Fire resistance of ultra high strength concrete filled steel tubular columns

FIRE RESISTANCE OF ULTRA-HIGH STRENGTH
CONCRETE FILLED STEEL TUBULAR COLUMNS



XIONG MINGXIANG





NATIONAL UNIVERSITY OF SINGAPORE
2013



FIRE RESISTANCE OF ULTRA-HIGH STRENGTH
CONCRETE FILLED STEEL TUBULAR COLUMNS



XIONG MINGXIANG
(B.ENG. Wuhan University of Science and Technology
M.ENG. Huazhong University of Science and Technology)




A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2013




DECLARATION
I hereby declare that this thesis is my original work and it has been written by me in
its entirety. I have duly acknowledged all the sources of information which have been
used in the thesis.
This thesis has also not been submitted for any degree in any university previously.

Xiong Mingxiang
06 June 2013












i

Acknowledgements

It would not have been possible to write this doctoral thesis without the help and
support of the kind people around me, to only some of whom it is possible to give
particular mention herein.
First of all, I would like to express my deepest gratitude to my supervisor, Professor
Liew Jat Yuen, Richard, for his enthusiasm, encouragement, and resolute dedication
to my ideas in study. Thanks for his unsurpassed knowledge and excellent guidance as
I hurdle all the obstacles in the completion of this research work. I also would like to
thank Professor Zhang Min Hong for her patient explanations and invaluable
suggestions on my queries on concrete and paper review.
I would like to acknowledge the financial support from A*STAR for my research
project (SERC Grant No: 092 142 0045). I would like to thank the researchers in this
project, Dr. Wang Tongyun, Dr. Xiong Dexin, Mr. Yu Xin and Dr. Song Tianyi, for
their kind help and advice. Besides, I also would like to thank Professor Shu Ganping,
A/Professor Fan Shenggang, A/Professor Xu Ming, Mr. Xiao and Mr. Jiang for their
kind academic and technical supports when I conducted the fire tests in South East
University of China.
I would like to thank the staff in our structural lab, Mr. Lim, Ms. Annie, Ms. Li, Mr.
Ang, Mr. Koh, Mr. Choo, Mr. Yip, Mr. Wong, Mr. Ow, Mr. Martin, Mr. Kamsan, Mr.
Ishak and Mr. Yong, for their kind technical supports when I carried on my
experiments in our structural lab. I also would like to thank the staff in our department
and faculty, especially Mr. Sit, Ms. Lim and Mdm. Lee, for their kind administrative
assistances.
ii

I would like to thank my dear friends and colleagues, Dr. Chia Kok Seng, Dr. Ma
Chenyin, Dr. Du Hongjian, Dr. Li Ya, Dr. Liu Xuemei, Dr. Wang Junyan, Dr. Yan
Jiabao, Mr. Wang Yu. Thanks for your kind help.
Finally, I would like to thank my family, my parents and parents-in-law, for paying
out so much that I can focus on my study. Special gratitude and love to my wife, Ms.
Liu Fangfang, for her continuous patience and support when I am abroad, and for her

standing by me and cheering me up through the good and bad times.



iii

Table of Content
Acknowledgements i
Table of Content iii
Summary vii
List of Publications xi
List of Tables xiii
List of Figures xv
Chapter 1 Introduction 1
1.1 Background 1
1.1.1 Concrete Filled Steel Tubular Column 1
1.1.2 Fire Hazard 3
1.1.3 Concrete Filled Steel Tubular Column in Fire Hazard 4
1.2 Motivation and Objectives 5
1.3 Overview of Contents 7
Chapter 2 Literature Review 10
2.1 Overview 10
2.2 Mechanical Properties of Concrete at Elevated Temperatures 10
2.3 Spalling of High Strength Concrete at Elevated Temperature 13
2.4 Mechanical properties of Concrete after Heating 13
2.5 Mechanical Properties of Steel at Elevated Temperatures 14
2.6 Fire Resistance of Concrete Filled Steel Tubular Columns 16
2.6.1 Experimental Studies 16
2.6.2 Numerical Studies 19
2.6.3 Design Codes 19

