Long term behavior of FRP strengthened RC beams

LONG-TERM BEHAVIOR OF FRP-STRENGTHENED RC BEAMS MITHUN KUMAR SAHA NATIONAL UNIVERSITY OF SINGAPORE 2006 LONG-TERM BEHAVIOR OF FRP-STRENGTHENED RC BEAMS MITHUN KUMAR SAHA B. Sc. Engg. (Civil), BUET A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2006 i Acknowledgements ACKNOWLEDGEMENTS First of all, the author would like to express his sincere gratitude to his supervisor, Associate Professor Tan Kiang Hwee, for his precious guidance, immense patience, constant encouragement and availability of comments whenever approached. Many thanks are expressed to the staff of the Structural/Concrete laboratory for their constructive suggestions and kind assistance in conducting the experimental investigations. Grateful acknowledgement is extended to the National University of Singapore for providing financial support to the author through the award of research scholarship. The author is deeply indebted to his parents for their vital sacrifices and perfect guidance that brought the author to this successful stage of life. The author appreciates all his friends for their constant inspiration throughout this study. Finally, the author would like to dedicate any contribution of this work to his parents. ii TABLE OF CONTENTS Title Page i Acknowledgements ii Table of Contents iii Summary xi List of Tables xiii List of Figures xv Nomenclature xx CHAPTER INTRODUCTION 1.1 General 1.2 Long-Term Effect on Structural Behavior of FRP-Strengthened RC Members 1.2.1 Effect of Sustained Loading 1.2.2 Effect of Cyclic Loading 1.2.3 Effect of Weathering 1.3 Objective and Scope of Study iii 1.4 Research Significance 1.5 Thesis Structure CHAPTER LITERATURE REVIEW 2.1 Introduction 10 2.2 Long-Term Deflections 11 2.2.1 Effect of Concrete Creep and Shrinkage 11 2.2.2 Effect of Concrete Fatigue Damage 18 2.2.3 Effect of Weathering 21 2.3 Long-Term Crack Widths 22 2.3.1 Effect of Concrete Creep and Shrinkage 22 2.3.2 Effect of Concrete Fatigue Damage 24 2.3.3 Effect of Weathering 27 2.4 Residual Structural Behavior 28 2.5 Summary 31 Figures 34 CHAPTER LONG-TERM BEHAVIOR OF FRP-STRENGTHENED RC BEAMS UNDER SUSTAINED LOADING 3.1 General 37 3.2 Experimental Investigation 39 3.2.1 Test Program 39 3.2.2 Material Properties 40 3.2.2.1 Concrete Mix 40 iv 3.2.2.2 Steel Bars 41 3.2.2.3 Glass Fiber Reinforced Polymer System 41 3.2.3 Specimen Fabrication 42 3.2.4 Test Set-up and Instrumentation 43 3.3 Analytical Considerations 3.3.1 Calculation of Deflections 43 44 3.3.1.1 Short-Term Deflection 44 3.3.1.2 Time-Dependent Deflection 46 3.3.2 Estimation of Crack Widths 51 3.3.2.1 Short-Term Crack Width 51 3.3.2.2 Time-Dependent Crack Width 59 3.4 Test Results and Discussion 3.4.1 Deflection Characteristics 59 59 3.4.1.1 Effect of Sustained Loading 59 3.4.1.2 Effect of FRP Reinforcement Ratio 60 3.4.1.3 Comparison with Analytical Predictions 61 3.4.2 Cracking Behavior 63 3.4.2.1 Effect of Sustained Loading 63 3.4.2.2 Effect of FRP Reinforcement Ratio 64 3.4.2.3 Empirical Expressions for Time-Dependent Crack Width 65 3.5 Summary 66 Tables and Figures 68 v CHAPTER EFFECT OF CYCLIC LOADING ON LONG-TERM BEHAVIOR OF FRP-STRENGTHENED RC BEAMS 4.1 General 94 4.2 Experimental Investigation 96 4.2.1 Test Program 96 4.2.2 Material Properties 