modeling of frp-jacketed rc columns subject to combined axial and lateral loads

MODEL OF FRP-CONFINED CONCRETE CYLINDERS UNDER AXIAL COMPRESSION .... MODEL OF RECTANGULAR FRP-CONFINED CONCRETE UNDER AXIAL COMPRESSION.... 82 3.3 NEW MODEL FOR RECTANGULAR FRP-CONFINED

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UNIVERSITY OF CALIFORNIA, SAN DIEGO

Modeling of FRP-Jacketed RC Columns Subject to Combined Axial and Lateral Loads

A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy

in Structural Engineering

by

Chung-Sheng Lee

Committee in Charge:

Professor Gilbert A Hegemier, Chair

Professor David Benson

Professor Vitali Nesterenko

Professor Frieder Seible

Professor Chia-Ming Uang

2006

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3211782 2006

UMI Microform Copyright

ProQuest Information and Learning Company

by ProQuest Information and Learning Company

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Copyright

Chung-Sheng Lee, 2006

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“The fear of the LORD is the beginning of wisdom.”

Proverbs, 9:10a

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TABLE OF CONTENTS

SIGNATURE PAGE iii

TABLE OF CONTENTS v

LIST OF SYMBOLS xii

LIST OF FIGURES xix

LIST OF TABLES xxvi

ACKNOWLEDGMENTS xxviii

VITA, PUBLICATIONS AND FIELDS OF STUDY xxix

ABSTRACT OF THE DISSERTATION xxxii

CHAPTER 1 INTRODUCTION 1

1.1 BACKGROUND 1

1.2 FRP OVERLAY TECHNIQUE 7

1.3 CONFINED CONCRETE BEHAVIOR 8

1.4 EVALUATION OF STRUCTURAL RESPONSE UNDER BLAST LOAD (EQUIVALENT SINGLE-DEGREE-OF-FREEDOM SYSTEM) 10

1.5 PROBLEM STATEMENT AND RESEARCH OBJECTIVES 13

1.6 DISSERTATION ORGANIZATION 15

CHAPTER 2 MODEL OF FRP-CONFINED CONCRETE CYLINDERS UNDER AXIAL COMPRESSION 17

2.1 INTRODUCTION 17

2.1.1 Review of Existing Model Development 18

2.1.2 “Actual” Stain-Softening Response of Concrete in Uniaxial Compression 20

2.1.3 Unconfined Model by Pantazopoulou and Mills [54] 24

2.2 STUDY APPROACH AND SIGNIFICANCE 27

2.3 “ACTUAL” RESPONSES OF CONCRETE IN UNIAXIAL COMPRESSION 28

2.3.1 Basic Concrete Properties 28

2.3.2 Parametric Formula for β and εclim 29

2.3.3 Determination of Parameter C 30

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2.3.4 Validity of Modified P&M Model Predictions 33

2.4 PROPOSED FRP-CONFINED CONCRETE MODEL 36

2.4.1 Axial Secant Stiffness of FRP-Confined Concrete 38

2.4.2 Confinement Effectiveness and Confinement Ratio 40

2.4.3 Implementation of Proposed Model 43

2.5 VALIDATION OF PROPOSED MODEL 46

2.5.1 Tests by Picher et al [58] 48

2.5.2 Tests by Mastrapa [42] 49

2.5.3 Tests by Owen [52] 51

2.5.4 Tests by Xiao and Wu [88] 53

2.5.5 Tests by Rochette and Labossière [66] 55

2.5.6 Tests by Dias da Silva and Santos [13] 56

2.5.7 Performance of Ultimate Axial Strength and Strain Predictions 57

2.6 EXPLICITLY EXPRESSION FOR ULTIMATE AXIAL STRENGTH AND STRAIN 66

2.6.1 Validation and Accuracy 68

2.6.2 Axial Responses vs Confining Stiffness 71

2.7 SUMMARY AND CONCLUSIONS 73

CHAPTER 3 MODEL OF RECTANGULAR FRP-CONFINED CONCRETE UNDER AXIAL COMPRESSION 76

3.1 INTRODUCTION 76

3.2 EXISTING STUDIES ON FRP-CONFINED CONCRETE IN RECTANGULAR SECTIONS 77

3.2.1 Experimental Stress-Strain Relations 77

3.2.2 Deformation of FRP Jacket 79

3.2.3 Existing Models for Rectangular FRP-Confined Concrete Columns 81

3.2.3.1 Confinement Mechanism of FRP Jacket in Rectangular Section 81

3.2.3.2 Existing Model Approaches 82

3.3 NEW MODEL FOR RECTANGULAR FRP-CONFINED CONCRETE IN AXIAL COMPRESSION 84

3.3.1 Effective Confined Area 84

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3.3.2 Model of Rectangular FRP-Confined Concrete in Axial

