Parametric study revealed that flexural fatigue performance of CFFT beams could be enhanced by increasing reinforcement index and the effective

Transcription

1 ABSTRACT AHMAD, IFTEKHAR. Shear Response and Bending Fatigue Behavior of Concrete-Filled Fiber Reinforced Polymer Tubes. (Under the direction of Amir Mirmiran.) Recent field applications and research findings have demonstrated the effectiveness of concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) as an efficient and promising hybrid system for designing main components such as pier columns, girders and piles for a bridge system. The vision was to provide a cost-competitive unified system composed of FRP/concrete hybrid members, which may act as a viable alternative to conventional reinforced and prestressed concrete structural systems. To achieve their broad-based implementation in civil infrastructure, understanding of their behavior and developing analytical tools under full spectrum of primary and secondary load demands are essential. Response characterizations under primary load demands namely, axial compression, flexural and axial-flexural, and seismic loadings have already been reported. However, investigations under primary shear and secondary fatigue load demands remain to be addressed. The present study consists of two phases. In the first phase, an experimental and analytical investigation was undertaken to characterize the behavior of a CFFT beam. Study on shear was primarily focused on the deep beam behavior. Comparisons of behavior of deep, short and slender beams were also highlighted. A strut-and-tie model approach, pertinent to analysis of deep reinforced and prestressed concrete members, was proposed to predict the shear strength of deep CFFT beams. Prediction showed good agreement with test results. It was concluded that shear failure mode is only critical for beams with shear span less than their depth. In the second phase, a detailed study on flexural fatigue behavior and modeling was undertaken. The main objective was to evaluate the performance of beams under four basic criteria; i) damage accumulation ii) stiffness degradation, iii) number of cycles to failure, and iv) reserve bending strength. Effects of laminate fiber architecture, reinforcement index, load range, and end restraint on the fatigue response of CFFT beams were addressed. A fiber element was developed, capable of simulating sectional strain profile and moment curvature at any given time or number of cycles under single and two stages of loading. The model can also predict deflections at mid-span, and can analyze the reserve bending response of a fatigued CFFT beam. i

2 Parametric study revealed that flexural fatigue performance of CFFT beams could be enhanced by increasing reinforcement index and the effective elastic modulus in the longitudinal direction.

3 SHEAR RESPONSE AND BENDING FATIGUE BEHAVIOR OF CONCRETE-FILLED FIBER REINFORCED POLYMER TUBES by IFTEKHAR AHMAD A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy CIVIL, CONSTRUCTION AND ENVIRONMENTAL ENGINEERING Raleigh 2004 APPROVED BY: Dr. Sami Rizkalla Dr. James Nau Dr. Eric Klang Dr. Amir Mirmiran Chair

4 BIOGRAPHY Iftekhar Ahmad received his Bachelor of Science in Civil Engineering degree in 1996 from Bangladesh Institute of Technology, Chittagong, Bangladesh and his Master of Engineering degree in Structural Engineering in 2000 from the National University of Singapore. He successfully completed his doctoral degree in 2004 from North Carolina State University (NCSU) at Raleigh in Structural Engineering and Mechanics. His research at NCSU was under the supervision of Dr. Amir Mirmiran, P.E. Prior joining to NCSU as a Ph.D. student, he worked as a structural design engineer in Buro Engineering Pte. Ltd., Singapore. His research interests are primarily in the areas of Fiber Reinforced Polymer (FRP), fatigue, FRP and concrete hybrid system, and ferrocement. Technical Publications: Ahmad, I., and Mirmiran, A., (2004) Fatigue Response of Hybrid FRP-Concrete Bridge Girders, ACI Spring Convention, Session on Research and Progress, March, Washington D.C. Ahmad, I., Shao, Y., and Mirmiran, A., (2004) Low and High Cycle Fatigue Behavior of Concrete-Filled Composite Tubes, 9 th Aerospace Division of International Conference of Earth and Space, Houston, Texas. Mansur, M., Ahmad, I., and Paramasivam, P., (2000) Punching Shear Behavior of Restrained Ferrocement Slabs, ACI Structural Journal, ACI, V. 97, No. 5, pp Mansur, M., Ahmad, I., and Paramasivam, P., (2001) Punching Shear Strength of Simply Supported Ferrocement Slabs, Journal of Materials in Civil Engineering, ASCE, V. 13, No. 6, pp ii

