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BEHAVIOUR OF FIBRE REINFORCED POLYMER CONFINED REINFORCED CONCRETE COLUMNS UNDER FIRE CONDITION

by Ershad Ullah Chowdhury A thesis submitted to the Department of Civil Engineering In conformity with the requirements for the degree of Doctor of Philosophy

Abstract In recent years, fibre reinforced polymer (FRP) materials have demonstrated enormous potential as materials for repairing and retrofitting concrete bridges that have deteriorated from factors such as electro-chemical corrosion and increased load requirements. However, concerns associated with fire remain an obstacle to applications of FRP materials in buildings and parking garages due to FRP's sensitivity to high temperatures as compared with other structural materials and to limited knowledge on their thermal and mechanical behaviour in fire. This thesis presents results from an ongoing study on the fire performance of FRP materials, fire insulation materials and systems, and FRP wrapped reinforced concrete columns. The overall goal of the study is to understand the fire behaviour of FRP materials and FRP strengthened concrete columns and ultimately, provide rational fire safety design recommendations and guidelines for FRP strengthened concrete columns.

A combined experimental and numerical investigation was conducted to achieve the goals of this research study. The experimental work consisted of both small-scale FRP material testing at elevated temperatures and full-scale fire tests on FRP strengthened columns. A numerical model was developed to simulate the behaviour of unwrapped reinforced concrete and FRP strengthened reinforced concrete square or rectangular columns in fire. After validating the numerical model against test data available in literature, it was determined that the numerical model can be used to analyze the behaviour of concrete axial compressive members in fire.

Results from this study also demonstrated that although FRP materials experience considerable loss of their mechanical and bond properties at temperatures somewhat below the glass transition temperature of the resin matrix, externally-bonded FRP can be used in strengthening concrete structural members in buildings, if appropriate supplemental fire protection system is provided over the FRP strengthening system.

Acknowledgements There are a number of people who contributed to the completion of this thesis and I would like to recognize these people and express my gratitude to them. I would like to first recognize my supervisors. Many thanks go to Dr. Mark Green for his guidance encouragement, patience and support. My deepest gratitude goes to Dr. Luke Bisby, who was always available to respond to my questions and guide me throughout my time as a graduate student at Queen's University.

This research project would not have been possible without the support of our industrial partners: Fyfe Co. LLC, BASF, and Sika. The fire endurance tests in this thesis were conducted in the Fire Risk Management testing facility at the National Research Council of Canada. I would like to thank Dr. Noureddine Bénichou of the National Research Council of Canada for providing his invaluable technical expertise and experience to this research. I would also like to thank the technical officers at the National Research Council of Canada: John Latour, Jocelyn Henrie, Rick Rombough, Patrice Leroux and Roch Monette.

Throughout my time as a graduate student at Queen's University I have been surrounded by tremendous supportive individuals. Thanks go to Dr. Andy Take, Maxine Wilson, Cathy Wager, Fiona Froats, Lloyd Rhymer, Paul Thrasher, Neil Porter, Dave Tyron, Jamie Escobar, Waleed Shawkat, Masoud Adelzadeh, and Peter Mitchell. My deepest gratitude goes to Rob Eedson for his assistance to this research.

Without the sacrifices and moral support of my parents (Abbu and Amma), it would not have been possible to pursue this degree. I am forever indebted to my parents and I dedicate this thesis to my parents. My sister (Tona Apu) and brother-in-law (Dula Bhai) had a huge contribution early in my academic career. I would like to thank my wife, Muna, for her support and

encouragement on occasions far too many to mention. The last two persons that I would like to thank are my nephew (Nazheef) and niece (Suhailah).

Statement of Originality Any published (or unpublished) ideas and/or techniques from the work of others are fully acknowledged in accordance with the standard referencing practices.

Abstract ...........................................................................................................................................iii

Acknowledgements ......................................................................................................................... iv

Statement of Originality.................................................................................................................. vi

Table of Contents ........................................................................................................................... vii

List of Figures .................................................................................................................................. x

List of Tables ................................................................................................................................ xvi

Notations ...................................................................................................................................... xvii

Chapter 1 Introduction ..................................................................................................................... 1

1.1 General ................................................................................................................................... 1

1.2 Research Objectives ............................................................................................................... 3

1.3 Outline of Thesis .................................................................................................................... 6

Chapter 2 Literature Review ............................................................................................................ 7

2.1 General ................................................................................................................................... 7

2.2 Background on FRP-Confined Concrete ............................................................................... 7

2.3 Performance of FRP Confined Concrete under Eccentric Loading ..................................... 13

2.4 Methods of Calculation for Slender Concrete Columns ...................................................... 16

2.5 Philosophy for the Fire Endurance of FRP Strengthened Concrete Columns ..................... 17

2.6 Material Properties at Elevated Temperature....................................................................... 19

2.7 Behaviour of FRP Strengthened Concrete Structures in Fire .............................................. 23

2.7.1 FRP Strengthened Flexural Concrete Members............................................................ 23

2.7.2 FRP Confined Axial Concrete Members ...................................................................... 24

2.8 Summary .............................................................................................................................. 26

at Ambient Temperature ................................................................................................................ 31

3.1 General ................................................................................................................................. 31

3.2 Research Significance: Current Chapter .............................................................................. 32

3.3 Numerical Study .................................................................................................................. 32

3.3.1 Material Properties ........................................................................................................ 33

3.3.2 Development of Axial Load-Moment-Curvature Relationship .................................... 35

3.3.3 Numerical Integration of Column Deflections.............................................................. 37

3.3.4 Development of Slender Column Axial Load-Moment Interaction Diagrams ............. 39

3.4 Validation of Numerical Model ........................................................................................... 40

3.5 Summary .............................................................................................................................. 46

Chapter 4 Mechanical Characterization of FRP Materials at High Temperature .......................... 62

4.1 General ................................................................................................................................. 62

4.2 Research Significance: Current Chapter .............................................................................. 62

4.3 Experimental Procedure ....................................................................................................... 63

4.3.1 FRP specimen fabrication ............................................................................................. 63

4.3.2 Test Conditions and Instrumentation ............................................................................ 64

4.4 Proposed Analytical Model.................................................................................................. 67

4.5 Results and Discussion ........................................................................................................ 69

4.5.1 Physical and Mechanical Properties ............................................................................. 69

4.5.2 FRP-to-FRP Bond Properties ........................................................................................ 73

4.6 Implementation in a Structural Fire Model .......................................................................... 74

4.7 Conclusion ........................................................................................................................... 76

Chapter 5 Full-Scale Fire Tests of FRP Confined Circular Columns ............................................ 89

5.1 General ................................................................................................................................. 89

5.2 Research Significance .......................................................................................................... 90

5.3 Experimental Procedure ....................................................................................................... 91

5.3.1 Column Specimens ....................................................................................................... 91

5.3.2 Fire Endurance Test Conditions and Procedure ............................................................ 94

5.4 Results and Discussion ........................................................................................................ 95

5.4.1 Thermal Behaviour ....................................................................................................... 96

5.4.2 Structural Behaviour ..................................................................................................... 99

5.5 Summary ............................................................................................................................ 100

Confined Reinforced Concrete Columns in Fire.......................................................................... 112

6.1 General ............................................................................................................................... 112

6.2 Research Significance ........................................................................................................ 113

6.3 Numerical Model ............................................................................................................... 114

6.3.1 Heat Transfer Model ................................................................................................... 115

6.3.2 Mechanical Property Model at Elevated Temperature................................................ 120

6.3.3 Structural Model ......................................................................................................... 125

6.4 Validation of Numerical Model ......................................................................................... 130

6.4.1 Unwrapped Reinforced Concrete Columns ................................................................ 130

6.4.2 FRP Wrapped Reinforced Concrete Columns ............................................................ 137

6.5 Summary ............................................................................................................................ 143

Chapter 7 Conclusions ................................................................................................................. 169

7.1 Summary ............................................................................................................................ 169

7.2 Behaviour of FRPs at Elevated Temperatures ................................................................... 170

7.3 Behaviour of FRP Confined Concrete Columns Exposed to Standard Fires ..................... 171

7.4 Recommendations for Future Research ............................................................................. 173

References .................................................................................................................................... 177

Appendix A Load Calculations for FRP-Wrapped Concrete Columns 3 and 4........................... 192

Appendix B Load Calculations for FRP-Wrapped Concrete Column 5 ...................................... 207

Appendix C Thermal Properties .................................................................................................. 218

Appendix D Additional Heat Transfer Equations for Rectangular Columns............................... 222

Appendix E Column Specimens for Additional Fire Tests.......................................................... 225

Figure 2-1: Typical stress-strain behaviour of plain concrete and FRP confined concrete ........... 28

(adapted from Thériault and Neale, 2000) ................................................................ 28

Figure 2-3: Effective wrap confinement of rectangular ................................................................. 29

concrete with increasing temperature (Hertz, 2005) ................................................. 29

reinforced concrete member (reproduced from Kodur et al. 2006)........................... 30

under isothermal condition ........................................................................................ 30

(considering second-order effects) ............................................................................ 49

curvature relationship)............................................................................................... 50

Figure 3-3: Numerical integration of lateral deflection of a column ............................................. 51

number of vertical sections assumed in the analysis ................................................. 52

Figure 3-5: Details of column specimens tested by Fitzwilliam (2006) ........................................ 53

tested by Fitzwilliam (reproduced from Fitzwilliam, 2006)...................................... 54

eccentricity of 20 mm) .............................................................................................. 55

load (initial load eccentricity of 20 mm) ................................................................... 55

longitudinal directions (initial load eccentricity of 20 mm) ...................................... 56

data (Fitzwilliam 2006) ............................................................................................. 56

applicable to (b)) ....................................................................................................... 57

directions (initial load eccentricity of 20 mm) .......................................................... 58

layers of longitudinal FRP wraps under different initial load eccentricities ............. 59

reinforced concrete columns strengthened with one layer of FRP ............................ 59

is also applicable to (b)) ............................................................................................ 60

data (Ranger 2007) .................................................................................................... 61

clockwise).................................................................................................................. 82

Figure 4-4: Electrical resistance foil gauge (5 mm) on FRP coupons ........................................... 82

under isothermal condition ........................................................................................ 82

Figure 4-6: Results from (a) TGA, (b) DSC, and (c) DMTA ........................................................ 83

coupons specimens (a) 1, (b) 2, and (c) 3 .................................................................. 84

steady-state condition ................................................................................................ 85

after failure (photos rotated 90° clockwise) .............................................................. 86

................................................................................................................................... 87

clockwise).................................................................................................................. 88

Figure 4-13: FRP to FRP bond strength under steady-state and transient conditions.................... 88

Column 5 with SikaWrap Hex 103C ....................................................................... 104

Figure 5-3: Spray-applying MBrace insulation system on Column 4.......................................... 105

Column 5 ................................................................................................................. 105

and reinforcing steel, and (c) Strain guages on reinforcing steel ............................ 106

after fire test ............................................................................................................ 107

immediately after fire test........................................................................................ 107

the fire test ............................................................................................................... 108

immediately after fire test........................................................................................ 108

4, and (b) Columns 4 and 5 .................................................................................... 109

4 and 5 ..................................................................................................................... 110

5 ............................................................................................................................... 111

................................................................................................................................. 149

relationship) ............................................................................................................. 150

Figure6-5:Componentsoftotalstrainwithinconcreteatelevatedtemperatures.......................150

standard fire ............................................................................................................. 151

Figure 6-7: Confining action of the FRP wrap at the corner of the cross section ........................ 151

diagram for Column NSCD-B, (Luciano and Vignoli, 2008) ................................. 152

(b) along the line AC ( Lie and Woollerton, 1998) ................................................. 153

(b) along the line AC ( Lie and Woollerton, 1998) ................................................. 153

(b) along the line AC (Lie and Woollerton, 1998) .................................................. 154

LWE3 (Lie and Woollerton, 1998) ......................................................................... 155

increasing fire exposure time .................................................................................. 156

increasing fire exposure (Lie and Woollerton, 1998) .............................................. 157

LWE14 (Lie and Woollerton, 1998) with increasing fire exposure ........................ 158

LWE3 (Lie and Woollerton, 1998) with increasing temperature ............................ 158

the line AB, and (b) along the line AC .................................................................... 159

increasing temperature ............................................................................................ 159

(2005) and Lie (1992) for siliceous aggregate concrete .......................................... 160

experimental data .................................................................................................... 161

and 50 mm, and (b) load eccentricity of 100 mm and 150 mm............................... 162

of 1.5 mm and 50 mm, and (b) load eccentricity of 100 mm and 150 mm ............. 163

Figure 6-25: Flames emanating from the cracks forming at the side face ................................... 165

concrete column after 240 minutes assuming cracks in the insulation.................... 166

insulation ................................................................................................................. 167

specimen KC (Kodur et al., 2005) with increasing fire exposure ........................... 167

strengthened reinforced concrete column with increasing fire exposure ................ 168

Table 3-1: Mechanical properties of the FRP system used in Fitzwilliam's (2006) tests.............. 48

Table 3-2: Summary of observed axial and hoop strain in Fitzwilliam's (2006) tests .................. 48

Table 4-1: Tensile strength and modulus of FRP coupons under steady-state condition .............. 78

Table 4-2: Failure temperature and strain of FRP coupons under transient-state condition .......... 79

Table 4-3: Shear strength of FRP single lap-splice coupons under steady-state condition ........... 80

Table 5-1: Concrete mix proportions of column specimens (after Bisby, 2003) ......................... 102

Table 5-2: Summary of design load capacity for Columns 3 and 4 ............................................. 102

Table 5-3: Summary of design load capacity for Columns 5....................................................... 103

Table 5-4: Summary of fire endurance tests on Columns 3 and 4 ............................................... 103

tested by Luciano and Vignoli (2008) and Tao and Yu (2008) ................................. 144

the numerical model................................................................................................... 145

Kodur et al. (2005) ..................................................................................................... 145

................................................................................................................................... 146

Rochette and Labossière (2000)................................................................................. 147

Notations D# Surface area of an element through which heat is transferred by conduction; one of Ramberg-Osgood coefficients D#Ö Total area of concrete enclosed by the FRP wrap D#Ø Effective FRP confined area D#Ú Gross cross-section area of column D#å Ô × Surface area of an element through which heat is transferred by radiation D#æ ç Total area of steel in the column D=, D=, and D=7Fitting constants (Eqn. 5-1) 56

D$ One of Ramberg-Osgood coefficient D% One of Ramberg-Osgood coefficient D%Ö Compression force in the concrete D%¾ Environmental reduction factor D%æ Compression force in the steel D? Specific heat capacity D?Ö Specific heat capacity of concrete D?Ü Specific heat capacity of insulation D?Ù Specific heat capacity of FRP D?Ý á Heat capacity of an element located at a mesh point in the mth column and nth à, row at jth number of time step

D?æ Specific heat capacity of steel D?ê Heat capacity of water D@ Diameter of compression member of circular cross section D'6 Slope of the linear second portion of the confined stress-strain relation (Eqn. 2-5) at ambient temperature D':D6;Slope of the linear second portion of the confined stress-strain relation (Eqn. 6- 6

17) at temperature D6 Nñ Change in storage (elastic) modulus D' NñNñ Change in loss modulus D' D'Ö Elastic modulus of unconfined concrete at ambient temperature D':D6;Elastic modulus of unconfined concrete at temperature D6 Ö

D'Ö â á × Heat energy transferred by conduction D'Ù Tensile elastic modulus of FRP D'Ù å ã Ö Elastic modulus of FRP in compression at ambient temperature D'Ù :D6ÖE;lastic modulus of FRP in compression at temperature D6 åã

D'Ù å ã ç Elastic modulus of FRP in tension at ambient temperature D'Ù :D6çE;lastic modulus of FRP in tension at temperature D6 åã

D'Ü Heat energy transferring into an element located at a mesh point in the mth á ? à, á column and nth row D'â Heat energy transferring out of an element located at a mesh point in the mth è ç ? à, á column and nth row D'å Ô × Heat energy transferred by radiation

D'æ Elastic modulus of reinforcing steel at ambient temperature D':D6;Elastic modulus of reinforcing steel at temperature D6 æ

D'æ Ö â Secant modulus of unconfined concrete at ambient temperature D' :D6;Secant modulus of unconfined concrete at temperature D6 æÖâ D'æ ç ? à,Enáergy stored in an element located at a mesh point in the mth column and nth row DAÛ Eccentricity a at point h along the column length DBÖ Stress in concrete DB:D6; Stress in concrete at temperature D6 Ö

DBÖ Ö Stress in confined concrete DB:D6;Stress in confined concrete at temperature D6 ÖÖ

DNBñ Unconfined concrete specified compressive strength at ambient temperature Ö

DNBñ :D6;Unconfined concrete compressive strength at temperature D6 Ö

DNBñ Ö Ultimate compressive strength of FRP confined concrete at ambient temperature Ö

Nñ:D6;Ultimate compressive strength of FRP confined concrete at temperature D6 DBÖ Ö DBÙ Ø Effective stress in the FRP DBÙ å ã Stress in FRP DBÙå:Dã6;Stress in FRP at temperature D6 DBÙ å ã ç Tensile strength of FRP at ambient temperature DBÙ å:D6çT;ensile strength of FRP at temperature D6 ã

DBß Ù å ã Lateral confining pressure on the concrete within FRP jacket at ambient temperature DB Ù:D6ãL;ateral confining pressure on the concrete within FRP jacket at temperature D6 ßå

DBæ Stress in steel DB:D6; Stress in steel at temperature D6 æ

DBì Yield strength of steel at ambient temperature DB:D6;Yield strength of steel at temperature D6 ì

DD Length of the column cross-section DG Distance from the extreme compression fibre to the neutral axis; thermal conductivity between two adjacent elements; effective length factor DG5 Confinement effectiveness coefficient DG6 Strain enhancement coefficient DGÖ Confinement coefficient; thermal conductivity of concrete DGÙ Thermal conductivity of FRP DGÜ Thermal conductivity of insulation DGß Confinement parameter DG Empirical constant describing the severity of the mechanical property DI degradation of FRP with increasing temperature DGæ Shape factor; thermal conductivity of steel DGç å Constant used in Eqn. 6-35 D. Height of column DH Distance between two points between which heat is being transferred

D/Û Bending moment capacity at point h of the column DI Weibull exponent (Eqn. 5-2); Mesh point in the mth row DJ Mesh point in the nth column; number of FRP layers D2 Axial force D2 MÜechanical property value of FRP at room temperature ÜáÜç Ôß

D2á, à Ô ë Nominal axial force resistance of column D2Ë Residual value of the mechanical property of FRP D2å, à Ô ëMaximum factored axial force resistance of column D2 Predicted axial force resistance of column å, ã å Ø ×

D4Ö Corner radius of a square/rectangular column D4à, á Element located at a mesh point in the mth column and nth row D4á Power law modification factor to account for polymer resin decomposition of FRP DN Radius of gyration D5½ Specified dead load D5Å Specified live load D5Ë Design axial load D5Í Specified total load D6 Temperature D6 Temperature around which the mechanical property curve is nearly symmetrical D?DADJDPDND=DH

D6Ö å Critical softening temperature of FRP D6ÙÝ Temperature of the fire at jth number of time step D6Ú Glass transition temperature of polymer matrix D6à Melting temperature of FRP D6àÝ, á Temperature of an element located at a mesh point in the mth column and nth row at jth number of time step D6æ Tension force in the steel DP Thickness of the FRP jacket; time D8à, á Volume of an element located at a mesh point in the mth column and nth row DS Width of the column DT Coordinates in the x-direction DU Coordinates in the y-direction DUÛ Distance at point h along the column length from the origin DÙ Load factor DÙ½ Dead load factor DÙÅ Live load factor DÙ5 Multiplier on DNBñto determine intensity of an equivalent rectangular stress Ö

distribution for concrete DÚ5 Ratio of depth of equivalent rectangular stress block to depth of the neutral axis ? Increment or difference DÝÖ Strain in concrete

DÝ:D6;Strain in concrete at temperature D6 Ö DÝÖ, Ù Ô ÜFailure strain of concrete due to stress ßèåØ

DNÝñÖ Strain at peak stress of the unconfined concrete at ambient temperature, DNÝñÖ:D6;Strain at peak stress of the unconfined concrete at temperature D6 DÝÖ è Ultimate axial strain of unconfined concrete at ambient temperature DÝÖ:D6;Ultimate axial strain of unconfined concrete at temperature D6 è

DÝÖ Ö è Ultimate axial strain of FRP confined concrete at ambient temperature DÝÖ:D6;Ultimate axial strain of FRP confined concrete at temperature D6 Öè

DÝÙ Ø Effective strain level in FRP reinforcement attained at failure DÝÙ å ã è Ultimate tensile axial strain of FRP confined concrete at ambient temperature DÝÙ :D6U;ltimate tensile axial strain of FRP confined concrete at temperature D6 åãè

DÝÙ å ã Strain in FRP DÝÙå:Dã6;Strain in FRP at temperature D6 DÝÛ, å è ãHoop rupture strain of the FRP jacket at ambient temperature DÝÛ, å:D6H;oop rupture strain of the FRP jacket at temperature D6 èã

DÝà Ô ç Emissivity of the material with which the element is made of DÝÙ Ü å Ø Emissivity of the surrounding environment DÝà Ø, Ö Mechanical strain (or instantaneous stress-related strain) of concrete DÝà Ø, æ Mechanical strain in steel DÝæ Strain in reinforcing steel

DÝ:D6;Strain in reinforcing steel at temperature D6 æ DÝç Û, Ö Unrestrained thermal strain of concrete DÝç Û, æ Unrestrained thermal strain of steel DÝç Ö Total strain of concrete DÝç å, Ö Transient creep strain of concrete DÝç æ Total strain in steel DNÝñç Point of transition between the parabolic and linear portion of the confined stress- strain plot (Eqn. 2-4) at ambient temperature DNÝñç:D6;Point of transition between the parabolic and linear portion of the confined stress- strain plot (Eqn. 6-17) at temperature D6 DÝì Yield strain of steel at ambient temperature DÝ:D6;Yield strain of steel at temperature D6 ì

DÝæ è Ultimate strain of steel at ambient temperature DÝæ:D6;Ultimate strain of steel at temperature D6 è

Dß Strain efficiency reduction factor DàÛ Slope at point h along the column length DâÔ Efficiency factor for FRP reinforcement in determination of DNBñ Ö Ö

Dâ Efficiency factor for FRP strain to account for the difference between observed rupture strain in confinement and rupture strain determined from tensile tests Dé Density DéÖ Density of concrete

DéÙ FRP reinforcement ratio; density of reinforcing steel DéÜ Density of insulation DéÝ á Density of in an element located at a mesh point in the mth column and nth row à, at jth number of time step Déæ Density of reinforcing steel Déê Density of water Dê Stefan-Boltzman Constant Dö Strength reduction factor DöÖ Resistance factor for concrete DöÙ å ã Resistance factor for FRP DöÝ Moisture content (fraction of volumn) in an element located at a mesh point in à, á the mth column and nth row at jth number of time step Döæ Resistance factor for reinforcing steel DîÛ Curvature at point h along the column length DðÙ FRP strength reduction factor DñÛ Lateral deflection at point h along the column length

Chapter 1 Introduction 1.1 General In recent years, existing concrete structures in North America have reached a state where many of them can no longer safely resist the loads acting on them. This is due to deterioration caused by a combination of electro-chemical corrosion and increased load requirements, among other factors. Demolishing and rebuilding these structures is not an economically viable option.

Therefore, fibre reinforced polymers (FRPs) are being used to repair and retrofit many of these structures. Fibre reinforced polymers (FRPs) are composite materials comprised of slender high strength fibres (typically carbon, glass, or aramid) embedded in a polymer matrix (typically epoxy or vinylester) to provide beneficial ideal material properties for many civil engineering applications. Because of their numerous advantages, including high strength-to-weight ratios in comparison to steel and inherent resistance to corrosion, FRP materials have been successfully applied in the rehabilitation of bridges in Canada and elsewhere (Rizkalla and Labossière, 1999).

However, due to the comparatively high sensitivity of FRP materials to elevated temperatures and fire, their use in repairing or reinforcing concrete structural members in buildings and parking garages makes these structures particularly vulnerable to fire; this has for many years discouraged applications of FRPs in buildings.

When designing structural members in buildings, fire safety is taken into consideration by providing protective steps to prevent the spread of fire and smoke, and the local or global structural collapse of the building long enough to allow safe evacuation of building occupants, as well as protection to the property. These objectives can be achieved in part by providing adequate fire resistance to the building components. By definition, fire resistance is the ability of a structural assembly or element to endure the effects of fire for a required period of time without

the loss of structural integrity, stability and temperature transmission. Fire resistance of a building component can be assessed by conducting full-scale fire tests on representative samples of the structural members in a furnace as per ULC-S101 (2004) or ASTM E119 (2001) standards.

However, these full-scale fire tests are expensive and time consuming. Performance-based assessment involving detailed calculations and numerical simulations provides a cost-effective method of assessment. To conduct detailed calculations and numerical simulations of unwrapped reinforced concrete and FRP strengthened reinforced concrete structures in fire, a detailed knowledge of the thermal and mechanical behaviour of the constituent materials at high temperature is essential. Although some information exists on the material behaviour of concrete and reinforcing steel in fire, knowledge of the material behaviour on FRP systems that are currently being used for the purpose of strengthening concrete structures is extremely scarce.

One of the major challenges in using FRP materials in civil engineering is the lack of understanding of the behaviour of FRP composites at elevated temperatures. It is widely known that above the glass transition temperature the polymer resins of FRPs degrade rapidly (ACI, 2008) and, when the FRP experiences temperatures in this range in a fire situation, the polymer resin changes from a stiff, solid state into a flexible, rubbery state. When the temperature reaches the decomposition temperature, the polymer resin will begin to thermally degrade and this raises concerns such as flame spread along the surface of the composite, additional heat release, and smoke generation and toxicity from combustion of the FRP. Polymer resins, such as epoxies, act as binding agents which enable the transfer of stresses between fibres in an FRP and are also often used as adhesives to bond FRP composites to structural members. Burning out of the polymer resin would therefore result in complete deterioration of both the mechanical and bond properties of the FRP.

Given the above issues, a research study has been ongoing for more than eight years at Queen's University in collaboration with the National Research Council (NRC) of Canada and

industrial partners to investigate the fire performance of FRPs and FRP strengthened concrete structural members. In the past, much of the overall research work in the study was conducted on the behaviour of insulated FRP strengthened concrete beams and circular columns in fire. As part of this research study, the focus of the current doctoral research program reported herein is to investigate the fire performance of specific FRP materials, various different fire insulation materials and large scale FRP wrapped reinforced concrete columns. The goals of the current doctoral research program is, for the very first time, to conduct material tests to characterize the mechanical and bond behaviour of a specific FRP strengthening system at elevated temperatures, conduct full-scale column fire tests on an uninsulated FRP wrapped reinforced concrete column, examine two different fire insulation systems, and develop a numerical model that can simulate the heat transfer and structural behaviour of both short and slender FRP wrapped rectangular and square concrete columns. Each o f these goals represents are unique contributions to the field of engineering. Based on the experimental and numerical research work in the current doctoral research program, rational fire safety design recommendations and guidance for FRP strengthened concrete columns will be provided.

1.2 Research Objectives The main objective of this research study is to understand the behaviour of FRP materials and FRP strengthened reinforced concrete columns in fire. Until now, most studies on the fire behaviour of FRP confined columns have been on circular cross sections. Nevertheless, a preliminary experimental investigation was conducted as part of the ongoing research study by performing a fire test on an FRP confined square reinforced concrete column, where only the temperatures of FRP and insulation's surface were measured (Kodur et al., 2005). In this preliminary study, the FRP wrapped square column endured 4 hours of fire exposure under full service load without experiencing structural failure. However, to gain further insight into the

behaviour of FRP wrapped square columns, as well as the insulation materials used and the specific performance of the FRPs themselves, further investigation, both experimental and computational, is needed so that rational design recommendations and guidelines can be suggested.

Hence, a combined experimental and numerical investigation was conducted by the author to investigate the fire risk associated with using FRPs to strengthen concrete columns of both circular and square cross sections. The experimental work consisted of both small-scale material testing at elevated temperatures and full-scale standard fire tests, and the numerical methodology involved the implementation of a finite difference model that is able to predict the temperatures within a column and a two-dimensional fibre-element analysis that is able to predict the strength of these columns in fire. To achieve this overall aim, the following specific objectives were decided: ? Quantify the thermal and mechanical properties of FRP materials at high temperatures: Only limited information is available on the mechanical and bond properties of currently available externally bonded FRP strengthening systems for reinforced concrete structures at high temperatures. Experimental data on the behaviour of FRP materials at high temperatures or in fire is needed in developing a rational analytical stress-strain model that can predict their mechanical behaviour in fire, as is needed for numerical modelling to predict the fire performance of concrete structures strengthened with FRPs. The testing procedures should investigate the tensile strength, tensile stiffness and bond strength in pure shear.

? Experimentally investigate the fire behaviour of loaded full-scale circular reinforced concrete columns strengthened with currently available externally bonded wet lay-up FRP strengthening systems: FRP strengthening systems that are currently being used in strengthening concrete structures are adversely affected by elevated temperature exposure

and fire, thus requiring a supplementary fire protection system to achieve a satisfactory fire endurance rating for the structural member (in most cases). Studying the thermal behaviour of different insulation materials is essential for modelling and designing fire protection systems for FRP strengthened concrete structures. As part of the ongoing research project, full-scale fire tests were conducted previously on two FRP wrapped circular columns, which were protected from fire by a supplemental fire insulation system developed by one of the industry partners. Additional full-scale fire tests of FRP strengthened concrete columns were conducted using supplemental fire insulation systems developed by two different industry partners to investigate the fire performance of existing fire insulation systems that can be used to protect FRP strengthened concrete columns. Also, it is known that the confinement pressure due to the FRP wrap is less effective in square columns than in circular columns at ambient temperature. It is essential to understand the confinement behaviour due to FRP wrapping in circular cross sections prior to developing a numerical model for FRP wrapped square concrete columns.

? Develop numerical heat transfer and structural response models for rectangular FRP wrapped concrete columns under standard fire exposures: Numerical methods of analysis can considerably reduce the cost incurred in fire testing of full-scale specimens, provided that accurate material behaviour at high temperature and in fire is accounted in the analysis. A heat transfer model and structural response model were developed using the finite difference method and a two-dimensional fibre-element analysis, respectively, to investigate the thermal and structural behaviour of an FRP strengthened reinforced concrete column exposed to fire.

This thesis is divided into seven chapters and several appendices. Chapter 2 presents a brief review of the literature relevant to the behaviour of FRP materials and FRP confined concrete columns at elevated temperatures and in fire. Chapter 3 presents a numerical model which can be used to evaluate the structural behaviour of eccentrically-loaded reinforced concrete and FRP strengthened reinforced concrete circular columns under ambient conditions. This chapter begins with the development of the numerical model, followed by validation of the results obtained using the numerical model against test results from available literature. This work was required before it could be built on to achieve later objectives more closely relating to the analysis of FRP wrapped columns in fire. Chapter 4 presents the experimental test procedures used and results of the mechanical and bond property tests on FRP materials at elevated temperatures. An analytical model characterizing the mechanical behaviour of FRP material at elevated temperatures is also presented in Chapter 4. Chapter 5 presents the experimental procedures used and results of the full-scale fire tests conducted on FRP confined circular columns. Chapter 6 presents the development of a numerical model that can simulate the heat transfer and structural behaviour of FRP confined concrete square columns in fire. The numerical model developed in this chapter represents an extension of the numerical model presented in Chapter 3 for ambient temperature analysis.

Supplementary information is provided in the Appendices. Appendix A and B presents the detailed load calculations for determining the sustained applied loads during the various column fire tests. Appendix C presents the thermal property models used in the heat transfer models that are developed in Chapter 6. Finally, Appendix D presents the two-dimensional finite difference heat transfer formulae used in Chapter 6 to determine the temperatures within the concrete columns.

Chapter 2 Literature Review 2.1 General FRP materials are now widely applied to repair and retrofit deteriorating or deficient infrastructure. However, many engineers are hesitant to use FRPs in buildings and parking garages because of the lack of knowledge and understanding of their behaviour, and of FRP strengthened concrete structures in fire. This chapter presents a review of existing knowledge related to FRP wrapped reinforced concrete columns under both ambient and elevated or high temperature exposures. The chapter focuses on: (1) the ultimate condition and the stress-stain behaviour of circular and rectangular concrete columns confined with FRP under ambient temperature conditions, (2) the structural response of eccentrically-loaded short and slender FRP confined concrete columns; and (3) the behaviour of FRP strengthened concrete structures and their constituent materials at elevated high temperatures or in fire. Although the present study is interested predominantly in the fire performance of axially loaded members, existing knowledge on the behaviour of FRP strengthened concrete flexural members at high temperature is also reviewed.

2.2 Background on FRP-Confined Concrete Strengthening reinforced concrete columns with circumferential FRP wraps offers a lightweight and non-corrosive alternative to traditional steel jacketing. The FRP application process on a circular column involves applying a coat of primer on the surface of the concrete column before wrapping the column with resin saturated FRP sheets. The FRP layer is wrapped around the column in a manner such that the end of the FRP layer is extended to form an overlap

joint that is sufficient to achieve a strength-controlling failure mode. If more than one layer of FRP is used to wrap the column, the overlap joints are staggered to avoid the concentration of seam weakness. For rectangular columns, the corners are usually rounded prior to the application of the FRP wrap to enhance the effectiveness of the FRP confinement and to avoid stress concentration on the FRP wrap from sharp corners. The wraps are usually applied with the fibres oriented in the circumferential directions.

There has been extensive research performed on FRP confined concrete members under concentric compressive axial loading at ambient temperatures (e.g. Teng et al. 2002; Pessiki et al., 2001; Lilliston and Jolly, 2000; Xiao and Wu, 2000; Spoelstra and Monti, 1999; Saafi et al., 1999; Toutanji, 1999; Saaman et al., 1998; Karbhari and Gao, 1997; Fardis and Khalili, 1982;

Fam et al., 2003). These (and other) studies have shown that the lateral confining pressure developed by the FRP jacket increases the compressive strength and deformability of circular concrete columns under axial compression and combined axial-flexural loading. There are effectively two methods used in confining concrete using FRP jackets ? active and passive confinement. Active FRP confinement can be provided by injecting an expansive grout between the FRP jacket and the axial member or by prestressing the FRP jacket during wrapping.

However, in most cases, FRP confinement is passive in nature, that is, confining pressure is developed within the FRP jacket by the lateral expansion of the concrete during compression (Poisson's effect). This lateral confining pressure, denoted as DBß , on the concrete within the Ùåã FRP jacket is assumed to be uniform and is based on force equilibrium as given by Eqn. 2-1 (Lam and Teng, 2003).

·DÝ 2 · D P ·ÙD ' Û, å è ã DB L å ã Eqn. 2?1 ß Ù å ã D4 Where D'Ù is the tensile elastic modulus of the FRP, DPis the thickness of the FRP jacket, DÝÛ, ã åã åè is the hoop rupture strain of the FRP jacket, and D4is the radius of the concrete core. Failure of

the FRP confined concrete typically occurs when the FRP jacket reaches its hoop rupture strain DÝÛ, (Lam and Teng, 2003; Pessiki et al., 2001; Spoelstra and Monti, 1999). However, åèã premature failure can occur by separation of the FRP overlap at the lap-splice in the hoop direction due to insufficient overlap length. In most existing FRP confinement models, the hoop rupture strain is assumed to be the ultimate tensile strain of the FRP material as measure from tensile coupon tests; however, experimental results from many researchers (e.g. Lam and Teng, 2003) have shown that the FRP jacket often fails before it reaches the ultimate tensile strain of the FRP. The hoop rupture strain of carbon and glass FRP confined circular concrete was observed to be on average about 59% and 62% of the ultimate tensile strain of the FRP as measured from coupon tests, respectively. In Lam and Teng (2003), the hoop rupture strain for high modulus carbon FRP confined concrete was found to be 79% of the ultimate tensile strain. It is believed that the average hoop strain of the FRP jacket is observed to be less than the average ultimate axial strain of the FRP because the curvature of the FRP jacket, in a manner, affects the failure strain of the FRP and cracks in the concrete lead to non-uniform stress distribution in the FRP jacket, which may lead to premature failure of the FRP jacket. It should be noted that this observation was based on hoop strains at failure recorded using isolated foil gauges. In a recent study conducted by Bisby and Take (2009) using an optical measurement technique, it was found that, depending on the location of the strain measurement, the hoop strains over the surface of the FRP confined circular concrete cylinders varied by as much as 50% of the ultimate axial strain of the FRP. Although Pessiki et al. (2001) suggest that the hoop rupture strain can be related (as shown in Eqn. 2-2) to the ultimate strain of the FRP through an efficiency factor D,ßit should be noted that a thorough understanding of the strain distribution around the FRP jacket is lacking in the existing literature, which only presents isolated readings for the values for hoop strain around the circumference of the circular concrete specimens.

DÝÛ, L D ß · D Ý è Eqn. 2?2 å è ãÙ å ã

Jiang and Teng (2006) recommend using values of 0.5 and 0.7 for the strain efficiency reduction factor, D,ßin the case of carbon FRP (CFRP) and glass FRP (GFRP), respectively.

Studies (Lam and Teng 2003; Xiao and Wu, 2000, ACI, 2008) have found that, if a sufficient amount of FRP is used to confine the concrete, the FRP confined concrete demonstrates a monotonically ascending bi-linear shape as shown in Figure 2-1. However, in some cases, an FRP confined concrete column may demonstrate a post-peak descending branch; the maximum compressive strength is reached before the maximum axial strain (Xiao and Wu, 2000). Lam and Teng (2003) and ACI (2008) suggest that FRP confined concrete having confinement ratio ? Nñ R 0.c0a8n be considered as sufficiently confined to avoid a post-peak descending DBß DBÖå ã Ù

branch. Existing models for FRP confined concrete have three major deficiencies in predicting the compressive strength and strain at ultimate condition (Lam and Teng, 2003). Firstly, as mentioned earlier, the FRP jacket is assumed in many models to rupture when the strain in the FRP jacket reaches the ultimate tensile strain of the FRP material, whereas the true strain at failure is often observed to be less than this and the appropriate value for use in design is not currently known. Secondly, the predictions made using existing models do not reflect properly the effect of jacket stiffness on the ultimate axial strain of FRP confined concrete. Some existing models (Karbhari and Gao, 1997; Miyauchi et al., 1992) have assumed that the axial strain at the compressive strength of confined concrete can be linearly related to the maximum confining pressure, which was derived from studies on actively confined concrete and steel confined concrete (Lam and Teng, 2003; Richart et al., 1929; Candappa et al., 2001). In a number of studies (Samaan et al., 1998; Spoelstra et al., 1993; Pantazopoulou, 1995), researchers have observed that similar levels of lateral pressure do not produce similar ultimate axial strains of confined concrete, because the elastic modulus of FRP varies over a wide range (Lam and Teng, 2003). Thirdly, existing compressive strength and strain models predicting ultimate condition were developed using a limited experimental database of tests on small scale, short,

concentrically-loaded, unreinforced concrete cylinders rather than on realistic reinforced concrete columns. Bisby et al. (2005d) conducted a research study where result from an extensive experimental database on the ultimate strength and strain of FRP confined concrete (using different types and amounts of FRP) at failure were statistically was compared against the predictions of twelve different existing models. This study concluded that the model proposed by Karbhari and Gao (1997) and Lam and Teng (2001) were more accurate than the others, however, Lam and Teng (2001) was found to be slightly conservative. After careful consideration of the deficiencies found in existing models, Lam and Teng (2001), Teng et al. (2002), and Lam and Teng (2003) proposed a stress-strain model, which has been adopted in ACI (2008) and is presented in Eqn. 2-3, for FRP confined concrete.