Compression 86

3.3.3 Approximate Evaluation of Transverse Strains 88

3.3.4 Approximate Evaluation of Hoop Jacket Strains 90

3.3.4.1 Hoop Jacket Strain on Flat Parts 91

3.3.4.2 Hoop Jacket Strain in Corner Zones 92

3.4 MODEL VALIDATION 95

3.4.1 Tests by SEQAD [73] 97

3.4.2 Tests by Hosotani et al [23] 98

3.4.3 Tests by Pico [59] 99

3.4.4 Tests by Rochette and Labossière [65][66] 100

3.4.5 Tests by Masia et al [41] 103

3.4.6 Tests by Rocca et al [64] 105

3.4.7 Comparison of Maximum Jacket Strain Predictions 109

3.5 PARAMETRIC STUDY 114

3.5.1 Effect of Corner Radius on Stress-Strain Relation 114

3.5.2 Effect of Jacket Thickness on Axial Responses 115

3.6 SUMMARY AND DISCUSSIONS 119

CHAPTER 4 LOAD-DISPLACEMENT MODEL OF FRP-JACKETED RC COLUMNS UNDER SEISMIC LOADS 122

4.1 INTRODUCTION 122

4.2 CONSTITUTIVE MODELS FOR MATERIALS 123

4.2.1 Cover Concrete in Compression 123

4.2.2 Concrete in Tension 124

4.2.3 Steel Reinforcement 125

4.3 MOMENT-CURVATURE ANALYSIS 126

4.3.1 Segments of Column Section 128

4.3.2 Section Analysis 131

4.3.2.1 Neutral Axis Location 131

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4.3.2.3 First-Yield Moment, M y 133

4.3.2.4 Idealized-Yield Moment, M i 134

4.3.2.5 Ultimate Moment, M u 134

4.3.3 Validity of Moment-Curvature Curves 136

4.4 REVIEW OF DISPLACEMENT ASSESSMENT ON DOUBLE BENDING COLUMNS 141

4.4.1 First-Yield Displacement 143

4.4.2 Idealized-Yield Displacement 144

4.4.3 Post-Yield Displacement 144

4.5 REVIEW OF UCSD SHEAR STRENGTH MODEL 146

4.5.1 Concrete Mechanism Strength, V c 146

4.5.2 Steel Truss-Mechanism Component, V s 149

4.5.3 Axial Load Shear Contribution, V p 150

4.5.4 FRP Jacket Contribution, V j 151

4.6 RESIDUAL SHEAR MODEL FOR FRP JACKET AND STEEL HOOP CONTRIBUTIONS 151

4.7 MODEL CALIBRATIONS ON FRP-JACKETED CIRCULAR COLUMNS UNDER DOUBLE BENDING 153

4.7.1 Moment-Curvature Responses 157

4.7.2 Hoop Jacket Strain-Curvature Curves 159

4.7.3 Revised Plastic Hinge Length 160

4.7.4 Load-Displacement Predictions 163

4.7.5 Shear Strength Analysis 165

4.8 LOAD-DISPLACEMENT ANALYSIS OF CFRP-JACKETED RECTANGULAR COLUMN UNDER SINGLE BENDING 167

CHAPTER 5 COMBINED AXIAL AND LATERAL LOAD TESTS OF CFRP JACKETED RC COLUMNS (SIMULATED BLAST LOADS) 174

5.2 COLUMN SPECIMENS AND FRP JACKETS 176

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5.3 MATERIAL PROPERTIES 180

5.3.1 Concrete 180

5.3.2 FRP Jackets 181

5.3.3 Steel Reinforcement 181

5.4 TEST SETUP, INSTRUMENTATION AND TESTING PROCEDURE 182

5.4.1 Test Setup 182

5.4.2 Instrumentation 186

5.4.3 Testing Procedure 186

5.5 OBSERVED BEHAVIOR AND EXPERIMENTAL RESULTS 187

5.5.1 Overall Response 187

5.5.2 Lateral Deflected Shapes 191

5.5.3 Loads vs Mid-High Lateral Displacement 194

5.5.4 CFRP Jacket Behavior 198

5.5.4.1 Vertical Distribution of Hoop Jacket Strains 198

5.5.4.2 Circumferential Distribution of Hoop Jacket Strains 200

CHAPTER 6 ANALYSIS OF CFRP-CONFINED RC COLUMNS SUBJECT TO COMBINED AXIAL AND LATERAL (SIMULATED BLAST) LOADS 209

6.2 LOAD-DISPLACEMENT MODEL OF BLAST-EFFECT COLUMN TESTS 209

6.2.1 Curvature Distribution 211

6.2.2 First-Yield Displacement 213

6.2.3 Second-Yield Displacement 214

6.2.4 Post Yield Displacement 218

6.3 ARCHING ACTION 219

6.4 RESIDUAL SHEAR STRENGTH 220

6.5 ANALYSIS ON 14 ×14 CFRP-JACKETED COLUMNS 221

6.5.1 2-Wrap CFRP-Jacketed Column in Test 2 222

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6.5.1.1 Section Analysis 222

6.5.1.2 Load-Displacement Curves 225

6.5.1.3 Jacket Strain Predictions 226

6.5.4 Analysis of As-Built Column in Test 4 238

6.5.5 Summary of Model Analysis on the 14 × 14 Columns 241

6.5.5.1 Ultimate State Predictions 241

6.5.5.2 Performance of the 14 × 14 Columns 243

6.6 ANALYSIS OF RECTANGULAR CFRP-JACKETED COLUMNS IN TESTS 7 AND 9 246

6.6.1 3-Wrap 12 × 18 Column in Test 8 246

6.6.2 3-Wrap 18 × 12 Column in Test 9 252

6.6.3 Summary of Model Analysis of Rectangular CFRP-Jacketed Columns 259

CHAPTER 7 CONCLUSIONS AND FUTURE WORK 261

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7.1 CONCLUSIONS 261 7.1.1 Model of FRP-Confined Concrete Columns in Axial Compression 261 7.1.2 Load-Displacement Response of FRP-Jacketed RC Columns under

