistance of the column checked via the design

237

methodology proposed in this research. It was found that a 254 mm square HSS column with
12.5 mm thick walls and filled with carbonate aggregate concrete with a compressive strength of
35 MPa will provide equivalent load capacity at ambient temperatures, and a two hour fire
resistance rating.
The structure, with CFHSS columns was analyzed using SAFIR, results from the simulation
indicate that the structure fails at approximately 58 minutes due to instability in the plain
concrete floor system. Failure of the system initiated at point B indicated in Fig. 7.5. Mid-span
deflection in the slab at this location is plotted as a function of fire exposure time in Fig. 7.7.
From Fig. 7.7, and it can be seen that the floor system undergoes a sudden increase in the
defection rate at 58 minutes. Also of note from Fig. 7.7, is the observation that the deflection in
the center of the composite beam utilizing plain concrete reached a maximum of 650 mm before
failure of the floor system. This large deflection can be attributed to the composite action that
develops between the concrete slab and the beams. The composite action from the floor slab was
however insufficient to achieve the two hour fire resistance rating required for this building.
0

Deflection (mm)

-100
-200
-300
-400
-500
-600
-700
0

10

20

30

40

50

60

Time (min)

Fig. 7.7: Secondary beam mid-span deflection with time corresponding to Case 2 analysis

238

Case 3
In order to enhance the fire resistance of the floor system analyzed in Case 2, the floor system
was redesigned with SFRC in place of plain concrete. Fire resistant design of the SFRC floor
system was carried out according to the developed methodology, and the fire resistance analysis
carried out on the reconfigured structural system using SAFIR. Results from the SAFIR analysis
show that the use of SFRC in the floor system in place of plain concrete increased the fire
resistance to 118 minutes under ASTM E-119 fire exposure. The maximum deflection of the
SFRC slab prior to failure was 688 mm as observed in Fig. 7.8 (which plots floor deflections for
point B in Fig. 7.5).
0

Deflection (mm)

-100
-200
-300
-400
-500
-600
-700
0

30

60

90

120

Time (min)

Fig. 7.8: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 3 analysis
While this deflection is not significantly more than the deflection reached with plain concrete, it
should be noted that the failure (fire resistance) time is more than doubled through the use of
SFRC. This can be attributed to tensile membrane action in the floor slab that is facilitated by
the increased tensile strength of SFRC. Despite the significant increase in fire resistance, this is
239

still insufficient to provide the two hour fire resistance rating required for this type of building.
As such, consideration needs to be given to design fires to achieve fire resistance in a
performance-based environment
Cases 4 and 5
In order to assess the response of the structure under design fire exposure, alternate fire
exposures were developed and the fire resistance analysis carried out on the reconfigured
structural system. To that end, the model used in Case 3 was analyzed under the extreme design
fire shown in Fig. 7.4. Prior to conducting this analysis, the design methodologies developed
above were applied to the column and the SFRC floor system, and it was predicted that the floor
system would fail in the analysis. Results from the SAFIR analysis confirm this postulate, fire
resistance under the extreme fire exposure was observed to be 12.5 minutes. The maximum
deflection observed in the slab prior to failure was 450 mm as shown in Fig. 7.9. The early
failure in the floor system can be attributed to the local minimum in floor load capacity as shown
in Fig. 6.6. This local minimum is sufficiently below the applied load on the floor, that the
simulation returns failure very early in the fire exposure, never allowing the fire to reach the
decay phase, thus no advantage of modeling a design fire is realized.
Following completion of this analysis, a three story model of the structure was exposed to the
extreme fire scenario. Results of the one story model were confirmed in that the three story
model failed at 13 minutes due to a floor failure. The low failure time for the three story model is
attributed to the same factors indicated for the one story model.

240

0
-50
Deflection (mm)

-100
-150
-200
-250
-300
-350
-400
-450
-500
0

2

4

6

8

10

12

14

Time (min)

Fig. 7.9: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 4 analysis
Cases 6 and 7
The analysis corresponding to the structural configuration of Case 4 was repeated under the
severe fire exposure shown in Fig. 7.4. As in Case 4, the developed design methodologies
indicate that failure will occur in the SFRC floor system, results from the SAFIR analysis
confirm this postulate. Under severe fire exposure, the structure was able to withstand the severe
fire exposure for 37 minutes, reaching a maximum deflection of 510 mm prior to failure as
shown in Fig. 7.10. While failure of the floor system still occurs in a relatively short period of
time, fire resistance is enhanced appreciably as compared to Case 4.

This enhanced fire

resistance is attributed to the development of tensile membrane action in the SFRC slab. Due
however to the extreme temperatures reached early in the fire exposure, the extent of tensile
membrane action is insufficient for the structure to reach the decay phase of the fire exposure,
thus the structure fails in the simulation.

241

As was the case under the extreme fire exposure, a three story model of the structure was
simulated under the severe fire exposure. This simulation failed at 39 minutes due to failure of
the floor system as compared to the 37 minutes in the one story model, thus confirming the
results from the one story case.
0

Deflection (mm)

-100
-200
-300
-400
-500
-600
0

10

20

30

40

Time (min)

Fig. 7.10: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 6 analysis
Case 8
To further enhance the fire resistance of the assembly beyond that observed in Case 6, a medium
design fire was developed and the fire resistance analysis carried out. As was done in previous
cases, prior to conducting the analysis, the developed methodologies were applied to the
structure, and in this case, the prediction was made that both the CFHSS columns and the SFRC
floor slab would be able to survive the entirety of the design fire exposure, results from the
SAFIR analysis confirm this postulate. A maximum deflection of 566 mm was reached in the
floor slab at 160 minutes, approximately 40 minutes after the peak fire temperatures as seen in

242

Fig. 7.11. The ability of the floor system to survive the medium fire exposure is attributed to the
development of tensile membrane forces and composite action between the SFRC slab and the
steel beam facilitated by the development of large displacements. From this case, it can be seen
that composite construction can provide sufficient fire resistance for a structure to reach
compartment burnout in a performance-based environment.