5 ACKNOWLEDGEMENTS I would like to express my sincere appreciation and profound gratitude to my advisor Dr. Amir Mirmiran for his invaluable guidance, endless patience, constant encouragement through thick and thin, and finally for his sincere friendship. Deepest appreciations are due to Dr. Sami Rizkalla, Dr. James Nau, and Dr. Eric Klang for serving on my PhD committee. Also, thanks to all of you for offering wonderful courses in my graduate studies. Thanks are extended to Dr. Amir Fam for providing some of the tubes tested in this project. Many thanks are due to Mr. Jerry Atkinson and Mr. William Dunleavy of Constructed Facilities Laboratory for their assistance on testing the specimens. I do not have the words to express the priceless support of my fellow friend Mr. Zhenyu Zhu. It has been a real honor to have you as a friend in NC State. I am thankful to good friends Mr. Engin Reis, Mr. David Schnerch for their assistance. Finally, this undertaking would never have been completed without the love, support, and patience of my wife Wahida and family. iii

6 TABLE OF CONTENTS List of Tables... vii List of Figures... viii List of Symbols...xv 1 CHAPTER 1 : INTRODUCTION 1.1 Problem Statement Research Objectives Research Approach Thesis Outline CHAPTER 2 : SHEAR REPONSE OF CFFT 2.1 Introduction Literature Review Research Significance Experimental Program Test Results and Discussion General Behavior of Deep CFFT Beams Experimental Indication of Failure Mode Comparison of Slender, Short and Deep Beams Strut-and-tie Model for Deep CFFT Beams Parametric Studies on Shear Criticality Summary and Conclusions...19 iv

7 3 CHAPTER 3 : FLEXURAL FATIGUE : EXPERIMENTAL WORK 3.1 Introduction Literature Review Experimental Program Static Tests Results and Discussion Fatigue Tests Test Observations and Failure Modes Test Results and Discussion Characterization of Material properties of FRP CHAPTER 4 : MODELING OF CONRETE-FILLED FRP TUBES IN FLEXURE 4.1 Introduction Literature Review Static Analysis Constitutive Models Modeling Procedure Model Verifications Fatigue Analysis Constitutive Models Additional Modeling Assumptions Modeling Procedure Model Verifications Parametric Study v

8 5 CHAPER 5 : CONCLUSIONS AND RECOMMENDATIONS 5.1 Summary Conclusions Recommendations for Further Research REFERENCES APPENDIX A : DETAILED SHEAR TEST RESULTS APPENDIX B : DETAILED FATIGUE TEST RESULTS APPENDIX C : FLOW CHART AND SOURCE CODE vi

9 LIST OF TABLES Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 3.1 Table 3.2 Table 3.3 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Mechanical properties of GFRP tubes used in CFFT beam shear tests Test matrix for slender, shot and deep CFFT beams Details of laminate architecture Lamina properties for parametric study Mechanical properties of FRP tubes used in CFFT beam fatigue tests Test results of flexural fatigue Test matrix and results of tension coupon tests Values of creep fatigue model parameters Matrix of parametric study Ply properties of lamina Comparisons of effects of different parameters vii

10 LIST OF FIGURES Figure 2.1(a) Figure 2.1(b) Figure 2.2 Figure 2.3(a) Figure 2.3(b) Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure 2.8 Figure 2.9(a) Figure 2.9(b) Figure 2.9(c) Figure 2.9(d) Figure 2.10(a) Figure 2.10(b) Figure 2.10(c) Figure 2.10(d) Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Schematics of deep beam test setup and instrumentation A view of test setup Typical load-deflection behavior of deep CFFT beam Typical cracking pattern of deep beam with low reinforcement index Cracking pattern of deep beam with high reinforcement index Cracking patterns comparison of short and deep beams with different D o /t j and a/d o ratios Typical load vs. strain rosette response of a deep CFFT beam Effect of a/d o ratio on diagonal tension and flexural strains Comparison of load vs. deflection responses of deep, short and slender CFFT beams Comparison of load-slip responses of deep, short and slender CFFT beams Strut-and-tie model for deep CFFT beam Details of strut-and-tie model Equilibrium of truss model with internal force flow Qualitative shape of major compression strut and C-C-C node Effect of fiber architecture on shear criticality of CFFT beam Effect of a/d o ratio on shear criticality of CFFT beam Effect of D o /t j ratio on shear criticality of CFFT beam Effect of concrete strength ' f c on shear criticality of CFFT beam Details of the test parameters Schematics of static and fatigue test setup and instrumentation of CFFT beams CFFT beam F-5 subjected to four point bending fatigue without lateral restraint CFFT beam F-4 with lateral restraint to guide actuator CFFT beam F-3 with end restraint viii