97 4.2.3 Specimen Fabrication 98 4.2.4 Test Set-up and Instrumentation 99 4.3 Analytical Considerations 4.3.1 Factors Affecting Deflection and Crack Width under Cyclic Loading 100 100 4.3.1.1 Cyclic Creep of Concrete in Compression 100 4.3.1.2 Deterioration in Tensile Stiffening 102 4.3.1.3 Fatigue Damage of FRP Laminate in Tension 102 4.3.2 Calculation of Deflections 103 4.3.3 Estimation of Crack Widths 104 4.4 Test Results and Discussion 4.4.1 Deflection Characteristics 105 106 4.4.1.1 Effect of Load Range 106 4.4.1.2 Effect of FRP Reinforcement Ratio 107 4.4.1.3 Comparison with Analytical Predictions 108 4.4.2 Stiffness Degradation 109 4.4.2.1 Effect of Load Range 109 4.4.2.2 Effect of FRP Reinforcement Ratio 110 4.4.3 Strains in Concrete, Steel Bars and FRP Laminates 110 vi 4.4.4 Cracking Behavior 111 4.4.4.1 Effect of Load Range 111 4.4.4.2 Effect of FRP Reinforcement Ratio 111 4.4.4.3 Comparison with Analytical Predictions 112 4.4.5 Residual Structural Behavior 113 4.4.5.1 Static Flexural Strength 113 4.4.5.2 Failure Mode 115 4.4.5.3 Deflection and Stiffness 116 4.4.5.4 Ductility 118 4.4.5.5 Strains in Concrete, Steel Bars and FRP Laminates 118 4.4.5.6 Crack Width 120 4.5 Summary 121 Tables and Figures 123 CHAPTER EFFECT OF WEATHERING ON LONG-TERM BEHAVIOR OF FRP-STRENGTHENED RC BEAMS UNDER SUSTAINED LOADING 5.1 General 143 5.2 Experimental Investigation 144 5.2.1 Test Program 145 5.2.1.1 Small Specimens 145 5.2.1.2 Large Specimens 146 5.2.2 Material Properties 5.2.2.1 Concrete Mix 147 147 vii 5.2.2.2 Steel Bars 147 5.2.2.3 FRP Laminate 148 5.2.3 Specimen Fabrication 149 5.2.3.1 Beam Description 149 5.2.3.2 Curing of Beams and FRP Installation 149 5.2.4 Simulation of Sustained Loading 150 5.2.4.1 Small Specimens 150 5.2.4.2 Large Specimens 151 5.2.5 Weathering Factors and Simulation 152 5.2.5.1 Weathering Factors 152 5.2.5.2 Simulation of Tropical Weathering 152 5.2.6 Instrumentation of Beams 156 5.2.6.1 Sustained Loading 156 5.2.6.2 Static Loading 156 5.3 Analytical Considerations 5.3.1 Prediction of Deflection 157 157 5.3.1.1 Factors Affecting Deflection 157 5.3.1.2 Calculation of Deflection 160 5.3.2 Estimation of Flexural Strength 162 5.3.2.1 Concrete Properties under Sustained Loading and Tropical Weathering 164 5.3.2.2 Properties of FRP Laminate under Sustained Loading and Tropical Weathering 164 5.3.2.3 Calculation of Flexural Strength 166 viii 5.4 Test Results and Discussion 5.4.1 Serviceability Limit State 168 168 5.4.1.1 Effect of Weathering 168 5.4.1.2 Effect of GFRP Type 169 5.4.1.3 Effect of FRP Reinforcement Ratio 170 5.4.1.4 Comparison of Observed Deflections with Analytical Predictions 170 5.4.2 Ultimate Limit State 171 5.4.2.1 Flexural Strength 172 5.4.2.2 Ductility 174 5.4.2.3 Strains in Concrete, Steel Bars and FRP Laminates 175 5.4.2.4 Crack Widths and Failure Mode 175 5.4.2.5 Comparison of Test Results with Analytical Predictions 176 5.4.2.6 Comparison of Test Results with Beams Subjected to Weathering Only 177 5.5 Summary 178 Tables and Figures 180 CHAPTER CONCLUSIONS 6.1 Review of Work 213 6.2 Summary of Findings 215 6.2.1 Long-term Behavior of FRP-Strengthened RC Beams under Sustained Loading 215 6.2.2 Effect of Cyclic Loading on Long-Term Behavior of FRP-Strengthened RC Beams 216 ix Appendices 1.2 