i 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 UMI Number: 3211782 3211782 2006 Copyright 2006 by Lee, Chung-Sheng UMI Microform Copyright All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 All rights reserved. by ProQuest Information and Learning Company. ii Copyright Chung-Sheng Lee, 2006 All rights reserved. iv “The fear of the LORD is the beginning of wisdom.” Proverbs, 9:10a v 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 I NTRODUCTION 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 S TUDY 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 ε clim 29 2.3.3 Determination of Parameter C 30 vi 2.3.4 Validity of Modified P&M Model Predictions 33 2.4 P ROPOSED 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 V ALIDATION 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 E XISTING 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 N EW MODEL FOR RECTANGULAR FRP-CONFINED CONCRETE IN AXIAL COMPRESSION 84 3.3.1 Effective Confined Area 84 vii 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 I NTRODUCTION 122 4.2 C ONSTITUTIVE 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 M OMENT-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 4.3.2.2 Cracking Moment, M cr 132 viii 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 L OAD-DISPLACEMENT ANALYSIS OF CFRP-JACKETED RECTANGULAR COLUMN UNDER SINGLE BENDING 167 4.9 SUMMARY AND CONCLUSIONS 173 CHAPTER 5. COMBINED AXIAL AND LATERAL LOAD TESTS OF CFRP JACKETED RC COLUMNS (SIMULATED BLAST LOADS) 174 5.1 I NTRODUCTION 174 5.2 COLUMN SPECIMENS AND FRP JACKETS 176 ix 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 5.6 SUMMARY AND CONCLUSIONS 207 CHAPTER 6. ANALYSIS OF CFRP-CONFINED RC COLUMNS SUBJECT TO COMBINED AXIAL AND LATERAL (SIMULATED BLAST) LOADS 209 6.1 INTRODUCTION 209 6.2 L OAD-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 [...]... 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... model and an associated computational algorithm were developed and validated for the response and failure conditions of RC columns subject to combined axial and seismictype (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. .. Summary of Model Analysis of Rectangular CFRP-Jacketed Columns 259 6.7 SUMMARY AND CONCLUSIONS 260 CHAPTER 7 CONCLUSIONS AND FUTURE WORK 261 x 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. .. bottom Mc Moment at column mid-height Mt Moment at column top Mcr Cracking moment My First-yield moment Mu Ultimate moment P Axial load P0 Initial axial load Pi1 Axial load at first yield state Pi2 Axial load at second yield state Pmax Maximum axial load Pu Ultimate axial load Q Total lateral load Qi1 Total lateral load at first yield state Qi2 Total lateral load at second yield state Qmax Maximum lateral. .. continued guidance and encouragement throughout my research at the University of California, San Diego Special thanks also go to Professor Frieder Seible and Professor Chia-Ming Uang for their assistance and advice I also want to acknowledge Professor David Benson and Professor Vitali Nesterenko for participating in my doctoral committee I am deeply indebted to my parents, my sister and my brother-in-law... 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... Ultimate lateral confining pressure ft Tensile stress of concrete fto Modulus of rupture of concrete fs Stress of steel fsy Yield stress of steel fsu 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 lt Yield penetration length l’t Revised yield penetration length m Mass n Parameter of Popovics’s expression, related to. .. 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 xxx FIELDS OF STUDY Studies in Solid Mechanics Professor Gilbert A Hegemier Professor Vitali Nesterenko Professor Xanthippi Markenscoff Studies in Structural Analysis Professor... 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 cy Neutral axis at My cov Concrete clear cover d Distance from extreme tensile bar to top concrete edge dbl Diameter of longitudinal bar dc() Distance from the center of concrete strip to the top concrete edge dj() Distance from the center of jacket strip to the top concrete... 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 . i 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. Distribution of Hoop Jacket Strains 200 5.6 SUMMARY AND CONCLUSIONS 207 CHAPTER 6. ANALYSIS OF CFRP-CONFINED RC COLUMNS SUBJECT TO COMBINED AXIAL AND LATERAL (SIMULATED BLAST) LOADS 209 6.1. 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