11 Figure 3.6 Static responses of tube types used in fatigue study Figure 3.7 Typical mid-span profile of CFFT beam in static test Figure 3.8 Fatigue response of beam F-7 under two-stage loading Figure 3.9 Progressive growth of deflection in CFFT beam F-7 Figure 3.10 Evolution of longitudinal strains of CFFT beam for tube type III Figure 3.11 Mid-span longitudinal strain profile of beam F-3 Figure 3.12 Comparison of virgin and reserve strength responses of beam F-7 Figure 3.13 End slippage after 1.7 million cycles Figure 3.14 Tensile rupture in reserve strength test Figure 3.15 Typical responses of tube type I CFFT beams with two different failure modes Figure 3.16 Tensile failure mode in CFFT beam of tube type I Figure 3.17 Shear-compression failure mode of tube type I CFFT beam Figure 3.18 Flexural fatigue response of beam F-6 made with tube type II Figure 3.19 Compression failure mode in CFFT beam of tube type II Figure 3.20 Tensile failure mode in CFFT beam of tube type V Figure 3.21 Response of CFFT beam F-8 made with tube type II Figure 3.22 Effect of reinforcement index in fatigue behavior Figure 3.23 Comparison of slippage comparison of beams F-5, F-6 and F-7 Figure 3.24 Effect of fiber architecture on fatigue behavior Figure 3.25 Effect of load range and minimum load on fatigue behavior Figure 3.26 Comparison of slippage of beams F-1, F-4 and F-5 Figure 3.27 Effect of end boundary conditions on fatigue behavior Figure 3.28 Comparison of slippage for different end conditions Figure 3.29 Comparison of dynamic stiffness degradation of all CFFT beams of tube type I Figure 3.30 Typical tension coupon specimen Figure 3.31 Typical static, creep and fatigue test setup Figure 3.32 Static response and reserve tension response after fatigue of tube type I coupon Figure 3.33 Static tensile response of tube type II coupon ix

12 Figure 3.34 Figure 3.35 Figure 3.36 Figure 3.37 Figure 3.38 Figure 3.39 Figure 3.40 Figure 3.41 Figure 3.42 Figure 3.43 Figure 3.44 Figure 3.45 Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8(a) Figure 4.8(b) Static tensile response of tube type III coupon Static tensile response of tube type V coupon Tensile creep response at 25% and 50% of ultimate strength of tube type I coupon Tensile creep response at 25% of ultimate strength of tube type II coupon Tensile creep response at 25% of ultimate strength of tube type III coupon Modulus reduction rate of tube type I coupon in log-log scale Comparison of experimental and fatigue model stiffness degradations of tube type I Modulus reduction rate of tube type II coupon in log-log scale Comparison of experimental and fatigue model stiffness degradations of tube type II Modulus reduction rate of tube type III coupon in log-log scale Comparison of experimental and fatigue model stiffness degradations of tube type III Comparisons of stiffness degradations of three different tubes Constitutive models for static analysis of CFFT section Discretization of CFFT section and its strain and stress profiles Comparison of static analysis with experiments Linear viscoelastic surface expressing the stress-strain relationship over time Summary of generalized fatigue analysis Linear elastic stress-strain relationship for residual response after single stage loading Linear elastic stress-strain relationship for residual response after two stages of loading Comparison of curvature response with model for beam F-7 in two stages of fatigue Comparison of deflection response with model for beam F-7 in two stages of fatigue x