2.7 Summary 22
Chapter 3 Behavior of High Strength Steel at Elevated Temperatures 30
3.1 Overview 30
3.2 Chemical Compositions of High Strength Steel 30
3.3 Microstructure of High Strength Steel at High Temperature 31
3.4 Tensile Test at Elevated Temperature 33
3.4.1 Test Specimens 33
3.4.2 Test Equipment and Instrumentation 33
3.4.3 Test Setup 34
3.4.4 Test Methods 35
iv

3.5 Test Results 36
3.5.1 Relative Thermal Elongation 36
3.5.2 Elastic Modulus 37
3.5.3 Effective Yield Strength 38
3.5.4 Stress-Strain Relation 40
3.6 Critical Temperature 41
3.7 Summary 45
Chapter 4 Behavior of Ultra-High Strength Concrete after Heating 58
4.1 Overview 58
4.2 Effect of Types of Fibers on Prevention of Spalling 58
4.2.1 Test Specimens 58
4.2.2 Test Procedure 59
4.2.3 Test Results 59
4.3 Effect of Polypropylene Fibers on Prevention of Spalling 61
4.3.1 Test Materials and Procedure 61
4.3.2 Residual Strength 61
4.3.3 Residual Elastic Modulus 64
4.4 Effect of Curing Condition 65

4.4.1 Test Material and Curing Conditions 65
4.4.2 Test Results 66
4.5 Summary 67
Chapter 5 Behavior of Ultra-High Strength Concrete at Elevated
Temperatures 82
5.1 Overview 82
5.2 Compression Tests at Elevated Temperature 82
5.2.1 Test Specimens 82
5.2.2 Test Equipments 82
5.2.3 Test Setup 83
5.2.4 Test Method 84
5.3 Test Results 85
5.3.1 Compressive Strength 85
5.3.2 Elastic Modulus 87
5.4 Summary 88
Chapter 6 Fire Tests on Ultra-High Strength Concrete Filled Steel Tubular
Columns 96
6.1 Overview 96
v

6.2 Details of Concrete Filled Steel Tubular Columns 96
6.2.1 Specimen Design 96
6.2.2 Design of Supports 97
6.2.3 Concreting and Construction of Fire Protection Material 98
6.2.4 Locations of Steaming Holes and Thermocouples 99
6.3 Test Setup and Procedure 99
6.3.1 Test Apparatus 99
6.3.2 Test Setup 100
6.3.3 Fire Exposure 101
6.3.4 Test Procedure and Failure Criteria 101

6.4 Test Data 102
6.4.1 Temperature Distribution 102
6.4.2 Failure Temperature of Outer Steel Tube 103
6.4.3 Displacement-Time Relationship 106
6.5 Test Observations 108
6.5.1 Cross-Sectional Failure 109
6.5.2 Flexural Buckling Failure 112
6.6 Summary 112
Chapter 7 Fire Resistant Design of Concrete Filled Steel Tubular Columns .146
7.1 Overview 146
7.2 Heat Transfer Analysis by Finite Difference Method 146
7.2.1 Basics of Heat Transfer 146
7.2.2 Finite Difference Method 147
7.2.3 Temperature Calculations of Circular CFST and CFDST Columns 153
7.2.4 Temperatures of Square CFST and CFDST Columns 156
7.3 Simple Calculation Model 157
7.4 M-N Interaction Model 160
7.5 Effective Length of Column in Fire Test 162
7.5.1 Column Pinned at Both Ends 163
7.5.2 Column Fixed at Both Ends 165
7.5.3 Column Fixed at One End and Pinned at another End 167
7.5.4 Comparisons 170
7.6 Thermal Properties of Materials at High Temperatures 172
7.6.1 Steel 172
7.6.2 Concrete 172
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7.6.3 Fire Protection Material 173
7.7 Validation of Proposed Methods 174
7.7.1 Validation with 66 Tests from the Literature 174

7.7.2 Validation of Finite Difference Method 175
7.7.3 Validation of SCM and MNIM 176
7.8 Parametric Analysis 179
7.8.1 Introduction 179
7.8.2 Effects of Concrete Strength 180
7.8.3 Effects of Steel Strength 180
7.8.4 Comparisons between Circular and Square Columns 181
7.8.5 Comparisons between Columns with Single-Tube and Double-Tube . 182
7.9 Summary 183
Chapter 8 Conclusions and Recommendations 216
8.1 Review of Competed Research Work 216
8.2 Conclusions 218
8.3 Recommendations to Future Work 221
References 224