:D'F D6' D'· D Ý â 6 Nñ Ö F if 0 Q DÝQ D Ý DB LP âÖ Nñ Ö ç Eqn. 2?3 Ö Ö 4DBÖ Nñ Nñ DB Q D Ý Ö E·D'Ý if DÝ OÖD ÝÖ Ö è 6Ö ç Nñ Nñ where DBis the compressive strength of unconfined concrete, DÝis the point of transition between Öç the parabolic and linear portion of the confined stress-strain response profile (which is described in Eqn. 2-4) as shown in Figure 2-1, D'is the elastic modulus of unconfined concrete, D'is the Öâ 6 slope of the linear second portion of the confined stress-strain relation (characterized by Eqn. 2- Öè

2 · DNBñ Nñ L Ö Eqn. 2?4 DÝç D' F D ' Ö6 Nñ Nñ DBÖ FÖD B D'6 L Ö Eqn. 2?5 DÝÖ Ö è Nñand DÝ where, DBÖ is the ultimate compressive strength and axial strain of FRP confined ÖÖÖè concrete, respectively. Lam and Teng (2003) proposed a model for the ultimate compressive strength and axial strain of FRP confined concrete, which is given in Eqn. 2-6 and Eqn. 2.7.

Nñ · 1H E DFBßD GÙ å ã DBÖ NÖñ ·5 NñGI ÖL D B Eqn. 2?6 DBÖ Nñ DBß DåÝÛ, 4. 8 9 · 1.H75 ÙGl· ã åpIã L D Ý E DG è DÝ è · F Eqn. 2?7 Ö Ö Ö 6 DB DNÝñÖ Nñ Ö

and DG where, DG are the confinement effectiveness coefficient and strain enhancement 56 coefficient, respectively. Based on a large experimental database, DGand DGwere found to be 56 equal to 3.3 and 12, respectively.

Studies have shown that the effectiveness of the FRP jacket in confining concrete is not only dependent on the stiffness of the FRP jacket but also the shape of the concrete axial member (Thériault and Neale, 2000; Mirmiran et al., 1998; Rochette and Labossière, 2000; Wang and Restrepo, 2001). FRP confinement is very effective in columns having circular cross section in comparison to square or rectangular cross sections. This is because the lateral expansion of circular concrete under compression is uniformly confined in a circular column, unlike in rectangular cross sections (Figure 2-2). In square or rectangular columns, much of the confinement pressure from the FRP wrap is developed at the corners, which must typically be rounded to prevent premature failure of the FRP wrap. The FRP sheets along the flat column sides provide negligible resistance to the lateral expansion, thus resulting only in partial confinement from the FRP jacket (Thériault and Neale 2000). The effectiveness of FRP confinement in square concrete columns increases as the amount of FRP wrap and the corner radius increases (Wang and Wu, 2008). ACI 440 Committee (2008) and other researchers (Teng et al. 2002; Wang and Restrepo, 2001) have established that the effective confinement due to the FRP wrapping of square or rectangular concrete axial members can be evaluated based on the arching-effect theory, which has been previously used by Sheikh and Uzumeri (1980) to evaluate the confinement of tied square concrete columns. In this approach, it is assumed that the effectively confined areas are enclosed by second-order parabolas (Parabola 1, Parabola 2,

Parabola 3 and Parabola 4) extending between the rounded corners of the cross-section as shown in Figure 2-3 (Yan et al., 2006). In many of the existing theoretical models for FRP confined rectangular concrete (ACI, 2008; Teng et al., 2001; Mirmiran et al., 1998), the average compressive strength of the confined concrete is determined by relating a shape factor DGto the æ

lateral confining pressure DBß of fully confined concrete, which is calculated by transforming Ùåã the rectangular cross-section into an equivalent circular cross-section as follows.

2 · D P ·ÙD·'D Ý å è ã Nñ å Ûã, DBß L·æDãG Eqn. 2?8 Ù å ?DS6 E6D H Wang and Restrepo (2001) take a slightly different approach than other existing models to evaluate this partial confinement of FRP confined rectangular cross-section; the compressive strength within the confined and unconfined regions are calculated separately and then added together to obtain the average compressive strength of the confined concrete. Since there is no stress-strain model that has been specifically developed for FRP confined rectangular or square concrete, the existing stress-strain model for FRP confined circular concrete has been adapted for rectangular cross-sections using the assumed effectively confined areas mentioned above (ACI, 2008; Teng et al., 2001).

2.3 Performance of FRP Confined Concrete under Eccentric Loading All of the research studies discussed so far on FRP confined concrete were on columns or cylinders that are classified as ?short? according to the ACI 318 design code (2005) and under a concentric loading condition. However, concentrically-loaded columns rarely exist in reinforced concrete structures. In most cases, at least minimal load eccentricity is experienced by a column due to end conditions, inaccuracy during fabrication, or variation in the materials, even if the applied load is concentric (Wang et al., 2007). As mentioned earlier, FRP wraps can significantly increase the strength and deformability of ?short? reinforced concrete columns under a concentric

loading condition. Studies (Parvin and Wang, 2001; Li and Hadi, 2003; Hadi, 2006; Ranger, 2007; Fitzwilliam, 2006; Fam et al., 2003) have also shown that, even under eccentric-loading conditions, reinforced concrete ?short? columns of both circular and rectangular cross section show an increase in axial strength and ductility from FRP confinement, however, the strength benefits of confinement diminish with increasing eccentricity. Parvin and Wang (2001) suggested the use of a reduction factor when designing eccentrically loaded concrete columns;

however, they made no suggestions on the value of this reduction factor. Li and Hadi (2003) found that, between carbon and glass FRP, carbon FRP (CFRP) wraps were able to achieve higher lateral confining pressure than glass FRP (GFRP) and also suggested the use of externally- bonded FRP wraps, where the fibres are in the longitudinal direction, to enhance the flexural stiffness of the FRP confined concrete column under eccentric loading condition. In a similar study, Hadi (2006) found that increasing the stiffness of the FRP wrap could also significantly increase the strength and ductility of the eccentrically loaded FRP wrapped columns. In square concrete columns, the FRP wraps were observed to fail by rupturing of the FRP sheet at the corner of the cross-section (Parvin and Wang, 2001) that experience the highest compressive stress as shown in Figure 2-2, and also that the columns failed less violently with increasing load eccentricity.

Fitzwilliam (2006) observed that the ultimate axial strain at the extreme compression fibre was significantly greater in an eccentrically-loaded FRP confined concrete column than when it was concentrically loaded. This occurred because the eccentrically-loaded column experiences uneven dilation of the confined concrete cross section. Hence, using uniaxial compression and uniform confinement models to analyze FRP confined concrete columns under eccentric loads would produce conservative axial strength and deformability predictions.

Another issue relating to eccentrically-loaded FRP confined concrete column is whether the available confinement models, discussed so far only for concentrically-loaded FRP confined

(2001) conducted an analytical study where various existing stress-strain models for FRP confined circular concrete were used to calculate the axial load-moment (P-M) interaction diagram for circular CFRP confined reinforced concrete columns. Conventional sectional- analysis was used to calculate the axial load-moment interaction diagram. After comparison of the results using different FRP confined stress-strain models, it was found that the models predicted higher strength capacity for FRP confined reinforced concrete columns than unwrapped reinforced concrete columns; however, all the stress-strain models predicted different ultimate condition. It was found that the axial strength and the curvature of FRP confined reinforced concrete columns depended on the ultimate compressive strength and axial strain, respectively.

A reinforced concrete column which behaves as a ?short? column under existing axial loads may change its behaviour to ?slender? under increased axial service loads after FRP confinement (ISIS Canada, 2001b). This is because a slender column fails by buckling, which is dominated by the flexural rigidity of the column. Circumferential wrapping with FRPs increases concrete strength but does not greatly affect the elastic modulus, so that the flexural rigidity is not increased by FRP wrapping and the buckling load is not increased. Research studies (Fitzwilliam, 2006; Tao et al., 2004; Ghali et al., 2003; Tao and Yu, 2008) on slender concrete columns wrapped with externally-bonded FRPs under monotonic compressive loads are scarce.

Existing research studies have found that wrapping slender concrete columns with FRPs can increase the axial strength of both short and slender columns, but that the effects of the FRP confinement are more profound for short columns than slender ones. Although increasing the hoop stiffness of the FRP wrap can substantially increase the axial strength and deformability of the reinforced concrete columns, the benefits of FRP confinement diminish with increasing slenderness and load eccentricity because reinforced concrete columns experience no significant increase in flexural rigidity from the circumferential FRP wraps. Hence, the effects of

slenderness are more important for the axial capacity of FRP confined concrete columns rather than for unwrapped reinforced concrete columns. Fitzwilliam (2006), Tao et al. (2004) and Tao and Yu (2008) suggested the use of vertical FRP wraps, where the fibres run along the longitudinal axis of the column, to provide flexural resistance (rigidity) to the secondary moments due to the slenderness effect. When a column specimen is short, longitudinal FRP wraps have no effect on axial strength and deformability as the column experiences only small second-order lateral deflections. Tao et al. (2004) observed that the average axial strain corresponding to the peak load DÝÖof an FRP confined concrete column decreased with increasing column slenderness. Ö

This is because, with increasing column slenderness, the failure mode is shifting from axially dominated material failure to flexurally dominated stability failure. It should be noted that the reduction of axial strength with increasing column slenderness or eccentricity has yet to be rationally quantified, thus demonstrating the need for further research work in the aspect of eccentrically loaded FRP confined slender concrete columns (both circular and square/rectangular).

2.4 Methods of Calculation for Slender Concrete Columns Various design and analytical methods have been proposed for the structural or computational analysis of slender concrete columns and these can be found in many textbooks, such as Wang et al. (2007) and Chen and Atsuta (1976). There are two major methods used in designing slender reinforced concrete columns, namely, the Moment Magnifier Method, which has been adopted by design codes (ACI, 2005; CSA, 2005) in North America, and Nominal Curvature Method, which is used in Europe (BSI, 1997). The Moment Magnifier Method is based on an elastic column analysis wherein the lateral deflection can be determined provided that the section's flexural stiffness is known. In the Nominal Curvature Method, the lateral deflection of the critical section is related to the curvature at that section using an assumed

deformed shape. Both methods approximate the second-order moments by an amplification of the first-order moments to make use of the section strength in design.

Bazant et al. (1991) present a method of analyzing hinged reinforced concrete columns with equal end eccentricities. In this method, the deflected shape of the column is assumed to be a half sine wave and the analysis is based on equilibrium of moments at the critical section, which is at the mid-height of a hinged column with equal end eccentricities. Chen and Atsuta (1976) proposed another analytical method of analysis that involves numerical integration to predict both the primary and secondary lateral deflection of slender columns. This method is more sophisticated and versatile than the method adopted by Bazant et al. (1991). Pfrang and Siess (1961) and Cranston (1972) have successfully used this method to analyze reinforced concrete slender columns. In this method, the column is divided into a number of segments and then the lateral deflection along the longitudinal height of the column is calculated at each of the division points using a moment-curvature-axial load relationship for the column's cross-section. The advantage of using this numerical integration method is that it can be used to analyze columns with unequal end eccentricities. One of the methods presented in Chen and Atsuta (1976), namely the Column Deflection Curve (CDC) Method, has been used in this research study to analyze slender concrete columns; details of the analysis are discussed in Chapter 3.

2.5 Philosophy for the Fire Endurance of FRP Strengthened Concrete Columns The main objectives of fire engineering are to prevent the loss of life or injury and property loss during fire (Lie, 1992; Buchanan, 2001). Obviously, these objectives can be best achieved by preventing ignition (that is, the start of flaming combustion). However, in the case of a fire, the fire safety objectives are first addressed by active fire protection systems, such as sprinkler systems, to minimize the spread of fire and smoke generation before the fire fully

develops. If active fire protection measures are unable to contain the fire and the fire does become fully developed, the fire safety objectives are then addressed by ensuring the structural members have adequate fire resistance to prevent both the spread of fire and collapse of the structure for adequate period of time for safe evacuation of occupants and for safety of fire fighters. Hence, when retrofitting reinforced concrete structural members in buildings with FRPs, it is important to consider the fire performance of FRP materials with respect to their flammability, smoke generation and toxicity, and with respect to their structural integrity at high temperatures during fire (Bisby et al., 2005c). Because this thesis deals with the structural integrity of FRP in fire, the discussion does not elaborate on the performance of FRPs with respect to smoke generation and toxicity.

Figure 2-5 illustrates the interaction between strength and service load with increasing ambient temperature of an FRP retrofitted reinforced concrete member. Reinforced concrete members are designed according to North American design codes (CSA, 2005; ACI, 2005) to have an ultimate strength that is considerably greater than the service loads which is likely to act on the member (Kodur et al., 2006). When these reinforced concrete members are strengthened using FRPs, the ultimate strength of the members increases, thus allowing for higher service load to act on the members. During a fire event, the ultimate strength of the FRP strengthened reinforced concrete member would decrease with increasing temperature and failure of the member would occur when the ultimate strength drops below the applied service load. Therefore, to ensure fire safety, the strength of the reinforced concrete member retrofitted with FRP must remain greater than the strengthened service loads for the required duration of a fire event (Kodur et al., 2006).

Generally, fire safety requirements for structural members in buildings are satisfied by ensuring the structural members satisfy a specific fire rating, which is typically obtained by conducting expensive and time consuming full-scale fire-tests. Nowadays, design codes are moving towards performance-based design methods, where detailed calculations and simulations are sometimes conducted in lieu of full-scale tests. Clearly such models must be validated using results from full-scale tests before they can be applied with confidence.

To perform these performance-based detailed, temperature-dependent calculations and model the behaviour of both unwrapped reinforced concrete and FRP strengthened reinforced concrete structures, the thermal and mechanical properties of the constituent materials of the various structural materials at high temperature is needed. Hence, a brief review of available mathematical models for representing the thermal and mechanical properties of concrete, steel and FRP in the existing literature is presented herein. Existing knowledge on the behaviour of concrete and steel at elevated temperatures has been extensively reviewed previously in other research studies (Williams, 2004; Bisby, 2003; Lie, 1992; Bazant and Kaplan, 1995; Purkiss, 2007; Chowdhury, 2005).

Unlike for concrete and steel, relatively little is known about the mechanical and thermal properties of FRP composites at high temperature, particularly for the fibre/resin combinations used in infrastructure applications. The thermal and mechanical properties of FRPs depend on the type of fibre and the polymer resin matrix, the fibre volume ratio, and the modulus of elasticity of both the fibres and the matrix materials (El-badry et al., 2000).

Lie (1992) and the Structural Eurocodes (BSI, 1992) present relationships for the variation of the thermal and physical properties (such as, thermal conductivity, specific heat and density) of concrete and steel at elevated temperatures, which can be used to calculate the heat transfer within a reinforced concrete member's cross-section on heating. Bisby (2003) and

Williams (2004) have developed finite difference heat transfer analyses of FRP strengthened structural members that make satisfactorily accurate temperature predictions using the mathematical relationships given by Lie (1992) for both concrete and steel. Bisby (2003) presents a mathematical model for the thermal and physical properties of FRP based on limited research work presented by Griffis et al. (1984).

As FRP composite materials are sensitive to fire, FRPs are often protected using supplementary insulation systems, such as vermiculite-gypsum fire insulation, which are proprietary materials. Bisby (2003) estimated the thermal and physical properties of this type of insulation material from a variety of sources and satisfactorily performed a finite difference heat transfer analysis of FRP strengthened and insulated reinforced concrete columns, which produced satisfactory results. The mathematical relationships from Lie (1992) and Bisby (2003) for the variation of thermal and physical properties of concrete, steel, FRP and insulation are presented in Appendix C.

Youssef and Moftah (2007) presented a review of existing mechanical property models developed in the last century by various researchers representing the behaviour of concrete (such as compressive strength, tensile strength, compressive strain at peak stress, and transient creep strain) and steel (such as yield strength and bond strength) at elevated temperature. The rate of deterioration of mechanical properties of concrete at elevated temperatures is dependent mainly on the type of concrete and the level of initial compressive stress. Compressive strength loss occurs at a lower temperature in siliceous aggregate concrete than in carbonate and lightweight aggregate concrete as shown in Figure 2-4. Concrete, which experiences an initial compressive stress during heating, will tend to maintain higher compressive strength than equivalent unstressed concrete; this is because concrete develops thermal micro-cracks when exposed to elevated temperatures and these cracks are reduced when the concrete expereinces a compressive stress during heating. Stressed concrete can be up to 25% stronger than unstressed concrete at

elevated temperatures provided that the initial compressive stress is about 25 to 30% of the initial room temperature strength (Hertz, 2005). Youssef and Moftah (2007) recommend using mechanical models of concrete that take account of the aggregate type and the level of initial compressive stress. Research studies on the ultimate compressive strain at elevated temperature are very limited and scarce. Terro (1998) and Williams (2004) are the only two research studies that the author is aware of which propose mathematical models representing the behaviour of the ultimate compressive strain of concrete at elevated temperature. The reader should note that, because little test data exist in this area, the models that have been proposed have not yet been fully validated. Although there have been several studies examining existing models describing the transient creep strain experienced by a heated concrete (Youssef and Moftah, 2007; Li and Purkiss, 2005; Nielsen et al., 2002), it is not clear which models better describe the structural behaviour of concrete. The mechanical behaviour models for reinforcing steel presented in Lie (1992) and Hertz (2005) can be used in calculating the load carrying capacity of reinforced concrete members at elevated temperatures. Bisby (2003) and Williams (2004) have successfully used the mathematical relationship presented in Lie (1992) for reinforcing steel in their numerical models.

The mechanical behaviour of FRP composites at elevated temperatures depends to large extent on the behaviour of the polymer resin matrix/adhesive. Polymer resins soften at temperatures in the region of their glass transition temperature, D6, thus limiting the transfer of Ú

stress between the fibres (Bank, 1993) or to any substrate to which they are bonded. The D6of Ú

resin systems typically used in construction applications are in the range of 65 to 120°C (Bisby et al. 2005c). Blontrock et al. (2000) state that the strength and stiffness of FRP composites start degrading rapidly at temperatures close to the glass transition temperature of their constituent polymer resin. Furthermore, both epoxy and polyester based composites will quickly ignite when they are exposed to fire, typically at temperatures in the range of 300 to 400°C (Bisby, 2003).

Thus, the mechanical properties of FRP composites will considerably and irreversibly deteriorate due to combustion of the polymer resin at these temperatures (Mouritz, 2002). As reported by Bisby (2003), studies have shown that carbon fibres experience little to no change to their tensile strength up to temperatures of more than 1000°C (Bakis, 1993; Rostasy, 1992), thus demonstrating more resistance to high temperature than glass fibres, which (similar to mild steel reinforcement) lose 50% of their original tensile strength above 550° (Rehm and Franke, 1974;

Sen, 1993). The bond between FRP laminates and concrete is also an important issue because bond is often the limiting parameter when strengthening concrete structures with FRP (Ueda and Dai, 2005). Studies (Bizindavyi and Neale, 1999; Chen and Teng, 2001; Chen and Teng, 2003) have shown that, under room temperature conditions and without specific preventative measures, premature failure due to debonding of FRP laminates is the most common type of failure in FRP strengthened concrete beams and slabs. External application of FRP laminates requires them to develop and transfer high shear forces through the interface between the adhesive or polymer resin and the concrete substrate. The bond properties between concrete and FRPs deteriorate rapidly with increasing temperature, and this could eventually lead to delamination or debonding of the FRP and the ensuing loss of interaction between the FRP and the concrete (Gamage et al., 2005).

A number of mathematical functions have been explored by researchers to describe the mechanical and bond property versus temperature relationships for these materials. These typically follow a reverse S-shape as shown in Figure 2-6. More details on the various mathematical functions that can be used to describe the variation in mechanical and bond properties of FRPs with increasing temperature are given in Chapter 4.

2.7.1 FRP Strengthened Flexural Concrete Members Without fire protection, FRP strengthened concrete beams have shown superior performance in fire in comparison to steel plate-strengthened concrete beams (Deuring, 1994). However, the fire endurance of reinforced concrete members strengthened with FRP can be considerably improved by providing supplementary fire protection systems (Blontrock et al., 2001; Williams, 2004;

Chowdhury et al., 2005) provided that the insulation is capable of maintaining the internal concrete and reinforcing steel temperatures below about 200°C and 250°C, respectively (Williams et al., 2005); steel and stressed concrete experience only minimal deterioration in their mechanical properties (Drysdale et al., 1990; Lie, 1992) at these temperatures. Hence, reinforced concrete members strengthened with FRPs and provided with sufficient supplemental fire insulation are generally able to endure the elevated temperatures experienced during fire for more than four hours (Williams et al., 2008; Chowdhury et al., 2005). Furthermore, maintaining low internal temperatures in the concrete and reinforcing steel is beneficial to the post-fire or residual behaviour of the concrete members (Chowdhury et al., 2005; Drysdale et al., 1990; Lie, 1992).

By providing supplemental fire protection, the temperatures of the FRP can be maintained below the glass transition temperature D6of the epoxy polymer resin for about one Ú

hour (Williams et al., 2008). However, the beneficial effects of fire protection for the FRP strengthened reinforced concrete member could also have potentially negative consequences, since sudden loss of insulation during fire could contribute to rapid loss of the FRP and explosive spalling of concrete cover from the member due to thermal shock and steep thermal gradients (Chowdhury et al., 2008). Therefore, it is essential that the fire protection remains intact for the

duration of the required fire exposure to ensure that the reinforced concrete member achieves a satisfactory fire endurance rating.

While a number of medium and full-scale fire endurance tests have been performed on FRP strengthened reinforced concrete flexural members, there is relatively little information on the critical exposure temperature that results in loss of structural effectiveness of the specific FRP strengthening systems used. In previous studies (Williams et al., 2008; Chowdhury et al., 2008), it was difficult to observe the structural failure of the FRP (if it occurred at all) during the fire, as the FRP strengthening system was completely obscured during testing by the supplemental fire insulation. Blontrock et al. (2001) conducted fire tests on FRP strengthened beams where the FRP was entirely protected by insulation, but also where only the anchorage was protected by insulation. In this study, loss of bond between the FRP and the concrete was observed at temperatures between 66°C and 81°C, and the performance of the fully-protected beams was observed to be similar to the beam where only the anchorage zones of the FRP were protected.

This shows that protecting the anchorage zones of the FRP with insulation would allow the FRP sheet to maintain its contribution as tensile reinforcement in a fire situation.

approximately 2%, 4% 13% and 18% of their initial room temperature ultimate strength when they were exposed to temperatures of about 120°C, 135°C, 150°C and 180°C, respectively.

However, the degradation of axial strength due to heating was reduced after treating the cylinder with an epoxy based fireproofing coating and paint; the axial strength of the GFRP confined cylinders decreased by about only 3% and 10 % at about 150°C and 185°C, respectively. The mode of failure of the GFRP confined cylinders changed with increasing temperature. At lower temperature, fibre dominated failure modes were observed, whereas, resin dominated failure modes were observed at higher temperatures.

Bisby et al. (2005a) reported on fire endurance tests on both insulated and uninsulated FRP confined reinforced concrete circular columns, which were also able to endure a standard fire under service load for more than four hours in some cases. The temperature of the steel reinforcement and concrete for the columns was maintained below 200°C for up to 5.5 hours in some cases, and therefore these columns were able to maintain essentially all of their original room temperature strength during the fire tests. This was evident in the fact that these columns failed after more than five hours of fire exposure at higher axial loads than predicted for the nominal (unfactored) compressive strength for the unwrapped condition at room temperature. In this study, the insulation protecting the FRP confined reinforced concrete columns was able to maintain the temperature of the FRP below 100°C, which was higher than the glass transition temperature of 91°C, for up to four hours during fire, although it is again not known if the FRP strengthening system remained structurally effective for the full duration of the tests. As previously discussed for FRP strengthened beams, supplemental fire insulation is beneficial in increasing the fire endurance of FRP strengthened reinforced concrete circular columns, provided that the supplemental fire insulation remains intact.

Although some information is available on the fire behaviour of FRP strengthened concrete circular columns, limited data exist on the performance of FRP strengthened concrete

square columns. Kodur et al. (2005) present data on the only full-scale fire test on FRP strengthened reinforced concrete square column that has been performed to date. The reinforced concrete column was strengthened with GFRP composite and was provided with 38 mm of a spray-applied gypsum-based supplemental fire insulation system. Confining the square column with GFRP increased the ultimate axial strength by about 5%. The column was able to endure the standard fire exposure under full, strengthened service load for four hours. The supplemental fire protection system was able to maintain the temperature of the FRP wrap below 100°C for about 30 minutes. Although formation of some thermal cracks in the insulation was observed during the fire test, the insulation system remained essentially intact until the end of the fire test, when explosive spalling of the concrete caused the insulation to debond and the column to fail after 255 minutes.

2.8 Summary This chapter has presented a review of existing studies on or relevant to the behaviour of FRP confined concrete and FRP confined reinforced concrete columns under ambient and elevated temperatures. Based on these studies, a large amount of strength and deformability is gained by confining concrete columns with FRPs. Due to partial confinement effectiveness, the enhancement in strength and ductility achieved by a rectangular or square concrete column from FRP confinement is in general not nearly as much as for circular concrete columns. The stress- strain behaviour of concentrically-loaded FRP confined circular concrete is reasonably well understood and established from available studies; however, it remains somewhat uncertain for the case of FRP confined square or rectangular concrete columns. The strength benefits achieved from FRP confinement diminish with increasing load eccentricity and column slenderness.

Although longitudinal FRP wraps have no effect on FRP confined short columns, they have been

shown to provide flexural resistance to the secondary moments experienced by FRP confined slender columns.

Performance-based design is becoming more accepted in current design codes, and this requires a more detailed understanding of the behaviour of a structural member's constituent materials at elevated temperatures. There are many available studies on the fire behaviour of conventional concrete and steel structural members; however, there is still information lacking on the behaviour of the ultimate compressive strain of concrete at elevated temperature. Additional experimental studies are required to understand the transient creep behaviour of concrete so that it can be included into numerical models.

Research studies on the fire behaviour of currently available FRP strengthening systems are limited. However, based on these limited studies, the strength and stiffness of FRP composites start to degrade rapidly at temperatures close to the glass transition temperature of the polymer matrix. Researchers have explored a number of mathematical functions to describe the mechanical and bond properties with increasing temperature. However, because numerous different formulations of FRP materials are available, experimental tests should be conducted to investigate the behaviour in fire of any specific FRP system, considering different parameters such as FRP types, curing regime, bonded length, heating rate, sustained load level, etc.

Although FRP strengthening systems are vulnerable to high temperature, tests on specific reinforced concrete structural members strengthened with specific available FRP strengthening systems have shown that they can endure the high temperature of a fire by providing adequate supplemental fire protection.

Unconfined FRP confined ' f cc c ? Axial stress, ' f c Parabolic Linear portion portion ?? cu ccu Axial strain, ? c

Figure 2-1: Typical stress-strain behaviour of plain concrete and FRP confined concrete

Confined concrete Unconfined concrete FRP wrap Figure 2-2: Confined concrete in FRP wrapped (a) circular and (b) square concrete column (adapted from Thériault and Neale, 2000)

h h' = h - 2Rc c R ? w' = w - 2R c Rc w Parabola 4 Parabola 1 Parabola 2 Parabola 3 h/2 - 0.25w' 0.25w' Confined concrete Unconfined concrete

Figure 2-3: Effective wrap confinement of rectangular 1.5 C) o (20 1.0 c (T) / f 0.5 c f 0.0 Lightweight Carbonate Siliceous ' ' 0 200 400 600 800 1000 Temperature (oC) Figure 2-4: Variation of compressive strength of lightweight, carbonate, and siliceous aggregate concrete with increasing temperature (Hertz, 2005)

Figure 2-5: Interactions between service loads, strength, and temperature for a FRP retrofitted reinforced concrete member (reproduced from Kodur et al. 2006) Mechanical Property, P P initial T cr

P central T g P R TT central R Temperature, T Figure 2-6: Typical relationship between mechanical property and temperature of FRP composite under isothermal condition

Chapter 3 Modelling Eccentrically Loaded Slender FRP-Confined Reinforced Concrete Columns at Ambient Temperature

3.1 General Reinforced concrete columns in real structures are typically subjected to at least some eccentricity of axial loads. To date, most research studies on FRP confinement for axial strength enhancement of reinforced concrete columns have concentrated on short columns under concentric axial compressive loads. Only a few research studies (Fitzwilliam and Bisby 2006;

Mirmiran et al. 2001; Mirmiran et al. 1998; Pan et al. 2007; Tao et al. 2004) are available which have investigated FRP confinement of reinforced concrete columns under combined axial compression and bending resulting from axial load eccentricity. As a result, comparatively little is known about the performance of eccentrically loaded FRP confined reinforced concrete columns, particularly for members of larger slenderness which may be exposed to substantial second-order bending moments. Provisions in current published design guidelines and codes are limited to treat only short columns (ISIS Canada 2001b; ACI 2008). As already stated a reinforced concrete column which is behaving as a ?short? column under existing axial loads may change its behaviour to a ?slender? column under increased axial service loads after confinement with FRPs (ISIS Canada 2001b) and some such columns, when eccentrically-loaded may be susceptible to instability resulting from their slenderness (MacGregor et al. 1970); circumferential FRP wraps increase a column's crushing strength without significantly increasing its flexural rigidity under service loads (i.e., without increasing its elastic buckling strength). Hence, an analytical investigation has been conducted as part of the research presented in this thesis to better understand the behaviour of FRP confined circular reinforced concrete columns with increasing slenderness under eccentric axial loads. The model is also required as a first step toward producing a versatile and defensible model to rationally predict the performance of FRP

wrapped concrete columns in fire; a central goal of the current research. This chapter presents the development and validation of a numerical model that can simulate the behaviour of FRP confined concrete columns with increasing slenderness under variable eccentric axial compressive loads. The model is used to determine the axial load-bending moment strength interaction diagrams of both unwrapped and FRP wrapped reinforced concrete columns of various slenderness ratios. This is accomplished by calculating axial load-moment paths of these columns under selected eccentric loading conditions, as described below.

3.2 Research Significance: Current Chapter There have been few publications on the behaviour on slender columns wrapped with FRP; to the author's knowledge no such experimental studies have ever been performed on columns of realistic scale, thus limiting existing design guidelines and codes (with one exception (ACI, 2008)) only to short columns under concentric axial load. With increasing slenderness, FRP confined concrete columns may not attain their maximum design strength because the confining reinforcement (in the hoop direction only) does not typically provide increased bending or buckling strength to the column, thus potentially making the column structurally unstable under the increased loads due to second-order effects. Research is needed on the slenderness implications for FRP confined concrete columns to support the development of rational design guidelines and strengthening limits for these types of members.

3.3 Numerical Study The numerical model for the FRP confined reinforced concrete columns was developed by the author using FORTRAN. The model simulates the second-order deformations experienced by slender FRP confined concrete columns to generate axial load-moment load paths, and in the

process also establishes their axial load-bending moment strength interaction diagrams. The development of strength interaction diagrams for slender columns requires an elaborate analysis, wherein a realistic moment versus curvature relationship is calculated for the column's cross- section, followed by calculation of axial load-moment paths for the full-height column under various load eccentricities and for various levels of slenderness. The method of analysis is based on the following common concrete modelling assumptions: (1) plane sections remain plain;

(2) the axial strain in the internal steel reinforcement is equal to the strain in the concrete at the same location (that is, perfect bond);

and 3.3.1 Material Properties A modified version of the FRP confined stress-strain model for concrete described by Fam et al. (2003), which is itself a modified version of the Popovics (1973) model, is adopted in the current analysis because it is one of only a few existing FRP confinement models that can be used to generate the stress-strain behaviour of both unconfined and FRP confined concrete using a similar relationship for both cases, because the model includes the post-peak strain-softening behaviour of unconfined concrete. The concrete stress, DB, at a given axial strain, DÝ, is: ÖÖ

Nñ DlÝÖDpã DBÖ Nâñ DB L DÝÖ â Eqn. 3?1 Ö DÝ D ã lÖ pE FN1ñ DÝÖ â

where D ã /D:' , D;' Nñ Nñ Nñ The strain at peak stress of ÖLâDÖ' âFæD 'Ö Öâ L 4700D¥B /DÝ â Ö â æ Ö â âÖ Ö

the unconfined concrete, DNÝñÖ, is determined by the following empirical relationship as given by â

Collins and Mitchell (1997): DNBñ DM Nñ Ö âGl· p DÝÖ âL F Eqn. 3?2 D'Ö âD M F 1 where D M D:NBñ/17. ;The ultimate unconfined concrete strain, DÝ L 0.8Ö âE , is taken as 0.0035 in Öè accordance with CSA A23.3-06 (CAN/CSA 2005).

The FRP confined compressive strength, DNBñ, and ultimate axial strain, DÝ, are ÖÖ ÖÖè calculated according to the empirical FRP confinement model of Jiang and Teng (2006).

According to Jiang and Teng's model, which represents a mildly revised version of the widely accepted Lam and Teng (2003) model, the confined compressive strength and ultimate axial strain are determined as follows: DNBñ if Dé O 0.01 Nñ Ö â Þ DBÖ ÖLNñ Eqn. 3?3 DBÖ1> E3D.5:é F 0.0D1;é?if Dé R 0.01 âÞ Þ 4. < DÝ L DcÝ1.65 5. 8 9 E 6.5Dé Ö Ö è Dé g Eqn. 3-4 Öâ Þ D:'o/ Nñ Nñ Nñ L DkPD 'D4, D;é L D Ý /DÝ, D' L D B where Dé /DÝ, and DÝ L D ßD. ÝJiang ã Þ Ö âÖ â Û, å è Ùã å ç, è Ù å ãæ Ö â Û, å Öè âãæ Ö â ã å and Teng (2006) recommend using values of 0.5 and 0.7 for the strain efficiency reduction factor, D,ßin the case of carbon FRP (CFRP) and glass FRP (GFRP), respectively.

Nñ Nñ To allow for a smooth and gradual transition between DBand DB, Fam et al. (2003) Ö ÖÖ introduced a shape factor DÙinto the Popovics (1973) stress-strain model. This can be calculated by modifying the expression previously given in Equation 3-1 as: NñDÝÖ Ö è DB l pD:ÙD;ã Ö Nñ DâÝÖ â DBÖ L Eqn. 3?5 D:ÙD;ãF 1 Ö Ö è lE p DNÝñÖ â Nñand DÝ After calculating DBÖ from Equations 3-3 and 3-4, the expression in Equation 3-5 is used ÖÖÖè to solve for D.ÙAlthough this confinement model can be used for the case of variable eccentric

loading conditions according to a procedure described by Fam et al. (2003) for concrete-filled FRP tubes, a different procedure (described later in this chapter) has been used to determine the decrease in axial strength for eccentrically loaded FRP wrapped columns.

A simple bi-linear elastic-plastic stress-strain model is adopted for reinforcing steel according to Equation 3-6: D'DæÝ when 0 Q DÝQìD Ý DB L æ æ Eqn. 3?6 æ DB Q D Ý ì when DÝì QæD Ýæ è Where DÝæ èL 0.i1s2the assumed ultimate strain at tensile rupture of the steel. This stress-strain model applies to both the tension and compression behaviour of steel in the numerical model, meaning that local buckling of longitudinal steel bars in compression is not considered.

Since the stress-strain behaviour of FRPs is linear-elastic to failure, the following equation is used to model the behaviour of the longitudinal wrap: D'Ù DåÝÙ ãå çã FRP in tension DBÙ åLã Eqn. 3?7 D'Ù DåÝÙãåÖãFRP in compression

3.3.2 Development of Axial Load-Moment-Curvature Relationship

The moment-curvature relationship for a given (constant) axial load is calculated using an incremental iterative procedure. The procedure is described with the aid of Figure 3-1a and Figure 3-1b. A set of strength interaction diagrams, the derivation of which is described below, is shown in Figure 3-1a for initial assumed compressive strains ranging between the maximum compressive strain, which was 0.0114, and 0.00114 at the extreme compressive concrete fibre for illustrative purpose. However, it should be cautioned that the strength interaction diagrams demonstrated in Figure 3-1a do not represent the cross section failure envelop for the specified column unless the strength interaction diagram represents the maximum compressive strain (which was 0.0114 in this case) for the specified column cross section. Details of the example column (Fitzwilliam 2006) used for this illustration is presented in Section 3.4 of this thesis.

From these series of strength interaction diagrams, the moment-curvature relationships for different axial load levels can be derived and as an arbitrary example, the moment-curvature relationship for an axial load of 526 kN is shown in Figure 3-1b.

To derive the moment-curvature relationship, the concrete strain at the extreme compressive fibre is incrementally increased from zero to the ultimate axial concrete strain DÝÖ è and DÝÖ(depending on the type of analysis). The strength interaction diagrams for the increasing Öè concrete strains are shown in Figure 3-1a. The model derives the moment-curvature relationship for a given axial load D2Ú from these strength interaction diagrams by modifying the strain ÜéØá distribution, by varying the depth of the neutral axis, using bisection root finding method. For a given concrete strain, two neutral axis values, DGand DG, were assumed initially ? one of low 56 value and the other of high value. The sum of the two neutral axes DGand DGis divided in half to 56 obtain DG LD:G /2;. For each of the strain distributions based on these three , that is, DG E D G 7756 neutral axes DG,5DGand DG, the stresses and forces over the cross section of the column are 67 integrated to determine the ultimate axial loads (D2,5D2and D2)7by using a fibre section analysis as 6

shown in Figure 3-2. Therefore: L D B , ? ? ? . . o Eqn. 3-8 , DG, DB, DB, DB D%, D%, D6 D25 Ö 5 kÖDæÝÙ å Öã,æ æ D2 L D B , ? ? ? . . o Eqn. 3-9 , DG, DB, DB, DB D%, D%, D6 6 Ö 6 kÖDæÝÙ å Öã,æ æ L D B , ? ? ? . . o Eqn. 3-10 , DG, DB, DB, DB D%, D%, D6 D27 Ö 7 kÖDæÝÙ å Öã,æ æ After calculating the ultimate axial loads D2,5D2, and D2from the three strain distributions, a 67 66

L D 2 Eqn. 3-11 DB5 F D 2 é Ø á 5ÚÜ

L D 2 Eqn. 3-12 DB6 F D 2 é Ø á 6ÚÜ

L D 2 Eqn. 3-13 DB7 F D 2 é Ø á 7ÚÜ

If the product of functions DB is equal to DGfor the next and DBis greater than zero, then DG5 7 57 iteration, otherwise, DG for the next iteration. In this manner, DGand DGare is equal to DG 6 7 56 repeatedly divided in half to find the next subinterval in which the given axial load D2 exists. á ÚÜéØ After each iteration the two neutral axes DGand DG If the difference 6

between DGand DGis less than 1.0%, then the root for the given axial load D2 is assumed to be 5 6 ÚÜéØá found for the given concrete strain and, the bending moment D/and curvature Dîcorresponding to the proposed concrete strain distribution are determined.