13 Figure 4.9 Comparison of top and bottom strain for beam F-7 in two stages of fatigue loading Figure 4.10 Comparison of reserve bending response for beam F-7 after two stages of loading Figure 4.11(a) Effect of fiber architecture on deflection evolution Figure 4.11(b) Effect of fiber architecture on reserve strength Figure 4.12 Effect of reinforcement ratio D o /t j on deflection evolution Figure 4.13 Effect of load range on deflection evolution Figure 4.14 Effect of beam geometry L/D o on deflection evolution Figure A.1 Load vs. deflection response of deep CFFT beam S-1 Figure A.2 Load vs. strain rosette response of beam S-1 Figure A.3 Comparison of flexural strain and diagonal tensile strain of beam S-1 Figure A.4 Load vs. relative end slip responses of beam S-1 Figure A.5 Load vs. deflection response of deep beam S-2 Figure A.6 Load vs. strain rosette response of beam S-2 Figure A.7 Comparison of flexural strain and diagonal tensile strain of beam S-2 Figure A.8 Load vs. relative end slip responses of beam S-2 Figure A.9 Load vs. deflection response of short CFFT beam S-4 Figure A.10 Load vs. strain rosette response of beam S-4 Figure A.11 Comparison of flexural strain and diagonal tensile strain of beam S-4 Figure A.12 Load vs. relative end slip responses of beam S-4 Figure A.13 Load vs. deflection response of deep CFFT beam S-5 Figure A.14 Load vs. strain rosette response of beam S-5 Figure A.15 Comparison of flexural strain and diagonal tensile strain of beam S-5 Figure A.16 Load vs. relative end slip responses of beam S-5 Figure A.17 Load vs. deflection response of deep CFFT beam S-7 Figure A.18 Load vs. strain rosette response of beam S-7 Figure A.19 Comparison of flexural strain and diagonal tensile strain of beam S-7 Figure A.20 Load vs. relative end slip responses of beam S-7 Figure A.21 Load vs. deflection response of deep CFFT beam S-9 Figure A.22 Load vs. strain rosette response of beam S-9 xi

14 Figure A.23 Comparison of flexural strain and diagonal tensile strain of beam S-9 Figure A.24 Load vs. relative end slip responses of beam S-9 Figure B.1 Virgin static response of beam F-1 before applying Stage 1 fatigue Figure B.2 Static response after one million cycles at Stage 1 fatigue (F-1) Figure B.3 Comparison of static stiffness degradations at Stage 1 fatigue (F-1) Figure B.4 Static response at the beginning of Stage 2 fatigue (F-1) Figure B.5 Fatigue response of beam F-1 under two-stage loading Figure B.6 Progressive growth of deflections (F-1) Figure B.7 Evolution of longitudinal strains (F-1) Figure B.8 Strain distribution across the depth (F-1) Figure B.9 Movement of neutral axis (F-1) Figure B.10 Evolution of hoop strains (F-1) Figure B.11 Relative slips between concrete and FRP (F-1) Figure B.12 Rotations at support points (F-1) Figure B.13 Virgin static response of beam F-3 before applying Stage 1 fatigue Figure B.14 Static response after one million cycles before applying Stage 2 fatigue Figure B.15 Reserve bending response (F-3) Figure B.16 Comparison of static stiffness degradations (F-3) Figure B.17 Fatigue response of beam F-3 under two-stage loading Figure B.18 Progressive growth of deflections (F-3) Figure B.19 Evolution of longitudinal strains (F-3) Figure B.20 Strain distribution across the depth (F-3) Figure B.21 Movement of neutral axis (F-3) Figure B.22 Evolution of hoop strains (F-3) Figure B.23 Relative slips between concrete and FRP (F-3) Figure B.24 Rotations at support points (F-3) Figure B.25 Virgin static response of beam F-4 before applying single-stage fatigue Figure B.26 Fatigue response of beam F-4 under single-stage loading Figure B.27 Progressive growth of deflections (F-4) Figure B.28 Evolution of longitudinal strains (F-4) Figure B.29 Strain distribution across the depth (F-4) xii

15 Figure B.30 Figure B.31 Figure B.32 Figure B.33 Figure B.34 Figure B.35 Figure B.36 Figure B.37 Figure B.38 Figure B.39 Figure B.40 Figure B.41 Figure B.42 Figure B.43 Figure B.44 Figure B.45 Figure B.46 Figure B.47 Figure B.48 Figure B.49 Figure B.50 Figure B.51 Figure B.52 Figure B.53 Figure B.54 Figure B.55 Figure B.56 Figure B.57 Figure B.58 Figure B.59 Figure B.60 Movement of neutral axis (F-4) Evolution of hoop strains (F-4) Relative slips between concrete and FRP (F-4) Rotations at support points (F-4) Fatigue response of beam F-5 under single-stage loading Progressive growth of deflections (F-5) Evolution of longitudinal strains (F-5) Strain distribution across the depth (F-5) Movement of neutral axis (F-5) Evolution of hoop strains (F-5) Evolution of confining strains (F-5) Relative slips between concrete and FRP (F-5) Rotations at support points (F-5) Virgin static response of beam F-6 before applying Stage 1 fatigue Static response after one million cycles at Stage 1 fatigue Comparison of static stiffness degradations at Stage 1 fatigue Fatigue response of beam F-6 under two-stage loading Progressive growth of deflections (F-6) Evolution of longitudinal strains (F-6) Strain distribution across the depth (F-6) Movement of neutral axis (F-6) Evolution of hoop strains (F-6) Relative slips between concrete and FRP (F-6) Rotations at support points (F-6) Comparison of static stiffness degradations (F-7) Fatigue response of beam F-7 under two-stage loading Progressive growth of deflections (F-7) Evolution of longitudinal strains based on linear pot measurement (F-7) Evolution of longitudinal strains based on strain gage measurement (F-7) Strain distribution across depth based on linear pot measurement (F-7) Strain distribution across depth based on strain gage measurement (F-7) xiii