vii

Summary
The aim of this research is to evaluate the fire resistance of high strength tubular steel
columns infilled with ultra-high strength concrete with compressive strength up to
160MPa. Although research work has been done on concrete filled steel tubular
(CFST) columns and design codes are available for fire resistant design, guidelines on
high strength steel and concrete on CFST is not available. The present research aims
to extend the design codes by investigating the behaviors of these high strength
materials at elevated temperatures by means of experiments and analytical methods.
High strength steel (HSS) is heat-treated from mild steel. A total of 73 specimens
were tested in axial tension in order to obtain the temperature dependent mechanical
properties of high strength steel. The tests were carried out based on both steady-state
and transient-state methods. Compared with normal strength steel (NSS) in EN 1993-

1-2, the relative thermal elongations of HSS were smaller. Elastic modulus and
effective yield strength of HSS were reduced faster than NSS beyond 400
o
C. Thermal
creep exhibited significant effect on the elastic modulus but it was not significant on
the effective yield strengths. The mechanical properties obtained from the experiment
were essential to determine the critical temperature and then the fire resistance time of
columns with HSS.
UHSC is prone to spalling when it is subject to high temperature. Spalling behavior
and residual properties of UHSC after elevated temperatures were experimentally
investigated based on types of fiber, dosages of polypropylene fiber, heating rates,
and curing conditions. Test results revealed that steel fiber was not effective to
prevent spalling of UHSC but polypropylene (PP) fiber with dosage of 0.1% in
volume was effective. Residual compressive strength and residual elastic modulus of
viii

UHSC were affected by dosages of polypropylene fiber and heating rates but not by
the curing conditions.
A total of 27 cylindrical specimens were tested to measure the temperature dependent
compressive strength and elastic modulus of UHSC at elevated temperatures.
Experimental evidence showed that both compressive strength and elastic modulus
experienced sharp deteriorations at temperature around 100
o
C and then were partly
recovered after heating to 300
o
C. Compared with normal strength concrete (NSC) and
high strength concrete (HSC) in EN 1992-1-2, the compressive strength and elastic
modulus of UHSC were reduced slower beyond 300
o

C. The tested strength and elastic
modulus could be used to calculate the fire resistance of CFST columns with UHSC.
A total of 22 CFST columns of 3.81m were tested including both single-tube columns
and double-tube columns. These columns were heated in accordance with ISO-834
fire. The experimental investigation focused on the varied thickness of fire protection
material, cross-sectional size, boundary condition, load level, and eccentricity of load.
Temperature profiles, axial deformations, fire resistance time, and failure modes were
obtained from tests. The experimental observations showed that most columns were
failed by the overall buckling, except for three columns by the cross-sectional failure.
Transversal cracks on concrete were observed for columns failed by the overall
buckling; whereas longitudinal splitting were found on columns with the cross-
sectional failure. Welding tearing failure was found in one column due to the poor
welding quality.
Existing simple calculation model (SCM) in EN 1994-1-2 and proposed M-N
interaction model (MNIM) were used to predict the fire resistance time of CFST
columns and their validity was verified by comparing test data from present research
ix

with data from the literature. By using SCM and MNIM, the effective length of the
CFST column in the fire test was derived by solving the 4
th
-order differential equation
of the lateral displacement. The temperature profiles of columns were calculated
based on finite difference method (FDM). The comparisons between tested and
calculated fire resistance time indicated that MNIM exhibited more conservative and
less scattered calculation data than SCM due to more reasonable consideration for the
second-order effect under fire.
Parametric analyses were carried out based on the validated MNIM method and aimed
to investigate the effects of strengths of steel and concrete on the fire resistance time
of CFST columns. Analysis results showed that the fire resistance time of columns

with UHSC was slightly higher than that of columns with NSC and HSC. The fire
resistance time of columns with HSS was shorter than that of columns with NSS. The
parametric analyses further indicated that the circular and square columns with single-
tube would exhibit same fire resistance time if they have equal section factors.
However, the circular columns exhibited slightly higher fire resistance time than the
square columns in terms of equal section factors and double-tube. In addition, it is
difficult to determine the superiority between the single-tube columns and the double-
tube columns in fire situations. Larger section factor makes the double-tube columns
exhibited shorter fire resistance time. However, the double-tube columns have smaller
non-dimensional slenderness ratio which resulted in higher buckling capacity and thus
higher fire resistance time.