Additionally, the design

methodologies here developed are shown to accurately predict the survival of a structure
utilizing composite construction under the medium design fire exposure.

0

Deflection (mm)

-100
-200
-300
-400
-500
-600
0

60

120

180

Time (min)

Fig. 7.11: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 8 analysis
Case 9
To illustrate the ability of composite construction to enhance fire resistance through the
development of composite and tensile membrane action, an additional case was analyzed using
SAFIR under the mild fire exposure shown in Fig. 7.4. Results from the SAFIR analysis confirm
the predictions of the developed methodologies as the structure is able to survive complete

243

compartment burnout under the mild design fire exposure. A maximum deflection of 390 mm
was observed in the floor system as seen in Fig. 7.12. While survival of the structure is
attributed to the development of composite and tensile membrane action, the lesser deflections
under the mild fire exposure as compared to the medium fire are attributed to the lower fire
temperatures. The lower fire temperatures result in lower steel and concrete temperatures as well
as lower thermal gradients in the materials, as such, thermal and mechanical deflections are
reduced. The end result is overall lower deflections under the mild fire case as compared to the
medium fire case.
0

Deflection (mm)

-50
-100
-150
-200
-250
-300
-350
-400
0

60

120

180

Time (min)

Fig. 7.12: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 9 analysis
Cases 10 and 11
To illustrate the full capability of composite construction to enhance structural fire resistance
without the need for applied fire protection on columns of secondary beams, the three-story case
with CFHSS columns and SFRC floor systems was simulated under the medium and mild fire

244

exposures of Fig. 7.4. In both cases, a one hour delay in ignition for one story to the next was
assumed. The result is a 5 hour fire exposure time in place of the 3 hour fire exposures
considered in the one story models. Due to similarities between results from both the medium
and mild fire simulations, only the mild fire will be used to illustrate the behavior of the
structure, though the discussion applies to both fire exposures.
Results from the SAFIR simulations indicate that the structure was able to survive burnout of
three consecutive stories under both of the design fire exposures. Maximum deflections ranging
from 375 to 425 mm were observed in the floor system as shown in Fig. 7.13. Overall survival
of the structure is attributed to the development of composite and tensile membrane action, both
in the CFHSS columns and the SFRC floor slab. There are however two key observations that
can be made from Fig. 7.13. The primary observation is that the first floor of the structure is
noted to deflect more (~40 mm) than the subsequent stories. This is attributed the difference in
the column end conditions of the three floors.

The bottom floor has assumed boundary

conditions on the bottom of the columns; the second floor has a simulated floor on both sides
while the third floor has assumed boundary conditions at the top of the columns. The second
observation from Fig. 7.13 is that the second and third stories in the simulation “rebound”
between 20 and 60 minutes. This is attributed to the slow thermal expansion of the supporting
columns below these stories. As these columns elongate, they lift the structure above them, thus
causing the “rebound” of these stories prior to their experiencing fire exposure.
From the different cases presented above, it can be seen that the development of composite and
tensile membrane action contributes to overall fire resistance. Additional consideration of design
fires further enhances fire resistance such that elimination of applied fire protection from
columns and secondary beams can be achieved.

245

Both of these factors are taken into

consideration in the developed design methodologies, and the methodologies have been shown to
accurately predict the fire resistance of composite construction under a wide range of
configurations and design fires.
50
0
Deflection (mm)

-50
-100

Story 1
Story 2

-150

Story 3

-200
-250
-300
-350
-400
-450
0

60

120

180

240

300

Time (min)

Fig. 7.13: Mid-span deflection in the secondary beam as a function of fire exposure time
corresponding to Case 10 analysis
7.4

Summary

The case study presented in this chapter illustrates the use of the proposed simplified approaches
for developing alternate fire resistance strategies for steel framed structures.

Through

consideration of composite construction in a performance-based design environment, it is
illustrated that the required levels of fire resistance can be achieved in steel framed structures
without the need for applied fire protection to columns or secondary beams through the use of
CFHSS columns and SFRC floor systems and the subsequent development of composite action.
In addition to providing a cost effective alternative to applied fire protection, the fire resistance

246

provided through composite construction is inherent to the structure, and not easily damaged,
thus increasing the reliability of structures under fire exposure.
Performance-based design of structural members for fire resistance facilitated by the fire
resistance evaluation methodologies developed above. These methodologies provide a means for
practitioners to rapidly and accurately assess the fire resistance of composite structures without
the need for costly computational or time resources, thus saving further resources in the design
process.

247

CHAPTER 8
8
8.1

CONCLUSIONS AND RECOMMENDATIONS
General

Steel framed structures often utilize composite construction due to several advantages composite
structural systems offer over other types of construction. The composite action that develops
between steel and concrete significantly enhances structural performance under ambient and fire
conditions. However, the beneficial effects of composite action are not taken into consideration
in evaluating fire response of structures due to a lack of understanding and design
methodologies. With the aim of developing this comprehensive understanding and rational
design methodologies, both experimental and numerical studies were carried out as part of this
research. The experimental studies consisted of analyzing concrete filled HSS columns, and
evaluating the response of a steel beam-steel fiber reinforced concrete slab assembly to fire
exposure. In the experimental study on beam-slab assemblies, special attention was given to
monitor the development of composite action and tensile membrane action under realistic
loading, fire, and restraint conditions.
Data from the fire resistance experiments were used to validate composite column, beam slab
assembly, and full-scale steel framed structural models created in SAFIR computer program.
These validated models were applied to study the influence that several factors have on the fire
response of composite structural systems at the element, assembly, and system levels. Factors
investigated include the effect of fire exposure, load level, concrete properties, failure limit
states, member interaction, and development of tensile membrane action. Results from these
parametric studies are utilized to quantify the influence of various factors and to develop rational
design methodologies. At the element level, a methodology for predicting the survivability of

248

CFHSS columns under design fire exposure was developed.