16 Figure B.61 Figure B.62 Figure B.63 Figure B.64 Figure B.65 Figure B.66 Figure B.67 Figure B.68 Figure B.69 Figure B.70 Figure B.71 Figure B.72 Figure C.1 Comparison of neutral axes movements for linear pot and strain gage measurements Evolution of hoop strains (F-7) Relative slips between concrete and FRP (F-7) Rotations at support points (F-7) Static response of beam F-8S to failure Fatigue response of beam F-8 under three-stage loading Progressive growth of deflections (F-8) Evolution of longitudinal strains (F-8) Strain distribution across the depth (F-8) Movement of neutral axis (F-8) Comparison of deflection response with model for beam F-3 in singlestage fatigue Comparison of deflection response with model for beam F-6 in singlestage fatigue Flow chart of fatigue analysis program of a CFFT beam xiv

17 LIST OF SYMBOLS A = Material constant of FRP fatigue model A a = Actual delamination area in FRP A g = Gross area of concrete section A o = Total area of delamination a = Shear span C h = Horizontal component of compressive strut force in concrete C fh = Induced horizontal compressive force in FRP tube c = Depth of neutral axis from the top of concrete core cc = Factor used in concrete fatigue model c c = Material constant of FRP cc 2 = Degradation ratio of concrete cf = Factor used in FRP fatigue model cf 2 = Degradation ratio of FRP D = Fatigue damage at any given time or cycle instant D f = Damage state at failure D i = Inside diameter of FRP tube D if = Initial damage state before applying fatigue load D o = Outer diameter of FRP tube d = Depth of a layer from top of concrete core E = Secant modulus at any given time or number of cycles E c = Modulus of elasticity of concrete in tension E fc = Short-term compressive modulus of FRP laminate E ft = Short-term tensile modulus of FRP laminate E j = Modulus of elasticity of FRP tube in hoop direction E 1 = Elastic modulus of lamina in the principal direction; Elastic modulus of stressstrain curve at the end of Stage 1 E 1c = Initial elastic secant modulus of concrete E 2 = Elastic modulus of lamina in transverse direction; Elastic modulus of stress-strain curve at the end of Stage 2 E 2c = Second slope of confined concrete model E * = Modulus of completely delaminated composite E o = Uncracked elastic modulus of FRP F fu = Failure force of FRP tube perpendicular to failure plane in shear F 1c = Longitudinal compressive strength of a lamina xv

18 F 1t = Longitudinal tensile strength of a lamina F 2c = Transverse compressive strength of a lamina F 2t = Transverse compressive strength of a lamina F 6 = Shear strength of a lamina f = Frequency of fatigue loading f c = Axial stress in concrete f ce = Effective compressive strength of concrete f cr = Modulus of rupture of concrete f fc = Short-term compressive ultimate strength of FRP laminate f ft = Short-term tensile ultimate strength of FRP laminate f fu = Failure strength of FRP tube perpendicular to failure plane in shear f j = FRP tube strength in axial or in hoop direction f jh = FRP tube strength in hoop direction f o = Plastic stress in concrete model f max = Maximum applied stress 1 f max = Maximum applied load during Stage 1 fatigue loading 2 f max = Maximum applied load during Stage 2 fatigue loading f min = Minimum applied stress f r = Confining pressure f res = Arbitrary stress level at reserve stress-strain response ' f c = Unconfined concrete strength ' f cu = Confined concrete strength f α = Ultimate tensile strength of ply at winding angle α f(t) = Stress at any given time t f 1 (τ) = Function expresses nonlinear shear strain of FRP f 2 (τ) = Function expresses stiffness reduction due to applied number of cycles G F = Fiber shear modulus G M = Matrix shear modulus G s = Shear modulus at any given time or number of cycles o G s = Initial shear modulus G 12 = Shear modulus of a lamina g(d) = Damage function i = i th layer of CFFT cross section; i th level of stress in stress-strain diagram L = Span length L p = Complimentary probability xvi