x




xi

List of Publications
Xiong M.X, Liew J.Y.R, Zhang M.H. Fire behavior of high strength steel tubular
columns infilled with ultra-high strength concrete. The 23
th
KKCNN Symposium on
Civil Engineering, Taipei, China, 13-15 November, 2010.
Liew J.Y.R, Xiong M.X, Xiong D.X. Ultra-high strength composite columns for high-
rise buildings. The 3
rd

International Symposium on Innovative Design of Steel
Structures, Singapore, 28 June, 2011.
Xiong M.X, Liew J.Y.R, Zhang M.H. Fire resistance of high strength steel (steady-
state tests). The 7
th
International Conference on Steel and Aluminum Structures,
Sarawak, Malaysia, 13-15 July, 2011.
Xiong M.X, Liew J.Y.R. Experimental investigation on mechanical properties of high
strength steel at elevated temperatures (transient-state tests). The 10
th
International
Conference on Advances in Steel Concrete Composite and Hybrid Structures,
Singapore, 2-4 July, 2012.
Liew J.Y.R, Xiong D.X, Xiong M.X, Yu X. Design of concrete filled steel tube with
high strength materials. The 9
th
World Congress, CTBUH, Shanghai, China, 19-21
September, 2012.







xii



xiii

List of Tables
Table 3.1: Typical chemical compositions of HSS RQT701 and NSS (%) 48
Table 3.2: Effective yield strengths of HSS RQT701 at ambient temperature (MPa) 48
Table 3.3: Reduction factors of elastic modulus and effective yield strengths 49
Table 4.1: Mixing proportions of plain UHSC 69
Table 4.2: Mixing proportions of UHSC with additions of fibers 69
Table 4.3: The properties of steel fiber 69
Table 4.4: The properties of polypropylene fiber 69
Table 4.5: The residual strength of UHSC mixtures after 800
o
C 70
Table 4.6: The mix proportions of NSC C50 70
Table 4.7: Residual strengths (MPa) from different fiber dosage and heating rate 70
Table 4.8: Residual elastic modulus (GPa) from different fiber dosage and heating
rate 71
Table 4.9: Residual strength and elastic modulus from different curing conditions 71
Table 6.1: Details of CFST and CFDST column specimens for fire tests 115
Table 6.2: Failure temperatures on steel tubes and failure modes 116
Table 7.1: Reduction factors of mechanical properties of steel and concrete at elevated
temperature given in EN 1992-1-2 and EN 1993-1-2 186
Table 7.2: Details of columns in Lie and Chabot (1992) and Romero’s (2011) tests
and comparison of test and predicted results 187
Table 7.3: Comparisons between Author’s tested with calculated fire resistance time
188
Table 7.4: Specimens designed for parametric analysis-circular columns 189
Table 7.5: Specimens designed for parametric analysis-square columns 190

xiv



xv

List of Figures
Figure 1.1: Types of concrete filled steel tubular columns 9
Figure 1.2: Typical longitudinal displacement of CFST column exposed to fire 9
Figure 2.1: Reduction factor of compressive strength of NSC at elevated temperatures
24
Figure 2.2: Reduction factor of compressive strength of HSC at elevated temperatures
24
Figure 2.3: Reduction factor of elastic Modulus of concrete at elevated temperatures
25
Figure 2.4: Stress-strain curves of NSC at high temperatures 25
Figure 2.5: Stress-strain curves for HSC at high temperatures 26
Figure 2.6: Reduction factors of unstressed residual compressive strength 26
Figure 2.7: Reduction factors for unstressed residual elastic modulus 27
Figure 2.8: Typical stress-strain curves for ASTM A36 steel at high temperatures 27
Figure 2.9: Comparison between stress-strain curves of steel at elevated temperatures
28