At the assembly level, a

methodology was developed that allows the maximum load a composite steel beam-SFRC slab
can carry while surviving design fire exposure to be determined. At the system level, the various
factors to be considered in undertaking detailed fire resistance analysis of composite structures
are laid out.
The methodologies developed above were incrementally applied to an 8-story office building,
and the fire resistance of the building was evaluated at each increment and under different fire
scenarios. When the as-constructed building was considered without external fire protection on
the columns and secondary beams, the columns failed in less than 20 minutes. When the
beneficial effects of composite construction, tensile membrane action, design fire exposure,
realistic load levels, and structural failure limit states were accounted for according to the above
developed methodologies, the fire resistance of the structure was significantly enhanced.
Further, when the inherent fire resistance derived through composite construction was accounted
for, the fire response of the structure was sufficient to eliminate external fire protection from
columns and secondary beams.
8.2

Key Findings

Based on the information presented in this study, the following key conclusions can be drawn:


There is very limited information on the response of composite floor assemblies under
realistic fire scenarios, loading, and restraint conditions.



The current fire resistance provisions in codes and standards are prescriptive in nature
and do not facilitate the use of rational methods that accurately account for the beneficial
effects of composite action in evaluating fire resistance.

249

The use of composite

construction enhances fire resistance through the development of composite action and
tensile membrane behavior.


The main factors that influence the fire resistance of concrete filled HSS columns are
concrete type, fire exposure, column size, load level, length (slenderness), and failure
limit states. CFHSS columns made with bar and steel fiber reinforced concrete have
significantly higher fire resistance than those made with plain concrete, mainly due to
higher load carrying capacity and higher confinement effect provided by the presence of
reinforcement in the concrete core. Through the use of bar or fiber reinforced concrete, it
is possible to achieve three hours of fire resistance.



The main factors that influence the fire response of composite floor assemblies are the
development of tensile membrane action, concrete type, fire exposure, slab geometry, and
failure limit states. The use of SFRC in floor slabs in place of plain concrete leads to the
development of significant tensile membrane forces and this in turn enhances the fire
resistance of the floor slab. Through the use of SFRC in slabs, it is possible to achieve
two hours of fire resistance without any applied fire protection to secondary beams under
ASTM E-119 fire exposure.



The use of plain concrete in composite beam slab assemblies enhances fire resistance
above that of unprotected steel beams tested individually. The enhanced fire resistance
however does not meet the required levels, and alternate approaches for enhancing fire
resistance (SFRC) must be utilized.



The fire resistance of steel framed structures is further enhanced if a system level
approach is applied for evaluating fire resistance.

250

The main factors that are to be

considered in evaluating system level fire response are member interactions, composite
and tensile action, and type of fire exposure.


A simplified approach based on equivalent fire severity principals has been proposed for
evaluating fire resistance of CFHSS columns under design fire exposure.



A simplified approach based on equivalent fire severity principals has been developed for
evaluating the load carrying capacity of a composite SFRC slab under design fire
exposure has been proposed.



The methodologies developed to evaluate the fire resistance of CFHSS columns and steel
beam-SFRC slab assemblies are capable of predicting their survivability under design fire
exposures. For the data pools used in this research, the developed methodologies predict
an un-conservative response less than three percent of the time.



In steel framed office buildings, it is possible to eliminate external fire protection to
columns and secondary beams (and possibly primary beams under low level fires) by
taking into consideration the beneficial effects of composite construction and through the
application of a performance-based fire design.

8.3

Recommendations for Future Research

While this research has served to advance the state-of-the-art with respect to the response of
composite construction to fire exposure, there is still a considerable need for further research to
extend the concepts to other situations encountered in typical steel framed buildings. The
following are some of the key requirements for further research in this area:


The current models for design fire scenarios are based on limited experimental results,
thus, the applicability of these fire scenarios for a wider range of compartments needs to
be further validated. Computational fluid dynamics based modes should be utilized to

251

investigate probable fire exposures in a compartment, and results utilized to validate the
simplified approaches for design fire development.


The conventional approach of evaluating fire resistance of CFHSS columns under
standard fire exposure has a number of limitations with respect geometry, load
eccentricity, and load magnitude.

These limitations need to be overcome and a

comprehensive design methodology developed that can be readily utilized for a wider
range of column parameters.


Normal weight steel fiber reinforced concrete was used in the experimental and
numerical studies on CFHSS columns and beam slab assemblies. Consideration should
be given to the use of light weight steel fiber reinforced concrete to maximize the benefits
achieve through this higher weight system.



At the present, it is assumed that a ribbed composite deck can be modeled structurally as
a deck of uniform (average) thickness, this assumption and the influence of connections
on structural behavior need to be given consideration.



Slip between steel and concrete whether it be between the walls and the core of a CFHSS
column, or between the concrete slab and deck of a floor system, is not taken into account
in the current analyses due to the complexity of this interaction and the lack of data to
accurately model it. This interaction should be given further attention in future research
by modeling the components individually, joined at the interface through the use of
frictional elements.



Very limited information is available on the mechanical properties of SFRC at elevated
temperatures.

Studies should be undertaken to establish sound, statistically based,

252

constitutive models for SFRC over the full range of temperatures practically experienced
under fire exposure.


Currently, building information management (BIM) software is widely used in practice,
and contains all of the information regarding a structures geometry. Software should be
developed assess structural fire resistance utilizing the data in the BIM models.

8.4

Research Impact

The current prescriptive based fire design approach for steel framed structures is expensive, time
consuming, and has a number of drawbacks. The methods do not take into account critical
factors like composite construction, realistic loading, restraint, and fire exposure. Rather, fire
resistance is achieved through the provision of external fire protection on structural steel
members. Thickness of this protection is not based on sound engineering principals as they
neglect the inherent fire resistance achieved though composite construction. Thus, modern steel
structures do not utilize the inherent fire resistance within the structural system, thereby reducing
their cost effectiveness and life safety.
Use of composite construction offers a practical alternative to the current prescriptive methods of
achieving fire resistance. Through the use of composite construction in the form of steel fiber
reinforced concrete in floor slab assemblies and concrete filled HSS columns, fire resistance can
be achieved without the need for external fire protection. Composite systems exist in almost all
steel framed structures and would require only minor engineering alterations to attain the
required level of fire resistance in most cases. In addition to being a simple means of satisfying
fire resistance requirements, altering existing structural components in the design process is a
cost effective means of enhancing fire resistance both in terms of labor and material savings.
Such a rational approach to fire safety design, through the elimination of external fire protection

253

from secondary beams and columns, will make steel framed buildings more cost effective and
contribute to reduced loss of life and property damage in fire incidents.