3.3.3 Numerical Integration of Column Deflections Once the moment-curvature relationship for a given constant axial load is determined, a piecewise numerical integration method, namely the Column Deflection Curve method, presented previously by Chen and Atsuta (1976) is used to determine the slope and lateral deflection along the longitudinal height of the column at that axial load level. The numerical procedure involves dividing the column into a series of discrete segments and calculating the curvatures at each of the division points using the axial load-moment-curvature relationship. The curvatures are then integrated to obtain the slope and lateral deflection along the longitudinal height of the column.

This numerical integration method is needed as it accounts for the effect of secondary bending moments caused by the coupling of axial loads and lateral deflections. The procedure is described with the aid of Figure 3-3.

The discrete points DU,5DU, DU, and so on, are chosen with small vertical intervals. To 67 determine the number of vertical intervals, a sensitivity analysis was conducted on the maximum axial resistance calculated from the numerical model for assumed column specimens similar to those tested by Fitzwilliam (2006) having slenderness ratios of 10 and 33 under both unwrapped and FRP wrapped conditions, as shown in Figure 3-4. It was observed that the variations in the

sensitivity analysis depended on the column length and the level of axial load resistance of the equivalent short column. Column specimens having a slenderness ratio of 10 showed minimal variation in axial resistance under both unconfined and confined conditions when the number of vertical sections ranged between 30 and 80 in the numerical analyses. However, as the slenderness ratio of the column increased to 33, the variation began to minimize when 80 vertical sections were used in the numerical model. Therefore, the column was discretized into 80 vertical sections; that is, each vertical section was approximately15 ± 2 mm of length in the numerical analysis of these example columns.

The numerical procedure starts with an assumed initial slope Dà, from one end of the â

column where the distance of the discrete point DUlateral deflection Dñ, and curvature Dî ,â are ââ The moment D/ BÛ is equal to D2 unless the column is concentrically loaded (that is, D/ zero. â · D A â â

is zero), which is rarely (in fact never) achieved in real construction. At point DU, the lateral Û

deflection, Dñ, the initial eccentricity, DA , and slope, Dà Û , bending moment, D/, curvature, Dî , are ÛÛÛÛ approximated using Equations 3-14 to 3-17.

1 Dñ L D ñ D:U F DU;FDî D:U F DU;6 Eqn. 3?14 Û Û ?E5ÛDà?Û5 Û ?25 Û ?Û5 Û ? 5 DAâ F

L D à D:U F DU; Eqn. 3?17 DàÛ F D îÛ Û ? 5 Û ? 5Û

This procedure is repeated for every discrete point on the column until the lateral deflection Dñ and the moment D/ BÛ < at the other end of the column become zero and D2DA, 4 4 <4 < respectively, by successively modifying the assumed initial slope Dà.âFollowing this method of integration, an axial load-moment path for the column is determined by increasing the applied

load incrementally. In this manner, the numerical model can analyze slender columns having end <4

Two types of failure may occur in the case of a slender concrete column: (1) material failure and (2) stability failure (McGregor et. al. 1970). Material failure of the column is assumed to occur in the numerical model when the axial load and bending moment combination exceeds the strength of the cross section, that is, the axial load-moment path would intersect the cross sectional strength interaction diagram as shown in Figure 3-1c. Stability failure of the column is assumed in the numerical model when the column achieves its maximum axial capacity before the column achieves its cross sectional axial strength, that is, the axial load-moment path would not intersect the cross sectional strength interaction diagram ? this is essentially a global buckling mode of failure.

3.3.4 Development of Slender Column Axial Load-Moment Interaction Diagrams The axial load-bending moment strength interaction diagram for a slender column (i.e., the slender column interaction diagram) is determined by calculating axial load-moment paths for the slender column under various initially eccentric loading conditions. Figure 3-1c shows an example axial load-moment path for an FRP wrapped reinforced concrete column having an initial unwrapped slenderness ratio of 18 at some given initial load eccentricity. Failure occurs due to both primary and secondary moments when the axial load-moment path intersects the cross section interaction diagram at Point B. If the column was short and did not experience noticeable significant secondary moments, the axial load-moment path would have intersected the interaction diagram at Point C. For design purposes, the actual failure moment is expressed in terms of the moment corresponding to the actual failure load in the axial load-moment path for short column, which is at Point A in Figure 3-1c. In this manner, from various axial load-moment paths representing various eccentric loading conditions, the slender column axial load-bending

moment strength interaction diagram can be determined. This is an interaction diagram which inherently accounts for the slenderness of the column and hence the presence of secondary moments, rather than simply showing properties for a given column cross-section.

3.4 Validation of Numerical Model The numerical model developed as described above was validated by comparing its predictions against experimental results from studies presented by Fitzwilliam (2006), Fitzwilliam and Bisby (2006), and Ranger (2007). These studies investigated the behaviour of both unconfined and FRP confined reinforced concrete columns having different initial slenderness ratios and under varying eccentric axial compressive loading conditions. The small- scale columns in these studies were 152 mm in diameter and were reinforced internally with four 6.4 mm diameter deformed steel bars in the longitudinal direction and 6.4 mm diameter closed circular steel ties at 100 mm center-to-center spacing in the hoop direction, with a cover of 25 mm to the longitudinal reinforcement (refer to Figure 3-5). The concrete used in fabricating the column specimens in both studies was of normal density, however, the average compressive strengths of the concrete in the two studies were different because the concrete was from different batches. Detail concrete mix designs are presented by Fitzwilliam (2006) and Ranger (2007). The concrete used by Fitzwilliam (2006) and Ranger (2007) had an average compressive strength of 36 MPa and 33 MPa, respectively, at the time of testing. The reinforcing steel used by Fitzwilliam (2006) had an average 0.2% offset yield strength of 693 MPa, average ultimate strength of 733 MPa, average ultimate strain of 1.89%, and average elastic modulus of 196 GPa. Ranger (2007) used similar reinforcing steel as in Fitzwilliam (2006) to fabricate the reinforced concrete column specimens. The mechanical properties of the FRP composite, which had a manufacturer specified design thickness of 0.381

mm for a single layer of laminate, are provided in Table 3-1. The column specimens in both studies were tested monotonically in compression to failure with pinned-pinned end conditions under an initial load eccentricity. In Fitzwilliam (2006), the column specimens had varying slenderness and were tested under a constant initial load eccentricity of 20 mm, whereas the column specimens in Ranger (2007) had an initial unwrapped slenderness ratio of 18 but were tested under varying initial load eccentricities. During the tests, axial strains were measured using PI-type strain gauges, hoop strains using electrical resistance foil strain gauges, and lateral deflection using linear potentiometers (refer to Figure 3-5).

When validating the numerical model described previously, a modified Ramberg-Osgood function (Mattock 1973), as shown in Equation 3-18, was used to model the stress-strain behaviour of the 6.4 mm diameter longitudinal reinforcing steel, rather than using Equation 3-6.

This is due to the fact that the steel used in these columns was cold-drawn deformed wire with high yield strength and without a well-defined yield plateau.

1 FD# DBæ LDæDÝæ'eD# E - i æ Qè D B Eqn. 3?18 1:ED:$DÝ æÖÎ

The function in Equation 3-18 is defined by the four coefficients: D',æD,#D$, and D.%From tension tests on the steel bars, Fitzwilliam (2006) found the average values of D'to be 196 GPa and DB è ææ to be 733 MPa, and using non-linear least-squares regression analysis he found the constants D,# D$, and D%to be 0, 268.87 and 3.78, respectively. , D,#D$, These values for the four coefficients (D'æ and D)%was used in Eqn. 3-18 to analyze the column specimens in Fitzwilliam (2006) and Ranger (2007).

The numerical model was first verified by comparing its predictions against experimental results from Fitzwilliam (2006), which are presented in Figure 3-7 to Figure 3-11. The column

effective length factor DGin the numerical analysis was taken to be 1.0 for pinned-pinned end conditions and to calculate the initial column slenderness DG?D. DN , which was varied by Fitzwilliam between 10 and 33. In the numerical analysis, the tensile properties used for the FRP were the tested values taken from Fitzwilliam (2006), and the compressive properties were taken as the average values quoted by the FRP manufacturer (refer to Table 3-1).

According to Equations 3-3 and 3-4, the concentric axial compressive strength of the wrapped columns is predicted as 41.8 MPa, and the predicted ultimate compressive axial strain is 1.14%, which was determined by assuming the hoop strain at FRP rupture, DÝÙ , equal to the ã å ã, å è ultimate tensile strain of the FRP from coupon tests (rather than by imposing the suggested strain efficiency, D,ßof 0.5 for CFRP (Jiang and Tent, 2006)). In Fitzwilliam's tests, the ultimate compressive axial strains observed at the extreme compression fibre under eccentric load were in the range of 1.21% and 2.41%, which were considerably higher than the predicted value. Further reducing the hoop strain at failure to a value less than the ultimate tensile strain of the FRP from coupon tests, as recommended by Jiang and Teng (2006) for designing FRP wraps, would reduce the confined concrete ultimate compressive strain and strength even more, thus compromising the validation of the numerical model through over-conservatism (which may be appropriate for design but not for predictive analysis as performed here). Hence, the hoop strain at failure was taken as equal to the ultimate tensile strain of the FRP, DÝÙ , in the model only to predict the å ã ç, å è ã values of the confined concrete ultimate compressive strain and strength. It is worth noting that during Fitzwilliam's experimental study, the eccentrically-loaded columns experienced hoop strains in the FRP wrap which were generally less (in the range of 0.235 and 0.660%) than the ultimate tensile strain of the FRP, as has been observed also in other previous studies (Jiang and Teng 2006; Lam and Teng 2004) for concentrically-loaded FRP confined concrete. The actual axial compressive strains that can be achieved for FRP wrapped columns under eccentric loads,

and the various factors influencing both hoop and axial strain at failure remain unknown, and these topics warrant further experimental study.

In most cases, any deviations found in the predictions from the numerical model when compared against Fitzwilliam's experimental tests can be attributed to the assumed material behaviour models, especially the FRP confined concrete model described in Equation 3-3 and 3- 4, which is based on extending the uniaxial compression and uniform confinement case to the case of variable confinement under eccentric loads. This influences the assumed ultimate concrete compressive strain and therefore the assumed ultimate strength of the FRP confined concrete, as previously noted, with subsequent effects on the model predictions. However, it is felt that the approach taken herein is conservative based on the available understanding of the mechanics involved and the available test data.

Figure 3-7 to Figure 3-10 show the axial load-lateral deflection behaviour of both unconfined and confined concrete columns from Fitzwilliam's (2006) study compared against the predictions of the numerical model presented in this thesis. The comparisons show that the model can predict the maximum axial load carrying capacity with reasonable accuracy, and can also capture the overall structural behaviour of these slender FRP confined circular reinforced concrete columns. The model's prediction of lateral deflections is reasonable, although the lateral deflection at failure is not captured well in many cases. This is thought to be because of the uncertainties inherent in predicting the concrete axial and FRP hoop strains at failure (as discussed previously). To demonstrate the accuracy of the prediction achieved with the numerical model, Figure 3-10 shows a comparison of the maximum axial load and the corresponding lateral deflection predicted by the numerical model and obtained during experiments. Wrapping the reinforced concrete columns with FRPs, where the fibres were oriented in the hoop direction, enhanced the axial capacity and ductility of the columns (refer to Figure 3-7 and Figure 3-8). As the slenderness of the unwrapped and FRP wrapped column specimens increased, the ultimate

axial capacity of these column specimens decreased and the lateral deflections increased at failure. The performance of the columns is reasonably well predicted by the model.

In the experiments conducted by Fitzwilliam (2006), the load carrying capacity and lateral deflection behaviour of the FRP confined reinforced concrete columns were further improved after wrapping with FRP vertically for flexural strengthening in addition to laterally for confinement, with the fibres oriented in the longitudinal direction (Figure 3-9). This behaviour is less well captured by the model, which is likely due to inaccuracies in the compressive stress- strain behaviour assumed for the longitudinal wraps. However, the deviation observed between the model prediction and the experiment in Figure 3-9 with respect to the flexural stiffness of column specimen having an initial unwrapped slenderness ratio of 33, which was wrapped with one layer of hoop FRP and four layers of longitudinal FRP, is not thought to be because of any inherent defect in the numerical analysis. This particular column specimen also demonstrated higher flexural stiffness than expected in comparison with other columns tested as part of the experimental program (refer to Figure 3-12). This high flexural stiffness is not the result of the flexural strengthening. In fact, the contribution from flexural strengthening at low loads is minimal as the second-order deformation is insignificant when the column is behaving as a short column. This is evident in Figure 3-13, where it can be seen, that, the longitudinal wraps became effective and provided additional flexural resistance to FRP confined reinforced concrete columns of initial unwrapped slenderness ratio of 10 and 33, when they were experiencing second-order deformations at higher axial loads. The author believes that the FRP confined reinforced concrete column specimen in question may have inadvertently been tested under a load eccentricity lower than the intended 20 mm during the experimental program. Using the numerical model, it was estimated that that particular FRP confined column may have experienced a load eccentricity of only about 12 mm (refer to Figure 3-14).

Comparing with the experimental data, the model is able to calculate the second-order deformations satisfactorily, and is thus reasonably able to capture the trends of the axial load- lateral deflection and the maximum axial load capacity of the column specimens. In the experimental tests, as the slenderness of the column specimens increased, the failure mode shifted from axially dominated material failure to flexurally dominated stability failure, which was also observed in the numerical model's predictions (Figure 3-11). The model predicted stability failure modes for FRP strengthened reinforced concrete columns that had initial slenderness ratio larger than 30 as shown in Figure 3-11 and Figure 3-15. Stability failure of a column was established in the numerical model by setting a failure criterion where the column was assumed to have failed when the axial load-moment path showed a decreasing branch, as seen in the experimental program (Figure 3-11); that is, when the axial load capacity started decreasing before intersecting the cross section strength interaction diagram. Figure 3-15 clearly shows the predicted impact of increasing slenderness on column performance for the FRP wrapped columns.

Another key aim of the numerical model developed herein was to be able to predict the axial load-bending moment strength interaction diagram for eccentrically-loaded reinforced concrete columns. Figure 3-16 and Figure 3-17 show comparisons of the model prediction and experimental data from Ranger (2007) for strength interaction diagrams of both unwrapped and FRP wrapped reinforced concrete column having an initial unwrapped slenderness ratio of 18.

The model was able to predict the maximum axial load carrying capacity with reasonable accuracy for both unwrapped and wrapped reinforced concrete columns, however, the lateral deflection at maximum axial load is not captured well in many cases, especially for FRP confined columns (Figure 3-17a). The model prediction of the axial load-bending moment strength interaction diagram was reasonably close to the experimental data for the unwrapped reinforced concrete column case. However, for the FRP wrapped reinforced concrete columns, the model

prediction and the experimental data was different in most cases. Again, this deviation in the model prediction is not the result of any inherent defect in the numerical model. The lateral deflection data was collected by Ranger (2007) using linear potentiometers; the author suspects that the linear potentiometers may not have been aligned properly when it was measuring the lateral deflection of the column specimens; hence, discrepancy between the experimental and predicted result was observed. As expected, the unwrapped reinforced concrete columns behaved like short columns: second-order deformation was minimal (Figure 3-16a). However, the same reinforced concrete column, when wrapped with a single layer of FRP in the hoop direction, changed its behaviour to slender under increased axial loads (Figure 3-16b).

3.5 Summary A structural response model has been developed that can simulate the second-order deformation and axial-flexural load path of an eccentrically-loaded slender FRP strengthened concrete column (or a reinforced concrete column) with reasonable accuracy. Furthermore, the numerical model can predict the axial load-bending moment strength interaction diagrams for slender columns by calculating axial load-moment paths for the column for various eccentric loading conditions. The structural model has been validated by comparing it against experimental results from the available literature (Fitzwilliam 2006; Fitzwilliam and Bisby 2006; Ranger 2007). It has been shown that the model can predict the maximum axial load carrying capacity and can also capture the structural behaviour of slender FRP confined circular reinforced concrete columns satisfactorily. However, the model's prediction of lateral deflection at ultimate is not captured well in many cases. Accurate prediction of the structural behaviour at loads near ultimate depends on the material behaviour models and assumptions that are used in the numerical model, particularly with regard to the axial compressive strain in the concrete and the hoop strain in the FRP wrap at failure. The FRP confined concrete model used in the numerical

analysis is based on extending the uniaxial compression and uniform confinement case to the case of variable confinement under eccentric loads, which influences the axial compressive strain in the concrete and the hoop strain in the FRP wrap. Hence, additional work is needed in this area.

The extension of the model to treat the case of FRP confined columns in fire is discussed in later chapters.

Table 3-1: Mechanical properties of the FRP system used in Fitzwilliam's (2006) tests Property Average valuea Design valueb Tested valuec Tensile Strength (MPa) 894 715 1014 ± 127 Tensile Modulus (MPa) 65402 61012 89773 ± 9871 Tensile Elongation (%) 1.33 1.09 1.15 ± 0.113 Compressive Strength (MPa) 779 668 - Compressive Modulus (MPa) 67003 63597 - a Value from FRP coupon test series conducted by the manufacturer b Value stated by the manufacturer (mean minus 3 standard deviations) c Value from FRP coupon test series reported in Fitzwilliam 2006

Table 3-2: Summary of observed axial and hoop strain in Fitzwilliam's (2006) tests Ave. hoop strain at Peak hoop strain at Peak axial strain at Specimensa kL/r ultimateb (%) ultimate (%) ultimate (%) 10U 9.9 - - 0.341 18U 17.8 - - 0.391 26U 25.7 - - 0.199 33U 33.6 - - 0.267 10C-1-0 9.9 0.660 1.20 1.926 18C-1-0 17.8 0.235 0.373 1.211 26C-1-0 25.7 0.483 0.939 1.279 33C-1-0 33.6 0.326 0.781 2.415 10C-1-2 9.9 0.464 0.734 2.005 33C-1-2 33.6 0.413 0.820 2.012 33C-1-4 33.6 0.419 0.847 2.543 a For example, 10C-1-2 is unwrapped initial column slenderness ratio of 10, wrapped with carbon, 1 layer hoop FRP wrap, 2 layers of longitudinal FRP wrap FRP, 2 layers of longitudinal b Calculated as an average of all seven foil hoop strain gauges outside the FRP overlapping zone

Axial Load (kN) 1000 800 600 400 200 0 ?cc = 0.0114 526 kN ?cc = 0.00114 0 5 10 15 20 Moment (kN m) (a) Moment (kN m) 20

15 10 5 0 0.000 0.004 0.008 0.012 Curvature (rad) × 0.01 (b) Axial Load (kN) 1000 800 600 400 200

0 M = Plonge kL/r = 0 Pshort kL/r = 18 C B A Plong

M = P (e + ? ) max long h 0 5 10 15 20 Moment (kN m) (c) Figure 3-1: FRP wrapped circular reinforced concrete column (a) strength interaction diagrams for different values of assumed maximum concrete compressive concrete strain, (b) example moment-curvature prediction for an assumed constant axial load of 526 kN, and (c) construction of a slender column axial load-moment interaction diagram (considering second-order effects)

FRP layer, k = 1 Steel layer, j = 1 Concrete layer, i = 1 d s, 1 d c, 6 d c, N-1 d s, 2

k i=N k=N Steel layer, j = 2 Concrete stress at layer i = 1, f c

? ?c s, 1 ? c, 6 Concrete force at layer i = 6, C c, 6 ? c, N-1 ?s, 2 Cc, N-1 f s, 1 or Ts, 1 f f, 6 or T f, 6

f f, N-1 or T f, N-1 f s, 2 or Ts, 2 Idealized geometry Strain Stresses and forces Stresses and forces in of cross section distibution in concrete steel and longitudinal FRP

Figure 3-2: Fibre section analysis for determining the stresses and forces in concrete, steel and longitudinal FRP wrap at a given cross-section along the column's height (as required to derive the axial load-moment interaction diagrams and moment-curvature relationship)

? 1 P* M h ? yo o y 1 ? 1 y 2 ? 2 ? h-1 ? 2 y h-1

? h y h ? h ? h-1 Figure 3-3: Numerical integration of lateral deflection of a column

Axial resistance, kL/r = 10 455 450 445 kL/r = 10 kL/r = 33 420

415 410 Axial resistance, kL/r = 33 405 0 20 40 60 80 100 Number of vertical sections (a)

560 Axial resistance, kL/r = 10 555 550 545 kL/r = 10 kL/r = 33 445

440 435 Axial resistance, kL/r = 33 430 0 20 40 60 80 100 Number of vertical sections (b)

Figure 3-4: Variation in axial resistance of an (a) unconfined reinforced concrete column, and (b) reinforced concrete column confined with a single layer of FRP with an increasing number of vertical sections assumed in the analysis

AA 4 - 6.4 mm diameter bars 6.4 mm diameter steel ties at 100 mm c/c spacing FRP strengthening system Section A-A 25.0 51.0 Figure 3-5: Details of column specimens tested by Fitzwilliam (2006)

Top View A Top View B

LP Pi Gauges Strain Gauge FRP Wrapped Specimen Unwrapped Specimen

Strain Gauge Pi Gauge Pi Gauge Top View A Top View B

Figure 3-6: Instrumentation arrangement for both wrapped and unwrapped column specimens tested by Fitzwilliam (reproduced from Fitzwilliam, 2006)

Axial Load (kN) 500 400 300 200 100 0 kL/r = 10 kL/r = 18 kL/r = 26 kL/r = 33 Experimental Model 012345 Lateral Deflection (mm) Figure 3-7: Predicted and observed (Fitzwilliam, 2006) axial load-lateral deflection behaviour of for unwrapped reinforced concrete circular columns with increasing load (initial load eccentricity of 20 mm) Axial Load (kN) 800

600 400 200 0 kL/r = 10 kL/r = 18 kL/r = 26 kL/r = 33 Experimental Model 0 5 10 15 20 25 30 Lateral Deflection (mm) Figure 3-8: Predicted and observed (Fitzwilliam, 2006) axial load-lateral deflection behaviour for reinforced concrete circular column wrapped with one layer of FRP with increasing load (initial load eccentricity of 20 mm)

Axial Load (kN) 800 600 400 200 0 10C-1-2 33C-1-2 33C-1-4 Experimental Model 0 5 10 15 20 25 30 Lateral Deflection (mm) Figure 3-9: Predicted and observed (Fitzwilliam, 2006) axial load-lateral deflection behaviour of reinforced concrete circular columns wrapped with FRP in both the hoop and longitudinal directions (initial load eccentricity of 20 mm) Predicted Load Capacity (kN) 700 20

600 15

500 10

400 5

300 0 300 400 500 600 700 0 5 10 15 20 700 20

600 15

500 10

400 5

300 0 kL/r = 10 kL/r = 18 kL/r = 26 kL/r = 34

Unwrapped 1 hoop wrap (mm) 10C-1-2 33C-1-2 33C-1-4 Predicted Lateral Deflection at Max. Applied Load kL/r = 10 kL/r = 18 kL/r = 26 kL/r = 34

Unwrapped 1 hoop wrap 10C-1-2 33C-1-2 33C-1-4 300 400 500 600 700 0 5 10 15 20 Maximum Applied Load (kN) Lateral Deflection at Max. Applied Load (mm) (a) (b)

Figure 3-10: Performance of the numerical model in predicting (a) the maximum applied load and (b) the corresponding mid-height lateral deflection in comparison with experimental data (Fitzwilliam 2006)

Axial Load (kN) 500 0 Experimental kL/r = 10 Model kL/r = 18 kL/r = 26 kL/r = 33 Cross section interaction diagram 0 5 10 15 20 Moment (kN m) (a)

1000 Axial Load (kN) 500 0 0 5 10 15 20 Moment (kN m) (b)

Figure 3-11: Comparison of model predictions and experimental data (Fitzwilliam 2006) for axial load-moment paths of (a) unwrapped reinforced concrete columns and (b) reinforced concrete columns strengthened with a single layer of FRP (Legend for (a) is also applicable to (b))

Axial Load (kN) 800 600 400 200 0 33U 33C-1-0 33C-1-2 33C-1-4 0 5 10 15 20 25 30 Lateral Deflection (mm) Figure 3-12: Comparison of the axial load-lateral deflection behaviour of column specimens of initial unwrapped slenderness ratio of 33 from Fitzwilliam's (2006) experiments Axial Load (kN) 800

600 400 200 0 kL/r = 10 kL/r = 33 Unconfined 1 hoop wrap 1 hoop wrap & 2 longitudinal wrap 0 5 10 15 Lateral Deflection (mm) Figure 3-13: Summary of the predicted axial load-lateral deflection behaviour of reinforced concrete circular columns wrapped with FRP in both the hoop and longitudinal directions (initial load eccentricity of 20 mm)

600 Axial Load (kN) 400 200 0 Experimental Model, e = 20 mm Model, e = 12 mm 0 5 10 15 20 25 Lateral Deflection (mm) Figure 3-14: Predicted axial load-lateral deflection behaviour of column specimens of initial unwrapped slenderness ratio of 33, confined with 1 layer of hoop FRP wrap and 4 layers of longitudinal FRP wraps under different initial load eccentricities Axial Load (kN) 1200 1000 800 600 400 200 0 kL/r = 10 kL/r = 30 kL/r = 50 kL/r = 80 0 5 10 15 20 Moment (kN m) Figure 3-15: Predicted axial load-bending moment paths of various slenderness ratios for reinforced concrete columns strengthened with one layer of FRP

Axial Load (kN) 500 0 Experimental Cross section interaction diagram Slender interaction diagram Load moment paths 0 5 10 15 20 Moment (kN m) (a)

1000 Axial Load (kN) 500 0 0 5 10 15 20 Moment (kN m) (b)

Figure 3-16: Comparison of model prediction and experimental data (Ranger 2007) for strength interaction diagrams of (a) unwrapped reinforced concrete columns and (b) reinforced concrete columns strengthened with a single layer of FRP (Legend for (a) is also applicable to (b))

e = 1 mm e = 5 mm e = 10 mm e = 20 mm e = 30 mm e = 40 mm e = 1 mm e = 5 mm e = 10 mm e = 20 mm e = 30 mm e = 40 mm 10 Predicted Load Capacity (kN) 800

600 400 200 Unwrapped 1 hoop wrap Predicted Lateral Deflection at Max. Applied Load (mm) 5

0 Unwrapped 1 hoop wrap 200 400 600 800 0 5 10 Maximum Applied Load (kN) Lateral Deflection at Max. Applied Load (mm) (a) (b)

Figure 3-17: Performance of the numerical model in predicting (a) the maximum applied load and (b) the corresponding mid-height lateral deflection in comparison with experimental data (Ranger 2007)

Chapter 4 Mechanical Characterization of FRP Materials at High Temperature

4.1 General Fibre-reinforced polymer (FRP) materials are increasingly being used in strengthening or rehabilitating reinforced concrete structures that need to sustain loads higher than originally considered in design, or have deteriorated from damage such as electrochemical corrosion. In spite of many advantages of using FRPs, such as resistance to corrosion and ease of application, fire resistance remains a significant obstacle to strengthening structural members in buildings and parking garages because of these materials' susceptibility to degradation of mechanical and bond properties at elevated temperatures. As part of this research study, this chapter presents the results of tests to characterize the mechanical properties of a typical, currently available glass/epoxy FRP (GFRP) under various loading and thermal regimes, ranging from ambient temperature to 200°C. Although 200°C is considerably lower than temperatures normally experienced in a fire, it represents maximum temperature levels expected for an FRP strengthening system protected with external insulation during a standard fire (Bisby et al., 2005c). Results from the tests presented in this chapter are used to develop analytical models to represent the mechanical behaviour of GFRP for subsequent use in predictive fire simulation software, one example of which has been developed by the authors and is presented in Chapter 7.

4.2 Research Significance: Current Chapter Examining the performance of FRP strengthened reinforced concrete members by conducting full-scale standard fire tests is expensive and time consuming. As a result, a major component of the current research study involves developing numerical models that can simulate the behaviour of FRP strengthened concrete structural members at high temperature. To

accurately simulate the behaviour of FRP strengthened concrete structures, a detailed knowledge of the thermal and mechanical behaviour of FRP materials at high temperature, which is extremely scarce for the specific FRP systems under consideration, is critical. Rational and defensible numerical models could considerably reduce the costs incurred in standard fire testing of full-scale specimens. In addition, the critical temperature above which the FRP composite will have inadequate structural strength remains unknown. Such information is important for setting defensible service temperature limits for these systems.

4.3 Experimental Procedure 4.3.1 FRP specimen fabrication Under various loading and thermal regimes, FRP tensile and FRP single lap-splice strength tests were conducted to determine the mechanical and lap-splice bond properties, respectively. Details of the specimens for the two overall types of tests are shown in Figure 4-1.

GFRP coupon specimens for pure tension tests were made from two plies of saturated unidirectional glass fabric (Tyfo SHE-51A). Two 725 mm × 725 mm glass fabrics were cut and saturated with epoxy resin (Tyfo S resin), which was mixed according to the manufacturer's data sheet. The two saturated fabrics were then stacked on a glass plate with the longitudinal fibres oriented in the same direction in both fabrics. A second glass plate was then placed on top of the lay-up, and the lay-up was left to cure undisturbed for about 72 hours. In a similar manner, a single ply 725 mm × 725 mm GFRP panel was made to be used as gripping tabs during testing of the GFRP specimens to avoid failure in or near the wedge-action grips.

After 72 hours, both the double and single GFRP panels were removed from the glass plates and were cured in an air-conditioned laboratory at ambient room temperature and relative humidity ranging between 35 to 45% for approximately 28 days. Following the 28 days, four

glass tab strips were cut from the single ply GFRP panel to match the width of the double ply GFRP panel. The four glass tab strips were bonded to both sides to the two edges of the panel using epoxy putty (Sikadur 30), which was mixed as per the manufacturer specifications. The panels were again placed in between two glass plates and left undisturbed for at least 4 days.

After curing, the GFRP panels were cut into 38 ± 2 mm wide FRP coupons using a wet, abrasive diamond blade. The FRP coupons were left to dry about prior to testing.

Lap-splice FRP-to-FRP bond specimens were fabricated in a similar manner. However, in making these specimens, two 390 ± 2 mm long glass fabrics having a width of 25 mm were saturated with epoxy resin, and then carefully placed in between the two glass plates such that the two fabrics overlapped each other by 50 ± 2 mm. After removing the single lap-splice FRP panel from between the two glass plates and curing for 28 days, tabs were installed and the panel was cut into 38 ± 2 mm wide coupons for testing as was done for the direct tension coupons.

4.3.2 Test Conditions and Instrumentation Both steady state (heat then load) and transient state (load then heat) thermal regimes were considered. Prior to the tension tests, the thermal behaviour of the FRP was investigated.

The mechanical properties and bond strength of FRP materials are known to begin degrading at temperatures close to the glass transition temperature, D6,Úof the polymer resin component of the FRP material, which is typically between 65°C and 120°C (Bisby et al., 2005c). The glass transition temperature is generally considered to be the midpoint of the temperature range over which the polymer changes from a stiff, solid state into a flexible, rubbery state. Hence, the tests presented in this chapter were conducted at ambient temperature and at temperatures near the resin's D6.ÚPrior to the tension tests, differential scanning calorimetry (DSC) and dynamic mechanical thermal analysis (DMTA) were performed on samples of the polymer resin to investigate the thermal behaviour of the polymer using two different techniques and to obtain D6.Ú

Through DSC, the heat loss or gain from the resin was profiled as the resin was heated at a constant rate to determine the D6.ÚNote that DSC is a thermal, rather than physical, test method.

DSC measures the change in energy absorbed or emitted by the resin undergoing thermal transition as a function of temperature. DMTA measures, among other parameters, the change in Nñ NñNñ storage (elastic) modulus (D') and the change in loss modulus (D'). D6was measured in this test Ú

by identifying a dramatic change in the elastic modulus corresponding to a peak in the damping NñNñNñ behaviour as measured by tan DÜ ?D' L D' . DMTA is a physical test, and is therefore a more meaningful test method as compared with DSC when studying the mechanical response of FRPs at high temperature. Thermogravimetric analysis (TGA) was also conducted on the polymer resin, as well as on the bare fibres and cured FRP coupons, to observe the mass loss response with increasing temperature. The TGA helped determine temperatures at which thermal decomposition of the constituent materials occurred.

Based on the D6determined using DSC, the steady-state thermal condition tension tests Ú

presented herein were conducted on both tensile FRP coupons and single lap-splice FRP coupons at ambient temperature, 30°C and 15°C below D6, at D6, and 15°C above D6. Additional tests ÚÚ Ú

were conducted at 200°C to observe the material's performance at temperatures well above D6.Ú For the steady-state thermal condition tests, the FRP specimens were heated in the custom fabricated thermal chamber shown in Figure 4-2, to the desired temperature at 10°C/min, held at the specified temperature for 10 minutes to stabilize, and then loaded at a crosshead stroke rate of 3 mm/min to failure. This heating rate was chosen to simulate the heating that might be experienced by an insulated FRP strengthening system exposed to a standard fire, based on previous testing of full-scale FRP strengthened and insulated reinforced concrete members (Bisby et al., 2005c). The hold period was chosen to ensure that the entire sample was at a uniform temperature when it was loaded. The crosshead stroke was chosen to be half of the rate prescribed for FRP coupon testing at ambient temperatures by ACI (ACI 2004) to correlate with

the rate at which the images were being captured for the particle image velocimetry (PIV) and photogrammetry analysis ? a technique used to determine the axial deformation of the FRP specimens.

For the transient thermal condition tests, the FRP specimens were subjected to a specified sustained load for 10 minutes under ambient temperature and then heated at 10°C/min until failure. For tensile coupon tests, the sustained load was chosen to correspond to the highest strength achieved by any of the five coupons tested under steady-state conditions at 200°C, to ensure failure of the coupons under transient conditions. For the FRP-to-FRP bond strength tests at high temperature, the lap-splice specimens were loaded to either 10%, 20%, 40%, or 70% of their room temperature tensile. No investigation on the heating rate or the loading rate, both of which may be important, has been conducted thus far.

The tests were performed at elevated temperatures in an Instron Universal Testing Machine (UTM), which has a built-in thermal chamber with an internal dimension of 250 mm (width) × 250 mm (depth) × 300 mm (height), a maximum load capacity of 600 kN, and stroke capacity of 305 mm, as shown in Figure 4-2. Because of the well known difficulty of measuring strain during material testing at elevated temperatures, axial strains were measured using a unique deformation measurement technique based on particle image velocimetry (PIV) and close-range digital photogrammetry (White et al., 2003). In this measurement technique, digital images were captured of the FRP specimens inside the thermal chamber using a high-resolution digital camera.

Using PIV, 20 virtual strain gauges were created across the width of the coupons by defining 40 pixel ?patches? on the images of the FRP specimens as shown in Figure 4-3. The gauge length of these virtual strain gauges was approximately 40 ± 10 mm. During PIV analysis, the digital images were processed to track the movement of the pixel patches and hence measure differences in the displacements of the patches between two or more digital images. Based on the displacements measured from the image processing, the axial strain was calculated at several locations across the width of the coupons. This information was subsequently used to calculate

the elastic modulus of the coupons during testing as per ACI 440 requirements (ACI 2004). In addition to measuring axial strains using PIV, the FRP specimens that were tested at ambient temperature were instrumented with a 5 mm electrical resistance foil gauge to compare against the results obtained from PIV (Figure 4-4). All of the FRP specimens were also instrumented with two Type-K thermocouples on two different locations of the FRP surface (inside the thermal chamber) to observe the temperature distribution along the length of the FRP specimens.

4.4 Proposed Analytical Model There has been a broad interest in developing a generalized model for mechanical properties of FRP composites at high temperature. In recent years, research studies (Kulkarni and Gibson, 2003; Mahieux and Reifsnider 2001, 2002; Mouritz and Gibson, 2006; Gibson et al., 2006; Feih et al., 2007) have shown that the typical relationship between a mechanical property of a polymer composite and temperature under isothermal condition (that is, constant temperature throughout the material) is generally that shown in Figure 4-5. Since limited data exist on individual mechanical properties, such as modulus and strength, it is assumed for convenience that all mechanical properties can be fitted to the typical mechanical property versus temperature relationship shown in Figure 4-5. This analytical model assumes no significant change in the initial room temperature value of the mechanical property D2Ü until it reaches a critical áÜçÜÔß softening temperature D6, above which the mechanical property decreases with increasing Öå temperature to a residual value of D2, at which point the polymer composite has achieved a Ë

temperature of D6.ËThe mechanical property deceases beyond the critical softening temperature D6, because the polymer composite's polymer matrix begins to change from a hard and brittle Öå state to a viscous or rubbery state over the glass transition region. As previously discussed, the glass transition temperature D6of a polymer composite is often determined by either DSC or Ú

DMTA, and it is important to be aware of the nature of these tests and the meaning of their

outcomes, which can sometimes differ considerably for the same polymer resin, when using D6to Ú

set thermal performance limits for FRPs at high temperature. Beyond the temperature D6, the à

mechanical property decreases gradually. Research (Feih et al., 2007; Mouritz and Gibson, 2006) has shown that many polymer composites lose more than 50% of their mechanical properties before reaching D6.ÚHence, it is appropriate to describe the relationship between mechanical properties and temperature of a composite using the thermal properties of the polymer.

A number of mathematical functions have been explored by researchers to describe the mechanical property versus temperature relationship shown in Figure 4-5. Kulkarni and Gibson (2003) described the variation of the mechanical property with increasing temperature using a polynomial expression as shown in Eqn. 4-1: D2:D6;D 6 F D 6 D 6 F D 6 D 6 F D 67 Ü ÜáÜçÜÔß L 1 á Ü ç Ü Ô Üß á Ü çÜF Ô ß G Eqn. 4?1 FD = G FD = G F D = D2 5 D6 F D 6 6 D6 F D 6 7 D6 F D 6 Ü á Ü ç Ü Ô Úß Ú Ú

Where D2is:aDp6articu;lar property at temperature D,6D2Ü is the value of that property at room áÜçÜÔß temperature D6 , and D= , and D= Ü , D= are fitting constants. This empirical relationship requires á Ü ç5Ü6Ô ß 7 deducing the fitting constants D=,5D=, and D=for various configurations and types of FRP 67 material by performing small-scale fire tests of FRP materials.

Another model was derived from a physical basis by considering the effects on intermolecular bonds in the resin with increasing temperature (Mahieux and Reifsnider 2001, 2002; Mouritz and Gibson 2006). There are two major types of bonds in polymers ? primary and secondary. With increasing temperature, the primary bonds (which include the strong covalent intermolecular bonds) remain intact from the glassy to viscous state. The polymer undergoes transition when there is breakage or failure between the secondary bonds (such as, hydrogen, dipole, Van der Waals, etc.). Research studies (Mahieux and Reifsnider 2001, 2002; Mouritz and Gibson 2006) have derived an exponential relationship (Eqn. 5-2) based on the effects of

increasing temperature on these intermolecular bonds in the polymer resin. The model follows a Weibull distribution as a function of temperature: D6 à ED:2 e;xp F D2D:6;LËD 2 Ü á ÜF D 2 lF pG Eqn. 4?2 Ëç Ü ÔDß6 ÜáÜçÜÔß

Where, DIis the Weibull exponent having a value ranging between 15 and 21. Mahieux and Reifsnider (2002) validated Equation 4-2 successfully by fitting modulus versus temperature data.