Seismic Loads 264 7.1.3 Resistance Function of FRP-Jacketed RC Columns under Blast

Loads 264 7.2 FUTURE WORKS 266

Appendix A Performance of Existing Models in Prediction of Ultimate

Axial Strength and Strain on FRP-confined Concrete Cylinders 268 Appendix B Static Tests on CFRP-Confined RC Columns Subject to

Uniform Lateral Loading – Column Drawings and Instrument Locations 275 REFERENCES 288

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LIST OF SYMBOLS

CAPITAL LETTERS

A g Gross sectional area

A cu unconfined area

A e Effective confined area

A seg_c() Area of concrete strip

A seg_j() Area of jacket strip

A seg_s() Area of steel strip

B Column width

C The order of the nonlinear function of axial-lateral strain relation, P&M model

D Section diameter of concrete cylinder

D e Equivalent diameter

E c Initial stiffness of concrete

E j Elastic modulus of confinement material in the hoop direction

j

E Effective confining stiffness

E s Elastic modulus of steel

Esec Axial secant stiffness of concrete

F Peak force of blast pulse

H Column Depth

I Impulse

I eff Effective section inertia

I g Gross section inertia

K Initial Stiffness of SDOF system

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KE Kinetic energy

L c Clear column height

L eff Effective column height

L p Plastic hinge length

L pb Plastic hinge length at column bottom

L pc Plastic hinge length at column mid-height

L’ p Revised Plastic hinge length

M i Idealized-yield moment

M b Moment at column bottom

M c Moment at column mid-height

M t Moment at column top

M cr Cracking moment

M y First-yield moment

M u Ultimate moment

P Axial load

P 0 Initial axial load

P i1 Axial load at first yield state

P i2 Axial load at second yield state

P max Maximum axial load

P u Ultimate axial load

Q Total lateral load

Q i1 Total lateral load at first yield state

Q i2 Total lateral load at second yield state

Q max Maximum lateral load

Q y Ideal yield lateral load

Q u Ultimate lateral load

R y Yield Resistance

R( ∆) Resistance function

T Natural period of response of structure

U Strain energy

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V Shear force

V c Shear resistance of concrete

V n Normal shear capacity

V p Shear resistance of axial load

V s Shear resistance of transverse steel

V s Shear resistance of FRP jacket

WD Work done on structure

X theo Theoretical result of Variable X

X test Experimental value of Variable X

Z Elastic section modulus

LOWER CASE LETTERS

b The length of the flat side of column width

c Depth of neutral axis

c y Neutral axis at M y

cov Concrete clear cover

d Distance from extreme tensile bar to top concrete edge

d bl Diameter of longitudinal bar

d c() Distance from the center of concrete strip to the top concrete edge

d j() Distance from the center of jacket strip to the top concrete edge

d s() Distance from the center of steel strip to the top concrete edge

f ic Axial stress at the point of inflection in Attard and Setunge Model (1996)

f c Axial compressive stress on unconfined concrete

f cr Cracking stress of concrete

f c(i) Axial compressive stress on unconfined concrete at incremental step i

f c(u) Ultimate axial strength of unconfined concrete

f c,uc Axial stress in unconfined area, rectangular model

f’ c Unconfined concrete strength

f cc Axial compressive stress of confined concrete

f cc,e Axial stress in effective confined area, rectangular model

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f cc(i) Axial compressive stress of confined concrete at incremental step i

f cc(u) Ultimate axial strength of confined concrete

f’ cc Maximum axial strength of confined concrete

f l Lateral confining pressure

f le Effective confining pressure, rectangular concrete model

f l(i) Lateral confining pressure at incremental step I

f lmax Maximum confining pressure

f l(u) Ultimate lateral confining pressure

f t Tensile stress of concrete

f to Modulus of rupture of concrete

f s Stress of steel

f sy Yield stress of steel

f su Ultimate stress of steel

gap Gap between jacket and footing and load stub

h The length of the flat side of column depth

i Incremental step

l t Yield penetration length

l’ t Revised yield penetration length

n Parameter of Popovics’s expression, related to the compressive strain ratio

q Uniform lateral load

r Corner radius

r f Strength degradation factor of unconfined concrete

t j FRP jacket thickness

t d Duration of blast load

v 0 Initial Poisson’s ratio of concrete

GREEK LETTERS

∆ Lateral displacement on column

∆& Velocity

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∆f Lateral Flexural displacement on column

∆p1 Plastic displacement between first and second yield states

∆p2 Plastic displacement after second yield state

∆s Lateral Shear displacement on column

∆y Yield displacement

∆y1 First-yield displacement, column under blast load

∆y2 Second-yield displacement, column under blast load

∆’ y First-yield displacement, column under seismic load

∆u Ultimate lateral displacement

αc Factor related to aspect ratio, UCSD shear model

β Material constant, P&M model

βc Factor related to longitudinal steel ratio, UCSD shear model

εA Area strain of concrete cylinder

εic Axial strain at the point of inflection in Attard and Setunge Model (1996)

εc Axial strain of unconfined concrete

ε*

c Axial strain corresponding to zero volume strain of unconfined concrete

εclim Axial strain at the limit of the linear response of unconfined concrete

εc0 Axial strain at peak strength f’ c

εc(i) Axial compressive strain of unconfined concrete at incremental step i

εc(u) Ultimate compressive strain of unconfined concrete

εc,uc Axial strain in unconfined concrete, rectangular model

εcc Axial compressive strain of confined concrete

εcc,e Axial compressive strain in effective confined area, rectangular model

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εcc0 Axial compressive strain of confined concrete at maximum strength f’ cc