254

APPENDICES

255

APPENDIX A
E-mail Permission for Use of Copyrighted Cardington Figures
From: colin.bailey@manchester.ac.uk
Sent: Tuesday, December 14, 2010 2:16 AM
To: Rustin S. Fike
Subject: Re: Cardington Test Picture Permission
Yes of course
Colin
Sent from my BlackBerry® wireless device
-------------------------------------------------------------------------------From: "Rustin S. Fike" <Fikerust@msu.edu>
Date: Mon, 13 Dec 2010 21:04:59 -0500
To: <colin.bailey@manchester.ac.uk>
Subject: Cardington Test Picture Permission
Dr. Bailey,
I am currently completing my Ph.D. in structural fire engineering at Michigan State University
under Dr. Venkatesh Kodur. I have a section in my thesis about the tests conducted at
Cardington and would like to include some figures from the Cardington tests that are on your
website. Pursuant to copyright policy, I need you permission to use these figures in my thesis,
may I use the figures from your website in my thesis? If you would like I can indicate the exact
pictures.
Thank you,
Kind regards,
Rustin
________________________________________
Michigan State University
Civil and Environmental Engineering
3558 Engineering Building
E. Lansing, MI 48824
PH: (517) 423-1529
Cell: (402) 418 2263

256

APPENDIX B
High Temperature Material Relationships
Table B.1: High temperature constitutive relationships for concrete

Stress-strain relationships

ASCE Manual (1992)


f
 c ,T

c  

 f c ,T




2

 
   max,T  
1  
  ,    max,T 

   max,T  
 


 


2
 


1    max,T     ,   
max,T 
  3 max,T  

 
 








 max,T  0.0025  6.0T  0.04T 2  10 6

 f c , 20 C  T  450 C



 

 T  20  


f c ,T   f c  2.011  2.353 
, 450 C  T  874 C 

 1000  
 

 0 , 874 C  T




Thermal Capacity

Siliceous Aggregate Concrete

 0.005T  1.7 20 C  T  200 C 
 2.7 200 C  T  400 C





 c  0.013T  2.5 400 C  T  500 C 
10.5  0.013T 500 C  T  600 C 


 2.7 600 C  T



Carbonate Aggregate Concrete

 2.566 20 C  T  400 C

 0.1765T  68.034 400 C  T  410 C



 25.00671  0.05043T 410 C  T  445 C 


 2.566 445 C  T  500 C

 c

 0.01603T  5.44881 500 C  T  635 C 
 0.16635T  100.90225 635 C  T  715 C 


176.07343  0.22103T 715 C  T  785 C 
 2.566 785 C  T




257

Table B.1 (Continued): High temperature constitutive relationships for concrete

Thermal Strain

Thermal Conductivity

ASCE Manual (1992)
Siliceous Aggregate Concrete.

 0.000625T  1.5 20 C  T  800 C 
kc  

1.0 800C  T

Carbonate Aggregate Concrete.

1.355 20 C  T  293 C

kc  

 0.001241T  1.7162 293 C  T 
All types :





 th  0.004 T 2  400  6 T  20   106





258

Stress-strain relationships

Table B.1 (Continued): High temperature constitutive relationships for concrete
Eurocode (2004)
3  f c' ,T
c 
, 
3

   
 c1,T  2  
  c1,T  
 



 


 cu 1,T

For ε c1(T) < ε ≤ ε cu1(T) , the Eurocode permits the use
of linear as well as nonlinear descending branch in the
numerical analysis.
For the parameters in this equation refer to Table A2
Specific heat (J/kg C)

Thermal Capacity

c= 900,
for 20°C ≤ T ≤ 100°C
c = 900 + (T - 100),
for 100°C < T ≤ 200°C
c = 1000 + (T - 200)/2, for 200°C < T ≤ 400°C
c = 1100,
for 400°C < T ≤ 1200°C
3

Density change (kg/m )

ρ = ρ(20°C) = Reference density
for 20°C ≤ T ≤ 115°C
ρ = ρ(20°C) (1 – 0.02(T - 115)/85)
for 115°C < T ≤ 200°C
ρ= ρ(20°C) (0.98 – 0.03(T - 200)/200)
for 200°C < T ≤ 400°C
ρ= ρ(20°C) (0.95 – 0.07(T - 400)/800)
for 400°C < T ≤ 1200°C
Thermal Capacity = ρ × c

259

Table B.1 (Continued): High temperature constitutive relationships for concrete

Thermal Conductivity

Eurocode (2004)
All types :
Upper limit:

kc = 2 – 0.2451 (T / 100) + 0.0107 (T / 100)2
for 20°C ≤ T ≤ 1200°C
Lower limit:

kc = 1.36 – 0.136 (T / 100) + 0.0057 (T / 100)2
for 20°C ≤ T ≤ 1200°C
Siliceous aggregates:

Thermal Strain

4

εth = -1.8×10- +9×10-6T+2.3 × 10
for 20°C ≤ T ≤ 700°C
-3
εth = 14 × 10
for 700°C < T ≤ 1200°C
Calcareous aggregates:
-4

6

εth = -1.2×10 +6×10- T+1.4×10
for 20°C ≤ T ≤ 805°C
-3
εth = 12 × 10
for 805°C < T ≤ 1200°C

260

-11 4

T

-11 3

T

Table B.1 (Continued): High temperature constitutive relationships for concrete

Stress-strain relationships

Lie and Kodur (1995b)



 c
f c  f 'c 1   m ax

  m ax


    m ax
f c  f ' c 1   c

 3 m ax


w here





2




2
 
 
 