Further investigation was conducted by Gibson et al. (2006) on the effects of increasing temperature on intermolecular bonds by investigating a number of empirical equations to describe the mechanical behaviour of FRP composites. They found that the behaviour of FRP composites at elevated temperature can be well described by functions based on a hyperbolic tangent function (Gibson et al., 2006; Feih et al., 2007; and Mouritz and Gibson, 2006): D2Ü á ÜE DD2 F D 2 D2D:6;LF ËçFÜÔáßÜËçÜÔDß:6 FD6;oáGD4 tanh kàDG Ö Ø á ç å Ô ß Eqn. 4?3 22 where, DGis an empirical constant describing the severity of the property degradation with DI increasing temperature, D6 is the temperature around which the curve is nearly symmetrical, D?DADJDPDND=DH and D4is a power law modification factor to account for resin decomposition. D4áequals 1 when á

there has been no loss from decomposition and zero when the resin has been completely volatized. It should be noted that the D6 indicated in Eqn. 4-3 and Figure 4-5 is not D?DADJDPDND=DH necessarily equal to the glass transition temperature.

4.5 Results and Discussion 4.5.1 Physical and Mechanical Properties

(where D6Úwas determined on the second heating cycle) and 55± 2°C based on DMTA. During DSC, the resin specimen went through a heating and cooling cycle; the specimen was heated to 150°C, cooled to 0°C, and then heated again to 150°C. The D6value obtained from using DSC Ú

was higher than from using DMTA because, the polymer resin had undergone through a post- curing regime in the first heating and cooling cycle prior to determining the D6from the second Ú

heating cycle. Figure 4-6(b) shows results from the second heating cycle. Based on the measured D6values obtained from DSC, test temperatures were selected on the basis of recommended Ú

service temperature limits as per ACI 440 requirements (ACI, 2002; ACI, 2008) as 20°C (ambient), 45°C (D6? 30°C), 60°C (D6 ), 90°C (D6 Ú ? 15°C), 75°C (D6 + 15°C) and 200°C. From ÚÚÚ the TGA, the FRP composite and the resin polymer began to lose their initial room temperature mass at about 360°C. However, the fibres showed no major loss in their mass during the TGA, as expected. Around 500°C, the FRP composite and the polymer resin lost about 50% and 93% of their initial room temperature masses, respectively. During the DMTA, a sharp decrease in the resin's elastic modulus was observed beginning at about 35°C, and the resin lost about 50% of its initial elastic modulus at a temperature of approximately 48°C. Also, there was a dramatic change in the damping loss factor :ta)naDt aÜbout 55°C, thus identifying the D6of the resin Ú

Five tensile tests were performed under steady-state thermal conditions at each of the above temperatures. Figure 4-7 shows the stress-strain plots of GFRP tensile coupons at room temperature. To calculate the tensile strength, the recorded axial load was divided by the FRP specimen cross section area, which was calculated by multiplying the nominal thickness of the FRP coupon with the measured width of the FRP coupon. Axial strains in the coupons were measured using PIV analysis. The strain analysis was performed using twenty virtual axial strain gauges across the width of the coupons, and the axial strains were observed to vary by up to 0.5% strain across the width of the FRP coupon specimens at failure of the coupons. This variation can

presumably be attributed to non-homogeneities in the coupons, as well as uneven gripping at the ends of the coupons, which indicates that results from coupon tests using wedge action grips and an isolated strain gauge to measure axial strain should be viewed with some caution, particularly as far as strain measurements taken with single isolated foil gauges are concerned. Also shown in Figure 4-7 are the strains measured by a foil gauge bonded on the FRP specimen at the centreline, which was used to validate the optical technique. Good agreement is obtained between the foil and optical gauges since the foil gauge measurements fall within the range of variation of the optical measurements across the width of the coupon. The foil gauge on FRP tensile Coupon 2 may not have been aligned properly along the length of the FRP coupon and as a result the foil gauge on the coupon specimen recorded lower strains than the optical gauges. Additional validation of this optical technique for measuring strains in FRPs is given by Bisby and Take (2009) and Bisby et al. (2007). Despite the variation in observed axial strain over the coupon width, the axial strains from all 20 virtual strain gauges were averaged across the width to obtain a global stress-strain curve for the coupons. From this global stress-strain curve, the tensile chord modulus was calculated using stress values corresponding to 0.1% and 0.3% strain (ACI 2004).

At room temperature, the GFRP coupons had an average tensile strength of 412 ± 22 MPa and a tensile chord modulus of 18800 ± 1800 MPa, based on a nominal thickness of 2.6 mm (which is the nominal thickness of two layers of FRP).

Figure 4-8 and Table 4-1 show the normalized tensile strength and elastic modulus data with increasing exposure temperature. The GFRP coupons tested in this chapter experienced tensile strength losses of about 50 ± 9% (average ± one standard deviation) and losses of tensile elastic modulus about 70 ± 13% at 60°C or D6? 15°C. Comparable losses of strength and Ú

modulus were observed at 75°C (D6), 90°C (D6+ 15°C) and 200°C, with little apparent additional ÚÚ degradation in either strength or stiffness at these higher temperatures. This behaviour is likely due to loss of interaction and load sharing between fibres for all elevated temperature exposures,

due to matrix softening, such that the elevated temperature strength and stiffness values effectively represent the results that would be obtained by testing dry fibres without a resin matrix. The data also suggest that, with adequate anchorage maintained at low temperature, the GFRP strengthening system tested herein can retain at least 40% of its room temperature strength at temperatures up to 200°C. Additional testing is needed above 350°C, where the matrix component of the FRP begins to decompose rapidly, Figure 4-6a.

While considerable variability exists in the data shown in Figure 4-7 and Figure 4-8, it should be noted that none of the coupons failed near the grips. All the coupons that were tested above 60°C (D6-15°C) ruptured in the region of the FRP that was inside the thermal chamber, Ú

indicating that the reduced strength and stiffness was not a consequence of thermal degradation in the gripping region. There were a few coupons below 60°C (D6-15°C) that failed outside the Ú

thermal chamber but away from the grips at 45°C (D6-30°C), which is assumed to be a random Ú

phenomenon not associated with thermal exposure. Failure of the GFRP coupons at room temperature was sudden and violent (Figure 4-9). The failure mode for coupons tested at 45°C (D6- 30°C) and 60°C (D6- 15°C) was similar to the failure mode observed at room temperature, ÚÚ but was less violent than that observed at the higher temperatures. However, with increasing temperature above 75°C (D6), the coupons split longitudinally (refer to Figure 4-10) as they Ú

approached failure and thus failed much more gradually. This splitting behaviour is thought to be associated with loss of interaction between the individual fibre rovings due to resin softening at elevated temperature.

To investigate the behaviour of the GFRP coupons under transient thermal conditions, five coupons were subjected to a sustained axial stress of 203 MPa, which corresponded to the highest strength achieved by one of the five coupons tested at 200°C under steady-state thermal conditions and also approximately 50% of the room temperature average strength. The coupons

were then exposed to increasing temperature. Failure occurred in the GFRP coupons at 57 ± 3°C at a strain of 1.42 ± 0.07%.

4.5.2 FRP-to-FRP Bond Properties Figure 4-11, Table 4-2 and Table 4-3 show the normalized lap-splice bond shear strength data with increasing temperature under both steady-state and transient thermal conditions. The average FRP-to-FRP bond shear strength achieved by the single lap-splice GFRP specimens at room temperature was 9.2 ± 1.1 MPa. To calculate the FRP-to-FRP bond shear strength, the recorded axial load was divided by the lap-splice area, which was calculated by multiplying the overlap length of the FRP with the measured width of the FRP. With increasing temperatures, the single lap-splice GFRP coupons experienced shear strength losses of 30 ± 8% at 45°C (D6- 30°C) Ú

and 77 ± 1.3% at 75°C (D6)Úunder steady-state conditions. Comparatively, under transient conditions, the single lap-splice GFRP coupons experienced shear strength losses of approximately 29% at 54 ± 2°C and 80% at 71 ± 2°C. Little additional degradation was observed in the shear strength of the lap-splice beyond D6.ÚThe residual shear strength was about 16% and 10% of the average room temperature shear strength of the lap-splice under steady-state and transient conditions, respectively. All the coupons that were tested at elevated temperatures failed in the lap-splice region inside the thermal chamber as shown in Figure 4-12.

Based on the results from the two types of mechanical tests, the bond strength of the FRP lap-splice is more critical when designing FRP strengthened reinforced concrete columns in a fire situation because the degradation of the lap-splice bond shear strength is considerably more severe than degradation of the FRP's tensile strength with increasing temperature. This occurs because the FRP-to-FRP bond strength depends largely on the strength of the resin matrix which is much more susceptible to elevated temperature than the fibres. As the resin matrix degrades in

the GFRP tensile coupons, the load is transferred to the fibres; thus, the GFRP tensile coupons were able to retain more than 40% of their room temperature strength at 200°C.

These results from the lap-splice FRP specimens should be taken with caution because they represent the most severe possible test of FRP-to-FRP bond strength and are not representative of longer FRP bond/splice lengths used in practice. Thus, more research is required to investigate longer bond lengths and to determine the consequences for member performance in fire.

4.6 Implementation in a Structural Fire Model As previously mentioned, the long term objective in performing the tests presented above is to develop empirical/analytical relationships to describe the variation in mechanical and bond properties of various currently available FRP strengthening materials and systems with temperature for subsequent use in numerical fire simulation models. The author has, on the basis of previously published research on the high temperature performance of polymer composites (Kulkarni and Gibson 2003; Mahieux and Reifsnider 2001, 2002; Mouritz and Gibson 2006;

Gibson et al., 2006; Feih et al., 2007), selected a sigmoid curve based on a hyperbolic tangent function in to describe the mechanical and bond property degradation of GFRP composites. In this study, D4was taken to be 1.0 because, based on TGA, the resins do not experience any á

significant amount of decomposition until 350°C and D2Ü was the average of the observed áÜçÜÔß values of the property at room temperature. Hence Eqn. 4-3 becomes: D2Ü E DD2 FËD 2Ü Ô ß D2D:6;L á Ü ËçFÜ Ôá ßÜ ç · D:6 F D6;o Eqn. 4?4 tanh kàDG Ö Ø á ç å Ô ß 22 Using a non-linear multi-parameter least squares regression analysis, the terms D2,ËDG, and à

D6Ö in the above equation were determined using SigmaPlot? software to provide an ØáçåÔß approximation to the experimentally observed behaviour. Based on the values obtained from the

regression analysis, the sigmoid curves for the mechanical and lap-splice bond properties are The coefficient of determination, D46 plotted on Figure 4-8 and Figure 4-11. , which is a fraction between 0 and +1.0, was calculated using SigmaPlot? software to determine how well the predicted values from the estimated mathematical model (Eqn. 5-4) represents the set of test data.

The coefficient of determination, D46 , gives the percent of the data closest to the line of best fit, for example in Figure 4-8(a), D46 L 0.m90eans that 90% of the total variation in the test data can be explained by the estimated mathematical model and the other 10% of the total variation Higher values of D46 remains unexplained. indicate that the estimated mathematical model comes closer capturing the test data. To further determine the goodness-of-fit, a 95% confidence band was determined using SigmaPlot? software and is shown in Figure 4-8a. The confidence band shown in Figure 4-8a has a 95% chance of containing the true best-fit curve. This does not, however, mean that it will contain 95% of the data points. The predicted tensile and FRP-to-FRP bond shear strength curves in Figure 4-8 and Figure 4-11 show satisfactory D46 values, which are equal to or higher than 0.90, and the 95% confidence band was also found to be close to the predicted curves. Although the analytical curve in Figure 4-8b was able to capture the trend of the test data, substantial scatter was observed in the elastic modulus test data, hence the relatively low D46 value of 0.65, and the 95% confidence band for the elastic modulus curve was also found to be wider in comparison with the 95% confidence band obtained for the tensile and FRP-to-FRP shear bond strength curve. This may be due to the small number of data points used to fit the tensile modulus curve; however, the analytical curve was able to capture the trend of the test data.

After performing the regression analysis, the term D2was approximately the average Ë

value of the property at 200°C. The values of DGare presented in Figure 4-8 and Figure 4-11. à

Under transient conditions, the degradation of the FRP-to-FRP bond strength is slightly more severe than that observed under steady-state conditions (refer to Figure 4-13). Based on the

regression analysis, D6Ö Øwas found to be between 47°C and 52°C for the strength, stiffness, áçåÔß and lap-splice bond properties under steady-state conditions, whereas, under transient state condition, D6Ö Øwas found to be 58°C for the FRP-to-FRP bond properties. It is significant áçåÔß that the range of values obtained for D6Ö Øfrom regression analysis was close to the áçåÔß temperature (47°C) where the polymer lost 50% of its initial elastic modulus during DMTA. This indicates that it may be possible to use the storage modulus loss curve from DMTA as a proxy for lap-splice bond degradation in externally-bonded FRP strengthening systems. Once the analytical relationships are derived for strength, stiffness and bond properties, they will be incorporated into numerical models to predict the fire endurance of GFRP strengthened reinforced concrete columns. However, further tests and investigations are required on different FRP composites at elevated temperatures to recommend a range of values for DGàand to determine whether DMTA could be used to rationally estimate D6Ö without performing tension tests. ØáçåÔß

4.7 Conclusion This chapter presents the results of an ongoing experimental study aimed at developing a more complete understanding of the degradation in mechanical and bond properties of FRP strengthening systems for infrastructure at elevated temperatures. Based on the results of these tests on GFRP coupons, the wet lay-up glass/epoxy FRP material tested in this chapter experienced 50% loss in tensile strength, 30% loss in tensile elastic modulus, and 60% loss in FRP-to-FRP bond strength at temperatures 15°C below the glass transition temperature of its resin matrix. Furthermore, based on the data presented herein, the wet lay-up GFRP material, with sufficient anchorage, can maintain 40% of their tensile strength and 70% of their elastic modulus at temperatures well in excess of the glass transition temperature of their resins. Much of the mechanical and FRP-to-FRP bond property degradation occurred below the glass transition temperature. However, the degradation of the FRP-to-FRP bond strength was more severe than

the deterioration of the tensile strength and modulus. Approximately 90% of the FRP-to-FRP bond strength was lost at temperatures slightly above the glass transition temperature of FRP lap- splice specimens, which had an overlap length of 50 mm. The loss of strength and stiffness appears to be due to loss of load sharing between the individual fibre rovings, essentially resulting in dry fibre behaviour at temperatures close to or exceeding the glass transition temperature of the resin. The hyperbolic tangent function model in Eqn. 4-4 presented herein is able to describe the mechanical and bond property degradation satisfactorily. However, considerable amount of additional testing is required before the true behaviour of FRP strengthening systems, under load, at elevated temperature can be accurately and reliably described.

Table 4-1: Tensile strength and modulus of FRP coupons under steady-state condition

Tensile Strength Tensile Modulus FRP FRP Temperature (MPa) (GPa) Thickness Width (°C) Test (mm) (mm) Test value Average Average value 37.4 415 18970 37.8 388 410 16120 18800 20 2.6 37.3 434 ± 21400 ± 37.8 431 20 19140 1800 37.6 391 18330 38.4 340 20380 38.2 412 325 18640 16900 45 2.6 38.1 301 ± 15120 ± 37.6 273 55 16930 2700 37.8 290 13590 38.0 246 16180 38.0 207 210 13920 13100 60 2.6 37.0 207 ± 13530 ± 37.8 232 35 12430 2500 37.2 154 9440 38.4 225 16070 38.6 226 195 12790 14400 75 2.6 38.5 183 ± 13450 ± 37.4 160 30 15780 1400 37.7 186 14060 38.0 216 15290 38.8 177 180 13830 11700 90 2.6 37.6 150 ± 13840 ± 38.1 196 25 9180 3700 37.4 167 6550 38.1 203 17260 37.8 195 190 14530 15300 200 2.6 37.8 190 ± 16020 ± 38.0 178 10 16310 2000 37.8 179 12170

Table 4-2: Failure temperature and strain of FRP coupons under transient-state condition

Failure Failure Strain Sustained Load FRP FRP Temperature (°C) (%) (% of Ultimate Thickness Width Condition) (mm) (mm) Test Test Average Average value value 38.0 55 -- 37.8 61 57 1.425 1.428 50 2.6 37.7 55 ± 1.494 ± 37.5 58 3 1.365 0.065 37.8 62 1.397

Table 4-3: Shear strength of FRP single lap-splice coupons under steady-state condition

Shear Strength Overlap FRP Temperature (MPa) Length Width (°C) Test (mm) (mm) Average value 39.2 7.5 37.6 10.6 9.2 20 51 38.9 9.4 ± 38.7 9.3 1.1 40.0 9.5 37.9 6.6 38.7 6.4 6.5 45 51 38.7 5.8 ± 41.3 7.8 0.8 38.4 6.0 38.7 3.4 38.6 4.0 3.8 60 51 39.0 4.7 ± 38.1 3.2 0.6 39.9 3.8 38.8 2.2 39.6 2.2 2.1 75 51 37.3 1.9 ± 38.8 2.2 0.1 39.6 2.1 38.5 1.8 39.5 1.7 1.9 90 51 38.9 2.0 ± 40.5 1.9 0.1 37.9 2.0 39.4 1.3 40.4 1.0 1.3 200 51 38.0 1.4 ± 39.9 1.1 0.2 38.8 1.4

FRP specimen GFRP tabs 38 mm 65 mm 65 mm 725 mm

65 mm 65 mm

50 mm overlap (a) (b) Figure 4-1: FRP specimen schematics for (a) tensile tests, and (b) FRP-to-FRP bond overlap test (Dimensions are in mm)

(a) (b) (c) Figure 4-2: (a) Universal testing machine, thermal chamber, and data acquisition system, (b) thermal chamber, and (c) wedge-action gripping system outside the chamber

Figure 4-3: Test patches on FRP specimens for image processing using PIV (photo rotated 90° clockwise)

Foil strain gauge Figure 4-4: Electrical resistance foil gauge (5 mm) on FRP coupons Mechanical Property, P P initial T cr

P central T g P R TT central m Temperature, T Figure 4-5: Typical relationship between mechanical property and temperature of FRP composite under isothermal condition

% of Initial Mass 120 100 80 60 40 20 0 FRP Resin Fibres 0 100 200 300 400 500 Temperature (?C) (a) Heat Flow (W/g) 6 4 2 0 -2 -4 -6 Specimen 1 Specimen 2 0 25 50 75 100 125 150 175 Temperature (?C) (b) 100 % of Initial Modulus 50

0 T = 55oC = 48oC g T 50 1.5 % of Initial Modulus Tan ? 1.0 ? Tan 0.5

0.0 0 50 100 Temperature (oC) (c)

Axial Stress (MPa) 500 400 300 200 100 0 PIV strain gauges 1-20 Average strain Foil Gauge

E = 21400 MPa PIV E = 22200 MPa Foil 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Strain (%) (a) Axial Stress (MPa) 500 400 300 200 100

0 PIV strain gauges 1-20 Average strain Foil gauge E = 19140 MPa PIV E = 23850 MPa Foil 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Strain (%) (b) Axial Stress (MPa) 500 400 300 200 100

0 PIV strain gauges 1-20 Average strain Foil gauge E = 18330 MPa PIV E = 19670 MPa Foil 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Strain (%) (c)

Figure 4-7: Stress-strain plots of FRP tensile coupons at ambient temperature of FRP tensile coupons specimens (a) 1, (b) 2, and (c) 3

Test data Predicted 95% confidence band 1.5 Normalized Tensile Strength 1.0

0.5 0.0 T = 75?C g P = 0.46 R k = 0.0882 m T = 47?C central R2 = 0.90 0 50 100 150 200 250 Temperature (?C) (a)

Test data Predicted 95% confidence band 1.5 Normalized Tensile Modulus 1.0

0.5 0.0 T = 75?C g P = 0.67 R k = 0.1024 m T = 51?C central R2 = 0.65 0 50 100 150 200 250 Temperature (?C) (b)

Figure 4-8: Normalized (a) tensile strength and (b) modulus of FRP coupon specimens under steady-state condition

(a) (b) Figure 4-9: Failure of GFRP coupons at ambient temperature (a) just before failure, and (b) just after failure (photos rotated 90° clockwise)

(a) (b) Figure 4-10: Failure of GFRP coupons at 200°C (a) just before failure, and (b) just after failure. Loss of interaction between rovings is evident (photos rotated 90° clockwise)

Test data Predicted 95% confidence band 1.5 Normalized Shear Strength 1.0

0.5 0.0 P = 0.16 = 75?C R T g k = 0.0509 m

T = 52?C central R2 = 0.96 0 50 100 150 200 250 Temperature (?C) (a)

Test data Predicted 95% confidence band 1.5 Normalized Shear Strength 1.0

0.5 0.0 P = 0.10 = 75?C R T g k = 0.0677 m

T = 58?C central R2 = 0.95 0 50 100 150 200 250 Temperature (?C) (b)

Figure 4-11: Normalized shear strength of FRP under (a) steady-state and (b) transient conditions

Figure 4-12: Failure of GFRP lap-splice coupons at elevated temperatures (photos rotated 90° clockwise)

1.5 Normalized Shear Strength 1.0 0.5 0.0 Steady-state condition Transient state condition 0 50 100 150 200 250 Temperature (?C) Figure 4-13: FRP to FRP bond strength under steady-state and transient conditions

Chapter 5 Full-Scale Fire Tests of FRP Confined Circular Columns

5.1 General Research has demonstrated that FRPs can be used efficiently and safely in strengthening and rehabilitation of reinforced concrete reinforced concrete structures. Hence, FRP materials have been successfully applied in the rehabilitation of bridges in Canada and elsewhere, such as the Champlain Bridge, Webster Parkade, Country Hills Boulevard Bridge and Ste-Émélie-de- l'Énergie Bridge (Rizkalla and Labossière 1999). However, the use of FRPs in buildings has been limited due to uncertainties regarding their behaviour in fire. The matrix components of currently available FRPs are combustible, raising concerns as to the fire performance of FRP strengthened reinforced concrete columns in buildings, where fire is one of the primary design considerations. As part of this ongoing research project, between Queen's University and the National Research Council of Canada (NRC) and industrial partners, the fire performance of FRP wrapped reinforced concrete column is being studied. Based on these studies, design recommendations and rational guidance are being developed for FRP wrapped reinforced concrete axial members with respect to fire safety considerations. Previously, two fire tests on circular columns (Bisby, 2003; Bisby et al., 2005a) and one square concrete column (Kodur et al., 2005) were conducted. This chapter presents the results of fire tests conducted recently on three full-scale FRP wrapped reinforced concrete circular columns subjected to a sustained axial load and the ASTM E119 standard fire.

Many engineers are hesitant to use FRPs in buildings due, in part, to the relative lack of knowledge of their performance during fire (Harries et al., 2003; Karbhari et al., 2003). Based on the limited available information (Kodur, 2001; Kodur and Baingo, 1998; Bisby et al., 2005b), a number of fire risks are associated in using FRPs in buildings, such as smoke generation, toxicity, flame spread, etc. Furthermore, the polymer resins of FRPs degrade above their glass transition temperatures (ACI 2008), thus raising potential concerns regarding the structural integrity of FRP strengthened reinforced concrete columns during fire. Because of these concerns, the American Concrete Institute (ACI, 2008) suggests that, unless the FRP temperature remains below its critical temperature (which they recommend to be D6Ú F 15uBnd(er service condition and D6in a Ú

fire situation) during fire, the strength contribution from FRPs should be ignored in an FRP strengthened concrete structures. Thus, the reinforced concrete structure alone must be able to endure the fire for the required length of time.

Williams, 2004) have shown that FRP strengthened reinforced concrete structures with adequate supplemental fire protection can endure in excess of 4 hours of exposure to the standard fire.

However, the performance of FRP strengthened concrete columns without any supplementary fire protection has not yet been explored. This paper investigates the fire endurance of FRP strengthened reinforced concrete circular columns with and without fire protection, and also investigates the effectiveness of two new supplementary fire protection systems.

5.3.1 Column Specimens The portion of the overall experimental program presented in this thesis involved fire tests on three FRP wrapped circular concrete columns, two of which were insulated with new fire protection systems that were developed by industry partners. Because these test specimens were part of an ongoing study (following on from work by Bisby (2003)), the FRP wrapped column without protection was designated as Column 3, and the two FRP wrapped and insulated columns as Column 4 and Column 5. Other than the type of concrete, the three columns were identical, with 400 mm diameter and 3810 mm length from end plate to end plate. The cross-sectional dimensions and reinforcement details of the columns are given in Figure 5-1. The longitudinal steel reinforcement in the columns consisted of eight 19.5 mm diameter deformed bars that were symmetrically placed with 40 mm clear cover to the spiral reinforcement. The lateral reinforcement for the columns consisted of 11.3 mm diameter deformed steel spiral with a centre- to-centre pitch of 50 mm. The longitudinal reinforcing bars and the steel spiral had measured yield strength of 456 MPa and 396 MPa, respectively (Bisby, 2003) after performing tension tests.

Columns 3 and 4 were fabricated with siliceous (granite) aggregate concrete and Column 5 with crushed (carbonate) aggregate concrete. The mix proportions for the concrete are provided in Table 5-1. The average 28-day compressive cylinder strength of the siliceous and carbonate aggregate concretes were 32.7 MPa and 38.5 MPa, respectively, and the corresponding compressive strength of the siliceous and carbonate aggregate concretes on the day of the fire test were 32.9 and 40.1 MPa, respectively.

Prior to fire testing, two layers of carbon FRP (CFRP) were bonded to the exterior of the three circular columns using an epoxy saturant/adhesive (Figure 5-2). Two different CFRP

strengthening systems (MBrace CF130 and SikaWrap Hex 103C) were used in this portion of the project. MBrace® CF130 was used in strengthening columns 3 and 4, and SikaWrap Hex 103C in column 5. Details of the FRP wrap and insulation systems are provided in Table 5-4. The MBrace carbon FRP had an ultimate tensile strength of 3800 MPa and a tensile elastic modulus of 227 GPa (based on the nominal thickness of 0.165 mm as suggested by the manufacturer). The SikaWrap Hex carbon FRP had an ultimate tensile strength of 849 MPa and tensile elastic modulus of 70.5 GPa (based on the nominal thickness of 1.016 mm as suggested by the manufacturer). Note, the FRP properties stated herein were presented by the manufacturer (but were not tested by the author).

Columns 4 and 5 were insulated with two different types of spray-applied cementitious mortar-based fire protection systems (an MBrace insulation system and a Sika insulation system) each of which was developed by one of the industry partners. The MBrace insulation system was used on Column 4 and the Sika insulation system on Column 5. The MBrace insulation system is a spray-applied cementitious mortar-based fire protection system containing various insulating fillers (developed by the manufacturer), which prevents mechanical deterioration to concrete structures above 300°C (as stated by the manufacturer) and explosive spalling when concrete is exposed to high heating rate. The Sika insulation system is a spray-applied mortar-based protection system with vermiculite as the insulating filler, which gives its strong insulation properties (as stated by the manufacturer). The insulation systems were sprayed on to the surface of Columns 4 and 5 using a shotcreting rig (Figure 5-3 and Figure 5-4). During the spray application of the MBrace insulation system, an accelerant was used for rapid curing of the insulation system. Although no accelerant was used in the Sika insulation system, 3.2 mm diameter steel mesh having 50 mm by 50 mm openings was attached to the surface of the column to provide reinforcement for the Sika insulation system prior to the application of supplemental fire protection on Column 5 (Figure 5-4a). After installation of the insulating material, using a

shotcreting rig, the average thicknesses of the insulation on Columns 4 and 5 were measured to be 53 mm and 44 mm.

The design load capacity and superimposed loads that were imposed on the columns during testing, based on existing North American design codes and guidelines (ACI, 1995; ACI, 2005; ACI, 2002; ACI, 2008; CSA, 2005; CSA, 1994; CSA, 2002; ISIS Canada, 2001b) are presented in Table 5-2 and Table 5-3. Details of the load calculations are provided in Appendices A and B. The axial design capacity of unwrapped Columns 3 and 4 was calculated to be 2702 kN, and, for Column 5, it was 3151 kN according to ACI 318-05 (ACI, 2005). However, based on CSA A23.3-04 (CSA, 2005), the axial design capacity of the unwrapped Columns 3 and 4 was 2445 kN and, for Column 5, it was 2782 kN. The FRP strengthening systems theoretically increased the axial design capacity of Columns 3 and 4 by 25% and Column 5 by 27% based on the ACI 440 design document (ACI, 2008). However, based on CSA S806-02 (CSA, 2002), the increase in axial strength of Columns 3 and 4 was about 9% and, for Column 5, it was about 18%.

Columns 3 and 4 were fire tested during the year 2005, hence ACI 440-02 (ACI, 2002), CSA S806-02 (CSA, 2002), and ISIS guidelines (2001b) were all considered to determine the sustained superimposed load that should be imposed on the columns during the fire tests.

According to the ACI 440-02 design guidelines (ACI, 2002), the axial strength of the wrapped Columns 3 and 4 increased by about 63%, however, the axial strength increase was about 32% according to ISIS design guidelines (2001b). Because the strength increase calculated using the ACI 440-02 design guidelines (ACI, 2002) was considered unconservative (based on previously noted research by Bisby et al. (2005d)), the superimposed load for the fire tests of FRP wrapped Columns 3 and 4, which was taken as 2635 kN, was based on the wrapped design load capacity calculated using the ISIS Canada design guidelines (2001b). When the fire test of Column 5 was conducted, which occurred in the year 2008, the updated version of ISIS design guidelines had adopted the provisions in CSA S806-02 (2002) for designing FRP strengthened axial concrete

members and the ACI 440 design model had changed substantially. Hence, ACI 440-08 (ACI, 2008) and CSA S806-02 (CSA, 2002) design codes were considered to determine the superimposed load to be applied to Column 5 during its fire test. To maintain similar fire test load ratios as were used for Columns 3 and 4, the superimposed load for the fire test of FRP wrapped Column 5 was based on the wrapped design load capacity calculated using ACI 440-08 design code (2008), and was calculated to be 3054 kN.

5.3.2 Fire Endurance Test Conditions and Procedure Prior to testing, the columns were instrumented with chromel-alumel (Type K) thermocouples. Figure 5-5 shows the location and number of the sensors in the columns, with some minor differences noted for Columns 4 and 5. The column specimens were fire-tested in the full-scale column furnace at the National Research Council of Canada (NRC), Ottawa. This test furnace was designated to expose the column specimens to a standard time-temperature fire curve and to subject the columns to a sustained concentric axial load during the fire test, as prescribed by ASTM E119 (ASTM, 2001) or CAN/ULC S101 (ULC, 2004). The end plates of the column specimens were bolted to the test frame loading head at the top and to a hydraulic jack at the bottom, resulting in a fixed-fixed end condition. Both columns 3 and 4 were subjected to a concentric axial applied load of 2635 kN, which represented 56% of the ultimate strengthened design capacity according to ACI 440 (ACI, 2002) and column 5 to a concentric axial applied load of 3054 kN, which represented 76% of the ultimate strengthened design capacity according to the ACI 440-08 (ACI, 2008). These loads were held constant throughout the fire tests of the columns, until the hydraulic jack could not maintain the load, at which point the columns were assumed to have failed and the test was stopped. If the column specimen did not fail under the sustained axial load during the 5 hours of the test, the load was steadily increased until the column failed, at which point the test was stopped.

During the fire test of Column 5, the furnace abruptly stopped 3 hours into the fire test, and it took about 12 minutes to bring the temperature inside the chamber back to the prescribed temperature-time curve as stated in ASTM E119 (ASTM, 2001). After 4 hours, due to technical difficulty, the furnace was unable to maintain the temperature in the chamber similar to the standard temperature-time curve as stated in the ASTM E119 (ASTM, 2001). At this point, the load was steadily increased until Column 5 failed.

5.4 Results and Discussion Table 5-4 gives a summary of the results of the fire endurance tests. Column 3, which was not protected by supplementary insulation, resisted the sustained concentric load of 2635 kN for 210 minutes, at which point sudden failure occurred. Prior to failure of Column 3, spalling of the concrete cover was observed from the view ports along the walls of the furnace leading to the sudden crushing of the concrete core. Figure 5-6 shows Column 3 prior to and after the fire tests.

After close inspection (once Column 3 had cooled down), there was no obvious buckling of the longitudinal reinforcing bars nor deformation of the spirals in Column 3. The insulated Column 4, on the other hand, was able to maintain the applied load for 300 minutes, after which time the load was gradually increased to induce failure which occurred in a non-violent manner by apparent crushing of the concrete core at about 4583 kN. The supplemental insulation system remained intact for the entire duration of the fire test and even after failure of Column 4 (refer to Figure 5-7). However, minor cracks, not more than 5 mm wide by the end of the test, developed and widened during the fire test. The insulated Column 5 was able to maintain the applied load for 240 minutes, after which time the load was gradually increased until failure occurred at about 4984 kN. However, it should be noted that, due to furnace malfunction, it was decided to load the column to failure after 240 minutes rather than 300 minutes. Prior to the fire test, it was observed that minor cracks had developed on the surface of the insulation system (Figure 5-8). These

cracks gradually widened to about 5 to 8 mm during the fire exposure, which was estimated through visual inspection from one of the viewports on the side of the furnace chamber 120 minutes into the fire test, and soon after 150 minutes flames were observed emanating from these cracks (Figure 5-8) The widening of the pre-existing cracks on the surface of the insulation system was due to thermally-induced shrinkage of the insulation and the flaming was thought to be associated with localized burning of the polymer adhesive/matrix beneath the insulation at the location of the crack. Otherwise, the insulation system on Column 5 remained intact for 240 minutes until the column failed by apparent crushing of the concrete core (Figure 5-9). The steel mesh reinforcement within the insulation system prevented the spalling of the insulation from the column surface. Comparing the fire performance of uninsulated and insulated columns, the supplemental insulation provided at least an additional 90 minutes of fire endurance to the FRP strengthened column and increased the failure load by over 74%.

5.4.1 Thermal Behaviour Figure 5-10 shows the recorded temperature-time curves at the level of the FRP wraps, insulation, and reinforcing bars during the fire tests of Columns 3, 4 and 5. Early in the fire test, the FRP wrap on Column 3 ignited causing the temperature to rise rapidly within the FRP, thus demonstrating the sensitivity of FRP to combustion. Since concrete has a relatively low thermal conductivity, the temperature of the longitudinal reinforcing steel, which was 50 mm within the concrete, was much lower than the temperature recorded at the FRP/concrete interface. The highest temperature recorded on the longitudinal reinforcing steel during the Column 3 fire test (prior to failure) was about 517°C. However, the highest temperature recorded on the steel reinforcement during the fire tests of Column 4 and 5 was much lower (approximately 280°C for Column 4 and 145°C for Column 5). The reader should take note that the highest temperature recorded on the reinforcing steel in Column 4 was much higher than Column 5 because, Column

after 240 minutes into the fire test, the temperature recorded on the reinforcing steel of Column 4 was about 193°C, which was about 48°C greater than the temperature observed for reinforcing steel of Column 5. Even though these columns were thermally insulated, the temperature of the FRP/concrete interface surpassed the glass transition temperature of the FRP, which was 71°C for the carbon FRP system used on Column 4 and 85°C for the FRP system on Column 5, at about 34 minutes and 60 minutes into the fire tests of Column 4 and 5, respectively. Comparing the two insulation systems, the Sika insulation system having an average thickness of 44 mm performed better by maintaining the temperature of the carbon FRP system below the glass transition temperature for 30 minutes longer than the MBrace insulation system, which had an average thickness of 53 mm. Regardless, the insulation systems used on Columns 4 and 5 would likely not be able to protect the FRP system for the entire duration of the fire test because FRP systems are wildly thought to degrade at temperatures above their glass transition temperatures (ACI, 2002; ACI, 2008), as was observed during the tests presented in Chapter 4. Since the insulation system remained intact for the entire period of the fire test of Column 4, it was impossible to precisely identify the temperature at which the FRP system lost its mechanical properties and/or bond to the concrete surface. However, about 180 minutes into the fire test of Column 5, flames were noticed emanating from the pre-existing cracks, which were about 5 to 8 mm wide, on the surface of the insulation system. Hence, the manufacturer needs to try to ensure that these surface cracks do not appear when the Sika insulation system is curing at ambient temperature; if combustion of the FRP system needs to be prevented.

The insulation systems on both Columns 4 and 5 were, however, very successful in maintaining low internal temperatures within the columns (refer to Figure 5-11), such that they essentially retained their room temperature unwrapped strength for the full duration of the fire.

Column 4, which was wrapped with a carbon FRP system identical to that of Column 3, was thus

able to resist the sustained fire test load for more than 300 minutes, unlike the uninsulated Column 3, which failed under the sustained fire test load after 210 minutes of fire exposure. The insulated Column 5, which was wrapped with the Sika carbon FRP system, was able to resist the sustained fire test load for more than 240 minutes without structural failure.

The recorded temperature-time curves at various locations within the concrete of Columns 3, 4, and 5 are shown in Figure 5-11. As expected, the internal concrete temperatures were considerably lower in Columns 4 and 5 than in Column 3. The temperatures recorded within the concrete increased at a steady rate until they reached 100°C, after which point the temperatures increased at lower rate for a small period of time. This reduced rate of temperature increased has been observed previously (Bisby et al., 2005a, Williams et al., 2008, Williams, 2004, Chowdhury et al., 2008) and is attributed to moisture movement and evaporation within the concrete and the insulation. Column 3 failed by spalling of the concrete cover leading to crushing of concrete core. However, this cover spalling occurred after several hours of fire exposure, and thus the FRP wrap did not appear to significantly increase the propensity for cover spalling in these FRP strengthened columns. It should be noted that these columns were fabricated with closely spaced spiral steel lateral reinforcement and thus the internal core concrete was very well confined. This confinement would have reduced the likelihood of cover spalling (Kodur et al., 2004; Dwaikat and Kodur, 2009). More research should be conducted on columns with less steel lateral reinforcement to investigate the effect of internal lateral reinforcement on the cover spalling behavior of FRP strengthened columns. Furthermore, the concrete in these columns had compressive strengths close to 33 MPa, which is classified as normal strength concrete (NSC).

Generally, NSC columns are less prone to spalling than high strength concrete (HSC) columns (Kodur et al., 2004; Dwaikat and Kodur, 2009)

Figure 5-12 shows the axial deformations of Columns 3, 4 and 5 during the preload and fire test phase. The columns experienced an initial load of about 350 kN from the weight of the hydraulic jack prior to the start of the preload phase. Since the temperature at the level of the FRP exceeded the glass transition temperature of the epoxy resin/adhesive relatively early in the fire exposure for both Columns 3 and 4, it can be conservatively assumed that the FRP wraps were rendered structurally ineffective by the end of the fire tests. However, even though the FRP strengthening system was presumed to have been rendered ineffective by the end of the fire tests, the loss of the strength of the two columns was significantly different. Column 3 failed under the sustained fire test load of 2635 kN after 210 minutes. The tested strength of Column 3 was lower than the unfactored axial strength of an equivalent unwrapped column, which was 3806 kN, and close to the factored axial design strength, which was 2702 kN, when calculated according to ACI 318 design code (ACI, 2005). This indicates that Column 3, without supplementary fire protection, had experienced significant loss of strength during the fire exposure. On the other hand, Column 4, which was also wrapped with MBrace carbon FRP system like Column 3, resisted the sustained fire test load for more than 300 minutes, after which point the load was gradually increased until failure of the column occurred at 4538 kN, which was 59% and 19% higher than the factored strength and unfactored strength, respectively, of an equivalent unwrapped column. Clearly, Column 4 failed at a higher applied load than Column 3 because its internal temperatures were maintained at low values by the supplemental insulation system. For the same reason, Column 5 also failed at 58% and 11% higher than the factored strength (which was 3151 kN) and unfactored strength (which was 4501 kN), respectively, of an equivalent unwrapped column.