Series I Beams 1.0 95% Confidence Line 0.8 0.6 0.4 Eq. (2.43) 0.2 Test / Prediction TD/ST Crack Width 1.2 Series II Beams 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 2.5 Fiber Content (%) 0.2 0.4 0.6 0.8 1.0 Applied Load/Ultimate Load (a) Non-linear Regression Analysis and Comparison with Test Results 1.0 3678 0.6 370 0.4 230 140 0.0 Eq. (2.44) 2284 0.8 0.2 1.2 Series I Beams Test / Prediction TD/ST Crack Width 1.2 49 Days 0.0 0.5 Series II Beams 1.0 0.8 0.6 0.4 0.2 0.0 1.0 1.5 Fiber Content (%) 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 Applied Load/Ultimate Load (b) Linear Regression Analysis and Comparison with Test Results Fig. A.8 Regression Analysis and Comparison with Test Results for Long-Term Crack Widths 250 Applied Load (kN) Appendices 30 30 25 25 20 20 15 15 AO 10 A-50 Applied Load (kN) B-50 0 10 15 20 25 30 30 25 25 20 20 10 15 20 25 15 15 CO 10 DO 10 C-50 D-50 0 10 15 20 25 10 15 20 Mid-span Deflection (mm) 25 30 Applied Load (kN) BO 10 10 15 20 Mid-Span Deflection (mm) 25 25 20 15 EO 10 E-50 0 Fig. A.9 Comparison of Load-Deflection Characteristics between Original and Aged Beams (Series I) 251 Appendices 30 Load (kN) 25 EO DO CO 20 AO BO 15 10 0 0.1 0.2 0.3 Maximum Crack Width (mm) (a) Beams not Subjected to Sustained Loading 30 C-50 25 Load (kN) E-50 20 B-50 A-50 D-50 0.6 mm@25 kN 15 10 0 0.1 0.2 0.3 Maximum Crack Width (mm) (b) Beams after Ten-Year of Sustained Loading Fig. A.10 Comparison of Load-Maximum Crack Width Relations between Original and Aged Beams (Series I) 252 Appendices 30 Load (kN) 25 20 C-59 C-50 C-35 15 C-65 10 C-80 0 10 15 20 25 Mid span Deflection (mm) (a) Load-Deflection Characteristics 30 Load (kN) 25 C-35 C-50 C-59 C-80 C-65 20 15 10 0 0.1 0.2 0.3 0.4 Maximum Crack Width (mm) (b) Load-Crack Width Relation Fig. A.11 Deflection and Cracking Behavior of Series II Beams when Tested to Failure 253 Appendices APPENDIX Stress-Strain Relations of Concrete, Steel Bars, and Fiber Reinforced Polymer (FRP) Laminates The constitutive relations for concrete, steel bars and fiber reinforced polymer (FRP) laminates are idealized as shown in Fig. B.1. For concrete, the behavior is modeled using Hognestad Stress-Strain curve with the strain corresponding to maximum stress (fc/) is taken as 0.002 and the maximum crushing strain (εcu) is taken as 0.003. The behavior of tensile steel reinforcement bars, on the other hand, is assumed as bi-linear. That is, elastic up to yield load level and then followed by perfectly plastic plateau. The behavior of FRP composite laminate under load is taken as linear elastic until rupture. 254 Appendices Stress, fc Εc = tan α = 4730 f c' ⎡ ⎛ ε f c = f c' ⎢2⎜⎜ ⎢⎣ ⎝ ε co fc’ α ⎞ ⎛ ε ⎟⎟ − ⎜⎜ ⎠ ⎝ ε co ⎞ ⎟⎟ ⎠ ⎤ ⎥ ⎥⎦ Strain, εc εco = 0.002 εcu = 0.003 (a) Hognestad’s Parabolic Concrete Model Stress, fs fy Εs Strain, εs εy (b) Elastic-Perfectly Plastic steel model Stress, ffrp ffrp,u Εfrp εfrp,u Strain, εfrp (c) Linear Elastic FRP model Fig. B.1 Idealized Stress-Strain Relations for Concrete, Steel Bar and FRP Laminate 255 Appendices APPENDIX Design Example on Deflection and Crack Width of FRP-Strengthened RC Beam under Sustained Loading A simply supported concrete beam is to span a length of 5.5 m (Fig. C.1). Based on the allowable span-depth ratio of 16 specified