, c 

 m ax

, c 

 m ax

 m ax  0.003  (7.0 T  0.05T 2 ) x10 6

c : Concrete specific heat. (J/kg  C)

kc : Concrete thermal conductivity (W/m.  C)

fc : 28 days concrete compressive strength at room temperature (MPa)

fc,T : Concrete compressive strength at temperature T. (MPa)

T : Concrete temperature. ( C )
 or  c : Concrete mechanical strain.
 th : Concrete thermal strain.
 cu1,T : Concrete ultimate strain at temperature T. (Eurocode model)

 c1,T : Concrete strain at maximum stress at temperature T (Eurocode model)
 max,T : Concrete strain at maximum stress at temperature T (ASCE 1992 and Kodur et al. 2004 models)
 (T): Density of concrete at temperature T. (kg/m3 )
 (20C): Density of concrete at room temperature. (kg/m3 )
 c : Stress in concrete. (MPa)

261

Table B.2. Values for the main parameters of the stress-strain relationships for concrete at
elevated temperatures (Eurocode 2004)
Siliceous Agg.
Temp.
(°C)

'
fc,T
'
fc (20 C )

Calcareous Agg.

εc1,T

εcu1,T

'
fc,T
'
fc (20 C )

εc1,T

εcu1,T

20

1

0.0025

0.02

1

0.0025

0.02

100

1

0.004

0.0225

1

0.004

0.023

200

0.95

0.0055

0.025

0.97

0.0055 0.025

300

0.85

0.007

0.0275

0.91

0.007

0.028

400

0.75

0.01

0.03

0.85

0.01

0.03

500

0.6

0.015

0.0325

0.74

0.015

0.033

600

0.45

0.025

0.035

0.6

0.025

0.035

700

0.3

0.025

0.0375

0.43

0.025

0.038

800

0.15

0.025

0.04

0.27

0.025

0.04

900

0.08

0.025

0.0425

0.15

0.025

0.043

1000

0.04

0.025

0.045

0.06

0.025

0.045

1100

0.01

0.025

0.0475

0.02

0.025

0.048

1200

0

-

-

0

-

-

262

Table B.3. Strength reduction factors for SFRC as a function of temperature
SFRC (SFPE 2002)
Temp.
(°C)

'
fc,T

ft',T

'
fc (20 C )

ft' (20 C )

20

1

1.38

100

1.06

1.31

200

1.1

1.27

300

1.1

1.24

400

1.1

0.91

500

0.88

0.59

600

0.64

0.43

700

0.17

0.33

800

0

0.3

900

-

0.2

263

Table B.4: High temperature constitutive relationships of structural steel

Thermal
Conductivity
(W/m.°K)

ASCE manual(1992)

For T  900C

ks   0.022T  48

For T  900C

k s  28.2

For T  650C

Specific Heat (J/kg.°K)

(0.004  T  3.3)  106
CS 
S
For 650C  T  725C

(0.068  T  38.3) 106
CS 
S
For 725C  T  800C
(0.086  T  73.35)  106
CS 
S

For T  800C

Thermal strain(per °C.)

s

4.55  106
CS 
S
is the density of steel.

For T  1000C

 (0.004T  12)  106

For T  1000C


 16  106


264

Table B.4 (Continued): High temperature constitutive relationships of structural steel

 p

E s ,T  


 s     p

2
c3  Fy ,T

( c1  c2 ) F y ,T 

E s ,T


2
c2 Fy,T  c3Fy,T
 
Where p
Es,T  c1Fy,T

Coefficients used
in the equations

Yield Strength

Elastic Modulus

Temperature-stress-strain Relationship

ASCE manual(1992)

c1 = 12.5; c2 = 0.975; c3 = 12.5; c4 =900; c5 = 1,750;
c6 = 340; c7 = 0.34; c8 = 240; c9 = 2,000; c10 = 1,100;
c11 = 690; c12 = 0.69; and c13 = 53.5.

265

Table B.4 (Continued): High temperature constitutive relationships of structural steel

Thermal
Conductivity
(W/m.°K)

Eurocode 3 (2005)

For T  800C

ks  54  3.33x102 T

For T  800C
ks  27.3

For T  600 C :

Specific Heat (J/kg.°K)

cs  425  7.73  10 1T 
1.69  103T 2  2.22  106 T 3
For 600C  T  735C

cs  666 

13002
738  T

For 735C  T  900C
17820
cs  545 
T  731
For 900C  T  1200C

cs  650

Thermal strain (per °C.)

For T  750C


1.2105T 0.4108T2 2.416104

For 750C  T  860C


1.1  102

For 860C  T  1200C


 2  10 5 T  6.2  103

266

Table B.4 (Continued): High temperature constitutive relationships of structural steel

Temperature-stress-strain Relationship

Eurocode 3 (2005)

F p ,T

 
E s ,T


E s ,T  

 F p ,T
   c1

 E s ,T

b

F p ,T  c 
a 2  ( c1   ) 2
a

 c    c a n d T  4 0 0 C
3
 1
( F u , T  F y , T )   c 3 F y , T  c1 F u , T


( c 3  c1 )

 c3    c 4 a n d T  4 0 0 C

s 
Fu ,T

 c    c a n d T  4 0 0 C
5
 4
( c5   )

Fu ,T 

( c5  c 4 )

 c 2    c 4 a n d T  4 0 0 C

F y ,T

 c    c a n d T  4 0 0 C
5
 4


(  c 2 ) 
F y ,T  1 


( c3  c 2 ) 


  c
5

0 .0


Where

a 2  (c1  F p,T / Es,T )(c1  F p,T / Es,T  c / Es,T )

b 2  c (c1  F p ,T / E s ,T ) E s ,T  c 2
( Fy,T  Fp,T )2
c
(c1  Fp,T / Es,T ) Es,T  2( Fy,T  Fp,T )

267

Table B.4 (Continued): High temperature constitutive relationships of structural steel

Elastic Modulus

Eurocode 3 (2005)