The observed axial deformations of the columns were the result of a combination of load effects and thermal expansion. During the preload phase of the fire test, Column 3 had an axial

deformation of 8.8 mm from the sustained applied load, Column 4 had 6.6 mm axial deformation, and Column 5 had 7.3 mm axial deformation. Examining Figure 5-12, Column 3 began experiencing increasing axial deformations after about 100 minutes of fire exposure, around which time the average temperature of its reinforcing steel was 297°C (refer to Figure 5-10) and the internal temperature of concrete 50 mm within the column was 276°C (refer to Figure 5-11).

Concrete begins to lose its room temperature compressive strength at temperatures above 200°C and its room temperature elastic modulus at temperature above 50°C (Schneider 1988). At temperatures close to 300°C, reinforcing steel loses about 20% of its initial room temperature yield strength (Lie 1992). At failure, Column 3 had an axial deformation of about 32 mm. On the other hand, Columns 4 and 5 maintained a constant axial deformation value under the sustained applied load for the initial 300 and 240 minutes, respectively, of exposure (because the internal temperatures of their reinforcing steel and compressive concrete were relatively low as compared to Column 3). Columns 4 and 5 experienced additional axial deformation again after 300 and 240 minutes, respectively, from the increasing applied load. At failure, Columns 4 and 5 had axial deformations of about 22 mm and 29 mm, respectively.

5.5 Summary Based on the results of full-scale fire endurance tests on the two FRP wrapped (confined) reinforced concrete circular columns presented herein, FRP materials can be used in buildings to strengthened reinforced concrete columns. By providing appropriate fire insulation, reinforced concrete columns that have been confined with FRP wraps can endure elevated temperatures of fire under strengthened service loads for more than 240 minutes. The supplemental fire protection system used herein was able to maintain low temperatures in the concrete and reinforcing steel during the fire tests, thus enabling the concrete and steel to retain most of their room temperature strength during the fire endurance tests. Although the insulation systems used

in this research were effective fire protection systems for the reinforced concrete columns, the insulation system was not able to maintain the temperature of the FRP system below its glass transition temperature for the entire duration of the fire test. The temperature of the FRP system remained below its glass transition temperature for about 34 minutes with about 53 mm of MBrace insulation system and for 60 minutes with 44 mm of Sika insulation system.

Even though the temperature of the FRP strengthening system exceeded the glass transition temperature during the fire test, the insulated FRP strengthened reinforced concrete columns were able to resist the applied sustained load under exposure to standard fire for more than 240 minutes. Hence, the fire endurance of the insulated FRP strengthened concrete columns should be defined in terms of the time that the column can resist the service load carrying capacity during fire, rather than the time it takes for the temperature at the level of the FRP strengthening system to exceed the glass transition temperature of the FRP strengthening system.

Table 5-1: Concrete mix proportions of column specimens (after Bisby, 2003) Mix Parameter Columns 3 & 4 Columns 5 Aggregate Type Siliceous Carbonate Maximum Aggregate Size 14 14 Type 10 Cement (kg/m3) 280 280 Coarse Aggregate (kg/m3) 1020 1070 Fine Aggregate (kg/m3) 980 980 Water (kg/m3) 152 152 Slump (mm) Max 150 Max 150 Water-cement Ratio 0.54 0.54 Tested 28-day Strength 32.7 38.5 Test day Strength 32.9 40.1

Table 5-2: Summary of design load capacity for Columns 3 and 4 Design Codes Unwrapped Wrapped Increase in Calculated Strength Design Strength Applied Strength Test Load (kN) (kN) (%) (kN) ACI 318-95 (F)a 2895 -- -- -- ACI 318-05 (F) 2702 -- -- -- CSA A23.3 (F) 2445 -- -- -- ACI 440.2R-02 (F) -- 4727 63c 3597 ACI 440.2R-08 (F) -- 3375 25 -- CSA S806-02 (F) -- 2667 9 2018 ISIS Canada (F) -- 3235 32 2448 ACI 318-95 (U)b 3860 -- -- -- ACI 318-05 (U) 3860 -- -- -- CSA A23.3 (U) 3688 -- -- -- ACI 440.2R-02 (U) -- 6585 71 -- ACI 440.2R-08 (U) -- 4822 20 -- CSA S806-02 (U) -- 4057 10 -- ISIS Canada (U) -- 5004 36 -- a F ? refers to factored design load calculations (ultimate design capacities) bU ? refers to unfactored load calculations (predicted load calculations) c Strength increase based on ACI 318-95

Table 5-3: Summary of design load capacity for Columns 5 Design Codes Unwrapped Wrapped Increase in Calculated Strength Design Strength Applied Strength Test Load (kN) (kN) (%) (kN) ACI 318-05 (F)a 3151 -- -- -- CSA A23.3 (F) 2782 -- -- -- ACI 440.2R-08 (F) -- 4014 27 3054 CSA S806-02 (F) -- 3281 18 2483 ACI 318-05 (U)b 4501 -- -- -- CSA A23.3 (U) 4249 -- -- -- ACI 440.2R-08 (U) -- 5799 29 -- CSA S806-02 (U) -- 5080 20 -- a F ? refers to factored design load calculations (ultimate design capacities) bU ? refers to unfactored load calculations (predicted load calculations)

Table 5-4: Summary of fire endurance tests on Columns 3 and 4 Column Layers Insulation Date of Fire Test Failure Fire No. of Thicknessb Fire test Load Ratioc Load Endurance FRPa (mm) (mm/yyyy) (kN) (min.) 3 2 0 05/2005 0.78 2635 210 4 2 53 05/2005 0.78 4583 >300 5 2 44 10/2008 0.76 4984 >180 a Carbon FRP system for columns 3 and 4 had a nominal thickness of 0.165 mm per layer and column 5 b Insulation System was used in this portion of the research c Fire test load ratio is the applied load divided by the factored resistance according to ACI 440-08 (ACI, 2008). The applied load was determined in accordance with ULC S101 (ULC 2004).

SECTION A-A A 3810 3734 A 864 400 CONCRETE: 35 MPa 28-DAY STRENGTH 864 REINFORCEMENT: 8-19.5 mm DIAMETER BARS LONGITUDINAL 11.3 mm DIAMETER SPIRAL w/ 50 mm PITCH c/c 40 mm COVER TO SPIRAL 50 mm COVER TO PRINCIPAL REINFORCEMENT *All dimensions in mm

10M Spiral 50 mm pitch c/c RebarConcrete 38 mm Thick Steel Plate

13 mm Diameter Machined Bar Ends Figure 5-1: Elevation and cross-sectional details of Columns 3, 4 and 5 prior to strengthening

(a) (b) Figure 5-2: Application of FRP strengthening system on (a) Column 3 with MBrace CF130 and Column 5 with SikaWrap Hex 103C

Figure 5-3: Spray-applying MBrace insulation system on Column 4

(a) (b)

Figure 5-4: (a) Steel mesh installed on Column 5; (b) Spray-applying Sika insulation system on Column 5

1C3, 9C4, C5 D 16 C4 2345678 17 C4 5 TCs @ D/8 D/4 D/4 FRP

9C3, 1C4, C5 19 10 12 11 *C3, C4, C5 - Column 3, 4, and 5

1, 16 9, 17 18234567819 12 10 11 (a) Fire Insulation

SG1 13 15 SG2 14 SG4 SG3

*SG - Strain Gauge 14 15 13 (b) SG1 SG4 SG2 SG3 (c) Figure 5-5: Location and numbering of thermocouples and strain gauges at mid-height: (a) Thermocouples within the concrete and on FRP surface, (b) Thermocouples on spiral and reinforcing steel, and (c) Strain guages on reinforcing steel

(a) (b)

Figure 5-6: Column 3 ? FRP wrapped concrete column (a) before fire test, and (b) immediately after fire test

(a) (b)

Figure 5-7: Column 4 ? FRP wrapped and insulated concrete column (a) before fire test, and (b) immediately after fire test

(a) (b) Figure 5-8: (a) Cracks on the surface of the fire insulation system prior to the fire test, and (b) flame emanating from the cracks on the surface of the fire insulation system during the fire test

(a) (b)

Figure 5-9: Column 5 ? FRP wrapped and insulated concrete column (a) before fire test, and (b) immediately after fire test

Column 3: FRP/concrete interface Column 3: Longitudinal rebar Column 4: FRP/concrete interface Column 4: Longitudinal rebar Column 4: FRP/insulation interface ASTM E119 standard fire 1500 C) ? 1000 Timperature ( 500

0 0 60 120 180 240 300 360 Time (minutes) (a) FRP/concrete interface Longitudinal rebar FRP/insulation interface Average furnace temperature 1500 Column 4 Column 5 C) ? Timperature ( 1000

500 0 0 60 120 180 240 300 360 Time (minutes) (b)

Figure 5-10: Temperatures at the FRP, insulation and reinforcing bars within (a) Columns 3 and 4, and (b) Columns 4 and 5

Column 3: 0 mm Column 3: 50 mm Column 3: 100 mm Column 3: 150 mm Column 4: 0 mm Column 4: 50 mm Column 4: 100 mm Column 4: 150 mm 1500 C) Timperature (? 1000

500 0 0 60 120 180 240 300 360 Time (minutes) (a) 0 mm 50 mm 100 mm 150 mm 500 400 C) ? Timperature ( 300 200 100

0 Column 4 Column 5 0 60 120 180 240 300 360 Time (minutes) (b)

Figure 5-11: Temperatures in concrete at various depths of (a) Columns 3 and 4, and (b) Columns 4 and 5

Column 3 Column 3 Column 4 Column 4 Column 5 Column 5 6000 5000 Preload Fire Test Phase Phase 40 Applied Load (kN) 4000 3000 2000 1000 Axial Deformation (mm) Preload Fire Test Phase Phase 30

20 10 0 0 -120 -60 0 60 120 180 240 300 360 -120 -60 0 60 120 180 240 300 360 Time (minutes) Time (minutes) (a) (b)

Figure 5-12: (a) Applied load and (b) axial deformations during the fire tests of Columns 3, 4, and 5

Chapter 6 Modelling the Heat Transfer and Structural Behaviour of Reinforced Concrete and FRP Confined Reinforced Concrete Columns in Fire

6.1 General As previously stated, fibre reinforced polymers are widely recognized for their ease of application and effectiveness for repairing and retrofitting deteriorated concrete structures.

Confining reinforced concrete columns with FRPs increases both the strength and deformability of the columns. However, one of the greatest impediments to using fibre reinforced polymer (FRP) composites in buildings is their susceptibility to degradation when exposed to elevated temperature and the limited knowledge available on their thermal and mechanical properties at elevated temperature. At high temperatures, all polymer resins will soften and eventually ignite, causing the resin matrix to weaken and raising potential concerns regarding the structural integrity of FRP strengthened concrete structures during fire. Since little is known about the thermal and mechanical properties of currently available FRP systems used in strengthening concrete structures, small-scale FRP material tests were conducted and presented in Chapter 4 to characterize the mechanical and thermal properties a specific type of currently available glass FRP (GFRP) used for strengthening concrete structures by the external bonding technique.

Furthermore, full-scale fire endurance tests were conducted and presented in Chapter 5 on FRP confined reinforced concrete circular columns to investigate the fire behaviour of FRP strengthened concrete structural members. However, these full-scale fire endurance tests are time consuming and very expensive. Hence, a major portion of this thesis involved developing numerical models that can simulate the heat transfer within the FRP confined concrete columns and their structural response at high temperature.

columns (Mirmiran et al., 1998). This occurs because the FRP confinement is much less effective for strengthening square columns than circular columns, as shown schematically in Figure 2-2.

This essentially results in only partial confinement of the columns' cross-section. In square columns, most of the confinement pressure from the FRP wrap is developed at the corners (which must typically be rounded to prevent failure of the FRP wrap due to stress concentrations), whereas along the flat column sides, the FRP sheets provide negligible resistance to lateral expansion resulting from the concrete's dilation upon compressive loading, and hence negligible lateral confining pressure (Thériault and Neale 2000). Since FRP wraps are currently being used for strengthening square and rectangular concrete columns, the behaviour of FRP confined reinforced concrete square columns in fire should be thoroughly investigated, as should the remaining unknowns regarding the specific performance of the FRP and supplemental fire insulation materials under fire conditions. This chapter presents and discusses, for the very first time, the development and validation of a heat transfer and structural response model for square and rectangular FRP confined reinforced concrete columns. The numerical model developed in this chapter is the only available tool that can easily be used to evaluate the performance of both insulated reinforced concrete columns and insulated FRP strengthened reinforced square and rectangular columns in fire. Preliminary results from this numerical study are presented in Chowdhury et al. (2007a).

6.2 Research Significance Previous experimental and modelling work on the fire performance of FRP confined reinforced concrete columns (Bisby et al., 2005a, Chowdhury et al., 2007b) has focused on the performance of circular members. While these studies have provided a wealth of useful information on the important factors to consider in designing fire protection schemes for FRP confined reinforced concrete columns, it must be recognized that the majority of columns in

structures are rectangular (or square) and most are subjected to at least minor load eccentricities and secondary bending moments; very little information on the performance of these types of members when strengthened with FRPs (even regarding performance at ambient temperature) is available in the literature.

6.3 Numerical Model A numerical model was developed and programmed in FORTRAN, to predict the temperatures within these types of members, and this information was subsequently used to predict the structural behaviour of FRP confined/strengthened concrete square and rectangular columns in fire. An explicit finite difference method was used to predict the heat transfer within the column, since a similar technique has been successfully used in the past for modelling of conventional reinforced concrete structures (Kodur and Baingo, 1998; Lie, 1992; Lie and Irwin, 1993; Lie and Celikkol, 1991; Lie and Stringer, 1994), as well as FRP strengthened reinforced concrete structures (Bisby et al., 2005a; Williams et al., 2008). Previously, Bisby et al. (2005a) developed a numerical model that used the load-deflection method described in Lie and Celikkol (1991) to calculate the axial strength of an FRP wrapped reinforced concrete circular column under fire condition. Using this load-deflection method, Bisby et al. (1005a) was able to calculate only the ultimate moment capacity at mid-height of the column specimen having an end eccentricity ratio DA?5DAequal to 1.0. Furthermore, this method could only be used to analyze 6

However, in the current model, the structural behaviour in fire was determined using two- dimensional fibre-element analysis and invoking the Column Deflection Curve (CDC) method presented by Chen and Atsuta (1976), details of which are given in Chapter 3 for FRP confined reinforced concrete circular columns under room temperature conditions. Using the Column Deflection Curve (CDC) method, both short and slender column specimens having end

eccentricity ratio DA?5DAranging between -1.0 and 1.0 could be analyzed under fire condition. 6

Hence, the model accounts for the temperature-dependent non-linear thermal and mechanical response of the column's constituent materials, the confining effect of the FRP wraps, and the second-order moments in an axially-loaded slender columns resulting from lateral deflection.

A flowchart of the overall program logic is shown in Figure 6-1. Initially, all required information are entered as input into the program. This includes cross-section details, concrete aggregate type, FRP thickness, duration of fire, room temperature, etc. The cross-section is then discretized into a number of rectangular elements as shown in Figure 6-2. The point D2à,has á

coordinates D TD:JL·;F?D1aTnd D UD:IL ·F;?D1,Uwhere DJand DIare the node numbers in the x- and y-direction, respectively. The fire temperature is calculated at each instant for the duration of fire, with a time step dictated by a stability criterion for the explicit calculation procedure. In the numerical model, the temperatures to which the exterior of a member might be subjected in the event of a severe building fire are represented by a standard temperature-time curve (Eqn. 6- 1) according to ASTM E119 (ASTM, 2001):

Ý ? ¥Ý? ç9 9 7 E715@0·EDA7. ; = D6Ù L 20 AE 170.41D¥F?DP Eqn. 6?1 where, , D6Ý Ùis the temperature of the fire at time step DaFnd ?DPis the duration (in hours) between time step DaFnd D F . E 1 It should be noted that this fire is very similar to the Canadian (ULC, 2004), British (BSI, 2009) and European (ISO, 2009) standard fires.

6.3.1 Heat Transfer Model The heat transfer from the column's centreline to its exterior surface is calculated using a series of two-dimensional explicit finite difference formulae based on elemental energy balance.

The formulation of the finite difference equations and the maximum allowable time step to ensure

stability of the explicit finite difference algorithm are based on theory described in both Cengel (1998) and Lie (1992). The general heat equilibrium equation used to describe the heat transfer within the column due to conduction is given in Eqn. 6-2, which is based on the conservation of thermal energy with the column.

Dò DòD6Dò DòD6Dò DòD6 DòD6 DlG pE DlG pE DlG pE6DLMD éD ? Eqn. 6?2 DòDT DòDV DòDP DòDT DòDUDòDUDòDV where, DGis the thermal conductivity of the constituent material, D6is the temperature, DMis6the heat generated in the constituent material, Déis the constituent material's density, D?is the specific heat of the constituent material, and DPis the time. The first three terms in Eqn. 6-2 represents the thermal conduction in an element of the column in each of the three coordinate direction (x-, y- and z-direction) and the last term represents the stored energy in the element of the colomn.

Based on conservation of thermal energy (Eqn. 6-3), the derivation of the heat transfer equations is shown below in this chapter: D'æ L D ' F D ' ç ? à, á Eqn. 6?3 â èá Ü á ? à, ç ? à,

where, D'Ü and D' are the energies transferred into and out of the element D4 , á á ? à,âáè ç ? à, á à,

respectively, and D'æ is the energy stored in the element D4 during a time interval ?DP(in ç ? à, á à, á hours), which is given by equations 6-4 and 6-5.

DòD6 L D é · D ? · Eqn. 6?4 D'æ ç ? à, á · D@DT · D@DU · D@DV DòDP D6Ý >F5ÝD 6 D' L Ý Ý Ý à, á à,· Dá8 Eqn. 6?5 · D ? E ·Dé?· D ö o · æ kD é ê ê à, á ç ? à, á à, á à, á à, á ?DP In equations 6-4 and 6-5, D6Ýand DöÝare the temperature and moisture content of element à, á à, á

D4 at time step D,FDéÝand D?Ýis the density and heat capacity of element D4 at time step D,F à, á à, á à, á à, á

and D8à,is the volume of element D4 . á á à,

Heat energy is transferred into (D' ) and out of (D' ) an element by Ü á ? à, á â è ç ? à, á

conduction, convection and radiation. For the purposes of this study, conduction, D'Ö , and âá× radiation, D' , are the only two modes of heat transfer that are being considered in the numerical åÔ× model because convection accounts for only about 10% of the heat transfer and can reasonably be neglected (Lie 1992). Equations describing the heat transfer by conduction and radiation are shown in Eqn. 6-6 and Eqn. 6-7: DòD6 D'Ö L D×G · D @D U · D @D V · Eqn. 6?6 â á DòDT

Ý8Ý8 D' L D ê · D Ý Dd6@E 273A E 273 ho å · D Ý · D #å · Ô × E kD 6 Eqn. 6?7 Ô × à Ô Ùç Ü å Ø Ù à, á

In Eqn. 6-6 and Eqn. 6-7, DGis the thermal conductivity between two adjacent elements, Dêis the ?

2003)), D#å is the surface area of element D4 through which heat is transferred by radiation. Ô × à, á In Eqn. 6-6, the thermal conductivity DGbetween two elements (for example, D=and D)>was derived based on the theory that heat flow is analogous to electric current flow as shown in Eqn. 6-7 and Eqn. 6-7.

DHÔB DH DHÕ Õ L Ô E Eqn. 6?7 DG · D # ÔB·D # DG· D # DGÕ ÔB Õ ÕÔB ÕÔ ÔB Õ

Where, DGis the thermal conductivity of an element, D#is the surface area through which heat is transferred by conduction, DiHs the distance between two points between which heat is being transferred. In Eqn. 6-7, D,GD,#and DaHre accompanied by subscripts. Subscript D=or D>denotes that the property is of Element D=or D,>and subscript D = BdenoDte>s that heat is being transferred from ÔB Õ

DHÔB·D GÔ· D G DGÔB LDÕ:H· D G;EÕD:H· DÕG; Eqn. 6?8 ÔÕÕÔ

If the element is in the interior, heat energy is only transferred into element D4à,byá conduction from the neighbour elements D4à , D4 , D4 , and D4 (Figure 6-3(a)), ? 5, á á > 5 à, á ?à 5> 5, áà, which is described in Eqn. 6-9.

DG · D # :à B; :à B; CÍ ? 5,à,áá ? 5,à,áá Ý Ý CÐ · kD 6 F D 6o à ? 5, à, á CÎ DH á CÑ :à B; ? 5,à,áá CÎDG:à, B; · D#:à, B; CÑ á ?à,5á á ?à,5á Ý Ý CÎE · kD6 FDC6oÑ à, á ? à, á DH 5 :à, B; D' LCÎ á ?à,5á CÑ Eqn. 6?9 Ö â á × ·D# CÎDG:à B; :à B; CÑ > 5,à,áá > 5,à,áá Ý Ý E · kD 6 F D 6o CÎ à, CÑ DH à > 5, á á :à B; > 5,à,áá CÎ CÑ DG:à, B; · D#:à, B; CÎE á >à,5á á >à,5á Ý Ý CÑ · kD 6 F D 6o à, á > à, á CÏ DH 5CÒ :à, B; á >à,5á

If the element is exposed to the surrounding environment, heat energy is transferred into the element D4à,byáconduction from the neighbour elements and radiation from the surrounding environment. To derive two general heat transfer equations (Eqn. 6-10 and Eqn. 6-11) for D6àÝ, > 5 á

and DöÝ, w>hic5h will account both modes of heat transfer (conduction and radiation), Equations à, á 6-5, 6-7 and 6-9 were substituted in Equation 6-3.

?DP CÍ H CÐ ÝÝ Ý ·D? ·Dö o·D8 CÎ kDé E·Dé? CÑ à à ê ê à à, á CÎ DG:à B; · D#:à B; CÑ CÓ ? 5,à,áá ? 5,à,áá Ý Ý C× CÎ · kD 6 F D 6o CÑ à à, á DH ? 5, á CÖ :à B; CÖ CÎ ? 5,à,áá CÑ CÖ DG:à, B; · D#:à, B; CÖ CÎ á ?à,5á á ?à,5á Ý Ý CÑ CÖ E · kD 6 F D 6o CÖ à, à, á Ý > 5Ý DH á ? 5 CÎ :à, B; CÑ L D 6 á ?à,5á Eqn. 6?10 D6à à ECÖ CÖ CÎ DG:à B; · D#:à B; CÑ > 5,à,áá > 5,à,áá Ý Ý CÎ E · kD 6 F D 6o CÑ à à, á CÔ DH > 5, á CØ :à B; CÎ > 5,à,áá CÑ CÖ DG · D # CÖ :à, B; :à, B; CÎ á >à,5á á >à,5á Ý Ý CÑ CÖ E · kD 6 F D 6o CÖ à, à, á DH á > 5 CÎÖ CÑ :à, B; CÖ á >à,5á CÎÖ 8 CÖCÑ ÝÝ8 · D Ý Dd6@E 273A E 273 ho EDêà· DÝ · D #å · Ô × E kD 6 CÏÕ Ô Ùç Ü å Ø Ù à, á CÙCÒ

?DP CÍ H CÐ CÎ D:é ·;D 8 CÑ ê· D ãê à, á CÎ DG:à B; · D#:à B; á Ý Ý CÑ CÓ ? 5,à,áá ? 5,à, ákD 6 F D 6o C× · CÎ 5, à, á CÑ DH à ? á CÖ :à B; CÖ ? 5,à,áá CÎÖ DG · D # CÖCÑ CÎÖ E:à, B; :à, B; à,5á Ý Ý o CÖCÑ á ?à,5á á ? · kD 6 FàD5, 6á Ý > 5Ý ECÎÖ :à, B; CÖCÑ Dö L D ö á ?à,5á Eqn. 6?11 à à CÎ DG:à B; · D#:à B; à,áá Ý Ý CÑ CÎÔ E > 5,à,áá > 5, · kD 6 à, o CØCÑ à > F Dá6á DH 5, :à B; > 5,à,áá CÎÖ CÖCÑ CÎÖ DG:à, B; · D#:à, B; à, á Ý Ý o CÖCÑ E áDH>à,5á á > · 5 kD 6 FàD5, 6á à, á > CÎÖ :à, B; à, CÖCÑ á > 5á CÎÖ Ý 8CÖCÑ 8 EDêà··DÝ · D # · Dd6Ý@E 273A E E 273 ho CÏÕ Ô Ùç Ü å Ô ×Ù à, káD 6 CÙCÒ Ø

In Eqn. 6-11, Dãis the heat of vapourization of water. Heat transfer equations for a corner ê

element, as shown in Figure 6-3b, are given in Eqn. 6-12 and Eqn. 6-13 which were derived by modifying Eqn. 6-9 and Eqn. 6-10.

?DP CÍ H CÐ ÝÝ Ý CÎ k·Dé? E ·Dé?· D ö o · D 8 CÑ à à ê ê à à, á CÎ DG · D # CÑ :à B; :à B; CÓ ? 5,à,áá ? 5,à,áá Ý Ý C× CÎ · kD 6 F D 6o CÑ à ? 5, à, á Ý > 5Ý CÎÖ DH á CÑ CÖ :à B; CÖ L D 6 ? 5,à,áá D6à à E Eqn. 6?12 CÎ DG:à, B; · D#:à, B; CÑ á ?à,5á á ?à,5á Ý Ý CÎ E · kD 6 F D 6o CÑ à, á ? à, á CÔ DH 5 CØ CÎ :à, B; CÑ á ?à,5á CÎÖ 8 8CÑ CÖ ·DÝ·D#·Dd6Ý@E273AEÝkD6h EDêà· DÔÝÙç Ü å Ø E 273 o CÏÕ å Ô ×Ù à, á CÙCÒ ?DP CÍ CÐ D:é ·;D 8 CÎ · D ? CÑ ê ê à, á CÎ DG:à B; · D#:à B; CÑ CÓ ? 5,à,áá ? 5,à,áá Ý Ý C× · kD 6 F D 6o CÎ à ? 5, à, á CÑ Ý > 5Ý CÖ DH á CÖ :à B; Dö L D öE ? 5,à,áá Eqn. 6?13 à, á à, CÎ CÑ á DG:à, B; · D#:à, B; CÎH á ?à,5á á ?à,5á Ý Ý CÑ E · kD 6 F D 6o à, á ? à, á CÎCÔ DH 5 CÑ :à, B; CØ á ?à,5á CÎCÖ 8 8CÑ CÖ ·DÝ·D#·Dd6Ý@E273AEÝkD6h EDêà· DÔÝÙç Ü å Ø E 273 o CÏCÕ å Ô ×Ù à, á CÒ CÙ The maximum allowable time step is calculated for the stability of the finite difference formulation by having the coefficient of D6Ýin Eqn. 6-12 greater than or equal to zero. The à, á derivation of the maximum allowable time step is lengthy, hence it is presented in Appendix D.

The variations of the thermal properties of the materials have been taken into account using

Using Eqn. 6-10 and Eqn. 6-11, the temperature of any element in the column can be determined based on the temperatures and thermal properties of its adjacent elements from the previous time step. Thus, a complete history of temperature within the column can be obtained.

6.3.2 Mechanical Property Model at Elevated Temperature After the temperature distribution of the column cross-section has been determined at each time step, the mechanical properties of the materials are determined at their current temperatures. The compressive stress-strain model proposed by Lie (1992) for unconfined concrete (Eqn. 6-14) was used for the analysis of reinforced concrete columns.

Nñ 6 Nñ Ö Ö Nñ QDÝ Ö Nñ i if 0 ÖQ DÖÝ Ö DBÖ L 6 Eqn. 6?14 CÔ D:6;FNñD Ý Nñ Ö Nñ :D6;Q DOÝDÝ CÖ Ö Nñ i ifÖDÝ Ö Ö è 3·DÝ Ö

where, DBD:6a;nd DÝD:6a;re the compressive stress and strain in the concrete at temperature D6 ÖÖ Nñ Nñ (which is in degree Celsius), DBD:6is;the compressive concrete strength at temperature D,6DÝD:6; ÖÖ NñD:6a;t temperature D6(referred to is the corresponding axial strain for the compressive strength DBÖ as peak strain in this study), and DÝÖ:isDt6hefa;ilure strain of unconfined concrete at temperature è

NñD:6, m;odel proposed by Hertz (2005) for modelling the D.6The compressive concrete strength, DBÖ mechanical response of concrete at elevated temperatures, which is presented in Eqn. 6.15, was used in Eqn. 6-14.

CÓ 1 CÖNñ20:°C; f Ö Ø è æ 6 < : j8 CÖDBÖ æ Ü ·ß Ü D6 â D6 E@D6 D6 1 E E@A AE@ A CÖ 15000 800 570 100000 CÖ 1 NñD:6;L Nñ fç êD6Ø ÚD6Û ç6 D6 < D6 : j8 DB DB20:°C; · Eqn. 6?15 Ö Ö ßÜÚÛ Ü CÔ 1 E E@ AE@AE@A CÖ 100000 1100 800 940 CÖ CÖNñ Ø Då6 D6 1 6 D6 < D6 : j8 20:°C; f DBÖ â · çÛ 1 E E@ AE@AE@ A CÕ 100000 1080 690 1000 Nñ20:°C; Nñ Nñ where, DBÖ æ Ü , DB20:°C; , and DB20:°C; are the room temperature ß ÖÜ Ö Øß âÜ èÚ æÛ ç Öê Ø Üâ Úç Û çØ å compressive strength of siliceous aggregate concrete, lightweight aggregate concrete and other type of aggregate concrete, respectively. The Hertz (2005) model accounts for the effect of aggregate type and preload on the response of concrete at elevated temperatures. The initial stress from preload is assumed to reduce the micro-cracking within concrete at elevated temperatures; reducing the rate of decay of the compressive concrete strength. Preloaded concrete may be 25% stronger than an unloaded concrete at elevated temperatures provided that the initial compressive stress from the preload is about 25 to 30% of the initial room temperature NñD:6c;ould compressive strength (Hertz, 2005). The effect of initial compressive stress on DBÖ therefore be accounted for in the analysis by multiplying the value obtained for DBÖ Nñ Nñ 6-15 by 1.25. However, the maximum value for DBD:6w;as conservatively limited to DB20:°Cin; ÖÖ the current analysis. If the initial compressive stress from the preload is not known, it is conservative to assume the DBÖ The corresponding axial strain DNÝñD:6o;r peak strain at ultimate compressive strength Ö

NñD:6a;t temperature D6is described by the model proposed by Terro (1998) in Eqn. 6-16. DBÖ Nñ ? 7 ? : ? = 6 ? 5 76 DÝD:6;L 2.05 H 10 E 3.08 · D 6 E 6.17 · DH610E 6.58 H·1D06 Eqn. 6?16 Ö H 10 Research aimed at characterizing the concrete failure strain at elevated temperature DÝÖ:isD6; è

limited. Williams (2004) presented a model describing the unconfined concrete failure strain

DÝÖ:aDt 6eleva;ted temperature, which assumes that the failure strain DÝ:isDr6elate;d to the peak è Öè strain DNÝñÖ D:6a;t elevated temperature by the same stress-to-strain ratio as at ambient temperature.

This seems the most reasonable approach in the absence of any specific experimental data and is used in the current model.

DÝ Nñ è :D6; Eqn.6?17 :D6; · Ö è Ö L DÝ Ö

The compressive stress-strain model given in Eqn. 6-18 was proposed for confined concrete at ambient temperature by Lam and Teng (2002). This model was modified to account for high temperature deterioration of material properties and was used in the analysis for FRP strengthened reinforced concrete column specimens exposed to fire.

:D:'D6; 6 D' 6 6 Nñ :D6; Q DÝ :D6; F · D Ý if 0 Q DÝ :D6; · DÝ DB PÖ Ö Nñ Ö Ö ç Ö:D6; L 4DB:D6; Eqn. 6?18 ÖÖ Nñ Nñ :D6; Q DÝ :D6; O DÝ DBÖ :D6; if DÖÝ Ö Ö è 6Ö ç

Where, DNÝñç:isDt6hepo;int of transition between the parabolic and linear portions of the confined stress-strain plot, which is described in Eqn. 6-19, D'D:6is;the elastic modulus of unconfined Ö

concrete at elevated temperature D,6which is described by Eqn. 6-20 as proposed by Anderberg and Thelandersson (1978), D':isDt6hesl;ope of the linear second portion of the confined stress- 6

strain relationship, which is characterized by Eqn. 6-21, and DÝÖ:isDt6heul;timate axial strain of Öè FRP confined concrete at temperature D.6 Nñ 2 · D BÖ DÝD:6;L Eqn. 6?19 ç D:6;F D ' 6

2 · DNBñ D'D:6;L Ö Eqn. 6?20 Ö Nñ Ö

Nñ Nñ Ö :D6FD;B D'D:6;L Ö Ö Eqn. 6?21 Ö

The FRP confined concrete strength DNBñ:aDnd6ulti;mate axial strain DÝ:aDt 6; ÖÖ ÖÖè temperature D6were characterized in the numerical analysis by modifying the models proposed by Lam and Teng (2007) to account for deterioration at high temperature. This is expressed in the following equations.

DBßD:6; ã Nñ Nñ Ù å DBD:6;LD:6B·; F1 E 3.5 · G Eqn. 6?22 Ö Ö Ö Nñ Ö

DBß:D6DÝ;D:6è; ã Nñ Ù å ã Û, å DÝÖD:6;LD:6Ý·;1.H75 E 12 · F G · F GI Eqn. 6?23 è è Ö Nñ Nñ DBÖ DÝÖ Where, DBß D:6is;theãlateral confining pressure from the FRP wrap, which is given by Eqn. 6-24 Ùå

and DÝÛ, D:6is;the FRP hoop rupture strain, which is given by Eqn. 6-25. åèã

DB D:6;L Ù å ã ç Û, å è ã Eqn. 6?24 ßÙåã 66 ?DS E D H D:6;L D ß · D Ý DÝÛ, :ãD6è; Eqn. 6?25 åèãÙå

Where, Dßis the average ratio of hoop rupture strain to ultimate axial tensile strain of the FRP material. Lam and Teng (2003) suggested the value 0.63 for Dßin Eqn. 6-25.

An elastic-perfectly plastic relationship shown in Eqn. 6-26 was used to describe the stress-strain behaviour of the reinforcing steel, both in tension and in compression.

DÝ:D6; · D' :D6QD;Ý DB æ æ ì :D6; L J Eqn. 6?26 æ :D6; :D6PD;Ý DBì if DÝ:D6; æì

Where, DB D:6a;re the stress and strain of steel, respectively, at temperature D,6DB :aDnd6DÝ; :D6; ææ ì and DÝ:aDre6the y;ield strength and strain of steel at D,6respectively, and D':isDt6heel;astic ìæ modulus of steel at temperature D.6Equations 6-27 to 6-29 describe the aforementioned material properties for steel at high temperature.

CÓ D6 CÖ20:°C·;N1 E O DBì D6 20°C Q D6 Q 600°C DBD:6;L 900 · ln @ A Eqn. 6?27 ì 1750 CÔ CÖ 340 F 0.34 · D6 CÕ20:°C·; 600°C O D6 Q 1000°C DBì D6 F 240

CÓ D6 CÖ20:°C·; N1 E O D'æ D6 20°C Q D6 Q 600°C D'D:6;L 2000 · ln @ A Eqn. 6?28 æ 1100 CÔ CÖ 690 F 0.69 · D6 CÕ 20:°C·; 600°C O D6 Q 1000°C D'æ D 6 F 53.5 DÝD:6;L ì Eqn. 6?29 æ

Since the stress-strain behaviour of the FRP composites at high temperature was linear- elastic in the small-scale experimental tests conducted at high temperature in Chapter 4, the following equation is used to model the tensile behaviour of the FRP composite.

:D6; Q DÝ Eqn. 6?30 Ù Ù å ã Ù åif ãDÝÙ å ã è åãÙåãç

where, DBÙD:6a;nd DÝ:aDr6e the;stress and strain of the FRP at temperature D,6D' :isD6; åã Ùåã Ùåãç

the tensile elastic modulus of the FRP at temperature D,6and DÝÙ :isDt6heul;timate tensile åãè failure strain of the FRP at temperature D,6which is calculated using equation Eqn. 6-31.

DÝ D:6;L å ã Eqn. 6?31 Ùåãç

where, DBÙ :isDt6hete;nsile strength of the FRP at temperature D.6 åãç The hyperbolic tangent curve proposed in Chapter 4 to describe the high temperature degradation of the FRP's tensile strength DBÙ :aDnd6tens;ile elastic modulus D' :wDa6s use;d åãç Ùåãç in the model because, experimental results presently previously by Kodur et al. (2005) from a standard fire test on a full-scale GFRP wrapped and insulated square reinforced concrete column specimen is used later in this chapter to evaluate the performance of the numerical model. The tensile strength DBÙ D:6a;nd elastic modulus D' :oDf 6theF;RP are given in equations 6-32 åãè Ùåãç and 6-33.

CÍ DBÙ 2å0:°C;E 0.46 · D B CÐ åãç DB CÎ 2 CÑ D:6;L Eqn. 6?32 Ù å ã 20:°C;F 0.46 · D B CÑ FÙ å ã ç Ù ã taçnh k0.0882D:·6 F;o4C7Ò CÏ 2 CÍ Ù å ã ç Ù å ã ç CÐ D' å:D6CÎ; L 2 CÑ Eqn. 6?33 CÎ Ù 2å0:°C;F 0.67 · D 'å ã ç CÑ CÏF ã ç Ù tanh k0.1024D:·6 FC;oÒ51 2 where, DB 20:°Ca;nd D' 2å0:°Ca;re the tensile strength and tensile elastic modulus of the Ùåãç Ù ãç FRP at room temperature, respectively. Since equations 6-32 and 6-33 represent the mechanical behaviour of the FRP for temperatures between 20°C and 200°C, the FRP was conservatively assumed to be totally ineffective beyond 200°C in the numerical model. This assumption was conservative because, there was no significant increase in the rate of thermal decomposition of the GFRP composite until about 350°C according to the results of the TGA (Figure 4-6a).

Regardless, the author chose to be conservative because, there was no tension tests conducted on the GFRP composites beyond 200°C.

6.3.3 Structural Model The objective of the structural model is to determine the failure load for an eccentrically- loaded column at each time step. This requires the derivation of the moment versus curvature relationship for the column's cross section for increasing axial load levels, followed by calculation of axial load-moment paths for a given initial load eccentricity and column length.

The method of analysis has been based on the following standard assumptions: (1) plane sections remain plane after loading;

(2) the total strain in the reinforcement is equal to the total strain in the concrete at the same location (i.e., perfect bond between the concrete and the steel reinforcement);

(3) the longitudinal stress at any point in the cross-section is dependent on the longitudinal strain; and (4) the tensile strength of the concrete is negligible and can be ignored.