Figure 3.1: Phase transformation of steel at elevated temperature 50
Figure 3.2: Dimensions of coupon specimen (units in mm) 50
Figure 3.3: Test setup 51
Figure 3.4: Relative thermal elongations of HSS RQT701 and NSS at elevated
temperature 51
Figure 3.5: Comparison of E
a,θ
/E
a
ratio and temperature relation of HSS RQT 701 and
NSS 52
Figure 3.6: Reduction factor of effective yield strength at 0.2% offset strain at
elevated temperature 52
Figure 3.7: Reduction factors of effective yield strengths at 0.5% strain at elevated
temperature 53
Figure 3.8: Reduction factors of effective yield strengths at 1.5% strain at elevated
temperature 53
Figure 3.9: Reduction factors of effective yield strengths at 2.0% strain at elevated
temperature 54
Figure 3.10: Stress-strain curves of HSS RQT701 from steady-state tests at elevated
temperature 54
Figure 3.11: Stress-strain curves of HSS RQT701 from transient-state tests at elevated
temperature 55
Figure 3.12: Critical temperatures of columns with HSS RQT 701, S460, S355 and
S275 55
xvi

Figure 3.13: Critical temperatures of columns with HSS RQT701 based on different
buckling curves at room temperature 56
Figure 4.1: Steel fiber 72

Figure 4.2: Polypropylene fiber 72
Figure 4.3: Spalled UHSC specimens with steel fiber after taken out from oven 72
Figure 4.4: Failure modes after being subjected to the target temperatures and
compression 73
Figure 4.5: Comparison between reduction factors of residual strength of plain UHSC
and C50 without PP fiber 73
Figure 4.6: Effects of fiber dosage on reduction factors of residual strength of UHSC
mixtures-5
o
C/min 74
Figure 4.7: Effects of fiber dosage on reduction factors of residual strength of UHSC
mixtures-30
o
C/min 74
Figure 4.8: Effects of heating rate on reduction factors of residual strength of UHSC
mixtures-0.1% PP fiber 75
Figure 4.9: Effects of heating rate on reduction factors of residual strength of UHSC
mixtures-0.25% PP fiber 75
Figure 4.10: Effects of heating rate on reduction factors of residual strength of UHSC
mixtures-0.5% PP fiber 76
Figure 4.11: Comparison between reduction factors of residual strengths of UHSC
with addition of 0.1% PP fiber and concretes in literature 76
Figure 4.12: Comparison between reduction factors of residual elastic modulus of
plain UHSC and C50 without PP fiber 77
Figure 4.13: Effects of fiber dosage on residual elastic modulus factor of UHSC
mixture-5
o
C/min 77
Figure 4.14: Effects of fiber dosage on residual elastic modulus factor of UHSC
mixture-30

o
C/min 78
Figure 4.15: Effects of fiber dosage on residual elastic modulus factor of UHSC
mixture-0.1% PP fiber 78
Figure 4.16: Effects of fiber dosage on residual elastic modulus factor of UHSC
mixture-0.25% PP fiber 79
Figure 4.17: Effects of fiber dosage on residual elastic modulus factor of UHSC
mixture-0.5% PP fiber 79
Figure 4.18: Comparison between reduction factors of residual elastic modulus of
UHSC with addition of 0.1% PP fiber and concretes in literature 80
Figure 4.19: Effects of curing conditions on reduction factors of residual strength of
UHSC mixtures 80
Figure 4.20: Effects of curing conditions on reduction factors of residual elastic
modulus of UHSC mixtures 81
Figure 4.21: Comparison between reduction factors of residual strength and residual
elastic modulus under all curing conditions 81
xvii

Figure 5.1: Details of cooling plate 90
Figure 5.2: Test setup 91
Figure 5.3: Specimen without protection by steel casing 91
Figure 5.4: Specimen with protection by steel casing 92
Figure 5.5: Schematic illustration of preloading cycles applied on the test specimens
92
Figure 5.6: Comparison between reduction factors of strength and residual strength . 93
Figure 5.7: Comparison between strength reduction factors of UHSC and NSC as
given in EN 1992-1-2 93
Figure 5.8: Comparison between strength reduction factors of UHSC and HSC as
given in EN 1992-1-2 94
Figure 5.9: Comparison between strength reduction factors of UHSC and HSC with