T  1 0 0 C
 1 .0 ,
 c T  c , 1 0 0 C  T  5 0 0 C
7
 6
 c8 T  c9 ,
5 0 0 C  T  6 0 0 C
E s ,T

  c1 0 T  c1 1 , 6 0 0  C  T  7 0 0  C
Es
 c T  c , 7 0 0 C  T  8 0 0 C
13
 12
 c1 4 T  c1 5 , 8 0 0  C  T  1 2 0 0  C

1 2 0 0 C  T
 0 .0 ,

Yield Strength

1 .0,

c T
 16
c T
 18
c T
F p ,T
 20
 
Fy
 c2 2T

 c2 4T

 c2 6T

 0 .0 ,


1.0 ,
c T
 28
 c30T

F y ,T  c32T

Fy
 c34T
 c36T

 c38T
 0.0 ,


T  100 C
 c1 7 , 1 0 0  C  T  4 0 0  C
 c1 9 , 4 0 0  C  T  5 0 0  C
 c21 , 50 0 C  T  6 00  C
 c23 , 60 0 C  T  7 00  C
 c25 , 70 0 C  T  80 0 C
 c27 , 8 00 C  T  12 00 C
1200 C  T

 c29 ,

T  400 C
400 C  T  500  C

 c31 ,

500 C  T  600  C

 c33 ,

600 C  T  700 C

 c35 ,

700 C  T  800 C

 c37 , 800 C  T  900 C
 c39 , 900 C  T  1200 C
12 00 C  T

c ,
T  300C
40
Fu,T 

 c41T  c42, 300C  T  400C
Fy 
400C  T
1.0,


268

Table B.4 (Continued): High temperature constitutive relationships of structural steel

Coefficients used in the equations

Eurocode 3 (2005)

c1 = 0.02; c2 = 0.02; c3 = 0.04; c4 =0.15; c5 = 0.20; c6
-3
-3
= -1×10 ; c7 = 1.1; c8 = -2.9×10 ; c9 = 2.05; c10 = -3
-4
1.8×10 ; c11 = 1.39; c12 = -4×10 ; c13 = 0.41; c14 = -4
-3
2.25×10 ; c15 = 0.27; c16 = -1.933×10 ; c17 = 1.193;
c18 = -0.6×10-3; c19 = 0.66; c20 = -1.8×10-3; c21 =
-3
-4
1.26; c22 = -1.05×10 ; c23 = 0.81; c24 = -2.5×10 ; c25
-4
-3
= 0.25; c26 = -1.25×10 ; c27 = 0.15; c28 = -2.2×10 ;
c29 = 1.88; c30 = -3.1×10-3; c31 = 2.33; c32 = -2.4×103
-3
; c33 = 1.91; c34 = -1.2×10 ; c35 = 1.07; c36 = -5×10
4
-4
; c37 = 0.51; c38 = -2×10 ; c39 = 0.24; c40 = 1.25;c41
-3
= -2.5×10 ; and c42 = 2.

269

APPENDIX C
SAFIR Thermal Input File
% Anything above the space is considered notes
NPTTOT
1764
%Number of points of integration
NNODE 441
%Number of Nodes
NDIM 2
%Number of global axis (2 thermal 2,3 structural)
NDIMMATER 1
%dimension of material law (1 thermal)
NDDLMAX 1
%nodal Dofs (1 thermal)
EVERY_NODE
1
%assignment of DOFs
END_NDDL
%end current assignments
TEMPERAT
%Start thermal analysis at t = 0
TETA 0.9
%time integration parameter (0 to 1)
TINITIAL 20.0
%initial temperature
MAKE.TEM
%command to make .tem file
LARGEUR11 40000 %thermal stiffness matrix parameter (SAFIR will inform if too
%small
LARGEUR12
150
%thermal stiffness matrix parameter (must be higher than restrained
dofs)
NORENUM
%do not allow equation renumbering
ASTM150.tem
%Name of .tem file
NMAT 3
%number of materials used in the cross section
ELEMENTS
%start the elements information
SOLID 400
%number of solid elements
NG 2
%number if integration points in each direction (2 %recommended)
NVOID 0
%number of internal voids
END_ELEM
% End elements assignment
NODES
%start node assignments two choices nodes - square %coordinates
node number then coordinates (y,x), or nodes_cyd to use polar coordinates %node number then
coordinates (r,theta)
%nodes example:
NODE 1
0
0
%node_cyl example:
NODE 1
0.010015789 90
%these commands establish one node at a time, you can also repeat nodes using the following
REPEAT 12
0.01 0.00 5
%this will repeat the last 12 nodes (first number) incrementing nodes by 0.01 in the y
%direction and (second number) and by 0.00 in the x direction (third number) and will do %it 5
times (fourth number)
.............................................
NODELINE
0.203 0.0
%location of neutral axis (y,x)
YC_ZC
0.203 0.0
%location of center of torsion (y,x)
FIXATIONS
%start support sub group
END_FIX
%end support sub group
NODOFSOLID
%start element assignments
270

ELEM 1
1
2
23
22
2
0 %specify each element by the
%coordinates it connects this line creates the element 1 connecting nodes 1,2,23,22 %numbering
in ccw direction, followed by material assignment then residual stress.
%can also use the repeat command:
REPEAT 12 13
5
%this will repeat the last 12 elements, increasing the node number by 13, and will do %this for 5
time
..............................................
FRONTIER
%starts specification of the exposed sides
F
20
NO
ASTME119 NO
NO
%element to have the fire %exposure
specified using node number then either "no" of the fire name which can be inbuilt or "name.fct"
GF
400 NO
ASTME119 NO
NO 20 %this will increment the exposed
%nodes from 20 to 400 in increments of 20 for the same fire exposure
END_FRONT
%end frontier assignment
SYMMETRY
%start symmetry
REALSYM 421
441
%define the first axis of symmetry
REALSYM 1
421
%define second axis of symmetry
END_SYM
%end symmetry subgroup
PRECISION 1.E-3
%specify numerical precision (0.001 is good)
MATERIALS
%start material subsection
CALCONCEC2
%material name (inbuilt)
46 25 9 .56
%material properties for concrete (water content, hot %surface
convection coeff cold surface convection coeff, relative emissivity)
STEELEC3
%material name
25 9 .5
%material properties for steel (hot surface %convection coeff
cold surface convection coeff, relative emissivity)
TIME
%start time subgroup
60
14400
%time step and max time
END_TIME
%end time subgroup
IMPRESSION
%start output loop
TIMEPRINT
%increments at which to print output
60
14400
%time step of printing and final time
END_TIMEPR
%end time print group