For each element, the stresses and strains are assumed to be those at their central nodes (refer to Figure 6-2). Therefore, the temperature and strain in the longitudinal reinforcing steel are assumed to be the same as those for the concrete element that the centroid of the steel bar lies within. Since the FRP wrap is thermally thin and has slightly variable temperature around the perimeter of the column during the fire, the mechanical properties of FRP material were conservatively determined based on the highest temperature achieved by any of the elements within the FRP. This is particularly conservative and appropriate since the FRP wrap is hottest at the corners, which is where confinement is most activated.

Using an incremental iterative procedure, the moment-curvature response of the column's cross-section for a given axial load is calculated. Details of this procedure have already been described in Section 3.3.2. The stresses and internal forces in the concrete and steel were determined using two-dimensional fibre-element analysis (Figure 6-4). To derive the moment- curvature relationship, various strain profiles were assumed across the cross-section by incrementally increasing the depth of the neutral axis DGand the concrete strain DÝat the extreme Ö

compression fibre (up to the failure axial concrete strain at high temperature). Based on the assumption that the cross-section remains plane during the loading process, Figure 6-5 shows a linear distribution of the total strain DÝdue to an eccentric compressive load. In the analysis, the çÖ total strain DÝin a concrete element at elevated temperature consists of three strain components: çÖ unrestrained thermal strain DÝç, transient creep strain DÝ (which is specifically for concrete Û, Ö ç å, Ö

under a fire condition), and mechanical strain (or instantaneous stress-related strain) DÝà Ø, Ö (Youssef and Moftah, 2007).

DÝç ÖLçD ÝE D ÝE D Ý Eqn. 6?34 Û, ç å, àÖ Ø, Ö Ö

Knowing the total strain by invoking the plane-sections assumption, the mechanical strain, DÝà , Ø, Ö at elevated temperature can be calculated by subtracting the unrestrained thermal strain, DÝç, and Û, Ö

transient creep strain, DÝç (which is dependent on both thermal strain and constant stress acting å, Ö

on heated concrete). The unrestrained thermal strain for concrete DÝç is determined using the Û, Ö relationship proposed in Lie (1992), and given in Eqn. 6-35.

L0>.:008 · D6 ? : DÝç Û, Ö E;6H 10· ?D:6 F;20 Eqn. 6?35 The transient strain of concrete is dependent on the thermal expansion and the sustained compressive stress experienced by the concrete during heating (Anderberg and Thelandersson, 1978). The accumulated transient strain for concrete DÝç heated under constant stress DBwas å, Ö Ö modeled by using a uniaxial formula given by Anderberg and Thelandersson (1978), which has been successfully used and incorporated in other previous research studies (Thelandersson, 1987;

Nechnech et al., 2002) DÝ L Ö · D Ý Eqn. 6?36 ç å, ÖçFåD G ç Û, Ö DBÖ The value for constant DGin Eqn. 6-36 was taken to be 1.8 for siliceous aggregate concrete and çå 2.35 for carbonate aggregate concrete (Nechnech et al., 2002). If the initial stress DBis not Ö

known, the stress ratio DB ? Nñ Ö Ö is aDssBumed to be 0.30. Note that the minus sign before the constant DGaccounts for the fact that transient strain and thermal strain are of opposite signs. çå

The mechanical strain of concrete at failure, DÝÖ, , was taken to be DÝ:fDor6; Ù Ô Ü ß è å ØÖ è unwrapped reinforced concrete columns and for FRP confined reinforced concrete column Eqn. 6-37 was used.

DÝ:D6;D:B ;OD:B:D6; · D# :D6; · D# DÝ L Ö Ö è Ö if Ö Ö Ö Ø Ö, Ù Ô Ü ßè å Ø Nñ Nñ Eqn. 6?37 DÝ:D6;D:B ;RD:B:D6; · D# :D6; · D# Ö è Ö if Ö Ö Ö Ø

is the total area of concrete (that is, gross cross-sectional area D# where, D# minus the total area ÖÚ of longitudinal reinforcing steel D# is the effective FRP ) enclosed by the FRP wrap and D#Ø æç confined area enclosed by the four parabolas shown in Figure 2-2(b). Details of the calculation of the effective FRP confined area are given later in this chapter. Knowing the mechanical strain of concrete at failure, the ultimate concrete strain was determined by adding the unrestrained Û, Ö ç å, Ö

At elevated temperature, the total strain (Eqn. 6-38), DÝ, in the steel reinforcement çæ consisted of the mechanical strain, DÝà , and the thermal strain, DÝ , which are determined using Ø, æ ç Û, æ a model proposed by BSI (1992) and given in Eqn. 6-39.

DÝç L D ÝE D Ý æ Eqn. 6?38 æ à Ø, æç Û,

F2.416 H?108E 1.2 ? 9 ? < 6 20°C Q D6 Q 750°C · D 6 E 0.4 · DH610 H 10 DÝ L ] ? 7 Eqn. 6?39 ç 11.0 H 10 750°C O D6 Q 860°C Û, æ ? 7E 2.0 ?· D96 860°C O D6 Q 1200°C F6.2 H 10 H 10 From each proposed strain profile, an axial load and bending moment is obtained by performing two-dimensional fibre-element analysis. If the axial load is in close agreement with the given applied load, the curvature corresponding to the proposed strain profile is taken to be accurate. Otherwise, the strain profile is modified and the procedure is repeated, as previously described in Chapter 3. Again, once the moment-curvature relationship for a given axial load is determined, the slope and lateral deflection are calculated along the longitudinal height of the column using the Column Deflection Curve method described by Chen and Atsuta (1976).

Details of the numerical procedure and equations used in calculating the slope and lateral deflection are provided in Section 3.3.3. This numerical integration method accounts for the effect of secondary bending moments caused by the coupling of axial load and lateral deflection.

Both material and stability (or global buckling) failure modes are considered in the numerical analysis. For each time step, an axial load-moment path for the column is determined by

increasing the applied load incrementally. Thus, from these axial load-moment paths at various time steps, the failure axial load versus time of fire exposure can be predicted.

Unlike circular columns, rectangular columns are only partially confined when wrapped with FRP (refer to Figure 2-2). It is assumed in the current analysis that the effective confined areas are enclosed by the following second-order parabolas (1, 2, 3 and 4) extending between the rounded corners of the cross section (Figure 2-3).

1 Parabola 1: DU L 6 Nñ DT E 0.5DD F 0.25DS Eqn. 6?40 DSNñ

1 Parabola 2: DT L 6 Nñ DU E 0.5DS F 0.25DD Eqn. 6?41 DNDñ

1 Parabola 3: 6 Nñ DU L DTF F 0.5DD E 0.25DS Eqn. 6?42 DSNñ

1 Parabola 4: DU LDT6F Nñ Eqn. 6?43 F 0.5DS E 0.25DD DD where, DSis the width of the column cross-section, DDis the length of the column cross-section, DSNñ is equal to D S Nñ E 2D 4 , DD and D4 Ö is equal to D D E 2D 4is the corner radius. The FRP sheet along the ÖÖ sides of the rectangular section provides negligible reaction to the lateral expansion of the concrete, and the confinement forces are developed at the rounded corners of the cross section (Figure 6-7). A unique aspect of the structural model described herein is that, to account for the partial confinement of a square or rectangular column, the model calculates the compressive stresses in the concrete elements within the unconfined region using Eqn. 6-14, but Eqn. 6-18 is used for concrete elements within the confined region, rather than transforming the rectangular section into an equivalent circular section as is done in most procedures for dealing with variable confinement in square and rectangular columns such as in ACI (2008) and Teng et al. (2002). It should be noted, however, that the current approach should give the same result for the case of concentric axial compression.

The numerical model was validated by comparing its predictions against experimental results presented in literature (Luciano and Vignoli, 2008; Tao and Yu, 2008; Lie and Woollerton, 1998; Kodur et al., 2005; Lie and Irwin, 1993) on both concentrically- and eccentrically-loaded unwrapped reinforced concrete and FRP strengthened reinforced concrete square columns under both ambient and fire conditions.

6.4.1 Unwrapped Reinforced Concrete Columns The structural model was validated using results from Luciano and Vignoli (2008) on reinforced concrete slender square columns under ambient temperature conditions. Luciano and Vignoli (2008) presented axial load test results on reinforced concrete slender square columns made with different types of concrete (normal strength, high strength and self-consolidating concrete) under varying eccentric loading conditions. The results of reinforced concrete slender square columns made with normal strength were used for the purposes of validating the numerical model developed by the author. The column specimens had cross-sectional dimensions of 100 mm × 100 mm and an effective length of 2120 mm; hence, they had an initial slenderness ratio, DG?D. DN , of 71. According to the ACI 318 reinforced concrete design code (2005), these columns would be classified as ?slender?. The columns had two different reinforcement layouts, which were indicated as ?A? and ?B?. Column A had four 8 mm diameter longitudinal steel reinforcing bars, whereas, Column B had four 12 mm diameter longitudinal steel reinforcing bars. Both Column A and Column B had 6 mm diameter steel ties for transverse reinforcement. Details of the arrangement of the transverse steel ties in the columns are provided by Luciano and Vignoli (2008). Both Column A and Column B were designed to have a concrete cover of 15 mm.

Luciano and Vignoli (2008) conducted both cylinder and cube compressive tests to obtain the mechanical properties of concrete used for fabricating the column specimens. The mechanical

properties of concrete obtained from testing cylinders were used in validating the current numerical model.

Table 6-2 and Figure 6-8 show a comparison of the model predictions and the experimental data. Since the model was able to calculate the second-order deformations satisfactorily, it was able to capture the trend of the axial load-lateral deflection, the maximum axial load carrying capacity and the corresponding lateral mid-height deflection at maximum axial load. As expected, Column specimens having high end eccentricities achieved lower axial load carrying capacity. Figure 6-8 also shows the predicted axial load-bending moment strength interaction diagram for these columns. Because of the high slenderness ratio of the column specimens, they did not achieve the full strength of the reinforced concrete cross section, except for Column B-25, based on the results from the numerical analysis. However, the peak load points were located in close proximity to the strength interaction diagrams, indicating that the model satisfactorily predicts the load carrying capacity of slender, eccentrically-loaded, rectangular reinforced concrete columns.

The numerical model was also used to evaluate the behaviour of unwrapped reinforced concrete square columns in a standard fire situation and the numerical prediction was validated against experimental results from Lie and Woollerton (1998). The 305 mm column specimens tested by Lie and Woollerton (1998) were 3810 mm long and were reinforced internally with four 25.4 mm diameter (No. 8, Area = 509 mm2) deformed steel bars in the longitudinal direction and with 9.5 mm diameter (No. 3, Area = 71 mm2) ties at 406 mm center-to-center spacing, with a clear cover of 48 mm to the longitudinal reinforcement. The 25.4 mm diameter steel had a yield strength of 444 MPa and an ultimate strength of 730 MPa, whereas the 9.5 mm diameter steel had a yield strength of 427 MPa and an ultimate strength of 671 MPa. Both carbonate and siliceous aggregate concretes were used to fabricate the column specimens. The columns were bolted to a column testing frame at the National Research Council of Canada, resulting in fixed-fixed end

However, it was found in previous research studies (e.g., Lie and Celikkol, 1991), which were also conducted in the same test furnace at the National Research Council of Canada that, an effective column length of 2000 mm represents the experimental behaviour of columns because the higher stiffness of the unheated portion of the column contributes to a reduction in the effective length of the column specimens during fire and, also, while the applied load on the column during testing may be intended to be concentric, a small eccentricity always exists due to imperfections during column fabrication and from the loading device. Hence, an initial small eccentricity of 1 mm was assumed during the structural analysis. In the analysis, the initial moisture content was assumed to be 5% (Lie and Woollerton, 1998), except for column specimen LWC2 and LWE14 indicated in Table 6-3.

Figure 6-9 to Figure 6-11 show experimental and predicted temperatures within the concrete at various depths, and Figure 6-12 shows the steel temperature as a function of fire exposure time. The heat transfer model was able to predict the temperatures within the concrete and the steel temperature with reasonable accuracy. Figure 6-9 and Figure 6-10 show the temperatures within the concrete of Column LWC9 and Column LWC2, respectively. Although both Column LWC9 and Column LWC2 were made with siliceous aggregate concrete, in the analysis Column LWC9 was assumed to have a moisture content of 5% and Column LWC2 was assumed to be a dry specimen (i.e., zero percent moisture content). The numerical model predicted higher temperature for concrete elements near the fire exposed exterior surface of Column LWC9 and Column LWC2 than the experimental test result, however, the prediction was similar to the experimental result as the concrete depth increased. Considerable variability was observed between the predicted and experimental results for thermocouple 28, which was at a depth of 25 mm from the fire exposed face of Column LWC9. The deviation between the

predicted and experimental result may be due to uncertainty as to the exact location of the thermocouples located in the columns and also to the fact that the thermally induced moisture migration within concrete elements was not taken into account in the thermal analysis. The effect of moisture was taken into account in the heat transfer model only by assuming that, in each concrete element, moisture began to evaporate when the temperature reached 100°C, which was observed in the temperature profile (Thermocouple 31) by a rapid increase in temperature followed by a plateau near 100°C. This behaviour was absent in the predicted temperature profile near the concrete core of Column Specimen LWC2, which was analyzed assuming that it was a dry specimen (that is, it had no evaporable pore moisture in the concrete). As a result, the concrete core temperature of Column LWC9 was lower than concrete core temperature of Column LWC2. The numerical model was also used to analyze carbonate aggregate concrete column LWE3 and the predicted temperatures were in close agreement with the experimental result as seen in Figure 6-11. The model was able to predict the temperatures of the longitudinal steel in column specimens LWC2, LWC 9, and LWE3 with reasonable accuracy (Figure 6-12).

Table 6-4 and Figure 6-13 to Figure 6-15 present the predicted axial capacity of reinforced concrete square columns reported by Lie and Woollerton (1998) in a fire situation using the structural model. The structural behaviour of Column Specimen LWC2 was investigated considering both transient-state and steady-state conditions to understand the behaviour of reinforced concrete columns in fire under both conditions. Column Specimen LWC2 was evaluated assuming an initial applied load eccentricity of 1.0 mm acting on an equivalent pinned-end column with an effective length of 2000 mm (as justified previously).

When conducting transient-state structural analysis, the transient strain of concrete, which is caused by the thermal expansion and the sustained compressive stress experienced by concrete during fire, was taken into account to calculate the total strain in concrete as described in Eqn. 6- 29. As mentioned earlier in this chapter, an applied sustained load on the column can be expected

to decrease the rate of decay of the ultimate strength of concrete at elevated temperatures (Hertz, 2005). The Column LWC2 was analyzed using the numerical model by considering the ultimate strength of both unstressed and stressed concrete. Figure 6-13(a) presents the variation of the predicted axial capacity of Column LWC2 under a transient-state thermal condition. Lie and Woollerton (1998) reported that, under an applied sustained load of 1333 kN and exposure to ASTM E119 standard fire, Column LWC2 failed 176 minutes into the fire test. When unstressed concrete was considered during transient-state analysis, the predicted failure time of the column specimen was about 130 minutes; however, the predicted failure time increased to 145 minutes when stressed concrete was considered. Hence, it is safe and conservative to design reinforced concrete columns for fire based on unstressed concrete models, and all subsequent column specimens herein were analyzed considering unstressed concrete models.

Under a steady-state thermal condition, the column specimen would be exposed to standard fire for a given period of time and then loaded to failure. The transient strain of concrete would be ignored in Eqn. 6-29 under a steady-state condition. Based on the results from the numerical model, Column LWC2 would fail about 145 minutes after the start of the fire test, as shown in Figure 6-13(b). Note that the failure time based on steady-state thermal conditions is similar to the time of failure determined for the column specimen when transient-state condition was considered by explicitly accounting for the effects of transient strain of concrete and the ultimate strength of stressed concrete because, after being exposed to fire for more than 120 minutes, the ultimate concrete strength of the column specimen would have decreased to such an extent that the structural behaviour would not be influenced by the transient strain of the concrete.

However, prior to 120 minutes of fire exposure, the predicted axial capacity under steady-state conditions was determined to be considerably higher in comparison to the predicted axial capacity under a transient-state condition. Hence, ignoring the effect of transient strain produces unconservative estimates of load carrying capacity in some cases. The numerical model was also

used to generate strength interaction diagrams and load-moment path curves of Column LWC2 under both ambient and fire conditions, as shown in Figure 6-14. Based on these results, the column did not experience a reduction in strength due to slenderness effects of more than 5%, hence, the column behaved as a ?short? column under both ambient and fire conditions (ACI, 2005; Wang et al., 2007).

The numerical model was also used to evaluate the structural behaviour of Column LWE14, which had an applied load eccentricity of 24.5 mm (Figure 6-15). Again, the predicted results were conservative in comparison to the experimental results. In the experiment, column specimen LWE14 failed 186 minutes into the fire test under an applied sustained load of 1178 kN. However, the predicted failure time according to the numerical model was approximately 128 minutes. Figure 6-14 presents the load-moment path curves for Column LWE14 under both ambient and fire conditions, and from this analysis, even under eccentric load conditions, the column behaved as a ?short? column.

Results from the numerical model were further compared against test data obtained from the fire test of carbonate aggregate concrete Columns LWC12 and LWE3 (Lie and Woollerton, 1998), which are presented in Figure 6-16. During the fire test, the concentrically-loaded Column LWC12 failed after 216 minutes under a sustained applied load of 1778 kN. According to the numerical model, the failure time of Column LWC12 was determined to be 170 minutes, which was again a conservative prediction. However, the model prediction of the failure time for eccentrically-loaded Column LWE3 was different than the failure time observed in the fire test.

According to Lie and Woollerton (1998), the carbonate aggregate concrete Column LWE3, which had an initial moisture content of 5% and concrete strength similar to siliceous aggregate concrete Column LWE14 prior to the fire test, failed after 181 minutes under a sustained applied load of 1000 kN in the fire test. That is, siliceous aggregate concrete Column LWE14 performed slightly better under eccentric load condition than carbonate aggregate concrete Column LWE3, which

does not agree with the numerical model. Assuming an initial moisture content of 5%, the temperature within a 305 mm carbonate aggregate concrete column would be considerably lower than a siliceous aggregate concrete according to the numerical model (Figure 6-17). Furthermore, the concrete strength of siliceous aggregate concrete degrades rapidly than carbonate aggregate concrete (Figure 6-18) according to the Hertz (2005) concrete strength model which was used in the numerical model. Hence, based on the numerical model, carbonate aggregate concrete columns perform much better in fire than siliceous aggregate concrete columns.

Lie and Irwin (1993) present a numerical model that uses a finite difference method to calculate the temperatures within a concrete column and load-deflection analysis (Lie et al., 1984) to calculate the strength of a fire-exposed concrete column. Using this numerical model, Lie and Irwin (1993) evaluated Reinforced Concrete Column LIC1, which is of 305 mm square cross- section and has similar reinforcement details as in Lie and Woollerton (1998). Column LIC1, which had a test-day concrete strength of 36.1 MPa, was made of siliceous aggregate concrete and had an initial moisture content of 5% prior to fire exposure (Table 6-3). The 25 mm longitudinal reinforcement had a yield strength of 414 MPa. The numerical model developed herein was used to evaluate the strength of Column LIC1 when exposed to an ASTM standard fire and the results from the Author's numerical model was compared against the test data (Lie and Irwin, 1993) and the results obtained from the Lie and Irwin (1993) model. During the fire test, the Column LIC1 failed under a sustained applied load of 1067 kN after 208 minutes.

According to the author's numerical model, the failure time was 160 minutes (model prediction 1), which was obtained after considering the transient strain of concrete and the Hertz (2005) ultimate compressive strength DBÖ Comparing the results from the numerical models, the Lie and Irwin (1993) model predicted higher load carrying capacity because, Lie and Irwin's (1993) numerical model does not take account of the

transient strain of concrete in calculating the total strain of concrete, and also it uses the ultimate NñD:6m;odel proposed by the Lie (1992), which was calibrated to simulate the concrete strength DBÖ fire behaviour of stressed concrete. Figure 6-19 shows a comparison of the variation of the ultimate concrete strength with increasing temperature proposed by the Hertz (2005) model and the Lie (1992) model. Furthermore, model prediction 3 (which was obtained by ignoring the transient strain of concrete and by accounting the Hertz (2005) ultimate compressive strength NñD:6m;odel of stressed concrete) demonstrates that Lie and Irwin (1993) predicted higher load DBÖ carrying capacity for Column LIC1 because transient strain of concrete was ignored and the NñD:6m;odel proposed by Lie (1992) represents the behaviour of ultimate compressive strength DBÖ stressed concrete. According to model prediction 2, by taking account of the ultimate compressive strength of stressed concrete and transient strain of concrete, the failure time of Column LIC1 increased by about 25 minutes in comparison to model prediction 1, which demonstrates again that it is conservative to design reinforced concrete columns for fire based on unstressed concrete models.

From the above discussion we can conclude that model was able to make reasonable predictions of the temperatures within reinforced concrete columns. The structural model was able to capture the trends of the axial load-lateral deflection of slender concrete columns satisfactorily and was also able to make conservative predictions of the load carrying capacity of reinforced concrete columns in a fire situation. For safe design of concrete columns, it appears to be necessary to consider the effects of transient strain in the analysis.

6.4.2 FRP Wrapped Reinforced Concrete Columns Results from Masia et al. (2004) and Rochette and Labossière (2000) on FRP confined concrete square prisms, tested under ambient temperature conditions, were used to validate the predicted axial strength and axial peak strain predicted by the numerical model. The comparison

between the predicted and test results are presented in Table 6-6 and Figure 6-21. The numerical model was able to predict the axial strength of the FRP confined concrete square prisms with reasonable accuracy. The model was also able to predict the axial compressive peak strain in the concrete at the most compressed fibre with reasonable accuracy in comparison with the test results when the corner radius of the FRP confined concrete square prism was equal to or greater than 25 mm. When the corner radius is sufficiently large to produce DNBñ· D #greater than the Ö ÖØ maximum axial load capacity of a plain concrete prism, the failure strain of the concrete according to Eqn. 6-31 is DÝand the value of DÝis reasonably close to the value observed during ÖÖ ÖÖ experiments. However, when the corner radius is small so that the maximum axial load capacity Nñ· D # of the plain concrete prism is greater than DBÖ , the axial peak strain of FRP confined concrete ÖØ is limited to DÝin the analysis because the maximum axial capacity of the FRP confined concrete Öè square prism is achieved at DÝrather than at DÝ. Deviation was observed between the predicted Öè ÖÖ and the test values of axial peak strain when the corner radius was less than 25 mm. Regardless of this deviation, it should be noted that the model was able to predict the axial strength accurately in comparison with the experimental results. Based on the analysis conducted herein, the corners of the concrete square prisms need to be sufficiently rounded to increase the axial strength from FRP lateral confinement; this is widely acknowledged within the FRP strengthening industry (ACI 440, 2008). Providing additional layers of FRP wrap could also increase the axial strength of a square concrete prism, when the corner radius of the concrete square prism cannot be increased, although this would not make effective use of the FRP's tensile strain capacity. Additional research is needed on the level of lateral confinement that can be provided using FRP to a square prism or column.

The numerical model was further used to evaluate the behaviour of FRP strengthened reinforced concrete square columns that were tested by Tao and Yu (2008) under ambient conditions. Tao and Yu (2008) tested both unwrapped reinforced concrete and FRP strengthened

reinforced concrete slender square columns under varying eccentric axial loading conditions. The columns had a cross section of 150 mm × 150 mm and had an effective length of 3060 mm;

hence, the column had an initial slenderness ratio, DG?D. DN , of 68. All the specimens were reinforced with four 12 mm diameter deformed steel bars and 6 mm steel ties at 100 mm center- to-center spacing having a clear concrete cover of 15 mm. There were two sets of column specimens fabricated and tested in Tao and Yu (2008). The first set of columns investigated the behaviour of reinforced concrete columns wrapped with unidirectional FRP and the second set investigated bidirectional FRP.

The mechanical properties of the steel reinforcement and concrete used to fabricate the column specimens in Tao and Yu (2008) are presented in Table 6-1. Prior to the external wrapping, the corners of the reinforced concrete columns were rounded to have a radius of 25 mm. The columns were then strengthened by wrapping with two layers of CFRP. The average tensile strength and elastic modulus of the CFRP, which were based on a nominal thickness of 0.17 mm per layer, were 4212 MPa and 255000 MPa, respectively. Figure 6-22 and Figure 6-23 present the results from the numerical model and provide a comparison against the test results.

The numerical model was again able to predict the axial strength of the column specimens with reasonable accuracy, and was also able to calculate the second-order lateral deflection at maximum axial load. In the numerical model, stability failure of a column was established by setting a failure criterion where the column was assumed to have failed when the axial load- moment path showed a decreasing branch after reaching maximum axial load. Hence, the predicted axial load versus lateral deflection curves in Figure 6-22 and Figure 6-23 did not show a post-peak curve as was observed in the experimental tests. Since FRP wraps in the hoop direction do not significantly enhance the flexural stiffness of the column specimens, the eccentrically-loaded FRP wrapped ?slender? columns, whose failure is governed by flexural

rigidity rather than crushing strength, showed no significant increase in axial strength from the lateral FRP confinement.

A column specimen tested and presented in Kodur et al. (2005) was used to evaluate the structural performance of FRP strengthened reinforced concrete square column specimen (KC) in a standard fire situation using the numerical model. Similar to the columns tested by Lie and Woollerton (1998), the FRP strengthened 406 mm square reinforced concrete column in Kodur et al. (2005) was also 3810 mm long and had similar steel reinforcement details except that the concrete clear cover to the longitudinal reinforcing steel was 50 mm. Kodur et al. (2005) used reinforcing steel with a yield strength of 400 MPa. The FRP confined reinforced concrete column was fabricated with carbonate aggregate concrete. Prior to wrapping the column with FRP, the corners of Column KC were rounded to a 30 mm radius. The column was confined with three layers of externally-bonded circumferential glass FRP (GFRP) wraps, which had a specified design thickness of 1.3 mm for a single layer of laminate. The FRP wrap had a 300 mm overlap in the hoop direction and 25 mm overlap in the vertical direction. The tensile strength and elastic modulus of the GFRP were 575 MPa and 26100 MPa, respectively. The FRP confined square column was provided with 38 mm of a spray applied cementitious insulation system to protect the FRP strengthening system from elevated temperatures. The compressive strengths and moisture conditions of concrete in the column at the time of testing are provided in Table 6-3. The moisture content of the insulation was assumed to be 10% in the numerical analysis. The columns were exposed to the ASTM E119 (ASTM, 2001) standard fire and tested in compression to failure under fixed end conditions. Figure 6-24 presents a comparison between the predicted and observed temperatures at various locations on the FRP and insulation in Column KC during the fire exposure. The numerical model was able to predict the temperatures near the corners of the column specimen close to the temperatures observed during the fire tests. However, significant variation was observed between the predicted and the observed temperatures at the

side faces. This variation is due to the formation of cracks in the insulation near the middle of the column's side faces. About 40 minutes into the fire test, flames were observed emanating from cracks that had formed in the insulation (Figure 6-25). As a result, the temperatures at the side faces were higher than at the corners of the column. However, based on knowledge of heat transfer, the temperatures near the corners were expected to be higher than the temperatures at the side faces of the column, as shown in Figure 6-26(b). Based on this hypothesis, combined with visual observation and photos taken during the fire test, a modified analysis was conducted by assuming a crack in the insulation at the middle of the side face and these results were then compared against the experimental result (Figure 6-27). This was done to check if the hypothesis regarding side face heating was plausible. After assuming cracks in the insulation, the heat transfer model was able to predict the temperatures on the FRP and insulation accurately. While this result shows that cracking of the insulation may be important for predicting the heat transfer in insulated FRP wrapped square reinforced concrete columns, although such modelling is extremely difficult and is considered beyond the scope of the current project.

Figure 6-28 presents the axial load capacity of Column KC with increasing fire exposure using the numerical model. Using the model, the axial strength of the reinforced concrete column was calculated to be about 9206 kN. After wrapping the reinforced concrete column with three layers of GFRP, the axial strength was predicted to be increased only by about 5%, demonstrating that large amounts of FRP are required for axial strengthening of square columns with FRP wraps. Without any insulation, the model predicts that the reinforced concrete column would fail under a sustained load of 3093 kN in about 125 minutes into the fire exposure. However, the structural performance of the reinforced concrete column is significantly improved by providing fire protection insulation. Using the numerical model, the predicted variation in axial strength of an insulated reinforced concrete column and an insulated FRP strengthened reinforced concrete column with increasing temperature were compared to examine the failure time of the FRP

confinement. Assuming that the insulation remained intact, that there was no crack formation within the insulation for the duration of the fire exposure, and that the mechanical properties of the FRP wrapping material at elevated temperature can be described as discussed previously in Section 4.6, the effects of the FRP confinement began to diminish at about 60 minutes into the fire, and in about 120 minutes the FRP confinement was probably ineffective as the temperature of the FRP exceeded 200°C (note that this in no way implies structural collapse). This was evidenced in Figure 6-28 when the axial load capacity curve representing the FRP strengthened column converged with the axial load capacity curve representing reinforced concrete column after 120 minutes. However, the duration of the effectiveness of the FRP confinement was reduced when the formation of cracks in the insulation was assumed at the side faces of the column specimen as observed during the fire test (Figure 6-29). The effects of FRP confinement were predicted to have disappeared in about 80 minutes into the fire exposure. Based on the results from the numerical analysis, the axial load capacity of the column specimen was about 9000 kN after being exposed to fire for about 240 minutes. During the test, due to the sudden loss of insulation at about 350 minutes into the fire test, the concrete cover spalled off the column, thus exposing the longitudinal reinforcement to extreme temperatures. Shortly after the major spalling of the concrete cover, the column specimen failed under the sustained applied load. It should be noted that if the insulation had remained intact, the column specimen would almost certainly not have failed under the sustained applied load. Regardless, the column specimen achieved a tested four hour fire endurance rating. Based on the above discussion we can conclude that the FRP strengthening system used herein to strengthen a square reinforced concrete column could maintain its effectiveness for up to 120 minutes with an adequate amount of thickness. However, formation of cracks within the insulation layer could bring the ?effective? time down to 80 minutes (Figure 6-29).

Full-scale fire endurance column tests are a time consuming and expensive way to investigate the fire behaviour of concrete columns. A numerical model was developed in this chapter to simulate the heat transfer within columns using a finite difference method and to simulate their structural behaviour using a two-dimensional fibre-element analysis where the Column Deflection Curve method was used to determine the second-order deformations in columns caused by the columns' slenderness. Comparing the results from the numerical model against available test results, the numerical model can predict the temperatures within both unwrapped reinforced concrete and FRP strengthened reinforced concrete columns with reasonable accuracy. The model was able to capture the trend of the axial load-lateral deflection response of a slender column satisfactorily and was also able to make conservative predictions of the load carrying capacity for safe design of concrete columns in a fire situation. From this study, it appears that ignoring the effect of transient strain in the structural analysis of reinforced concrete columns in a fire situation produces unconservative prediction of the column's load- carrying capacity. Also, in a fire situation the FRP strengthening system used to confine the reinforced concrete column presented by Kodur et al. (2005) could have maintained its effectiveness for at least 120 minutes with adequate fire insulation over it, however, this time had come down to about 80 minutes with the formation of cracks within the insulation. In spite of this, the reinforced concrete column sustained the carried applied load for about four hours.

Table 6-1: Mechanical properties of concrete and steel reinforcement used in column specimens tested by Luciano and Vignoli (2008) and Tao and Yu (2008)

Concrete Steel reinforcement Column a 28-day Test-day Yield Ultimate Molulus of specimen strength strength Steel strength strength elasticity (MPa) (MPa) type (MPa) (MPa) (MPa) 12 541.3 641.7 200000c NSCD-A & B a 47.36 50.65 8 549.3 614.1 200000 c 6 604.1 638.4 200000 c

US-1, 2, 3 & 4 b 50 61.5 12 388.7 557.9 196000 6 397.3 548.1 216000

BS-1, 2, 3 & 4 b 50 61.5 12 358.1 520.5 186000 6 382.2 456.5 211000 a The designation for the column specimens as presented in Luciano and Vignoli (2008) b The designation for the columns specimens as presented in Tao and Yu (2008) c Typical value for the modulus of elasticity of steel was used in the analysis as no value was presented in Tao and Yu (2008)

Table 6-2: Experimental results from Luciano and Vignoli (2008) versus predicted results from the numerical model

Test results Predicted results Mid-height Mid-height lateral lateral Column deflection at Peak deflection at Peak specimen Eccentricity peak load load peak load load (mm) (mm) (kN) (mm) (kN) NSCD-A-8 7 13.0 297.0 13.0 300.0 NSCD-A-13 13 15.0 216.0 13.0 224.0 NSCD-A-25 24 26.0 126.0 20.0 130.0 NSCD-B-8 6 14.0 327.0 13.5 341.0 NSCD-B-13 12 17.0 249.5 14.0 255.0 NSCD-B-25 24 30.0 164.0 22.0 160.0

Table 6-3: Details of specimens from Lie and Woollerton (1998), Lie and Irwin (1993), and Kodur et al. (2005)

Column Aggregate Moisture Concrete Specimen Cross Section Steel Type Content Strength (mm × mm) (%) (%) (MPa) LWC2 305 × 305 2.19 Siliceous 0 36.9 LWC9 305 × 305 2.19 Siliceous 5 38.3 LWE14 305 × 305 2.19 Siliceous 0 40.0 LWC12 305 × 305 2.19 Carbonate 5 39.9 LWE3 305 × 305 2.19 Carbonate 5 39.9 LIC1 305 × 305 2.19 Carbonate 5 36.1 KC 406 × 406 1.21 Carbonate 5 52.0

(2005) Failure Time Column Applied (minutes) Specimen Eccentricity Load (mm) (kN) Test Predicted 1.0 LWC2 1333 170 130 (minimum) LWE14 24.5 1178 183 125 1.0 LWC12 1778 216 170 (minimum) LWE3 24.5 1000 181 -- 1.0 LIC1 1067 208 160 (minimum) 1.0 KC 3093 256 -- (minimum)

Table 6-5: Details of specimens from Masia et al. (2004) and Rochette and Labossière (2000)

Specimen size, Concrete FRP Type and FRP Specimen Source Strength Properties Thickness b × h × r designation (MPa) (mm) (mm × mm × mm) Masia et al. 27.2 CFRP; 0.26 100 × 300 × 25 M1 2004 DBÙ å Lã35è00 M;Pa 0.26 125 × 375 × 25 M2 D'Ù åLã230 G;Pa 0.26 150 × 450 × 25 M3 ç Rochette 42.0 CFRP; 0.90 152 × 500 × 5 RL1 and 42.0 DBÙ å Lã12è65 M;Pa 0.90 152 × 500 × 25 RL2 Labossière 2000 42.0 D'Ù å Lã 82.7 G; Pa 0.90 152 × 500 × 38 RL3 ç 43.9 1.50 152 × 500 × 5 RL4 43.9 1.20 152 × 500 × 25 RL5 43.9 1.50 152 × 500 × 25 RL6 35.8 1.20 152 × 500 × 25 RL7 35.8 1.50 152 × 500 × 25 RL8 35.8 1.20 152 × 500 × 38 RL9 35.8 1.50 152 × 500 × 38 RL10

Table 6-6: Comparison between predicted results and test results from Masia et al. (2004) and Rochette and Labossière (2000)

Peak Axial Strain Wrapped Strength Specimen (%) (MPa) Source Designation Test Model Test Model Masia et al. M1 1.76 1.87 51.4 44.8 2004 M2 1.63 1.57 40.5 37.0 M3 1.22 1.37 36.2 31.5 Rochette RL1 0.69 0.30 39.5 44.1 and RL2 0.92 1.17 42.4 40.0 Labossière 2000 RL3 1.12 1.17 48.9 53.1 RL4 1.02 0.30 43.9 46.5 RL5 1.35 1.39 50.9 51.0 RL6 0.90 1.65 47.9 56.1 RL7 2.04 1.62 52.3 45.4 RL8 2.12 1.94 57.6 50.4 RL9 1.92 1.62 59.4 54.0 RL10 2.39 1.94 68.7 60.0

Start Input: Member details (e.g. cross section, concrete aggregate type, FRP thickness, etc.), fire duration, etc.

Discretization of column into elements Calculation of fire temperatures Calculation of maximum time step Calculation of thermal properties of constituent materials Calculation of element temperatures using explicit finite difference method Calculation of mechanical properties of constituent materials for specified temperatures Determine load-moment interaction diagram for various temperatures ? For given loads, determine moment-curvature relationship using equilibrium and compatibility relationship ? Using the moment-curvature relationship, determine the load and deflection at mid-height; subsequently determine the load-moment interaction diagram.

Output: Temperature data for specified elements Output: Load-moment interaction diagrams at specified

End Figure 6-1: Flowchart showing the procedures for the fire resistance calculation of columns

?y (M-1)?y y = (m-1)? y y ?x x = (n-1)? x (N-1)?x Insulation layer FRP layer Concrete Nodes

x Figure 6-2: Discretization of one-quarter cross-section of an insulated and FRP strengthened concrete square column (Nodes within the FRP and insulation layer are not shown) (a) Rm+1, n

Rm, n-1 m, R n Rm, n+1 Rm-1, n E cond(m+1, n) E cond(m, n-1) E cond(m, n+1)

E cond(m-1, n) (b) Rm, n-1 Rm, n Rm-1, n E rad, fire E cond (m, n-1) E rad, fire

E cond (m-1, n) Figure 6-3: Heat transfer mechanism within (a) an interior, and (b) exterior corner element

Steel layer, j = 1 FRP layer, k = 1 Concrete layer, i = 1 d s, 1 d c, 6 d c, N-1 d s, 2

k i=N k=N Steel layer, j = 2 Concrete stress at layer i = 1, f c

? ?c s, 1 ?c, N-1 ? s, 2 ?c, 6 Concrete force at layer i = 6, Cc, 6 Cc, N-1 f s, 1 or Ts, 1 f f, 6 or Tf, 6

f f, N-1 or Tf, N-1 f s, 2 or Ts, 2 Idealized geometry Total strain Stresses and forces Stresses and forces in of cross section distibution in concrete steel and longitudinal FRP

Figure 6-4: Two-dimensional fibre analysis for determining the stresses and forces in concrete and reinforcing steel at a given cross-section along the column's height (as required to derive the axial load-moment interaction diagrams and moment-curvature relationship)

? tot,c Total strain ? th,c = + ?? tr,c me,c

+ Thermal strain Transient strain Mechanical strain

Figure 6-5: Components of total strain within concrete at elevated temperatures

300 150 Y-Axis Y-Axis 150 300 150 150 100 50 0 -50 -100 -150 900 900 750 750 600 600 450 900 600 450 300 150 300 450 750 600 600 150 750 300

150 300 450 450 750 600 600 150 600 300 300 450 750 450 450 600 600 750 750 750 900 150 100 50

0 -50 -100 -150 0.018 0.018 0.009 0.018 0 005 0.018 0 005 0.009 0.

0.018 0 013 . 0.0090.013 0.0090.013 0.005 0.005 0.018 0.013 0.009 0.013 .