results from previous researches 94
Figure 5.10: Comparison between reduction factors of elastic modulus and residual
elastic modulus 95
Figure 5.11: Comparison between reduction factors of elastic modulus of UHSC and
HSC as given in previous researches 95
Figure 6.1: Dimensions of circular CFST columns 117
Figure 6.2: Dimensions of square CFST columns 118
Figure 6.3: Dimensions of circular CFDST columns 119
Figure 6.4: Dimensions of square CFDST columns 120
Figure 6.5: Welding details of boxed columns 121
Figure 6.6: Pinned support allowing free rotation 121
Figure 6.7: fixed support with fixer plate to prevent rotation 122
Figure 6.8: Supports in fire test 122
Figure 6.9: Casting of concrete 123
Figure 6.10: CFST columns applied with fire protection material 123
Figure 6.11: Locations of steaming holes 124
Figure 6.12: Locations of thermocouples 124
Figure 6.13: Furnace for standard fire test 125
Figure 6.14: Test setup 125
Figure 6.15: Measurements of axial displacements of columns 126
Figure 6.16: Measured temperatures in tested columns 129
Figure 6.17: Stub composite columns to illustrate the effects of cross-sectional size
and load level on the failure temperature of outer tube 130
Figure 6.18: Curves of vertical displacements versus fire exposure time of column
LC-2-1 ~ LC-2-6 130
xviii

Figure 6.19: Curves of vertical displacements versus fire exposure time of column
LC-3-1, LC-3-2, and LC-4-1 131
Figure 6.20: Curves of vertical displacements versus fire exposure time of column

LSH-2-1 ~ LSH-2-6 and LS-2-1 131
Figure 6.21: Curves of vertical displacements versus fire exposure time of column
LDC-2-1, LDC-2-2 and LDC-2-3 132
Figure 6.22: Curves of vertical displacements versus fire exposure time of column
LDSH-2-1, LDSH-2-2 and LDSH-2-3 132
Figure 6.23: Failure modes of tested CFST columns 138
Figure 6.24: Comparions between failure modes of circualr single-tube columns 138
Figure 6.25: Comparions between failure modes of square single-tube columns 139
Figure 6.26: Comparions between failure modes of double-skin columns 139
Figure 6.27: Faliure observations at cross sections 140
Figure 6.28: Relation of section classification and temperature for circular external
tubes with S355 steel 140
Figure 6.29: Relation of section classification and temperature for square external
tubes with S690 steel 141
Figure 6.30: Longitudinal splitting of concrete by cross-sectional failure 141
Figure 6.31: Weld tearing of welded box section 142
Figure 6.32: Intact welding of welded box section 142
Figure 6.33: Transversal cracking of concrete by flexural buckling failure 143
Figure 6.34: Local bulge of inner tube 144
Figure 6.35: Relation of section classification and temperature for circular inner tubes
with S355 steel 144
Figure 6.36: Relation of section classification and temperature for square inner tubes
with S690 steel 145
Figure 7.1: Discretization of 2-D heat transfer 191
Figure 7.2: Discretization of circular CFST column 191
Figure 7.3: Discretization of circular CFDST column 192
Figure 7.4: Discretization of square CFST column 192
Figure 7.5: Discretization of square CFDST column 193
Figure 7.6: M-N interaction curve and corresponding stress distributions in fire
situation 194

Figure 7.7: Diagram for calculation of effective length of pinned-pinned column 195
Figure 7.8: Diagram for calculation of effective length of fixed-fixed column 195
Figure 7.9: Diagram for calculation of effective length of fixed-pinned column 196
Figure 7.10: Coefficients of effective lengths of columns in author’s fire tests 196
Figure 7.11: Coefficients of effective lengths of fixed-fixed columns under fire 197
xix

Figure 7.12: Coefficients of effective lengths of fixed-pinned columns under fire 197
Figure 7.13: Coefficients of effective lengths of pinned-pinned columns under fire 198
Figure 7.14: Comparison between calculated and measured temperatures in Lie’s tests
204
Figure 7.15: Comparison between measured and calculated temperatures in author’s
tests 208
Figure 7.16: Comparisons between tested and calculated fire resistance time based on
SCM 209
Figure 7.17: Comparisons between tested and calculated fire resistance time based on
MNIM 209
Figure 7.18: M-N curves of column LC-2-4 under fire 210
Figure 7.19: M-N curves of column LDC-2-2 under fire 210
Figure 7.20: M-N curves of column LSH-2-4 under fire 211
Figure 7.21: M-N curves of column LDSH-2-2 under fire 211
Figure 7.22: Effect of strength of concrete 212
Figure 7.23: Effect of strength of steel 213
Figure 7.24: Ratio of fire resistance time per section factor between circular and
square columns with single-tube 214
Figure 7.25: Ratio of fire resistance time per section factor between circular and
square columns with double-tube 214