by ACI Building Code (2005) , the minimum beam depth should be 340 mm; however, due to architectural reason the beam depth needs to be kept within 300 mm. The beam width is selected as 250 mm. The beam is reinforced with T25 bars (1470 mm2 in tension) and T20 bars (628 mm2 in compression) (Table C.1). The cover to the reinforcement bars is 40 mm. The ultimate moment capacity of the beam is calculated as 195 kN-m. It is proposed to bond the tension face of the beam (depth = 300 mm) with three layers of FRP laminates (ρfrp = 1.02%) as described in Table C.2 to keep the deflection and crack width after years under sustained loading of 10 kN/m (dead load of 1.8 kN/m and live load of 8.2 kN/m) within allowable limits. The calculations are as follows: 256 Appendices (a) Mid-Span Deflection after Years Procedure Calculation Equation No. Ec = 4730*√35 = 27983 MPa Step 1: Calculate elastic modulus of concrete, depth of neutral axis of uncracked section, gross moment of inertia based on transformed section Step 2: Calculate the depth of neutral axis based on cracked section Step 3: Calculate cracked moment of inertia Step 4: Calculate modulus of rupture, cracking moment, effe-ctive moment of inertia x = (250*300*300/2+37000/27983*250*3.05*300) /(250*300+37000/27983*250*3.05) = 152 mm It = 250*3003/12 + 250*300*(152-150)2 + 200000/27983*(260-152)2 + 37000/27983 *250*3.05*(300-152)2 = 7.39*108 mm4 3.3 x = 109 mm 3.6, 3.7 Icr = 250*1093/3 + 200000/27983*1470* (260109)2 + (200000/27983-1)*628*(109-40)2 + 37000/ 27983*250*3.05*(300-109)2 = 4.03*108 mm4 3.5 fcr = 0.623*√35 = 3.69 MPa Mcr = 3.69*7.39*108/(300-152) = 1.84*107 N-mm Ie = (1.84*107/3.78*107)3*7.39*108 + [1(1.84*107/3.78*107)3]*4.03*108 = 4.41*108 mm4 3.2 Step 5: Calculate instantaneous deflection due to live load (and compare with allowable value) and total load ΔiL = 5*8.2*55004/(384*27983*4.41*108) = 7.91 mm ([...]... modulus of concrete Ee,N = effective cycle-dependent modulus of concrete xx Ef = elastic modulus of fiber reinforcement Efrp = elastic modulus of FRP laminate Efrp,N = elastic modulus of FRP laminate after N cycles of loading Efrp,t = elastic modulus of FRP laminate at time t under sustained loading Efrp,w = elastic modulus of FRP laminate due to sole effect of weathering Efrp,wt = elastic modulus of FRP. .. under different load ranges The residual structural behavior of GFRP -strengthened RC beams after cyclic loading would also be investigated (3) Effect of tropical weathering on long- term deflection, crack width, and residual strength of GFRP -strengthened RC beams under sustained loading Long- term deflection and crack width of RC beams strengthened with GFRP system subjected to outdoor and simulated weathering... Behavior of FRP Laminate (Holmes and Just 1983) Fig 5.9 Effect of Weathering on Long- Term Serviceability Fig 5.10 Effect of GFRP Type on Long- Term Serviceability Fig 5.11 Effect of FRP Reinforcement Ratio on Long- Term Deflection Fig 5.12 Comparison of Observed Deflections with Analytical Predictions Fig 5.13 Degradation in Flexural Strength Fig 5.14 Load-Deflection Behavior of Small RC Beams Strengthened. .. (Unidirectional) GFRP System Fig 5.15 Static Behavior of Large RC Beams Strengthened with GFRP Laminates xvii Fig 5.16 Load-Deflection Behavior of