εcc(i) Axial compressive strain of confined concrete at incremental step i

εcc(u) Ultimate axial compressive strain of confined concrete

εcr Tensile cracking strain of concrete

εj Pure tensile jacket strain

εj ( ) hoop jacket strain

εj(u) Theoretical jacket rupture strain

εl Lateral (transverse) strain of concrete cylinder

εl0 Lateral (transverse) strain at peak strength f’ c

εl(i) Lateral (transverse)strain at incremental step i

εl(d) Design rupture strain of FRP jacket

εl(u) Experimental rupture strain of FRP jacket

εs Strain of steel

εsh Strain-hardening strain of steel

εs_h Strain of transverse steel

εsu_h Ultimate Strain of transverse steel

εsy Yield strain of steel

εsu Ultimate strain of steel

εt Tensile strain of concrete

εtop Strain at the top concrete edge

εv Volumetric strain of concrete cylinder

φ Section curvature

φb Curvature at column bottom hinge

φc Curvature at column mid-height hinge

φcr Section cracking curvature

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φp Plastic curvature

φpb1 Plastic curvature at column bottom between first and second yield states

φpb2 Plastic curvature at column bottom after second yield state

φpc Plastic curvature at column mid-height

φy Idealized-yield curvature

φ’y First-yield curvature

φu Ultimate curvature

γc Factor related to curvature, UCSD shear model

ϕ Angle between the vertical axis and shear cracks

ϕp Angle between the vertical axis and the compression of vertical load

ϕq Angle between the compression strut and axial load (arching action)

µ∆ Displacement ductility

µφ Curvature ductility

θb Rotation at column bottom end

θpb1 Plastic rotation at column bottom end between first and second yield states

θpc Plastic rotation at column mid-height

ρh hoop steel ratio

ρl longitudinal steel ratio

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LIST OF FIGURES

Figure 1.1: Murrah Federal Building after Bombing Attach, 1995 [51] 2

Figure 1.2: Proof-of Concept Test, 4-Story “Building” during Blast [20][38] 4

Figure 1.3: Performance of CFRP-Jacketed (left) and As-Built (right) Columns after Blast [20][38] 4

Figure 1.4: Field Test Setup [20] 6

Figure 1.5: UCSD Quasi-Static Test Setup [20] 6

Figure 1.6: Application of FRP Composite Overlays on a RC Column 8

Figure 1.7: Influence of Confinement Levels on the Responses of a Circular Confined Concrete Cylinder 9

Figure 1.8: Single-Degree-Of-Freedom Model for Blast Analysis 11

Figure 2.1: Schematic Stress-Strain Responses of Uniaxial Compression Concrete [50] 21

Figure 2.2: Uniaxial Strain-Softening Curves by Attard and Setunge (1996) 24

Figure 2.3: Volume-Axial Strain Model by Pantazopoulou and Mills [54] 26

Figure 2.4: Effect of Parameter C on P&M Model Predictions 31

Figure 2.5: Rates of Lateral Dilatancy, C and C0 33

Figure 2.6: “Actual” Responses of Unconfined Concrete by Modified P&M Model 34

Figure 2.7: Comparison of proposed εclim vs ε 0 35

Figure 2.8: Axial stress level at εclim 36

Figure 2.9: Schematic Constitutive Relations between unconfined and FRP-Confined Concrete Cylinders under Axial Compression 37

Figure 2.10: Secant Stiffness vs Lateral Strain 39

Figure 2.11: Triaxial Test Data vs Confined Strength Envelopes 42

Figure 2.12: Implementation of Proposed FRP-Confined Concrete Model 44

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Figure 2.13: Model of 38-MPa Concrete Cylinder Confined with Different

Amounts of FRP Composite Confinement 45

Figure 2.14: Poisson’s Ratios on FRP-confined Concrete Cylinders (f’ c = 38 MPa) 46

Figure 2.15: Comparison of Proposed Model with Tests by Picher et al [58] 49

Figure 2.16: Comparison of Proposed Model with Tests by Mastrapa [42] 50

Figure 2.17: Comparison of Proposed Model with Tests by Owen [52] 52

Figure 2.18: Comparison of Proposed Model with Tests by Xiao and Wu [88] 54

Figure 2.19: Model Comparison with Tests by Rochette and Labossière [66] 56

Figure 2.20: Model Comparison with Tests by Dias da Silva and Santos [13] 57

Figure 2.21: Performance of Model Predictions on Ultimate Axial Strength, f cc(u) 64

Figure 2.22: Performance of Model Predictions on Ultimate Axial Strain, ε cc(u) 65

Figure 2.23: Normalized Axial Stress-Lateral Strain Curves for Unconfined Concrete with Peak Strength from 20 to 55 MPa (3 to 8 ksi) 67

Figure 2.24: “Actual” Confinement Effectiveness vs Confinement Ratio 69

Figure 2.25: Relation of Increased Strain Ratio vs Confinement Effectiveness 69

Figure 2.26: Increased Axial Strength Ratios vs Rupture Strain 72

Figure 3.1: Influence of Corner Radius to the Axial Responses [66] 78

Figure 3.2: Influence of Number of FRP Jacket Plies to the Axial Responses [66] 79