271

APPENDIX D
SAFIR Structural Input File
% Anything above the space is considered notes
NPTTOT
1764
%Number of points of integration
NNODE 441
%Number of Nodes
NDIM 2
%Number of global axis (2 thermal 2,3 structural)
NDIMMATER 1
%dimension of material law (1 thermal)
NDDLMAX 1
%nodal Dofs (1 thermal)
FROM 1 TO 41 STEP 1 NDDL 3
%assignment of Dofs
END_NDDL
%end current assignments
STATIC PURE_NR
%specifies convergence criterion
NLOAD 1
%number of load vectors
OBLIQUE 0
%number of oblique supports
COMEBACK
1
%allow calculation back step
LARGEUR11 40000 %thermal stiffness matrix parameter (SAFIR will inform if too
%small
LARGEUR12
150
%thermal stiffness matrix parameter (must be higher than restrained
dofs)
NORENUM
%do not allow equation renumbering
NMAT 3
%number of materials used in the cross section
ELEMENTS
%start the elements information
BEAM 20 2
%type of element (truss, shell, beam), number of those %elements
present and the number of thermal cross sections in the 20 elements
NG 2
%number if integration points in each direction (2 %recommended)
NFIBER 1600
%Number of longitudinal fibers (elements for the thermal %analysis)
END_ELEM
%end the elements subsection
NODES
%start node assignments, coordinates (x,y)
NODE 1
0.00 0.20 %Node example
%these commands establish one node at a time, you can also repeat nodes using the following
GNODE 41 0.00000 6.00000 1 %this will generate nodes from the previous %number to
41, the 41st node has coordinates 0,6 (x,y) and the step in node number will %be one
.............................................
FIXATIONS
%start support sub group
BLOCK 1
F0
F0
F0 %block restrict movement in the dofs when F0 %(f
zero) is put in that spot, other supports can also be specified)
END_FIX
%end support sub group
NODOFBEAM
%start importing thermal data
ASTM150.TEM
%name of thermal file to import (must be done for as many
%sections as specified above)
TRANSLATE 1 1
%specify that thermal material correspond to structural in
reference to the following order
………………………
END_TRANS
%end translation of materials

272

ELEM 1 1 2 3 2
%element subgroup is started, defines element one %to
connect nodes 1,2,3 with the cross section 2 just defied. Note beam elements have %three nodes,
the center must have one dof while the ends at least 3
…………………………………..
PRECISION 1.E-3
%specify numerical precision (0.001 is good)
LOADS
FUNCTION FLOAD
%specifies loading function FLOAD is a default
NODELOAD 41
0
-4870000
0
%Applies a node load at node 41 in %the
directions stipulates (x,y,x)
END_LOAD
%ends the load subgroup
MATERIALS
%start material subsection
CALCONCEC2
%material name (inbuilt)
0.25 48.1E6 0
0
%material properties for concrete (Poisson’s ratio,
%compressive strength, tensile strength, place holder (0)
STEELEC3
%material name
210.E9
0.3 350.0E6
%material properties for steel (elastic modulus, Poisson’s
%ratio, material strength
TIME
%start time subgroup
60
14400
%time step and max time
END_TIME
%end time subgroup
LARGEDISPL
%allow large displacements
EPSTH
%Print stress information
IMPRESSION
%start output loop
TIMEPRINT
%increments at which to print output
60
14400
%time step of printing and final time
END_TIMEPR
%end time print group
PRINTMN
%print internal forces for beam elements
PRINTREACT
%print reactions

273

APPENDIX E
CFHSS Column Design Example
A CFHSS column located in a room 3 m high with a 6 m by 4 m floor that has a fuel load of 550
2
MJ/m (of floor area) is to be designed. The room has one window opening 3 m wide by 2 m
high. In this compartment, the architect has proposed a 273 mm diameter circular HSS column
filled with plain concrete made with siliceous aggregate. The height of the column needs to be
3.81 m (to accommodate the drop ceiling and utilities) with fixed connections on both ends. The
building code requires the column to have a 2-hour fire resistance rating. Now it is desired to
know if this column will satisfy the code requirements by withstanding complete burnout of the
fire that would occur within the compartment.
Room properties
Room dimensions: 6 m wide by 4 m deep by 3 m high
Ventilation: one window, 3 m wide by 2 m high
2
Fire load: 550 MJ/m
Lining material: concrete with the following properties
Thermal conductivity: k = 1.6 W/mK
3
Density: ρ = 2300 kg/m
Specific heat cp = 980 J/kg K
Column properties:
Length: 3.81 m
Effective length factor: 0.65
Concrete compressive strength: 27.4 MPa
Diameter: 273.1 mm
Load: 750 kN
F = 0.07 (siliceous aggregate) 0.08 (carbonate aggregate)
Calculation of design fire as per Eurocode
Thermal inertia of concrete:

b  kpc p  1.6* 2300  980  1900 Ws 0.5 / m2 K
Floor area:

A f  6 * 4  24 m 2
Area of internal surface:

At  6 * 4* 2  3*6* 2  3* 4* 2  108 m 2
Ventilation factor:

Fv  Av H v / At  (3* 2) 2 /108  0.079 m0.5
Fuel load energy density:

274

e f  550 MJ / m 2
Total fuel load:

E  e f A f  550* 24  13, 200 MJ
Duration of fire:

td  0.00013E /( Av H v )  0.00013*13200 /(6* 2)  0.202 hours
Imaginary time used in Eurocode time-temperature relationship:
t*  td ( Fv / 0.04) 2 /(b /1900) 2  0.202(0.079 / 0.04) 2 /(1900 /1900) 2  0.789 hours
Time temperature relationship:

T  1325(1  0324e0.2t * 0.204e1.7t *  0.472e19t * )
Fire decay rate
Interpolate between a decay rate of 625 °C/hr for fire lasting ½ hour or less and 250 °C
for fires lasting more than 2 hours = 553 °C/hr after 0.789 hours of combustion, see Fig. 6.4 for
graphical representation of time temperature relationship for the design and standard fire
Calculation of ASTM fire resistance based on Eq. 1
st
1 Iteration:
The fire resistance (R) of a CFHSS column under standard fire exposure can be computed
using Eq. [2.1]
( f 'c  20) 2 D
(27.4  20)
273.1
R f
D
 0.07
(273.1)2
 101min
( KL  1000)
C
(3810*.65  1000)
750
Area under ASTM E-119 time-temperature curve at 101 min: 1462 min°C
Area under the design fire time-temperature curve at 101 min: 1503 min°C
Since the area under the standard fire curve is less than that under the design fire the column will
fail in the design fire. An alternative must be selected since this does not satisfy the 2 hour fire
rating required for the column.
nd

2

Iteration:
By changing the aggregate type used in the concrete from siliceous to carbonate, the fire
resistance of the column can be enhanced.
( f 'c  20) 2 D
(27.4  20)
273.1
R f
D
 0.08
(273.1)2
 116 min
( KL  1000)
C
(3810*.65  1000)
750
Area under ASTM E-119 time-temperature curve at 116 min: 1701 min°C
Area under the design fire time-temperature curve at 116 min: 1626 min°C
Since the area under the standard fire curve is greater than that under the design fire the column
will not fail in the design fire, thus the CFHSS column can be used in this application.

275

A detailed finite element analysis was carried out on this CFHSS column using the computer
program SAFIR. Results from the analysis indicate that the column does not fail under the
design fire but rather survives compartment burnout when carbonate aggregate are used. This is
in agreement with the predictions from the proposed equivalent area approach that requires
significantly less time and effort.

276

APPENDIX F
SFRC Floor Design Example
A room 3 m high with a 6 m by 4 m floor (with secondary beams spanning in the 6 m direction)
2
and a fire load of 5.25 kN/m is to be designed. The room has one window opening 3 m wide by
2 m high. The architect has indicated that the room below the considered compartment has the
2
same dimensions and will have a fuel load of 550 MJ/m (of floor area). Now, it is desired to
know what thickness the floor needs to be to satisfy the code requirements by withstanding
complete burnout of the probabilistic fire that would occur within the compartment.
Room properties
Room dimensions: 6 m wide by 4 m deep by 3 m high
Ventilation: one window, 3 m wide by 2 m high
2
Fire load: 550 MJ/m
Lining material: concrete with the following properties
Thermal conductivity: k = 1.6 W/mK
3
Density: ρ = 2300 kg/m
Specific heat cp = 980 J/kg K
Calculation of design fire as per Eurocode
Thermal inertia of concrete:

b  kpc p  1.6* 2300  980  1900 Ws 0.5 / m2 K
Floor area:

A f  6* 4  24 m 2
Area of internal surface:

At  6 * 4* 2  3*6* 2  3* 4* 2  108 m 2
Ventilation factor:

Fv  Av H v / At  (3*2) 2 /108  0.079 m0.5
Fuel load energy density:

e f  550 MJ / m2
Total fuel load:

E  e f A f  550* 24  13, 200 MJ
Duration of fire:

td  0.00013E /( Av H v )  0.00013*13200 /(6* 2)  0.202 hours
Imaginary time used in Eurocode time-temperature relationship:

277

t*  td ( Fv / 0.04) 2 /(b /1900) 2  0.202(0.079 / 0.04) 2 /(1900 /1900) 2  0.789 hours
Time temperature relationship:

T  1325(1  0324e0.2t * 0.204e1.7t *  0.472e19t * )
Fire decay rate
Interpolate between a decay rate of 625 °C/hr for fire lasting ½ hour or less and 250 °C
for fires lasting more than 2 hours = 553 °C/hr after 0.789 hours of combustion, see Fig. 6.12 for
graphical representation of time temperature relationship for the design and standard fire
Determination of ASTM fire resistance
18.00
Load Capacity (KN/m2)

100 mm

15.00

125mm
150 mm

12.00
9.00
6.00
3.00
0.00
4.00

6.00

8.00

10.00

12.00

14.00

Span (m)

Fig. F.1: Load capacity of strip floor to achieve two hour fire resistance rating under ASTM E119 fire exposure
st

1 Iteration:
Using Fig. E.1, the length of the span is found on the X-axis and a vertical line is drawn until the
line for the desired slab thickness is intersected, in the case illustrated above when the slab
2
thickness is 100 mm, the load capacity of the slab is found to be 5.5 kN/m
Based on a maximum design fire temperature of 1089 °C, the design fire burnout load is:

278

ASTM Load Capacity
5.5KN / m2
Design Load Capacity 

 5.08KN / m 2
t
1089C 100mm

100
1006C 100mm
Given that the previous iteration yielded a load capacity less than the applied load capacity it is
necessary to reiterate the process with a thicker floor slab assembly
nd

2 Iteration:
By entering Fig. E.2 (reproduced below to avoid confusion with multiple iterations) the load
2
capacity of the 112.5 mm thick floor system is fond to be 8.5 kN/m

Load Capacity (KN/m2)

18.00
100 mm

15.00

125mm
150 mm

12.00
9.00
6.00
3.00
0.00
4.00

6.00

8.00

10.00

12.00

14.00

Span (m)

Fig. F.2: Load capacity of strip floor to achieve two hour fire resistance rating under ASTM E119 fire exposure
Based on this load capacity, the burnout load capacity of the slab is found as follows

ASTM Load Capacity
8.5KN / m 2
Design Load Capacity 

 6.98KN / m 2
t
1089C 112.5mm

100
1006C 100mm

279

2

Since the burnout load capacity of the floor (6.98 kN/m ) is greater than the applied load of 5.25
2

kN/m the floor is sufficient to withstand compartment burnout and there is no need for applied
external fire protection on the secondary beams,

280

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