Small RC Beams Strengthened with Type 2 (Bidirectional) GFRP System Fig 5.17 Degradation in Ductility Fig 5.18 Strains at Mid-Span Sections in Small RC Beams Strengthened with Type 1 (Unidirectional) GFRP System Fig 5.19 Strains at Mid-Span Sections in Small RC Beams Strengthened. .. locally because of an economical balance of cost and specific strength properties (ACI Committee 440R 1996) 1.4 Research Significance This research yields valuable results regarding the long- term structural behavior of FRP- strengthened RC beams The investigation on the effect of tropical weathering on FRP- strengthened RC beams is unique as the effect of sustained loading is combined with that of weathering... fiber reinforcement as its primary objective Focus would be placed on the application of externally bonded glass FRP (GFRP) systems in RC beams The scope of this study covers: (1) Experimental and analytical investigation on long- term deflection and crack width of GFRP -strengthened RC beams under sustained loading Long- term deflections and crack widths would be observed and compared among beams strengthened. .. different FRP ratios and subjected to different levels of sustained loading Analytical models would be developed for the calculation of deflection and crack width of strengthened beams under sustained loading (2) Effect of cyclic loading on long- term deflection and crack width of GFRPstrengthened RC beams Experimental and analytical study would be carried out on beams strengthened with different FRP ratios... the cracking of FRP- strengthened RC members under sustained loading Cracks may result due to premature debonding of external FRP systems, thereby reducing the service life of such structures (Teng et al 2002) 5 Chapter 1: Introduction 1.3 Objective and Scope of Study In view of the above discussion, this research is carried out to investigate the long- term structural behavior of RC beams strengthened. .. xii List of Tables Table 3.1 Test Program Table 3.2 Properties of FRP Laminate and its Component used in Current Study Table 3.3 Details of Test Beams Table 3.4 Properties of FRP Systems used in Previous Studies Table 3.5 Expressions for Short -Term Crack Width (in Imperial Units) in FRPStrengthened RC Beams Table 3.6 Expressions for Short -Term Crack Width (in SI Units) in FRPStrengthened RC Beams Table... reinforced concrete (RC) members due to its high strength to weight ratio and the ease of installation compared to other systems However, not much attention has been given to the long- term behavioral aspects of such strengthened members This research was aimed at investigating, both experimentally and analytically, the long- term deflection, cracking and residual structural behavior of RC beams strengthened . Review of Work 213 6.2 Summary of Findings 215 6.2.1 Long-term Behavior of FRP-Strengthened RC Beams under Sustained Loading 215 6.2.2 Effect of Cyclic Loading on Long-Term Behavior of FRP-Strengthened. LONG-TERM BEHAVIOR OF FRP-STRENGTHENED RC BEAMS MITHUN KUMAR SAHA NATIONAL UNIVERSITY OF SINGAPORE 2006 LONG-TERM BEHAVIOR OF. Loading on Long-Term Behavior of FRP-Strengthened RC Beams 216 ix 6.2.3 Effect of Weathering on Long-Term Behavior of FRP-Strengthened RC Beams under Sustained Loading 217 6.3 Recommendations