Figure 3.3: Deflected Shape of FRP jacket in Rectangular Section 80

Figure 3.4: Typical Shape of Effective Confined Area 82

Figure 3.5: Proposed Equivalent Diameter and Effective Confined Area 85

Figure 3.6: Proposed Transverse Deformation Model on Rectangular Concrete Core 90

Figure 3.7: Proposed Flexural Deflection on FRP Jacket 91

Figure 3.8: Analysis Algorithm of Rectangular FRP-Confined Concrete Model 94

Figure 3.9: Model Analysis vs Test Results of SEQAD [73] 97

Figure 3.10: Comparison of Model Analysis with Test Results of Hosotani et al [23] 99

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Figure 3.11: Comparison of Model Analysis with Test Results of Pico [59] 100 Figure 3.12: Model Analysis vs Test Results of Rochette and Labossière [65] 101 Figure 3.13: Model Analysis with Test Results of Rochette and Labossière [66] 102 Figure 3.14: Model Analysis vs Test Results of Rochette and Labossière [66] on

AFRP-Confined Concrete Columns 103 Figure 3.15: Comparison of Model Analysis with Test Results of Masia et al [41] 104 Figure 3.16: Comparison of Model Analysis with Test Results of Rocca et al [64] 106 Figure 3.17: Corner Jacket Strain Ratio vs B/r 113

Figure 3.18: Jacket Strain Ratio at Side Center vs B/r 113

Figure 3.19: Effect of Corner Radius on Stress-Strain Responses 115 Figure 3.20: Effect of Jacket Thickness on Maximum Axial Strength 117 Figure 3.21: Effect of Jacket Thickness on Compression Capacity 118 Figure 4.1: Stress-Strain Responses for Cover Concrete 124 Figure 4.2: Stress-Strain Relation of Reinforcing Steel 126 Figure 4.3: Flow Chart of Moment-Curvature Program FSCC 127 Figure 4.4: Segments of Circular Section 129 Figure 4.5: Segments of Rectangular Section 130 Figure 4.6: Moment-Curvature Curves 135 Figure 4.7: Column Section in Tests of Sheikh and Yau [77] 137 Figure 4.8: Stress-Strain Curves of Steel Bars in Tests of Sheikh and Yau [77] 137 Figure 4.9: Stress-Strain Curve of CFRP and GFRP in Tests of Sheikh and Yau

[77] 138 Figure 4.10: Moment-Curvature Analysis on As-Built Specimen S-2NT 138 Figure 4.11: Moment-Curvature Analysis on GFRP Jacketed Column ST-2NT 139 Figure 4.12: Moment-Curvature Analysis on CFRP Jacketed Column ST-3NT 139 Figure 4.13: Moment-Curvature Analysis on CFRP Jacketed Column ST-4NT 140 Figure 4.14: Moment-Curvature Analysis on GFRP Jacketed Column ST-4NT 140

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Figure 4.15: Moment and Shear Diagrams of Columns under Double Bending 142 Figure 4.16: Curvature Distributions of the Lower Cantilever 143 Figure 4.17: Reduction Factor γc (UCSD Shear Strength Model [32]) 148 Figure 4.18: Steel Truss Mechanism 149 Figure 4.19: Axial Load Shear Contribution 150 Figure 4.20: Details of As Built Column in Tests ACTT-9513 [71] and ACTT-

9519 [26] 155 Figure 4.21: FRP Jacket Layouts 156 Figure 4.22: Moment-Curvature Analysis on Test ACTT-9513 [71] 158 Figure 4.23: Moment-Curvature Analysis on ACTT-9519 [26] 158 Figure 4.24: Hoop Jacket Strain-Curvature Curves 159 Figure 4.25: Jacket Strain-Displacement Predictions on GFRP-Jacketed Column 162 Figure 4.26: Jacket Strain-Displacement Predictions on CFRP-Jacketed Column 162 Figure 4.27: Jacket Rupture at Column Top End, Test ACTT-9519 [26] 164 Figure 4.28: Load-Displacement Analysis on GFRP-Jacketed Column 164 Figure 4.29: Load-Displacement Analysis on CFRP-Jacketed Column 165 Figure 4.30: Shear Capacity Analysis on GFRP-Jacketed Column 166 Figure 4.31: Shear Capacity Analysis on CFRP-Jacketed Column 167 Figure 4.32: Column Dimensions and Jacket Layout in Test ACTT9503 [70] 170 Figure 4.33: Jacket Rupture at Column Bottom End, Test ACTT9503 [70] 171 Figure 4.34: Moment-Curvature Analysis on Test ACTT9503 171 Figure 4.35: Load-Displacement Analysis on Test ACTT9503 172 Figure 4.36: Shear Capacity Analysis on Test ACTT9503 172 Figure 5.1: Finished FRP-Retrofitted Specimens 178 Figure 5.2: Application of CFRP Strips and Jacket; 180 Figure 5.3: Experimental Stress-Strain Curves for Grade 60 #6 Bar 182 Figure 5.4: Elevation View of Specimen Placement and Lateral Load Setup 184

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Figure 5.5: Elevations of Vertical Load Setup: 185 Figure 5.6: Photographs for As-Built Column Tests 188 Figure 5.7: Photographs of Retrofitted Column Test Specimens 189 Figure 5.8: Crack Pattern on Confined Concrete Surface, Test 3 190 Figure 5.9: Typical Deflected Shapes of As-built and Retrofitted Specimens (left:

Test 4, right: Test 10) (1 in = 25.4 mm) 192 Figure 5.10: Deformed Shapes of Specimens after Testing [20] 193 Figure 5.11: Load-Displacement Curves in Tests 1 to 6, and 10 196 Figure 5.12: Load-Displacement Curves in Tests 7 to 9 197 Figure 5.13: Vertical Distribution of Hoop Jacket Strain in Test 2 199 Figure 5.14: Vertical Distribution of Hoop Jacket Strain in Test 3 200 Figure 5.15: Hoop Jacket Strain Profiles at Column Height of 3”, Test 8 203 Figure 5.16: Hoop Jacket Strain Profiles at Column Height of 3”, Test 9 204 Figure 5.17: Hoop Jacket Strain Profiles at Column Height of 3”, Test 10 205 Figure 5.18: Variations of Hoop Jacket Strain at Corners, at 3” Height, Test 8 206 Figure 5.19: Variations of Hoop Jacket Strain at Corners, at 3” Height, Test 9 206 Figure 6.1: Static Loading Condition in UCSD Blast-Effect Column Tests 211 Figure 6.2: Curvature Distributions on Lower Half Column 212 Figure 6.3: Behavior of Column between First- and Second-Yield States 215 Figure 6.4: Assumed Stress-Strain Curve of Steel Bars for 14 ×14 Columns 222 Figure 6.5: Maximum P-M diagram for Test 2 223 Figure 6.6: Modified Bilinear Moment-Curvature Curve for Test 2 224 Figure 6.7: Bilinear Model of Moment and Jacket Strain εj(b/2, t j/2) for Test 2 225 Figure 6.8: Load-Displacement Predictions, Test 2 226 Figure 6.9: Jacket Strains at 6-in (152-mm) Height above Footing, Test 2 227 Figure 6.10: Maximum P-M diagram for Test 10 228 Figure 6.11: Modified Moment-Curvature Curve for Test 10 229

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Figure 6.12: Bilinear Model of Moment and Jacket Strain at Flat Side Centers,

Test 10 230 Figure 6.13: Bilinear Model of Moment and Jacket Strain at Corners, Test 10 230 Figure 6.14: Load-Displacement Predictions on Test 10 232 Figure 6.15: Hoop Jacket Strains at 3-in Height above Footing, Test 10 233 Figure 6.16: Jacket Corner Strains at 6-in Height above Footing, Test 10 233 Figure 6.17: Maximum P-M diagram for Test 3 234 Figure 6.18: Modified Moment-Curvature Curve for Test 3 235 Figure 6.19: Bilinear Model of Moment and Jacket Strain at Flat Side Centers 236 Figure 6.20: Load-Displacement Predictions, Test 3 237 Figure 6.21: Hoop Jacket Strains at 3-in Height above Footing, Test 3 238 Figure 6.22: Maximum P-M diagram for Test 3 239 Figure 6.23: Modified Moment-Curvature Curve for Test 4 240 Figure 6.24: Load-Displacement Prediction on As-built Column in Test 4 241 Figure 6.25: Number of Wraps vs Lateral Displacement Ductility on 14 × 14

Columns 245 Figure 6.26: Number of Wraps vs Lateral Strength Increase on 14 × 14 Columns 245 Figure 6.27: Maximum P-M diagram for Test 8 247 Figure 6.28: Modified Moment-Curvature Curve for Test 8 247 Figure 6.29: Bilinear Model of Moment and Jacket Strains at Flat Side Centers,

Test 8 248 Figure 6.30: Bilinear Model of Moment and Jacket Strain at Corners, Test 8 249 Figure 6.31: Load-Displacement Predictions, Test 8 250 Figure 6.32: Hoop Jacket Strains on Short Sides at 3-in Height above Footing,

Test 8 251 Figure 6.33: Hoop Jacket Strains on Long Sides at 3-in Height above Footing,

Test 8 251 Figure 6.34: Jacket Corner Strains at 3-in Height above Footing, Test 8 252

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Figure 6.35: Maximum P-M diagram for Test 9 253 Figure 6.36: Modified Moment-Curvature Curve for Test 9 254 Figure 6.37: Bilinear Model of Moment and Jacket Strains at Flat Side Centers,

Test 9 255 Figure 6.38: Bilinear Model of Moment and Jacket Strain at Corners, Test 9 255 Figure 6.39: Load-Displacement Predictions, Test 9 256 Figure 6.40: Hoop Jacket Strains on Long Sides at 3-in Height above Footing,

Test 9 257 Figure 6.41: Hoop Jacket Strains on Long Sides at 3-in Height above Footing,

Test 9 258 Figure 6.42: Jacket Corner Strains at 3-in Height above Footing, Test 9 258

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LIST OF TABLES

Table 2.1: Uniaxial Model of Attard and Setunge [4] 23 Table 2.2: Variables of Adopted Tests 47