19 l g = Gage length of coupon l d = Width of bearing plate under load and support point l dl = Effective length of bearing plate k 1 = Coefficient of confinement effectiveness M = Mid-span moment M app = Maximum applied moment M rest = Resistant moment at any given time t M static = Static moment capacity m = Creep model constant of FRP N = Number of cycles N f = Number of cycles at failure N s = Number of compressive struts N 1 = Number of fatigue cycles at the end of Stage 1 N 2 = Number of fatigue cycles applied in Stage 2 n c = Constant representing gradient of creep curve n f = Material constant of FRP fatigue model n s = Curve shape parameter of concrete model n w = Number of winding angles P = Probability of failure P cr = Total cracking load P u = Total load to fail in flexure or in shear P max = Total maximum applied load P min = Total minimum applied load P static = Ultimate total static load P reserve = Total load at failure for reserve bending response P uflexure = Total load at failure in flexure P ushear = Total load at failure in shear R = Ratio between minimum and maximum applied load; Stress ratio S = Arbitrary maximum stress level S c = Characteristic stress level S max = Ratio between maximum stress applied and static confined strength S min = Ratio between minimum stress applied and static confined strength avg S max = Ratio between average maximum stress applied and static strength T f = Tie force T o = Entire duration of cyclic loading V c = Concrete contribution to shear xvii

20 V j = FRP tube contribution to shear V n = Shear capacity of RC or CFFT beams t = Time t j = Thickness of FRP tube t 1 = Duration of applied fatigue loading in Stage 1; time instant in creep curve t 2 = Duration of applied fatigue loading in Stage 2; time instant in creep curve u = Relative slip between concrete and FRP V f = Fiber volume fraction f = Differential change in stress t = Differential time increment top ε res = Differential increment in residual strain at top of concrete core δ = Mid-span deflection of beam δ static = Deflection of CFFT beam at failure during static response ε c = Axial strain in concrete ε fc = Short-term compressive strain of FRP laminate at failure ε ft = Short-term tensile strain of FRP laminate at failure f ε o = Stress-dependent and time-dependent elastic strain of FRP 1 ε o = Short-term static strain at the end of Stage 1 fatigue loading 2 ε o = Short-term static strain at the end of Stage 2 fatigue loading ε cr = Creep strain in concrete f ε cr = Time-dependent viscous strain of FRP t ε cr = Tensile cracking strain of concrete 1 ε cr = Creep strain at the end of stage 1 fatigue loading 2 ε cr = Total creep strain at the end of Stage 2 top ε cr = Creep strain at top of concrete core ε cu = Ultimate strain of confined concrete ε e = Combined short term and fatigue strain in concrete ε eff = Effective short-term response in post fatigue analysis top ε fat = Fatigue strain at top of concrete core 1 ε fat = Fatigue strain at the end of Stage 1 fatigue loading 2 ε fat = Fatigue strain due to Stage 2 fatigue loading xviii

21 ε o = Maximum total strain in first load cycle or short-term static strain top ε o = Short-term initial strain at top of concrete core ε res = Actual total residual strain 2 ε res = Actual residual strain at the end of Stage 2 top ε res = Reference total residual strain at the top of concrete core ε bottom = Strain at the centroid of bottom FRP layer in static analysis ε top = Strain at top of concrete core during static analysis ε total = Total strain in concrete; total strain in any layer of CFFT cross section top ε total = Reference total strain at the top of concrete core α = Winding angle; A factor used with D o to represent lever arm β = Material constant for fatigue of concrete γ = A factor accounts for reduced shear mechanism δ = Deflection θ = Failure plane of FRP with respect to longitudinal axis θ i = Angle of i th ply with respect to crack angle 45 o ω = Reinforcement index φ = Stiffness reduction factor for FRP ψ = Curvature of the CFFT section at any given time t ν 1 = Efficiency factor ν 2 = Efficiency factor ν 12 = Major Poisson s ratio of a FRP lamina xix