0.009 0.005 0.018 0.013 0.009 0.013 0.005 0.005 0.018 018 0 013 . 0.009 0.009 0.013 0.013 0.018 0.018 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 X-Axis X-Axis (a) (b)

Figure 6-6: Predicted two-dimensional (a) temperature distribution, and (b) ultimate concrete strain distribution within column specimen LWC2 after 1 hour of ASTM E119 standard fire

E t? frpt h,rup d f flrp 45° E t? frpt h,rup

Figure 6-7: Confining action of the FRP wrap at the corner of the cross section

400400 300300 Axial Load (kN) 200 100 0 Model A-8 Experiment A-13 A-25 Applied Load (kN) 200 100

0 0 1000 Applied Load (kN) 500 0 10 20 30 40 50 60 Lateral Deflection (mm) (a) Model B-8 Experiment B-13 B-25 0 10 20 30 40 50 60 Lateral Deflection (mm) (b)

Model A-8 Experiment A-13 A-25 Strength Interaction Diagram 1000 Applied Load (kN) 500

0 Model B-8 Experiment B-13 B-25 Strength interaction diagram 0 5 10 15 0 5 10 15 Moment (kN m) Moment (kN m) (c) (d)

Figure 6-8: (a) Axial load versus mid-height lateral deflection of Column NSCD-A; (b) axial load versus mid-height lateral deflection of Column NSCD-B; (c) axial load-moment interaction diagram for Column NSCD-A; and (d) axial load-moment interaction diagram for Column NSCD-B, (Luciano and Vignoli, 2008)

y 305 mm A (0, 0) 305 mm C Furnace/ TC 37 (144, 144) ASTM fire TC 36 (135, 135) TC 26 (140, 0) TC 35 (125, 125) x TC 28 (127, 0) TC 34 (108, 108) B TC 29 (89, 0) TC 33 (81, 81) TC 30 (51, 0) TC 32 (45, 45) TC 31 (0, 0) 1500 Test Predicted 1500 C)

C) Temperature (o 1000 500 Temperature (o 1000 500 0 0 Test Predicted 0 60 120 180 240 0 60 120 180 240 Time (minutes) Time (minutes) (a) (b)

Figure 6-9: Variation in concrete temperature within Column LWC9 (a) along the line AB, and (b) along the line AC ( Lie and Woollerton, 1998)

y 305 mm A (0, 0) 305 mm C Furnace/ TC 36 (144, 144) ASTM fire TC 36 (135, 135) TC 26 (140, 0) TC 35 (125, 125) x TC 28 (127, 0) TC 34 (108, 108) B TC 29 (89, 0) TC 33 (81, 81) TC 30 (51, 0) TC 32 (45, 45) TC 31 (0, 0) 1500 Test Predicted 1500 Temperature (C) 1000

500 Temperature (C) 1000 500 0 0 Test Predicted 0 60 120 180 0 60 120 180 Time (minutes) Time (minutes) (a) (b)

Figure 6-10: Variation in concrete temperature within Column LWC2 (a) along the line AB, and (b) along the line AC ( Lie and Woollerton, 1998)

y 305 mm A (0, 0) 305 mm C Furnace/ TC 37 (144, 144) ASTM fire TC 36 (135, 135) TC 26 (140, 0) TC 35 (125, 125) x TC 28 (127, 0) TC 34 (108, 108) B TC 29 (89, 0) TC 33 (81, 81) TC 30 (51, 0) TC 32 (45, 45) TC 31 (0, 0) 1500 Test Predicted 1500 C)

C) o Temperature ( 1000 o 500 Temperature ( 1000 500 0 0 Test Predicted 0 60 120 180 240 0 60 120 180 240 Time (minutes) Time (minutes) (a) (b)

Figure 6-11: Variation in concrete temperature within Column LWE3 (a) along the line AB, and (b) along the line AC (Lie and Woollerton, 1998)

Temperature (C) 500 0 TC 4 TC 10 TC 3 TC 9 Predicted 0 60 120 180 Time (minutes) (a)

1000 oC) Temperature ( 500 0 TC 4 TC 10 TC 3 TC 9 Predicted 0 60 120 180 240 Time (minutes) (b)

1000 oC) Temperature ( 500 0 TC 4 TC 10 TC 3 TC 9 Predicted 0 60 120 180 240 Time (minutes) (c)

Figure 6-12: Variation in reinforcing steel temperature in columns (a) LWC2, (b) LWC9, and (c) LWE3 (Lie and Woollerton, 1998)

Axial Load (kN) 5000 4000 3000 2000 1000 0 kL/r = 0 kL/r = 23 Lie and Woollerton, 1998

' f c, unstressed ' f c, stressed 0 60 120 180 Time (minutes) (a) Axial Load (kN) 5000 4000 3000 2000 1000

0 kL/r = 0 kL/r = 23 Lie and Woollerton, 1998 With transient strain Without transient strain 0 60 120 180 Time (minutes) (b)

Figure 6-13: The effect of (a) ultimate strength of stressed concrete and (b) transient strain on the variation of axial capacity of Column LWC2 (Lie and Woollerton, 1998) with increasing fire exposure time

Axial Load (kN) 5000 4000 3000 2000 1000 0 0 minutes 60 minutes 120 minutes 180 minutes Strength interaction diagram Load-moment path

0 50 100 150 200 Moment Capacity (kN m) (a) Axial Load (kN) 5000 4000 3000 2000 1000

0 Strength interaction diagram Load-moment path 0 50 100 150 200 Moment Capacity (kN m) (b)

Figure 6-14: Strength interaction diagram for columns (a) LWC2, and (b) LWE14 with increasing fire exposure (Lie and Woollerton, 1998)

Axial Load (kN) 5000 4000 3000 2000 1000 0 kL/r = 0 kL/r = 23 LWC2 LWE14

e = 1.0 mm e = 24.5 mm 0 60 120 180 240 Time (minutes) Figure 6-15: Variation of axial capacity of siliceous aggregate concrete columns LWC2 and LWE14 (Lie and Woollerton, 1998) with increasing fire exposure Axial Load (kN) 5000 4000 3000 2000 1000

0 kL/r = 0 kL/r = 23 LWC12 LWE3 e = 1 mm e = 24.5 mm 0 60 120 180 240 Time (minutes) Figure 6-16: Variation of axial capacity of carbonate aggregate concrete columns LWC12 and LWE3 (Lie and Woollerton, 1998) with increasing temperature

y C 305 mm A (0, 0) 305 mm TC 26 (140, 0) TC 37 (144, 144)) x TC 28 (127, 0) TC 36 (135, 135) B TC 29 (89, 0) TC 35 (125, 125) TC 30 (51, 0) TC 33 (81, 81) TC 31(0, 0) TC 32 (45, 45) 1500 C) Temperature (o 1000

500 0 Siliceous Carbonate 1500 C) o Temperature ( 1000 500 0 Siliceous Carbonate 0 60 120 180 240 0 60 120 180 240 Time (minutes) Time (minutes) (a) (b)

Figure 6-17: Comparison between siliceous and carbonate aggregate concrete column (a) along the line AB, and (b) along the line AC

1.5 C) o (20 1.0 c (T) / f 0.5 c f 0.0 Siliceous Carbonate ' ' 0 500 1000 Temperature (oC) Figure 6-18: Variation of compressive strength of siliceous and carbonate aggregate concrete with increasing temperature

Hertz, 2005 (unstressed) Hertz, 2005 (stressed) Lie, 1992 1.5 C) o (20 1.0 c ' (T) / f 0.5 c ' f 0.0 0 500 1000 Temperature (oC) Figure 6-19: Comparison between the ultimate compressive strength model proposed by Hertz (2005) and Lie (1992) for siliceous aggregate concrete

Model prediction 1 Model prediction 2 Model prediction 3 Test (Lie and Irwin, 1993) Model (Lie and Irwin, 1993) 5000 Axial Load (kN) 4000 3000 2000 1000

0 Failure time during test 0 60 120 180 240 300 360 Time (minutes) Figure 6-20: Variation of axial capacity of siliceous concrete column LIC1 (Lie and Irwin, 1993) with increasing temperature (Note that, Model prediction 1 considers E¿ :aEn?d ; ExE?,E? Nñ Nñ unstressed E?:, ME?odel;prediction 2 considers E¿ :aEn?d str;essed E?:, aEn?dM;odel E? ExE?,E? E? prediction 3 ignores E¿ Nñ ExE?,E? E?

Peak Axial Strain from Model (%) 2.5 2.0 1.5 1.0 0.5 0.0 Masia et al. 2004 Rochette and Labossiere 2000 0.0 0.5 1.0 1.5 2.0 2.5 Peak Axial Strain from Experiment (%) (a) Axial Strength from Model (MPa) 80

60 40 20 0 Masia et al. 2004 Rochette and Labossiere 2000 0 20 40 60 80 Axial Strength from Experiment (MPa) (b)

Figure 6-21: Performance of the numerical model in predicting (a) the peak axial strain and (b) the axial strength of FRP wrapped square concrete prism in comparison with experimental data

Axial Load (kN) 1000 500 0 Predicted Tao and Yu (2008) e = 1.5 mm e = 50 mm 0 50 100 Lateral Deflection (mm) (a) Axial Load (kN) 250 200 150 100 50

0 Predicted Tao and Yu (2008) e = 100 mm e = 150 mm 0 50 100 Lateral Deflection (mm) (b)

Figure 6-22: (a) Axial load versus mid-height lateral deflection of unwrapped reinforced concrete square column specimen (Tao and Yu, 2008) having (a) load eccentricity of 1.5 mm and 50 mm, and (b) load eccentricity of 100 mm and 150 mm

Axial Load (kN) 1000 500 0 Predicted Tao and Yu (2008) e = 0 mm e = 50 mm 0 50 100 Lateral Deflection (mm) (a) Axial Load (kN) 250 200 150 100 50

0 Predicted Tao and Yu (2008) e = 0 mm e = 50 mm 0 50 100 Lateral Deflection (mm) (b)

Figure 6-23: (a) Axial load versus mid-height lateral deflection of FRP strengthened reinforced concrete square column specimens (Tao and Yu, 2008) having (a) load eccentricity of 1.5 mm and 50 mm, and (b) load eccentricity of 100 mm and 150 mm

2 6 Insulation 1 5 7 3

GFRP 8 4 Furnace/ ASTM fire TC 2 (Insulation/FRP bond) TC 6 (FRP/concrete bond) 1500 Test Predicted 1500

10001000 Temperature (C) 500 Temperature (C) 500 0 0 0 60 120 180 240 Time (minutes) (a) Furnace/ ASTM fire TC 1 (Insulation/FRP bond) TC 5 (FRP/concrete bond) 1500 Test Predicted 1500

10001000 Temperature (C) 500 Temperature (C) 500 0 0 0 60 120 180 240 Time (minutes) (c) Furnace/ ASTM fire TC 4 (Insulation/FRP bond) TC 8 (FRP/concrete bond) Test Predicted

0 60 120 180 240 Time (minutes) (b) Furnace/ ASTM fire TC 3 (Insulation/FRP bond) TC 7 (FRP/concrete bond) Test Predicted

0 60 120 180 240 Time (minutes) (d)

Figure 6-24: FRP and insulation temperature on column specimen KC (Kodur et al. 2005)

Figure 6-25: Flames emanating from the cracks forming at the side face

100 Y-axis (mm) 0 -100 800 C -200 800 C 600 C 400 C 200 C 800 C

800 C 200 C 600 C 400 C 200 C 200 C 400 C 600 C 800 C 200 800 C 600 C 400 C 100 Y-axis (mm) 0 400 C -100 600 C -200 240 200 C 200 C 240 200 C 240 200 C 240 -200 -100 0 100 200 -200 -100 0 100 200 X-axis (mm) X-axis (mm) (a) (b) 200

100 Y-axis (mm) 200 C 0 -100 -200 240 200 C 280 240 200 C 200 C 200 C 240 200 240 80 200 C 240 200 C 240 280 200 C 240 C 20 C 200 C 200 0C -200 -100 0 100 200 X-axis (mm) (c)

Figure 6-26: Temperature distribution of (a) Reinforced concrete column after 120 minutes, (b) insulated FRP strengthened reinforced concrete column after 240 minutes assuming no cracks within the insulation, and (c) insulated FRP strengthened reinforced concrete column after 240 minutes assuming cracks in the insulation

Furnace / ASTM fire TC 1 (Insulation/FRP interface) TC 5 (FRP/concrete interface) 1500 C) ? 1000 Temperature ( 500

0 0 60 120 180 240 Time (minutes) Figure 6-27: FRP and insulation temperature on column specimen KC assuming cracks in the insulation

RC Insulated-RC Insulated & FRP-RC Experiment 10000 Axial Capacity (kN) 5000

0 0 60 120 180 240 300 Time (minutes) Figure 6-28: Variation of axial load capacity of FRP strengthened reinforced concrete column specimen KC (Kodur et al., 2005) with increasing fire exposure

Insulated-RC Insulated & FRP-RC (without crack) Insulated & FRP-RC (with crack) 10000 Axial Capacity (kN) 9500

9000 8500 0 60 120 180 240 Time (minutes) Figure 6-29: Axial capacity of insulated reinforced concrete column and insulated FRP strengthened reinforced concrete column with increasing fire exposure

Chapter 7 Conclusions 7.1 Summary The overall objective of this thesis was to investigate the fire risk associated with using externally-bonded FRPs to strengthen reinforced concrete columns of both circular and square cross section. To achieve this objective, full-scale fire tests of FRP strengthened reinforced concrete circular columns were conducted using supplemental fire insulation systems. These full- scale fire tests examined the fire performance of two different fire insulation systems and determined the ultimate axial strength of these columns when exposed to fire. Although these full-scale standard fire tests provided a wealth of useful information on the important factors to consider when designing FRP confined reinforced concrete columns, such these tests are expensive and time consuming. Hence, a major part of this research program was devoted to developing a numerical model that can simulate the behaviour of reinforced concrete and FRP strengthened reinforced concrete columns. Since a numerical model was developed previously and presented by Bisby (2003) for circular concrete columns, this thesis focused on the development of a numerical model for square/rectangular concrete columns, although some tangential research devoted to modelling the performance of slender and eccentrically-loaded FRP wrapped reinforced concrete columns was performed as presented in Chapter 3. An explicit finite difference method was used to predict the heat transfer within the column and a two- dimensional fibre-section analysis was used to determine the structural behaviour. The Column Deflection Curve (CDC) method presented by Chen and Atsuta (1976) was invoked in the numerical model to calculate the second-order lateral deflection of a slender column. A significant obstacle to accurately simulating the behaviour of FRP strengthened concrete structures was the lack of knowledge on FRP's thermal and mechanical behaviour at elevated

temperatures. Hence, a small-scale material testing program was conducted to investigate the thermal behaviour of the FRP material and also to characterize the mechanical and bond properties of glass/epoxy FRP (GFRP) under various loading and thermal regimes, ranging from ambient to 200°C.

7.2 Behaviour of FRPs at Elevated Temperatures Under a number of loading and thermal regimes, GFRP tensile and single lap-splice strength tests were conducted to investigate the mechanical and bond properties, respectively.

Based on the observations and results from the small-scale experimental test program, which were presented in Chapter 3, the following conclusions were drawn: 1. Much of the mechanical and FRP-to-FRP bond property degradation occurs below the glass transition temperature of the FRP. The GFRP material tested in the current study experienced a 50% loss in tensile strength, a 30% loss in tensile elastic modulus, and a 60% loss in FRP-to-FRP bond strength at temperatures 15°C below the glass transition temperature of its epoxy resin matrix.

2. The GFRP material tested in the current study can, with sufficient anchorage, maintain 40% of its tensile strength and 70% of its elastic modulus at temperatures considerably in excess of the glass transition temperature of their resins.

3. Approximately 90% of the FRP-to-FRP bond strength was lost at temperatures slightly above the glass transition temperature of FRP lap-splice specimens, which had an overlap length of 50 mm. Although the degradation of the FRP-to-FRP bond strength was more severe than the deterioration of the tensile strength and modulus, it should be cautioned that the results presented on the lap-splice FRP specimens herein represent the most

severe possible loading case for load transfer in the FRP-to-FRP bond and such tests are not representative of longer FRP lap-splice lengths which are used in practice.

4. The hyperbolic tangent function model given by Eqn. 4-3 is able to describe the mechanical and bond property degradation of the specific GFRP material tested in the current study satisfactorily. Hence, this model was used in numerical model presented in Chapter 6 to analyze the fire behaviour of FRP strengthened concrete axial members.

7.3 Behaviour of FRP Confined Concrete Columns Exposed to Standard Fires A numerical model was developed in Chapter 6 to predict the temperatures within a unwrapped reinforced concrete and FRP strengthened reinforced concrete square/rectangular column and, subsequently using this information, to simulate the structural behaviour of these concrete columns in fire. As a first step, an analytical structural model was developed and validated in Chapter 3 that can simulate the behaviour of FRP confined concrete circular columns with increasing slenderness under variable eccentric axial compressive loads at ambient temperature. In addition to the numerical study presented in Chapters 3 and 6, full-scale fire tests were conducted on three FRP wrapped reinforced concrete circular columns, two of which were protected with one of two different insulation systems (denoted as the MBrace insulation system and the Sika insulation system). Results from these fire tests are presented and discussed in Chapter 5. Based on the analytical and experimental investigation, the following conclusions were drawn on the behaviour of FRP confined concrete columns under both ambient room temperature and fire conditions: 1. The analytical model was able to predict the maximum axial load carrying capacity and capture the trend of the axial load-lateral deflection of a slender column satisfactorily at ambient room temperature. However, in many cases the model was not able to accurately

predict the axial load carrying capacity and lateral deflection of a slender column at ultimate condition. This was because the FRP confined concrete model used in the numerical model could not accurately determine the axial compressive strain in the concrete and hoop strain in the FRP wrap at failure for the case of variable confinement under eccentric loads, and also because of suspected inaccuracies in the applied load eccentricity in the tests used for model validation.

2. The numerical model confirmed the following observations, many of which have been made in previous research studies (Fitzwilliam, 2006; Tao and Yu, 2008). Wrapping the reinforced concrete columns with FRP, where the fibres are oriented in the hoop direction, enhanced the axial capacity and axial and lateral deformability of the reinforced concrete columns at ambient temperature. However, as the column slenderness increased, the ultimate axial capacity of both unwrapped and FRP wrapped concrete columns decreased and the lateral deflections increased at failure.

3. Based on the results of full-scale fire endurance tests presented in Chapter 5, externally- bonded FRPs can be used in buildings to strengthen reinforced concrete circular column, if a supplemental fire protection system is provided over the FRP strengthening system.

By providing appropriate fire insulation, the reinforced concrete columns that have been confined with FRP wraps can endure the elevated temperatures of the standard fire under strengthened service loads for more than 240 minutes.

4. The insulation systems used in the fire tests presented herein were effective fire protection systems for the FRP wrapped reinforced concrete columns. However, the insulation systems were not able to maintain the temperature of the FRP strengthening systems below their glass transition temperatures for the entire duration of the fire tests.

The temperature of the FRP system remained below its glass transition temperature for about 34 minutes with about 53 mm of the MBrace insulation system and for 60 minutes

with 44 mm of the Sika insulation system. Based on the results presented in Chapter 4 on the mechanical behaviour of FRP materials at elevated temperature, it appears that by providing an appropriate insulation system an FRP confined reinforced concrete column can maintain its increased axial load carrying capacity for at least 60 minutes of exposure to the standard fire.

5. The fire endurance of the insulated FRP strengthened concrete columns should be defined in terms of the time that the column can resist the service load carrying capacity during fire, rather than the time it takes for the temperature at the level of the FRP strengthening system to exceed the glass transition temperature of the FRP strengthening system.

6. The numerical models developed in this research study can be used in the safe design of concrete columns under both ambient room temperature and fire conditions. Based on the results presented in Chapter 6, the numerical model was able to make reasonable predictions of the temperatures within both unwrapped reinforced concrete and FRP strengthened reinforced concrete square columns. The numerical model made conservative predictions of the load carrying capacity for safe design of unwrapped reinforced concrete and FRP strengthened reinforced concrete columns in a standard fire situation. Using the numerical, it appears that ignoring the effect of transient strain in the structural analysis of concrete columns in a fire situation produces unconservative estimates of load carrying capacity of the column.

7.4 Recommendations for Future Research The primary focus of this thesis was to understand the behaviour of FRP strengthened concrete columns in fire. Several important conclusions were drawn from this research study, however, further research is required to fully characterize the complex behaviour of FRP

materials and FRP strengthened concrete structural members at high temperature. The following are suggestions based on the research study presented herein for future studies into the fire behaviour of FRP wrapped reinforced concrete columns: 1. To the best of the author's knowledge, Kodur et al. (2005) present the results of the only fire test that has been conducted on an FRP strengthened reinforced concrete square column to date and the author used the results of this test to validate the predictions of the numerical model presented in Chapter 6. Additional full-scale fire tests on FRP confined reinforced concrete square/rectangular columns are required to understand the behaviour of these types of structural members in fire, as well as to validate the numerical model against additional test results.

2. Detailed information on fire insulation systems are proprietary in most cases, and therefore only limited information about their temperature dependent thermal properties is available. Because the insulation system used in Kodur et al. (2005) was similar to the insulation system used by Bisby (2003), the author used the thermal property model of the insulation system presented in Bisby (2003) in the numerical model. However, the precise thermal behaviour of existing insulation systems (such as the MBrace and Sika insulation systems) is unknown. Hence, thermal analyses, including TGA and thermal conductivity testing using for example a Hot Disk? System need to be conducted on the existing insulation system to the characterize their thermal properties with increasing temperatures and subsequently be used in the numerical model.

3. FRP is a versatile material. Innumerable combinations of fibres and resin polymer materials can be combined to create an FRP composite. In this research study, tensile tests and FRP-to-FRP bond shear tests were conducted on one specific, wet lay-up, glass/epoxy FRP strengthening system to characterize the mechanical and bond property degradation of this type of FRP with increasing temperature. Similar small-scale FRP

material tests needs to be conducted on other types of FRP composites to fully understand their behaviour in fire. Based on the experimental work on this specific GFRP material, a mathematical model was presented describing the mechanical and bond degradation of the FRP. The additional tests would help determine the range of values for the constants in Eqn. 5-3 for different types of available FRPs.

As mentioned earlier, the FRP-to-FRP bond shear strength tests were conducted on FRP lap-splice specimens having approximately 50 mm lap-splice length. The results from these tests represent the most severe possible case and do not represent the longer FRP bond/splice lengths used in practice. Hence, the effect of different lap-splice length on the degradation of FRP-to-FRP bond shear strength needs to be examined, as does the strength when FRP is bonded to other substrates such as concrete or steel. Furthermore, compression tests on FRP confined circular cylinder and square/rectangular concrete prisms, and FRP-to-concrete bond strength tests at elevated temperatures are needed.

4. In Chapter 6, a numerical model was developed to simulate the heat transfer within a concrete column. Results from the numerical model were validated against fire test data obtained from normal strength concrete columns. Generally, normal strength concrete columns are less prone to spalling than high strength concrete columns (Kodur et al., 2004; Dwaikat and Kodur, 2009) because high strength is concrete is much denser than normal strength concrete, hence, permeability within high strength concrete is low. The low permeability of high strength concrete prevents the moisture in the pores within the concrete to move away from the heating source quickly enough to relieve the internal pressure that is developing in the pores, which makes high strength concrete prone to spalling. This thermally induced moisture migration within concrete elements was not taken into account in the numerical model presented in Chapter 6, as the model for analysing normal strength concrete columns. To enable analysis of high strength

concrete column using this model, thermally induced moisture migration within concrete needs to be incorporated into the model based on mass transfer, which may eventially allow the model to predict spalling of concrete.

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Appendix A Load Calculations for FRP-Wrapped Concrete Columns 3 and 4

A.1 General This appendix presents detailed load calculations for the reinforced concrete columns that were tested at the National Research Council of Canada, Ottawa on 2005. For unwrapped reinforced concrete columns, the loads have been calculated using CSA A23.3-94 (CSA 1994) and ACI 318/318R-95 (ACI 1995), and for FRP strengthened concrete columns, the loads were calculated using ISIS Canada design guidelines (ISIS 2001a, ISIS 2001b), ACI 440.2R-02 design guideline (ACI 2002), and CSA S806-02 (CSA 2002). Fire endurance tests loads were calculated in accordance with ULC S101 (CSA 2004), which is equivalent to ASTM E119 (ASTM 2001).

All calculations have been performed in SI units. In all design equations including American codes, Canadian rebar designations and properties were used. The actual tested properties have been used where available in design calculations for all materials involved. The material properties were as following: ? Nñ 28-day Compressive Strength, DBÖ L 32.7 MPa ? Nñ Test day Compressive Strength, DBÖ L 32.9 MPa ? Yield Strength of Longitudinal Reinforcing Steel: DBì L 456 MPa ? Ultimate Tensile Strength of FRP System: DBÙ L 3800 MPa åãç

? Ultimate Strain of FRP System: DóÙ L 1.67% åãè ? Elastic Modulus of FRP System: D'Ù L 227 GPa åãç

A.2 Axial Load Capacity of Reinforced Concrete Column A.2.1 ACI 318/318R-95

The maximum axial design strength for a spirally reinforced concrete column according to ACI 318/318R-95, CL. 10.3.5.1 is taken as: L D öD 2 Nñ D# g EAq?n1. kD#F D #o E D B D2å, L 0.85Dö c0.85DBæ ç ì æ ç á, à Ô ë Ö Ú àÔë

Where Döis equal to 0.75 (CL. 9.3.2.2), D#is the gross cross-sectional area of concrete, and D#is ç Úæ the area of the longitudinal reinforcing steel in compression. For the columns tested herein this equation becomes: D2å, L 0.85 · 0.705>.85 ·<32.9 · D:è · 2006 F 8 · 300;=E45<6 · 8:· 300;=? àÔë

D2 N7 å, à LÔ 28ë95 H 10 D2å, à LÔ 28ë95 kN Having the member reduction factors equal to 1.0 in Eqn. A-1 for axial load capacity gives the predicted strength of the columns according to ACI 318 design code. Thus, D2å, L 0.85 · 1.00>·.85 ·<32.9 · D:è · 2006 F 8 · 300;=E45<6 · 8:· 300;=? ãåØ×

D2 L 3860 N7 å, ã å Ø × H 10 D2å, L 3860×kN ãåØ

A.2.2 ACI 318/318R-05 The maximum axial design strength for a spirally reinforced concrete column according to ACI 318/318R-05, CL. 10.3.6.1 is taken as:

D2å, à L D öD 2L 0.85Dö NñkD# EBq?n1. Ô áë, à Ô ë c0.85DB o D# g Ö Ú F D #ç E D B æ ìæç

Where Döis equal to 0.70 (CL. 9.3.2.2), D#is the gross cross-sectional area of concrete, and D#is Ú æç the area of the longitudinal reinforcing steel in compression. For the columns tested herein this equation becomes: D2å, L 0.85 · 0.700>·.85 ·<32.9 · D:è · 2006 F 8 · 300;=E45<6 · 8:· 300;=? àÔë

D2 L 2702 N7 å, à Ô ë H 10 D2å, à LÔ 27ë02 kN Having member reduction factors equal to 1.0 in Eqn. B-1 for axial load capacity gives the predicted strength of the columns according to ACI 318/318R-05. Thus, D2å, L 0.85 · 1.00>·.85 ·<32.9 · D:è · 2006 F 8 · 300;=E45<6 · 8:· 300;=? ãåØ×

L 3860 N7 D2å, ã å Ø × H 10 D2å, L 3860×kN ãåØ

Therefore, the design strength and the predicted strength as per ACI 318/318R-05 are 2702 kN and 3860 kN, respectively.

A.2.3 CSA A23.3-94 and CSA A23.3-04 The maximum axial design strength for a spirally reinforced concrete column according to CSA A23.3-94, CL.10.10.4 is taken as: D2 L 0.85D 2 Nñ D# g Eqn. A?2 å, L 0.85 ·DöDcBDkÙD#F D #o DBE D öç à Ô ë á, à Ô ë 5 ÖÖ Ú æ ç æì æ

Where Döis equal to 0.6 (CL. 8.4.2), Döis equal to 0.85 (CL 8.4.3), DÙis equal to 0.80 Öæ5 (CL.10.1.7). Thus, this equation becomes:

D2 L 0.85D 2 L 0.850.>·80 · 0.60 · 32.9 · D:è · 2006 F 8 · 300;E 0.85 · 4568·:· 300;? å, à Ô ë á, à Ô ë

D2å, à LÔ24ë45 N7 H 10 D2å, à LÔ 24ë45 kN Having material resistance factors equal to 1.0 in Eqn. A-2 for axial load capacity gives the predicted strength of the columns according to CSA A23.3 design code. Thus, D2å, L 0.850.>·80 · 1.0 · 32.9 · D:è · 2006 F 8 · 300;E 1.0 · 4568·:· 300;? ãåØ×

D2 L 3688 N7 å, ã å Ø × H 10 D2å, L 3688×kN ãåØ

A.3 Axial Load Capacity of FRP Strengthened RC Column A.3.1 ACI 440.2R-02

The design strength of the FRP confined columns is calculated in accordance with Chapter 11 of ACI 440.2R-02. The wrap consists of a double layer of FRP. The effective confining pressure in the jacket at ultimate is calculated as follows, with notation modified for consistency within this appendix. The confinement reinforcement ratio Déis calculated as Ù

4 · D J · D4P· 2 · 0.165 DéÙ L L L 0.0033 Eqn. A?3 D@ 400 The effective ultimate strength of the FRP wrap is taken as the product of the ultimate strength and an environmental reduction coefficient D%as follows: ¾

DBÙ L·D%B L 1.0 · 3800 L 3800 MPa Eqn. A?4 Ø¾Ùåãè

Where D%is taken to be 1.0 for CFRP as test specimens were not exposed to any severe ¾

environmental condition prior to testing. The confining pressure at ultimate can subsequently be determined as (with DâÔ L 1fo.0r a circular column): Dâ · D B · D é 1.0 · 0.0033 · 3800 DB Ô Ù Ù Ø ß L L L 6.27 MPa Eqn. A?5 22 And the confined ultimate strength of the concrete is calculated using the Mander equation:

7.9 · DBß2 · D Bß DNBñ Nñ2L.25 · 1¨ F 1.25M Eqn. A?6 Ö ÖLÖD B E Nñ F Nñ DBÖ DBÖ

7.9 · 6.27 2 · 6.27 DNBñ ÖL 32.92L·.25 · 1¨ E F F 1.25M Ö 32.9 32.9

Nñ L 63.5 MPa DBÖ Ö Using an additional reduction factor Dð(CL. 11.1), the ultimate strength of the FRP-wrapped RC column can now be determined as: L 0.85Dö Nñ D# g Eqn. A?7 DB kD#F D #o E D B D2å, c0.85ÖDÚð æ ç ì æ ç à Ô ë ÙÖ

D2å, L 0.85 · 0.750.>·85 · 0.95 · 63.5 · D:è · 2006 F 8 · 300;E 4568·:· 300;? àÔë

D2 L 4727 7 å, à Ô ë HN10 D2å, à LÔ 47ë27 kN Having the reduction factors equal to 1.0 in Eqn. A-7 results in the following predicted strength for the FRP confined columns L 0.85Dö Nñ D# g Eqn. A?8 DB kD#F D #o E D B D2å, c0.85ÖDÚð æ ç ì æ ç ã å Ø × ÙÖ

D2å, L 0.85 · 1.0.>·85 · 1.0 · 63.5 · D:è · 2006 F 8 · 300;E 4568·:· 300;? ãåØ×

D2å, ã L 6585 kN åØ× Therefore, the design and predicted strengths as per ACI 440R-02 are 4727 kN and 6585 kN, respectively.

A.3.2 ACI 440.2R-08 The design strength of the FRP confined columns is calculated in accordance with Chapter 12 of ACI 440.2R. The wrap consists of a double layer of FRP. The effective strain level in the FRP at failure is DÝÙ L·DâÝ å ã è Eqn.B?3 ØÙ

Where, Dâis a strain efficiency factor accounting for the premature failure of the FRP system, which is equal to 0.55.

DÝÙ L 0.55 · 0.0167 L 0.00921 Ø The maximum confinement pressure is calculated using Eqn. B-4 2D'DÙJDÙPDØÝ DBß L Eqn. B?4 D& 2 · 227000 · 2 · 0.165 · 0.00921 DBß L L 3.45 MPa 400 The minimum level of confinement required by ACI 440.2R design guideline is 0.08. The confinement ratio is of the current strengthening system DBß 3.45 Nñ L L 0.105 P 0.08 Eqn. B?5 DBÖ 32.9 Therefore, having two layers of FRP satisfies the minimum confinement ratio requirement. The confined concrete strength is calculated using Eqn. B-6

Nñ Nñ E 3.3Dâð DBÖ ÖLÖD B ÙDÔBß Eqn. B?6 Where, the reduction factor DðÙis equal to 0.95 and the efficiency factor Dâis equal to 1.0 Ô

Nñ L 32.9 E 3.3 · 0.95 · 1.0 · 3.45 L 43.7 MPa DBÖ Ö The ultimate strength of the FRP-wrapped RC column can now be determined as: D2 L 0.85Dö Nñ D# g Eqn. B?7 kD#F D #o E D B å, c0.8Ú5DBæ ç ì æ ç àÔë ÖÖ

D2å, L 0.85 · 0.70.>·85 · 43.7 · D:è · 2006 F 8 · 300;E 4568·:· 300;? àÔë

L 3375 7 D2å, à Ô ë HN10 D2å, à LÔ 33ë75 kN Having the reduction factors equal to 1.0 in Eqn. B-7 gives a confined concrete strength of 54.7 MPa, which results in the following predicted strength for the FRP confined columns D2å, L 0.85 · 1.0.>·85 · 43.7 · D:è · 2006 F 8 · 300;E 4568·:· 300;? ãåØ×

D2 L 4822 7 å, ã å Ø × HN10 D2å, L 4822×kN ãåØ

Therefore, the design strength and the predicted strength as per ACI 440R is 3375 kN and 4822 kN, respectively.

A.3.3 CSA S806-02 According to CSA S806-02, the ultimate strength of the FRP is limited to 0.004 · D'Ù orå ã å Ùã å ã è Ù å ã

0.004 · D'Ù åLã0.004 · 227000 L 908 MPa Eqn. A?9 DöÙ · D B L 0.75 · 3800 L 2850 MPa Eqn. A?10 å Ùã å ã è

Therefore, the confining pressure at ultimate is calculated as follows: 2 · 2:· DP·;D B 2 · 2: H 0.16·5;908 DB L Ù åLã L 1.50 MPa EqAn?.11 ß D@ 400 The confined ultimate strength of the concrete is determined from Nñ L 0.85N·ñD B · D B · D G Eqn. A?12 DBÖ Ö Ö EßD GÖ ß Where DGis equal to 1.0 for circular and oval columns Ö

ß · D B L 6.25 Eqn. A?13 Öß

Thus, the confined ultimate strength of the concrete is Nñ L0.:85 · 32.9;E6.:25 · 1.0 · 1.5;L 37.3 MPa DBÖ Ö Eqn. A?14 And, the design strength of the FRP confined column is determined from D2 L 0.85 · Nñ D# g DöDB kD#F D #o DBE D ö Eqn. A?15 å, cD ÙÚ æ ç æì æ ç à Ô ë 5 ÖÖ Ö

D2å, L 0.850.>·80 · 0.60 · 37.3 · D:è · 2006 F 8 · 300;E 0.85 · 4568·:· 300;? àÔë

D2 L 2667 N7 å, à Ô ë H 10 D2å, à LÔ 26ë67 kN Even after omitting the FRP material reduction factor in Eqn A-10, 0.004 · D' is still the Ùåã limiting FRP strength. Therefore, the confined ultimate strength for calculating the predicted strength remains 37.3 MPa. Omitting member reduction factors in Eqn. A-15 for axial load capacity gives the predicted strength of the columns according to S806-02. Thus, D2å, ã L 0.850.>·80 · 1.0 · 37.3 · D:è · 2006 F 8 · 300;E 1.0 · 4568·:· 300;? åØ×

L 4057 H710 D2å, ã å Ø × N D2å, L 4057 kN ãåØ×

Therefore, the design strength and the predicted strength as per CSA S806-02 is 2667 kN and 4057 kN, respectively.

A.3.4 ISIS Canada According to the ISIS Canada design guidelines, the confining pressure at ultimate is calculated as follows: 2 · D J · D ö· D B · D P 2 · 2 · 0.75 · 3800 · 0.165 Ù êè DB L å Ùã å ã L L 4.70 MPa Eqn. A?16 ß D@ D@ Where DöÙ is equal to 0.75 for CFRP with an interior conditioned exposure. The ISIS Canada åã guidelines specify a maximum effective confinement pressure as follows: DNBñ 1 32.9 1 DBß, L Ö l F DpöL l F 0.6pL 9.48 MPa Eqn. A?17 àÔë Ö 2 · D Ùã DGØ 2 · 1.0 0.85 Ö

Where DÙã ÖL 1an.0d DGØ L 0.f8o5r unexpected eccentricities. The volumetric confinement ratio is calculated as: 2 · D B 2 · 4.70 Dñê L Nßñ L L 0.4762 Eqn. A?18 Dö 0.60 · 32.9 ·ÖD BÖ The confined ultimate strength of the concrete is determined from: Nñ Nñ L13:2.9E· 1.0 · 0.4762;L 48.6 MPa DB L D B · D ñ o Eqn. A?19 Ö · k1 ãEÖDêÙ ÖÖ

Finally, the design strength of the FRP-wrapped column is determined from D2 L 0.85 · Nñ D# g Eqn. A?20 DöDB kD#F D #o DBE D ö å, cD ÙÚ æ ç æì æ ç à Ô ë 5 ÖÖ Ö

D2å, L 0.850.>·80 · 0.60 · 48.6 · D:è · 2006 F 8 · 300;E 0.85 · 4568·:· 300;? àÔë

D2 L 3235 N7 å, à Ô ë H 10 D2å, à LÔ 32ë35 kN

Omitting member reduction factors in Eqn. A-20 for axial load capacity gives the predicted strength of the columns according to S806-02. Thus, D2å, L 0.850.>·80 · 1.0 · 48.6 · D:è · 2006 F 8 · 300;E 1.0 · 4568·:· 300;? ãåØ×

L 5004 N7 D2å, ã å Ø × H 10 D2å, L 5004×kN ãåØ

Therefore, the design strength and the predicted strength as per ISIS Canada design guideline is 3235 kN and 5004 kN, respectively.

A.4 Summary of Load Capacity Table A1 presents an overview of the various column strength calculations. Examination of the data in Table A1 reveals that the ACI 440.2R-02 design guide predict a 63% increase in the design axial load capacity of the column due to FRP-wrapping, while the ISIS Canada design guidelines and CSA-S806-02 predict an increase of 32% and 9%, respectively. Although it is possible that a 63% increase in the load capacity would be observed in tests of these columns, it is unlikely that such a large increase would be used in a design situation. Hence, it is appropriate that the lower ultimate load capacity value obtained from ISIS Canada design guidelines and CSA codes will be used to determine the load for the fire endurance tests.

A.5 Superimposed Loads for Columns Exposed to Fire using ULC S101-04

As stated in ULC S101-04, a superimposed load must be applied to the test specimens to simulate the stress level under full specified service load or maximum working load during a fire endurance test. Using the ultimate and service load capacities of the specimens, the applied load for the tests can be calculated.