Table 2.3: Comparison of Experimental Results [58][42] with Proposed Model 60

Table 2.4: Expressions of Adopted Models for Comparison 70 Table 2.5: Comparison of Model Accuracy 71 Table 3.1: Mechanical Characteristics of Concretes in Rectangular Section 88 Table 3.2: Specimen Properties for Model Comparisons 95 Table 3.3: Comparison of Maximum Jacket Strain Predictions 111 Table 4.1: Details of As-Built Column in Adopted Tests 154 Table 4.2: FRP Jacket Properties in Each Test 154 Table 4.3: Moment-Curvature Analysis on Tests ACTT-9513 [71] and ACTT-9519 [26] 157 Table 4.4: Summary of Plastic Hinge Lengths in Adopted Tests 161 Table 4.5: Load-Displacement Predictions for Tests ACTT-9513 and 9519 163 Table 4.6: Properties of Reinforcement Steel and Concrete in Test ACTT-9503 [70] 168 Table 4.7: CFRP Jacket Properties in Test ACTT-9503 [70] 168 Table 5.1: Test Matrix and Specimen Characteristics [20][21] 175 Table 5.2: Details of As-built Columns 177 Table 5.3: Properties of CFRP lamina provide by manufacturer [9] 178 Table 5.4: Properties of CFRP Strips (Sika CarboDur® S1012) 179 Table 5.5: Concrete Strength and Properties of CFRP Jackets 181 Table 5.6: Maximum Load Reached in Each Test [20][21] 195 Table 5.7: Maximum Measured Jacket Strains in Tests 202 Table 5.8: Increase ratios of Loads and Displacement of vs Number of FRP Wraps208

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Table 6.1: Moment-Curvature Characteristics in Figure 6.6 for Test 2 224 Table 6.2: Moment-Curvature Characteristics in Figure 6.11 for Test 10 229 Table 6.3: Moment-Curvature Characteristics in Figure 6.18 for Test 3 235 Table 6.4: Moment-Curvature Characteristics in Figure 6.23 for Test 4 240 Table 6.5: Summary of Ultimate State Predictions on the 14 × 14 Columns 242 Table 6.6: Summary of Load-Displacement Analyses of 14 × 14 Columns 244 Table 6.7: Influence of Number of CFRP Wraps on Column Ultimate Performance 244 Table 6.8: Moment-Curvature Characteristics in Figure 6.28 for Test 8 248 Table 6.9: Moment-Curvature Characteristics in Figure 6.36 for Test 9 254 Table 6.10: Summary of Load-Displacement Analyses of Tests 8 and 9 259

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I am deeply indebted to my parents, my sister and my brother-in-law for their everlasting support and encouragement To my wife Ming-Hua and my daughter Ashley, I thank you for your love and prayers I would like to acknowledge my Lord Jesus Christ for leading me throughout my Ph.D., and I give all the praise to Him

The text of CHAPTER 2, in part, is a reprint of the material as it appears in “A Constitutive Model for FRP-Confined Concrete Cylinders in Axial Compression” has been submitted to ACI Structural Journal for publication I was the primary author and the co-author listed in this publication directed and supervised the research which forms the basis for this chapter

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VITA, PUBLICATIONS AND FIELDS OF STUDY

VITA

1992 B.S in Engineering,

Chung Yuan Christian University, Taiwan

1994 M.S in Structural and Mechanical Engineering,

National Central University, Taiwan

2000-2006 Graduate Student Researcher,

Department of Structural Engineering, University of California, San Diego

2006 Ph.D in Structural Engineering

University of California, San Diego

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PUBLICATIONS Journal Papers:

1) Lee, C S, and Hegemier, G A., “A Constitutive Model for FRP-Confined

Concrete Cylinders in Axial Compression,” ACI Structural Journal,

Submitted

Research Reports

1) Hegemier, G A., Frieder, S., Rodriguez-Nikl, T., Lee, C S., Budek, A M.,

and Dieckmann, L., “FRP-Based Blast Retrofit Design Strategies – Laboratory Tests on Rectangular RC Columns,” Report No SSRP-2002/04, UCSD, March

2002

2) Hegemier, G A., Frieder, S., Lee, C S., and Rodriguez-Nikl, T “FRP-Based

Blast Retrofit Design Strategies – Laboratory Tests on Rectangular RC Columns – Part II,” Report No SSRP-2002/17, UCSD, October 2003

3) Lee, C S., and Hegemier, G A., “Model of FRP-Confined Concrete Cylinders

in Axial Compression,” Report No SSRP-04/05, UCSD, May 2004

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FIELDS OF STUDY Studies in Solid Mechanics

Professor Vitali Nesterenko Professor Xanthippi Markenscoff

Studies in Structural Analysis

Professor John Kosmatka Professor Almed Elgamal Professor André Filiatrault

Studies in Structural Design

Professor Chia-Ming Uang Professor Robert E Englekirk Professor M J Nigel Priestley

Studies in Finite Element Method

Professor David Benson

Studies in Advanced Composite Materials

Professor Vistasp M Karbhari Professor John Kosmatka Professor Francesco Lanza Di Scalea

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ABSTRACT OF THE DISSERTATION

Modeling of FRP-Jacketed RC Columns Subject to Combined Axial and Lateral Loads

by Chung-Sheng Lee

Doctor of Philosophy in Structural Engineering University of California, San Diego, 2006

Professor Gilbert A Hegemier, Chair

To successfully use the fiber-reinforced-polymer (FRP) overlay technique for the seismic retrofit and the blast-hardening of RC columns, the mechanical behavior of the FRP-confined concrete needs to be understood and its response needs to be accurately predicted Although a number of studies have been conducted to-date, it is still not clear how the main parameters affect the axial stress-strain response of a FRP-confined concrete cylinder In particular, while it is understood that FRP jackets inhibit dilatancy, current models do not capture the physics that leads to ascending or strain-softening responses vs the level of lateral confinement

In this dissertation, a dilatancy-based analytical model for FRP-jacketed circular concrete cylinders in axial compression was developed The proposed theory