22 Chapter 1 Introduction CHAPTER 1 INTRODUCTION 1.1 PROBLEM STATEMENT Use of fiber reinforced polymer (FRP) composites has recently gained wide acceptance as an economical technique for strengthening and rehabilitation of existing concrete structures. Thriving incorporation of FRP in retrofit measures has led to the development of an innovative hybrid construction concept (Mirmiran and Shahawy 1995) that utilizes FRP tube and concrete as its two basic materials for member design. Basic role of FRP tube in this system is to replace steel, while concrete serves the same purpose as that in conventional reinforced concrete (RC) structures. In addition, FRP tube renders itself as permanent formwork, protective jacket, confinement, and shear and flexural reinforcement, whereas concrete provide the compressive strength as well as stability to the tube against its lateral buckling. The composite system thus formed is commonly referred to as concrete-filled FRP tubes (CFFT), and is found a viable alternative to reinforced or prestressed concrete for use as columns, piles and beams (Karbhari et al. 2000, Mirmiran et al. 2000, 2003a, 2003b). A recent survey on highway bridges indicates that there over 583,000 bridges in the United States, 200,000 are steel, 235,000 are conventional RC, and some 108,000 are constructed using prestressed concrete. Nearly 15% of the bridges are structurally deficient, primarily due to corrosion of steel or steel reinforcement. Direct annual of cost of corrosion repair for highway bridges is estimated as $8.93 billion dollars consisting of $2.93 billion dollars for maintenance of superstructure alone (Koch et al. 2001). The key problems identified for bridge deterioration include the exposure of steel to aggressive environments and permeability of concrete that causes steel rebar to corrode. In addition, a substantial number of bridges are in need of replacement as they have exceeded their design life. One potential solution to mitigate the corrosion problem in the new bridges is to utilize the concept of CFFTs. To demonstrate the effectiveness of the 1

23 Chapter 1 Introduction system, CALTRANS (California Department of Transportation) recently (Seible et al. 1999) designed and built Kings Storm Water Channel Bridge in Riverside County, CA. Concrete-filled carbon tubes were used in superstructure as bridge girders. Performance of this application has broadened the scope of CFFT, especially to bridge girders, and has proved the feasibility of this innovative concept. A follow-up project on I-5 Gilman Bridge across the University of California, San Diego campus in La Jolla, CA, is being designed with CFFT as primary structural members for girders and pylons (Seible et al. 1999, Zhao et al. 2000). In the last decade, considerable amount of research effort has been directed towards characterizing the CFFT system under axial compression (Samaan et al. 1998, Harmon et al. 1998, Fam and Rizkalla 2001), flexural and axial-flexural loading (Mirmiran et al. 2000, Davol et al. 2001, Fam and Rizkalla 2002), simulated seismic loading (Seible et al. 1996, Shao and Mirmiran 2004) as well as long-term sustained loading (Naguib and Mirmiran 2001 and 2002). Superior performances, comparable to reinforced and prestressed concrete, have been documented under static and pseudo-static loading. Significant amount of modeling work has also been carried out to better understand the behavior of the CFFT system, and subsequently establish necessary design guidelines for practical implementation. However, previous studies indicate that response under short-term static shear loading and long-term dynamic fatigue loading have received little or no attention. It is obvious that in real applications, such as those stated earlier, the CFFT system will be subjected to shear and fatigue loading in addition to other loads due to self-weight and transient heavy traffic. Therefore, it is recognized that the increasing use of CFFT system in bridge construction will depend fully on the development of proper analytical tools capable of addressing responses under all primary and secondary types of load demands. Hence, a thorough understanding of the shear behavior and bending fatigue response of CFFT is warranted. 1.2 RESEARCH OBJECTIVES This present study is aimed at providing basic technical information on shear behavior and bending fatigue response of CFFT beams at the member level. The research is divided into two components, depending on the type of load demand studied. A number of research objectives are identified and systematically listed below in the two stated areas for the proposed experimental and analytical development. 2

24 Chapter 1 Introduction Shear of CFFT Observe failure modes and evaluate the behavior and performance of CFFT beams under shear loading, and in particular assess the effect of the following parameters: o Laminate architecture; o Reinforcement index of the tube, i.e., over-and under-reinforced section; and o Shear-span-to-depth a/d o ratio, where a is the shear span and D o is the outside diameter of the tube. Develop an analytical model to predict the shear strength of deep CFFT beam Employ the analytical model to predict the critical a/d o ratio, below which shear becomes the governing mode of failure for CFFT system. Flexural Fatigue of CFFT Observe failure modes and evaluate the behavior and performance of CFFT beams under fatigue loading, and in particular assess the effect of the following parameters: o Laminate architecture; o Reinforcement index and stiffness of the tube; o Load range; o Damage accumulation and stiffness degradation through single and two stages of loading; and o End restraints. Develop and validate an analytical tool for predicting the fatigue behavior of CFFT beams under single and two stages of loading. Extend the model to predict reserve bending response after removal of fatigue loading; Utilize the analytical tool to study the fatigue behavior of CFFT under the different influencing factors, particularly the fiber reinforcement and load range; and Recommend a safe load level for design, below which fatigue will not be a critical factor in design of CFFT systems. 3