The total specified load D5comprises of the specified dead load D5and the specified live load D5. Í½Å Factoring the specified load gives the following relationship.

DÙDÍ5LD5Ù ED5Ù Eqn. A?21 ½½ ÅÅ

Where DÙis an overall factor applied to the total load, DÙis the dead load factor and DÙis the live ½½ load factor.

Rearranging Eqn. A-21, DÙD½5 ED5Ù D Ù L½ Å Å Eqn. A?22 D5½ EÅD 5 According to ULC S101-04, a dead to live load of 2.5 may be used to reflect the actual in-service conditions. Then , Eqn. A-22 can be expressed as ½ EDÙ EDÙ D Ù L ½ Å L ½ ½ Eqn. A?23 3.5D5Å 3.5 The factored total axial load is DÙDÍ5LËD 5 Eqn. A?24 Where, D5is the design axial capacity of the column specimen Ë

Rearranging Eqn. A-23 D5Ë 3.5D5Ë D5Í L L Eqn. A?25 ½ EDÙ Å

A.5.1 Superimposed Load from ACI 440.2R-02 The ultimate load capacity using ACI 440.2R was calculated to be 4727 kN. As per 318/318R-05 code, the dead load factor DÙand live load factor DÙare 1.2 and 1.6, respectively. Using the ½Å

derived Eqn. A-25, the superimposed load was calculated as below. In Eqn. A-25, the dead load only includes the self-weight of the specimen.

3.5 · 4727 D5Í L L 3597 kN Therefore, the test load using ACI 440.2R is 3597 Kn

A.5.2 Superimposed Load from CSA S806-02 The ultimate load capacity using the CSA S806-02 was calculated to be 2667 kN. As per CSA code, the dead load factor DÙand live load factor DÙare 1.25 and 1.5, respectively. Using ½Å the derived Eqn. A-25, the superimposed load was calculated as below. In Eqn. A-25, the dead load only includes the self-weight of the specimen 3.5 · 2667 D5Í L L 2018 kN 2.:5 · 1.25 E 1.5;

A.5.3 Superimposed Load from ISIS Canada The ultimate load capacity using the ISIS Canada was calculated to be 3235 kN. As per CSA code, the dead load factor DÙand live load factor DÙare 1.25 and 1.5, respectively. Using ½Å the derived Eqn. A-25, the superimposed load was calculated as below. In Eqn. A-25, the dead load only includes the self-weight of the specimen 3.5 · 3235 D5Í L L 2448 kN 2.:5 · 1.25 E 1.5;

A.6 Strengthening Limits The ACI 440.2R-08 design code (CL. 9.2) states that careful consideration should be given to determine reasonable strengthening limits. These limits must be imposed to guard against collapse of the structure should complete failure of the FRP system occur due to unforeseen circumstances such as fire or vandalism. ACI 440 recommends that the existing strength of the structure should be sufficient to resist a level of load described by: á E 0.75D5 Ø ê Eqn. A?26 Ø ë Ü æ ç½Ü á ÚÅ á

Where, D:öD4; is the existing strength of the member to be strengthened with FRP, D5is áØ ë Ü æ ç Ü á Ú ½ the strengthened service dead load, and D5is the strengthened service live load. According to Å

ULC S101-04, a dead to live load of 2.5 may be used to reflect the actual in-service conditions, that is, D5 L 2.5D 5 ½ .ÅTo check the strengthening limits, the load capacity from the service loads obtained from ACI 440 design guideline were calculated. Therefore, E D 5 Eqn. A?27 2.5D5Å Å L 2448 2448 D5Å L L 699 kN 3.5 D5½ L 2.5 · 699 L 1749 kN 2895 R1.:1 · 1749 E 0.75 · 699;L 2448 kN Hence, strengthening limits satisfied for an applied load of 2448 kN.

A.7 Serviceability Limitations To prevent radial cracking or yielding of internal reinforcing steel in the column under service load conditions, ACI 440.2R-02 (CL. 11.1.3) limits the stress in the concrete at service condition to 0.60DNBñ .ÖAlso, to avoid plastic deformation the stress in the steel must be below

ineffective, the concrete stress corresponds to as shown below

Nñ 6 ;L 2481 kN L 0.60 · D B L 0.60 · 32.9D·:è · 200 Eqn. A?28 D2å, · D #Ú àÔëÖ

Using the serviceability limitations, the service axial load is 2481 kN, which is larger than the load calculation from Eqn. B19. Thus, the applied load of 2448 kN calculated from ACI 440 design guidelines would be used for fire testing the columns specimens.

Table A-1: Summary of design load calculations for Columns 3 and 4

Calculated Unwrapped FRP-wrapped Increase in Increase in Applied Strength Strength Strength Strength Test Load Design Codes (kN) (kN) (kN) (%) (kN) ACI 318-95 (F)a 2895 -- -- -- -- ACI 318-05 (F)a 2702 -- -- -- -- CSA A23.3 (F) 2445 -- -- -- -- ACI 440.2R-02 (F) -- 4727 1832 63 3597 ACI 440.2R-08 (F) -- 3375 673 25 -- CSA S806-02 (F) -- 2667 222 9 2018 ISIS Canada (F) -- 3235 790 32 2448 ACI 318-95 (U)b 3860 -- -- -- -- ACI 318-05 (U)b 3860 -- -- -- -- CSA A23.3 (U) 3688 -- -- -- -- ACI 440.2R-02 (U) -- 6585 2725 71 -- ACI 440.2R-08 (U) -- 4822 962 20 -- CSA S806-02 (U) -- 4057 369 10 -- ISIS Canada (U) -- 5004 1316 36 -- a F ? refers to factored design load calculations (ultimate design capacities) bU ? refers to unfactored load calculations (predicted load calculations)

Appendix B Load Calculations for FRP-Wrapped Concrete Column 5

B.1 General This appendix presents detailed load calculations for the reinforced concrete columns that were tested at the National Research Council of Canada, Ottawa on 2008. For unwrapped reinforced concrete columns, the loads have been calculated using CSA A23.3-05 (CSA 2005) and ACI 318/318R-05 (ACI 2005), and for FRP strengthened concrete columns, the loads were calculated using ACI 440.2R-05 design guideline (2005) and CSA S806-02 (CSA 2002). Fire endurance tests loads were calculated in accordance with ULC S101 (CSA 2004), which is equivalent to ASTM E119 (ASTM 2001). All calculations have been performed in SI units. In all design equations including American codes, Canadian rebar designations and properties were used. The actual tested properties have been used where available in design calculations for all materials involved. The material properties were as following: ? Nñ 28-day Concrete Compressive Strength: DBÖ L 38.5 MPa ? Nñ Test day Concrete Compressive Strength: DBÖ L 40.1 MPa ? Yield Strength of Longitudinal Reinforcing Steel: DBì L 456 MPa ? Ultimate Tensile Strength of FRP System: DBÙ å Lã84è9 MPa ? Ultimate Strain of FRP System: DóÙ L 1.12% åãè

? Elastic Modulus of FRP System: D'Ù åLã70552 MPa ? Thickness of single layer of FRP, DPê L 1.016 mm

B.2 Axial Load Capacity of Reinforced Concrete Column B.2.1 ACI 318/318R-05

The maximum axial design strength for a spirally reinforced concrete column according to ACI 318/318R-05, CL. 10.3.6.1 is taken as: L D öD 2 Nñ D# g EBq?n1. kD#F D #o E D B D2å, L 0.85Dö c0.85DBæ ç ì æ ç á, à Ô ë Ö Ú àÔë

Where Döis equal to 0.70 (CL. 9.3.2.2), D#is the gross cross-sectional area of concrete, and D#is ç Úæ the area of the longitudinal reinforcing steel in compression. For the columns tested herein this equation becomes: D2å, L 0.85 · 0.700>·.85 ·<40.1 · D:è · 2006 F 8 · 300;=E45<6 · 8:· 300;=? àÔë

D2 N7 å, à LÔ 31ë51 H 10 D2å, à LÔ 31ë51 kN Having member reduction factors equal to 1.0 in Eqn. B-1 for axial load capacity gives the predicted strength of the columns according to ACI 318/318R-05. Thus, D2å, L 0.85 · 1.00>·.85 ·<40.1 · D:è · 2006 F 8 · 300;=E45<6 · 8:· 300;=? ãåØ×

D2 L 4501 N7 å, ã å Ø × H 10 D2å, L 4501×kN ãåØ

Therefore, the design strength and the predicted strength as per ACI 318/318R-05 are 3151 kN and 4501 kN, respectively.

B.2.2 CSA A23.3-04 The maximum axial design strength for a spirally reinforced concrete column according to CSA A23.3-04, CL.10.10.4 is taken as: L 0.85D 2 Nñ D# g Eqn. B?2 D2å, L 0.85 ·DöDcBDkÙD#F D #o DBE D öç à Ô ë á, à Ô ë 5 ÖÖ Ú æ ç æì æ

Where Döis equal to 0.65 (CL. 8.4.2), Döis equal to 0.85 (CL 8.4.3), DÙis equal to 0.80 Öæ5 (CL.10.1.7). Thus, this equation becomes: D2å, L 0.85D 2 L 0.850.>·80 · 0.65 · 40.1 · D:è · 2006 F 8 · 300;E 0.85 · 4568·:· 300;? à Ô ë á, à Ô ë

D2 L 2782 N7 å, à Ô ë H 10 D2å, à LÔ 27ë82 kN Having the material resistance factors equal to 1.0 in Eqn. B-2 for axial load capacity gives the predicted strength of the columns according to CSA A23.3-04 Thus, D2å, L 0.850.>·80 · 1.0 · 40.1 · D:è · 2006 F 8 · 300;E 1.0 · 4568·:· 300;? ãåØ×

D2 L 4249 N7 å, ã å Ø × H 10 D2å, L 4249×kN ãåØ

Therefore, the design strength and the predicted strength as per CSA A23.3-04 are 2782 kN and 4249 kN, respectively.

B.3 Axial Load Capacity of FRP Strengthened RC Column B.3.1 ACI 440.2R-08

The design strength of the FRP confined columns is calculated in accordance with Chapter 12 of ACI 440.2R. The wrap consists of a double layer of FRP. The effective strain level in the FRP at failure is DÝÙ L·DâÝ å ã è Eqn.B?3 ØÙ

Where, Dâis a strain efficiency factor accounting for the premature failure of the FRP system, which is equal to 0.55.

DÝÙ L 0.55 · 0.0112 L 0.00616 Ø The maximum confinement pressure is calculated using Eqn. B-4 DJDP 2D'Ù DÝÙ Ø DBß L ê Eqn. B?4 D& 2 · 70552 · 2 · 1.016 · 0.00616 DBß L L 4.42 MPa 400 The minimum level of confinement required by ACI 440.2R design guideline is 0.08. The confinement ratio is of the current strengthening system DBß 4.42 Nñ L L 0.110 P 0.08 Eqn. B?5 DBÖ 40.1 Therefore, having two layers of FRP satisfies the minimum confinement ratio requirement. The confined concrete strength is calculated using Eqn. B-6

Nñ Nñ L D B DB Eqn. B?6 DBÖ E 3.3Dâðß ÖÖ ÙÔ

Where, the reduction factor Dðis equal to 0.95 and the efficiency factor Dâis equal to 1.0 ÙÔ

The ultimate strength of the FRP-wrapped RC column can now be determined as: L 0.85Dö Nñ D# g Eqn. B?7 kD#F D #o E D B D2å, c0.8Ú5DBæ ç ì æ ç àÔë ÖÖ

D2å, L 0.85 · 0.70.>·85 · 53.9 · D:è · 2006 F 8 · 300;E 4568·:· 300;? àÔë

D2 7 å, à LÔ40ë14 HN10 D2å, à LÔ 40ë14 kN Having the reduction factors equal to 1.0 in Eqn. B-7 gives a confined concrete strength of 54.7 MPa, which results in the following predicted strength for the FRP confined columns D2å, L 0.85 · 1.0.>·85 · 54.7 · D:è · 2006 F 8 · 300;E 4568·:· 300;? ãåØ×

D2 L 5799 7 å, ã å Ø × HN10 D2å, L 5799×kN ãåØ

Therefore, the design strength and the predicted strength as per ACI 440R is 4014 kN and 5799 kN, respectively.

B.3.2 CSA S806-02 According to CSA S806-02, the ultimate strength of the FRP is limited to 0.004 · D'Ù orå ã å Ùã å ã è Ù å ã

0.004 · D'Ù åLã0.004 · 70552 L 282 MPa Eqn. B?8 DöÙ · D B L 0.75 · 849 L 637 MPa Eqn. B?9 å Ùã å ã è

Therefore, the confining pressure at ultimate is calculated as follows: 2 · D P 2 · 2: H 1.01·6;282 ê· D B å ã DBß L Ù L L 2.87 MPa Eqn. B?10 D@ 400

The confined ultimate strength of the concrete is determined from Nñ L 0.85N·ñD B DBÖ Ö Ö E·ßDG·ÖD Bß Eqn. B?11 Where DGis equal to 1.0 for circular and oval columns Ö

DGß ·ÖD B L 6.71.:·0 · 2.87; L 5.60 E.qBn?12 ß

Thus, the confined ultimate strength of the concrete is Nñ L0.:85 · 40.1;E5.:60 · 1.0 · 2.87;L 50.1 MPa DBÖ Ö Eqn. B?13 And, the design strength of the FRP confined column is determined from D2 L 0.85 · Nñ DöcD Ù Eqn. B?14 DB kD#F D #o DBE D ö å, à Ô ë 5 ÖÖ ÖÚ æ ç æDì#æ gç D2å, à L 0.850.>·80 · 0.60 · 50.1 · D:è · 2006 F 8 · 300;E 0.85 · 4568·:· 300;? Ôë

D2 L 3281 H710 å, à Ô ë N D2å, à LÔ 32ë81 kN Even after omitting the FRP material reduction factor in Eqn. B-9, 0.004 · D' is still the Ùåã limiting FRP strength. Therefore, the confined ultimate strength for calculating the predicted strength remains 50.1 MPa. Having the material resistance factors equal to 1.0 in Eqn. B-14 for axial load capacity gives the predicted strength of the columns according to S806-02. Thus, D2å, L 0.850.>·80 · 1.0 · 50.1 · D:è · 2006 F 8 · 300;E 1.0 · 4568·:· 300;? ãåØ×

L 5080 N7 D2å, ã å Ø × H 10 D2å, L 5080×kN ãåØ

Therefore, the design strength and the predicted strength as per CSA S806-02 is 3281 kN and 5080 kN, respectively.

B.4 Summary of Load Capacity Table A1 presents an overview of the various column strength calculations. Examination of the data in Table A1 reveals that the ACI 440.2R design guide predict a 27% increase in the design axial load capacity of the column due to FRP-wrapping, while the CSA-S806-02 predict an increase of 18%, respectively. The ultimate load capacity obtained from the ACI 440.2R is used to determine the load for the fire endurance tests.

B.5 Superimposed Loads for Columns Exposed to Fire using ULC S101-04

As stated in ULC S101-04, a superimposed load must be applied to the test specimens to simulate the stress level under full specified service load or maximum working load during a fire endurance test. Using the ultimate and service load capacities of the specimens, the applied load for the tests can be calculated.

The total specified load D5comprises of the specified dead load D5and the specified live load D5. Í½Å Factoring the specified load gives the following relationship.

DÙDÍ5LD5Ù ED5Ù Eqn. B?15 ½½ ÅÅ

Where DÙis an overall factor applied to the total load, DÙis the dead load factor and DÙis the live ½½ load factor.

Rearranging Eqn. B-15, DÙD½5 ED5Ù D Ù L½ Å Å Eqn. B?16 D5½ EÅD 5 According to ULC S101-04, a dead to live load of 2.5 may be used to reflect the actual in-service conditions. Then , Eqn. B-16 can be expressed as ½ EDÙ EDÙ D Ù L ½ Å L ½ ½ Eqn. B?17 3.5D5Å 3.5

The factored total axial load is DÙDÍ5LËD 5 Eqn. B?18 Where, D5is the design axial capacity of the column specimen Ë

Rearranging Eqn. B-17 D5Ë 3.5D5Ë D5Í L L Eqn. B?19 ½ EDÙ Å

B.5.1 Superimposed Load from ACI 440.2R-08 The ultimate load capacity using the ACI 440.2R was calculated to be 4014 kN. As per 318/318R-05 code, the dead load factor DÙand live load factor DÙare 1.2 and 1.6, respectively. ½Å Using the derived Eqn. B-19, the superimposed load was calculated as below. In Eqn. B-19, the dead load only includes the self-weight of the specimen 3.5 · 4014 D5Í L L 3054 kN 2.:5 · 1.2 E 1.6;

B.5.2 Superimposed Load from CSA S806-02 The ultimate load capacity using the CSA S806-02 was calculated to be 3281 kN. As per CSA code, the dead load factor DÙand live load factor DÙare 1.25 and 1.5, respectively. Using the ½Å derived Eqn. B-19, the superimposed load was calculated as below. In Eqn. B-19, the dead load only includes the self-weight of the specimen 3.5 · 3281 D5Í L L 2483 kN 2.:5 · 1.25 E 1.5;

B.6 Strengthening Limits The ACI 440.2R-08 design code (CL. 9.2) states that careful consideration should be given to determine reasonable strengthening limits. These limits must be imposed to guard against collapse of the structure should complete failure of the FRP system occur due to unforeseen circumstances such as fire or vandalism. ACI 440 recommends that the existing strength of the structure should be sufficient to resist a level of load described by: á E 0.75D5 Ø ê Eqn. B?20 Ø ë Ü æ ç½Ü á ÚÅ á

Where, D:öD4; is the existing strength of the member to be strengthened with FRP, D5is áØ ë Ü æ ç Ü á Ú ½ the strengthened service dead load, and D5is the strengthened service live load. According to Å

ULC S101-04, a dead to live load of 2.5 may be used to reflect the actual in-service conditions, that is, D5 L 2.5D 5 ½ .ÅTo check the strengthening limits, the load capacity from the service loads obtained from ACI 440 design guideline were calculated. Therefore, E D 5 Eqn. B?21 2.5D5Å Å L 3054 3054 D5Å L L 873 kN 3.5 D5½ L 2.5 · 873 L 2182 kN 3151 R1.:1 · 2182 E 0.75 · 873;L 2596 kN Hence, strengthening limits satisfied for an applied load of 3054 kN.

B.7 Serviceability Limitations To prevent radial cracking or yielding of internal reinforcing steel in the column under service load conditions, ACI 440.2R-02 (CL. 11.1.3) limits the stress in the concrete at service condition to 0.65DNBñ .ÖAlso, to avoid plastic deformation the stress in the steel must be below 0.60DB,ìwhich is 273.6 MPa. If it is assumed that the vertical reinforcing steel and FRP-wrap are ineffective, the concrete stress corresponds to as shown below

Nñ 6 ;L 3275 kN · D # L 0.65 · 40.1D·:è · 200 Eqn. B?22 D2å, L 0.65 ·ÖD BÚ àÔë

Using the serviceability limitations, the service axial load is 3275 kN, which is larger than the load calculation from Eqn. B-19. Thus, the applied load of 3054 kN calculated from ACI 440 design guidelines would be used for fire testing the columns specimens.

Table B-1: Summary of design load calculations for Column 5 Calculated Unwrapped FRP-wrapped Increase in Increase in Applied Strength Strength Strength Strength Test Load Design Codes (kN) (kN) (kN) (%) (kN) ACI 318 (F)a 3151 -- -- -- -- CSA A23.3 (F) 2782 -- -- -- -- ACI 440.2R (F) -- 4014 863 27 3054 CSA S806-02 (F) -- 3281 499 18 2483 ACI 318 (U)b 4501 -- -- -- -- CSA A23.3 (U) 4249 -- -- -- -- ACI 440.2R (U) -- 5799 1298 29 -- CSA S806-02 (U) -- 5080 831 20 -- a F ? refers to factored design load calculations (ultimate design capacities) bU ? refers to unfactored load calculations (predicted load calculations)

Appendix C Thermal Properties The thermal property relationships of concrete, reinforcing steel and FRP material, and physical constants used in the heat transfer model are presented in this Appendix.

C.1 Concrete C.1.1 Thermal Capacity For Siliceous Aggregate Concrete: 0.:0005 · D6 E;1.7H 1:0 0 Q D6 Q 200B( CÓ : 200B( O D6 Q 400B( CÖ2.7 H 10 DéD? L0.:013 · D6 : Eqn. C?1 Ö Ö F;2.5H 10 400B( O D6 Q 500B( CÔ:F0.013 · D6 E;1H0.51:0 500B( O D6 Q 600B( CÖ CÕ : 2.7 H 10 D6 P 600B( For Carbonate Aggregate Concrete: 2.566 : 0 Q D6 Q 400B( H 10 CÓ0.:1765 · D6 F 68.0;34H 1:0 400B( O D6 Q 410B( CÖ CÖ : :F0.05043 · D6 F 25.0;0H6710 410B( O D6 Q 445B( CÖ 2.566 : 445B( O D6 Q 500B( H 10 DéDÖ?Ö L : Eqn. C?2 CÔ0.:01603 · D6 E 5.448;81H 10 500B( O D6 Q 635B( CÖ0.:16635 · D6 E 100.902;25H 1:0 635B( O D6 Q 715B( CÖ:F0.22103 · D6 E 176.0;7H3431:0 715B( O D6 Q 785B( CÕ : D6 P 785B( 2.566 H 10

C.2 Steel C.2.1 Thermal Capacity 0.:004 · D6 E;3.3H 1:0 CÓ0.:068 · D6 E3;8.3H 1:0 DéDæ?æ L CÔ:F0.086 · D6 E;73H.351:0 CÕ : 4.55 H 10

C.2.2 Thermal Conductivity F0.022 · D6 E 48 DGæ LD 28.2

C.3 FRP C.3.1 Specific Heat 0.95 CÓ1.25 E · D6 CÖ 325 CÖ 2.8 · D:6 F3;25 2.2 E CÖ 18 CÖ 0.15 D? L5.0 F · D:6 F3;43 Ù 167 CÔ 3.59 CÖ · D:6 F5;10 4.85 F CÖ 28 CÖ 1.385 CÖ1.265 E · D:6 F5;38 2778 CÕ0

C.3.2 Density 1.6 0.35 DéÙ L1^.6 F · D:6 F5;10 28 1.25 0 Q D6 Q 650B( 650B( O D6 Q 725B( Eqn. C?5 725B( O D6 Q 800B( D6 P 800B(

0 Q D6 Q 900B( Eqn. C?6 D6 P 900B( 0 Q D6 Q 325B( 325B( O D6 Q 343B( 343B( O D6 Q 510B(Eqn. C?7 510B( O D6 Q 538B( 538B( O D6 Q 3316B( D6 P 3316B(

0 Q D6 Q 510B( 510B( O D6 Q 538B(Eqn. C?8 D6 P 538B(

C.3.3 Thermal Conductivity 1.1 CÓ1.4 F · D6 0 Q D6 Q 500B( CÖ 500 DGÙ L 0.1 Eqn. C?9 CÔ1.4 F · D:6 F5;00 500B( O D6 Q 650B( CÖ 150 CÕ0.2 D6 P 650B(

C.4 Insulation C.4.1 Specific Heat 1.1763 CÓ 1.3058 F 1.1763 CÖ1.1763 E · D:6 F;20 CÖ 78 F 20 CÖ 6.9066 F 1.3058 1.3058 E · D:6 F;78 CÖ 125 F 78 CÖ 6.9066 F 1.3722 CÖ6.9066 E · D:6 F1;25 CÖ 137 F 125 1.3722 F 1.0136 D?Ü L1.3722 E · D:6 F1;37 CÔ 153 F 137 CÖ 1.0136 F 0.8509 CÖ1.0136 E 610 F 153 · D:6 F1;53 CÖ 1.6976 F 0.8509 CÖ0.8509 E · D:6 F6;10 CÖ 663 F 610 CÖ 1.6976 F 0.9167 CÖ1.6976 E 690 F 663 · D:6 F6;63 CÕ0.9167

C.4.2 Density 351 351 F 287 DéÜL3^51 F ·D:6 F1;00 200 F 100 287

220 0 O D6 Q 20B( 20B( O D6 Q 78B( 78B( O D6 Q 125B( 125B( O D6 Q 137B( 137B( O D6 Q 153B(Eqn. C?10 153B( O D6 Q 610B( 610B( O D6 Q 663B( 663B( O D6 Q 690B( D6 P 690B(

C.4.3 Thermal Conductivity 0.1158 0 Q D6 Q 100B( CÓ 0.1158 F 0.0726 CÖ0.1158 F · D:6 F1;00 100B( O D6 Q 101B( CÖ 101 F 100 0.0726 101B( O D6 Q 400B( DGÜ L 0.1224 F 0.0726 Eqn. C?12 CÔ0.0726 F · D:6 F4;00 400B( O D6 Q 800B( CÖ 800 F 400 CÖ 0.2087 F 0.1224 CÕ0.1224 F1000 F 800· D:6 F8;00 D6 P 200B(

C.5 Water C.5.1 Thermal Capacity DéD? L 4.2 :H 10 êê

C.5.2 Heat of Vapourization Dãê L 2.3 :H 10 C.6 Physical Constants

Stefan-Boltzmann constant, DÙ L 5.67 ?H<10 Emissivity of fire, DÝÙ L 1.0 ÜåØ

Emissivity of concrete, DÝÖ â á L 0.9 ÖåØçØ Emissivity of steel, DÝæ L 0.9 çØØß

Emissivity of FRP, DÝ¿ Ë LÉ0.9 Emissivity of insulation, DÝÜ á æ èL 0.9 â ßÔçÜ á

Appendix D Additional Heat Transfer Equations for Rectangular Columns

D.1 Stability Criteria The equation for the maximum allowable value of the time step for the rectangular column is derived from Equation 6-11, which is again shown below.

?DP CÍ H CÐ CÎ kÝDéÝ · D öÝ o · D 8 CÑ à· D ? ê à à, á àê CÎ DG · D # CÑ CÎÓ :à, á :à, B;?à,5 kÝD 6 Ý oá CÑ B;?à,5á á · áà, á FD6 C× Ý > 5Ý ECÎÖ DH ? à5, CÑ :à, B; CÖ D6 L D 6 á ?à,5á à à CÎ DG:à B; · D#:à B; CÑ > 5,à,áá > 5,à,áákÝD 6 F D 6 CÎ E DH:à 5, áá · à > 5, àÝ, o CÑ CÎÔ á á CÑ >B; à, CØ CÎÖ 8 CÑ 8CÖ ED# · D ê · D Ý Dd6Ý@E 273A F Ý E 273 ho CÏÕ å Ô ×B à, · D ÝÙç Ü å Ø kD 6 CÒ áÔ Ù à CÙ For simplicity, let D&represent the term kÝDéÝ E ·Dé? ; Eoquation 6-11 then becomes: à· D ?à ê · D öÝ êà

?DP CÍ H CÐ CÎ D & · D 8á CÑ à, CÎ DG:à, B; · D#:à, B; CÑ CÓ á ?à,5á á ?à,5á Ý Ý C× · kD 6 F D 6o Ý > 5Ý CÎÖ DH:à, B; à, á à, á CÑ ?5 D6 L D 6 á ?à,5á CÖ à à ECÎ DG · D # CÑ Eqn. D?1 :à B; :à B; CÎ E > 5,à,áá > 5,à,áá Ý Ý CÑ · kàD 6> F D 6o 5, à, á CÎÔ DH:à B; á CØCÑ > 5,à,áá CÎÖ 8 CÖCÑ Ý E 273A Ý 8 EDå# · D ê · D Ý· D Ý Dd6@ F kD 6 h CÏÕ Ô ×B à, Ô Ùç Ü å Ø E 273 o á Ù à CÙCÒ

CÍ D6àÝ CÐ CÎ ?DP · DG · D # · D 6Ý CÑ E :à, à,5áà, á ? 5 B;?à,5:à, B; CÎ CÑ D & · D·8DH:à, B; CÎ à, á á ?à,5á CÑ CÎ ?DP · DG · D # · D 6Ý CÑ CÎ F :à, CÑ B; :à, B; á ?à,5á á ?à,5áà, á D & · D·8DH:à, B; CÎ à, á á ?à,5á CÑ CÎ ?DP · DG · D # · D 6Ý CÑ E :à à > 5, á >B;5,à,áá:à B; > 5,à,áá CÎ D & · D 8 CÑ à,· DH:à B; á > 5,à,áá CÎ Ý CÑ CÎ ?DP · DG · D # · D 6 CÑ F :à B; :à B; à, á > 5,à,áá > 5,à,áá CÎ D & · D 8 á CÑ à,· DH:à B; á > 5,à,á CÎ 8 CÑ CÎ ?DP · D# · D ê · D Ý · D@6ÙÝ CÑ å Ô à, · D Ý A ×B à áÔ Ùç Ü å Ø CÎ E D & · D 8 CÑ CÎ à, á CÑ 7 CÎ 1092 · ?DP · D# · D ê · D Ý · D@6ÝACÑ å Ô à, · D Ý åÙ Ø ×B à áÔ Ùç Ü >CÎ5E CÑ D6àÝ L D & · D 8 CÑ Eqn. D?2 CÎ à, á CÎ ÝC6Ñ 447174 · ?DP · D# · D ê · D Ý · D@6A CÎ å Ô à, · D Ý åÙ CØÑ ×B à áÔ Ùç Ü E CÎ D & · D 8 CÑ à, á CÎ CÝÑ 81385668 · ?DP · D# · D ê · D Ý · D 6 CÎ å Ô à, · D Ý Ü CåÑ E ×B à áÔ Ùç Ù Ø CÎ D & · D 8 CÑ à, á CÎ Ý 8 CÑ CÎ ?DP · D# · D ê · D Ý · kDo6 CÑ F å Ô ×B à · D Ý åà Ø à, áÔ Ùç Ü CÎ D & · D 8 CÑ à, á CÎ Ý 7CÑ CÎ 1092 · ?DP · D# · D ê · D Ý kDo6 F å Ô ×B à, · D Ý · åà ØCÑ à Ô Ùç Ü á CÎ D & · D 8 CÑ à, á CÎ ÝC6Ñ CÎ447174 · ?DP · D# · D ê · D Ý · kDCo6Ñ F å Ô à, · D Ý åà Ø ×B à áÔ Ùç Ü CÎ D & · D 8 CÑ à, á CÎ CÑ CÎ81385668 · ?DP · D# · D ê · D Ý Ý F å Ô à, · D Ý · D 6CÑ ×B à áÔ Ùç Ü àå Ø CÏ D & · D 8 CÒ à, á

The stability criteria is satisfied if the coefficient of D6àÝin Equation D-2 is greater than or equal to zero, which is equated in Equation D-3

CÍ ?DP · DG D# CÐ CÎ F :à, CÑ B; :à, B; á ?à,5á· á ?à,5á D & · D·8DH:à, B; CÎ à, á á ?à,5á CÑ CÎ ?DP · DG · D # CÑ :à B; :à B; F > 5,à,áá > 5,à,áá R 0 EqDn?.3 CÎ D & · D·8DH:à B; CÑ à, á > 5,à,áá CÎ CÝÑ CÎ81385668 · ?DP · D# · D ê · D Ý F å Ô ×B à, · D Ý · D 6CÑØ áÔ Ùç Ü àå CÏ D & · D 8 CÒ à, á

Therefore, the required time step · DH:à, B; · DH:à B; Q D & · D 8á á ?à,5á > 5,à,áá ?DP à, Eqn. D?4 DG:à, B; · D#:à, B; · DH:à B; á ?à,5á á ?à,5á > 5,à,áá N EDG B; · D#:à B; · DH:à, B; O :à > 5,à,áá > 5,à,áá á ?à,5á F81385668 · D# · D ê · D Ý· D Ý · DH:à, B; · DH:à >B;5,à,áá å Ô ×B à áÔ Ùç Ü å Øá ?à,5á à,

Appendix E Column Specimens for Additional Fire Tests E.1 General

Two full-scale fire tests of reinforced concrete square columns, which will be strengthened with FRP and insulated for fire protection, are to be conducted in this ongoing research project.

The objective of the square column fire tests is to investigate the behaviour of FRP strengthened concrete square columns with insulation under elevated temperatures, as well as to obtain official fire endurance ratings from the Underwriters' Laboratories of Canada (ULC) for the FRP strengthening and insulation systems to be tested. These strengthened and insulated columns will be subjected to the ULC-S101 standard fire under sustained service load (that is, the load that the columns would be expected to experience in an actual fire situation).

E.2 Column Fabrication Two full-scale reinforced concrete square columns have been fabricated, cured and partially instrumented by the Author in the Structures Testing Laboratory at Queen's University.

The overall height of the column specimens is 3810 mm, as shown in Figure E-1, which is based on the height of the column furnace at the National Research Council (NRC). The cross section of the column was chosen as 400 mm square, and the resulting reinforcements were designed based on CSA A23.3-94 requirements (CSA, 1994). To test the columns in the column furnace at the National Research Council (NRC), 38 mm thick steel end plates were welded to the longitudinal bars at both ends as shown in Figure E-2(a). The average compressive strength of concrete after testing three concrete cylinders after 7 days was 27 ± 2 MPa and after 28 days was 36 ± 3 MPa. The primary longitudinal reinforcing steel bars have yield strength of 477 MPa and

ultimate strength of 695 MPa, which was obtained from the mill report. The column specimens were cast using hand scoops in three lifts through rectangular openings into the formwork as shown in Figure E-2(b). After each lift, the concrete was vibrated with a wand vibrator to ensure adequate consolidation (Figure E-2(c)). Following the removal of the formwork, which was after 24 hours, the column specimens and the aforementioned cylinders were cured under a plastic enclosure as shown in Figure E-2(f), for approximately 28 days at ambient temperature and relative humidity. The chamfered corners of the column specimens will be rounded at a later date using a concrete grinder to have a minimum radius of 25 mm as currently recommended by most suppliers of FRP strengthening systems for reinforced concrete structures. The full-scale columns were transported to the Fire Research Laboratory of the National Research Council (NRC), Ottawa, where they will be wrapped with FRP and insulated with a proprietary fire insulation system prior to fire testing.

E.3 Instrumentation Both columns were partially instrumented during the fabrication process with thermocouples and electrical resistance strain gauges (on the vertical reinforcing steel) at the column mid-height as shown in Figure E-3. The thermocouples on the FRP strengthening surface and the fire insulation system will be installed when the columns are being wrapped with FRP and insulated. The locations of the thermocouples are shown in Figure E-4. Chromel-alumel (Type K) thermocouples, which have an accuracy of ± 1°C, as stated by the manufacturer, have been installed and will be used to measure the internal temperatures of concrete, reinforcing steel, FRP surface and insulation. Type K thermocouples are graded by the manufacturer for a temperature range between -200°C to 1250°C. To locate the thermocouples, at specific locations within the concrete columns, a steel welding-rod was tied, using plastic ties, to the steel reinforcement cage and the thermocouples were secured to the rod using wire and 5-minute epoxy

as shown in Figure E-4(a). Kyowa? KFU-5-120-C1-11 high temperature strain gauges were installed on the reinforcing steel as shown in Figure E-4(c), to study the effectiveness of the FRP and detect any bending in the column during the fire endurance tests. The information from the strain gauges could be used in validating the portion of the numerical model (developed by the Author for this research study) that determines the structural response of the columns during fire.

E.4 Proposed Plan for Fire Test Both column specimens will be tested in the column furnace at the National Research Council (NRC), Ottawa (Figure E-5). This furnace was built specifically for testing loaded full- scale reinforced concrete columns during fire exposure according to ULC-S101 (2004). After the column specimens are placed inside the chamber, the end plates of the column are bolted to the hydraulic jack at the bottom and to the hydraulic jack can apply a maximum load of 9790 kN.

The heating chamber of the furnace, which is lined with insulating material that can effectively transfer the heat to the specimens (that is, it has an emissivity close to 1.0), is 2640 mm square and 3050 mm high. The heat in the chamber is supplied by 32 propane burners with a total heating capacity of 4200 kW, arranged in 8 vertical lines. Temperatures in the heating chamber are recorded by eight thermocouples located at various heights throughout the chamber (Figure E-6).

The sustained applied load to be applied during the fire tests will be based on the requirements of ULC-S101 (2004) and ASTM-E119 (2001). According to ULC-S101, a full- scale fire test of a reinforced concrete column is considered successful if the column specimen is capable of carrying the sustained applied service load without structural failure for the desired duration during exposure to a standard fire.

machined to 25 mm rounded corners 15 15 A 3810 3734 Steel Plate 25M Rebar 10M Ties

25M rebar through and welded to the steel plate Weld 38 mm thick steel plate *N.T.S **All dimensions in mm

Figure E-1: Column dimensions and reinforcement details 228 SECTION A-A 864 305 NO. OF SPECIMENS: 2 square columns CONCRETE: 28 MPa 28-day design strength REINFORCEMENT: 4 - 25M longitudinal rebars 10M ties spaced at 305 mm c/c and 136 mm overlap 40 mm concrete cover to ties 50 mm concrete cover to principal reinforcement

Welded steel rebar (a) (b)

(c) (d)

Figure E-2: (a) Primary steel reinforcement welded to steel end plates; (b) Concrete poured into the formwork using hand scoops; (c) Concrete being vibrated; (d) Rectangular opening being sealed; (e) Concrete being poured from the opening at the top of the formwork; and (f) Curing the columns

(e) (f) Figure E-2 (continued): (a) Primary steel reinforcement welded to steel end plates; (b) Concrete poured into the formwork using hand scoops; (c) Concrete being vibrated; (d) Rectangular opening being sealed; (e) Concrete being poured from the opening at the top of the formwork; and (f) Curing the columns

(a) (b)

(c) (d)

Figure E-3: Instrumentation on column specimens ? (a) Top view of thermocouple locations; (b) Side view of thermocouple locations; (c) Strain gauge on primary steel rebar; and (d) Waterproof sealant over the strain gauge

51.0 65.0 26.0 12.0 23 11 12 13 24 14 25 15 26 22

27 16 17 45.0 2845.0 18 1925.0 29 3026.0 20 11.5 21 31 (a) 35

34 3365.6 3225.2 114.5 (b) Figure E-4: Location of thermocouples and strain gauges within the specimens (dimensions shown in figure are in mm): (a) Thermocouples in the concrete, (b) Thermocouples on the longitudinal reinforcing steel, (c) Thermocouples on the FRP and insulation, (d) Strain gauges on the longitudinal reinforcing steel

36 37 38 41 39 (c) SG1 SG2 SG4 SG3 42 43

Insulation FRP (d) Figure E-4 (continued): Location of thermocouples and strain gauges within the specimens (dimensions shown in figure are in mm): (a) Thermocouples in the concrete, (b) Thermocouples on the longitudinal reinforcing steel, (c) Thermocouples on the FRP and insulation, (d) Strain gauges on the longitudinal reinforcing steel

Figure E-5: Column furnace at the National Research Council (NRC) of Canada, Ottawa (http://irc.nrc-cnrc.gc.ca/fr/facilities/column_e.html on 16August, 2006)

505 505 816 5, 6 1, 2 3, 4 7, 8 Furnace door 2642 Furnace chamber

5 6 1, 7 3 2, 8 4 610 610 3048 610 * All dimensions are in mm 610

Figure E-6: Thermocouple locations in the column furnace at NRC, Ottawa (reproduced from Bisby 2003)

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