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is applicable to both the heavily confined case with ascending axial loaded vs axial strain response, and the lightly confined specimen with strain-softening behavior As

an extension of the circular model, a new model for rectangular FRP-confined sections was then developed In addition to jacket membrane strain, the jacket flexural strains caused by the cross-sectional shape were taken into account, and the rupture strain of the FRP jacket in the corner zone was predicted The present model was validated via

a large set of existing test results, and excellent agreement with experimental data was observed

As the application of the proposed concrete model, a load-displacement model and an associated computational algorithm were developed and validated for the response and failure conditions of RC columns subject to combined axial and seismic-type (lateral) loads On the other hand, excluding the strain rate effects on material parameters from modeling, an analytical procedure was also developed to predict the resistance function of FRP-jacketed RC columns subject to combined axial and uniform lateral (simulated blast) loads The model was validated via the results of the UCSD quasi-static tests on “blast columns”, and satisfactory correlation with the experimental load-displacement curves were observed The present models and the analytical procedures proposed in this dissertation can serve as design/analysis tools for the FRP overlay technique as applied to the seismic retrofit as well as the blast-hardening of RC columns

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CHAPTER 1 INTRODUCTION

1.1 Background

A column is a critical vertical structural member that must support a vertical load from the superstructure (the floors and roof) and transmit this load to the foundation In a steel-reinforced concrete (RC) column, especially in seismic regions, the transverse steel is usually designed in a relatively dense layout in an effort to restrain the lateral dilatancy (expansion) of the concrete core under vertical compression, and to increase the shear resistance With the aid of the confinement effects of this transverse steel, the failure of the concrete core is delayed and the column response becomes more ductile under a seismic load In contrast, where designed to sustain a vertical load only (i.e., a gravity design), the transverse steel in a

RC column in a nonseismic region is usually spaced roughly the column width, which provides relatively low restraint of the concrete dilatancy and shear resistance [37] As

a result, for a lateral load such as an impact or a blast pressure, the RC column typically fails in shear due to a low shear capacity Such a failure can lead to a catastrophic collapse

A dramatic example of this occurred, on April 19, 1995, in the bombing of the Murrah Federal Building in Oklahoma City, where 168 lives were lost, numerous people were injured, and over 75 buildings in the surround area were damaged On the north and south sides of the Federal Building, the car bomb destroyed several exterior columns at the street level, and the upper portion of the building suffered a

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catastrophic collapse as a consequence [49][51] Figure 1.1shows the Murrah Federal Building after the attack Following an investigation of the building collapse [49], the ASCE engineers on the Building Performance Assessment Team (BPAT) reported:

“The building was designed and constructed in accordance with the applicable codes, but did not provide any deliberate resistance against a vehicular bomb attack.”

In another paper [82], they concluded: “In combination with continuity

reinforcement, column shear reinforcement would have greatly reduced progressive collapse.”

Figure 1.1: Murrah Federal Building after Bombing Attach, 1995 [51]

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Since the tragedy of the Federal Building bombing, the need for the evaluation and design of civilian buildings to withstand the effects of bombing is evident In response to this need, a “blast-hardening” technique based on the use of fiber-reinforced polymers (FRPs) as an additional “shear reinforcement” on RC columns was developed by researchers from UCSD and elsewhere The concept of the FRP overlay technique was originally developed by UCSD for the seismic retrofits of reinforced concrete elements (columns, beams, masonry walls …… and etc.), and the efficacy has been confirmed by full-scale test validations in UCSD’s Powell Labortories[20][21][26][27]

To validate the FRP overlay technique for blast loads, the Technical Support Working Group (TSWG) and the Defense Treat Reduction Agency (DTRA) conducted a proof-of-concept test on a 4-story RC “building” retrofitted with CFRP jackets and subjected to blast loading A photo of the “building” under blast loading is shown in Figure 1.2 Figure 1.3 is a photo of the target column after the blast As seen from Figure 1.3, when compared with the deflected shape of the as-built column, the success of the FRP overlay technique for “blast-hardening” of RC columns is evident [20][38] The following description of “blast-hardening” has been adopted by the

National Research Council [51], “Blast-hardening of a structure refers to all

measures that are taken, either in the design phase or in subsequent (retrofit) action, to reduce or eliminate the effects of an explosion.”

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Figure 1.2: Proof-of Concept Test, 4-Story “Building” during Blast [20][38]

Figure 1.3: Performance of CFRP-Jacketed (left) and As-Built (right) Columns after

Blast [20][38]

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In addition to the demonstration test, a field test series and a corresponding quasi-static test series on the FRP-jacketed columns were initiated by TSWG/DTRA and conducted at Kirkland Air Force Base (KAFB) in New Mexico, and in UCSD’s Powell Laboratories, respectively Figure 1.4shows the field test setup In the UCSD quasi-static tests, the specimens were first loaded vertically and fixed in the vertical displacement to simulate the actual boundary condition during blast The specimens were then quasi-statically loaded in the lateral direction via an array of three hydraulic actuators to simulate blast effects Figure 1.5shows the UCSD quasi-static test setup

The purpose of the UCSD quasi-static test was to evaluate candidate retrofit designs, which were then tested under blast loading in the field [20] In addition, the objective of the UCSD quasi-static tests was to better understand the failure mechanisms of the CFRP-jacketed column under blast effects and to empirically derive so-called “resistance functions” for the jacketed columns The test results are summarized in Chapter 5 in this dissertation They are adopted in this study to validate the proposed load-displacement model, which is described in Chapter 6

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Figure 1.4: Field Test Setup [20]

Figure 1.5: UCSD Quasi-Static Test Setup [20]

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