25 Chapter 1 Introduction 1.3 RESEARCH APPROACH A detailed work plan was developed to attain the above mentioned objectives in a sequential manner. As usual for relatively new undertakings, plan comprises of experimental observations followed by analytical development. The experimental and analytical modeling phases of this project consist of the following components: 1. Tests performed in the earlier research on flexure of CFFT beams with varying a/d o ratios are evaluated, and a new test program for shear was devised as a part of the continuing research on the CFFT system. Similar tubes are used to extend the range of findings from large a/d o ratios to the lowest practical limit of about 1, or in other sense, from slender beams to very short and deep beams. An optimized number of beams were selected for testing to identify shear criticality, or lack thereof, of CFFT beams. 2. Pure bending fatigue tests were conducted on CFFT beams under four point bending, using different tube properties and laminate architecture to compare their performances under repeated loading up to a predetermined and practical number of cycles. Constant amplitude fatigue with loading and unloading cycles was applied to simulate fatigue condition. Subsequently, if the specimen withstood the first stage of loading, tests continued to stages of fatigue loading to replicate the simplest form of variable amplitude loading, which is typical in actual structures. Similar tubes as those used in shear test program were used for fatigue testing. 3. Flexural response of CFFT beams was evaluated based on four basic criteria, namely, i) damage accumulation, ii) stiffness degradation, iii) number of cycles to failure, and iv) reserve bending strength. Effect of laminate fiber architecture, reinforcement index, load range, and end restraint on the behavior and performance of CFFT beam were addressed. 4. The analytical modeling of shear was mainly focused on extending the state-of-the-art on deep reinforced concrete beams. Strut-and-tie model was developed to predict the shear strength of deep CFFT beams. A parametric study was carried out to identify the critical a/d o ratio. Also effect of fiber architecture, D o /t ratio, and concrete strength were highlighted. 4

26 Chapter 1 Introduction 5. An elaborate fiber section model was developed to trace the fatigue response of CFFT beams using available short-term and long-term material models of concrete and FRP. The model is capable of simulating strain distribution at cross section and moment curvature at any given time or number of cycle under single and two stages of loading. The model also generates deflection at mid-span and predicts the reserve bending response of a fatigued CFFT beam. A parametric study was carried out to better understand the effect of different factors affecting the fatigue behavior. 1.4 THESIS OUTLINE This dissertation proposal consists of five chapters and three appendices. Chapter 1, this chapter, focuses on providing problem statement for the research, and identifying the research objectives and research approach. Chapter 2 summarizes the shear test results and presents the shear strength model of CFFT. Chapter 3 presents the previous experimental work on fatigue at both material and structural levels, and summarizes the present tests on flexural fatigue of CFFT, as well as creep and fatigue property characterization of FRP. Chapter 4 reports on the available analytical work in the literature for modeling concrete and FRP fatigue response. Thereafter, it focuses on the analytical model development for flexural fatigue, followed by model verification and parametric study. Chapter 5 summarizes the research undertaken in this study, and provides concluding remarks in addition to recommendations for future research. It is important to note that Chapters 2-4 are prepared to serve as standalone and concise papers on their respective topics. Therefore, additional test data on shear response and flexural fatigue of CFFT are provided in Appendix A and B, respectively. Appendix C describes the flow chart and the source code of the program developed for flexural fatigue. 5

27 Chapter 2 Shear Response of CFFT CHAPTER 2 SHEAR RESPONSE OF CFFT 2.1 INTRODUCTION An analytical and experimental study was undertaken to investigate the behavior of slender, short and deep beams made of concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) under three and four point transverse loading. A total of ten beams were tested to study the effect of fiber architecture, shear-span-to-depth ratio, reinforcement index, and diameter-to-thickness ratio of the tube. Four different tube types were used to fabricate the beams. Test results suggest that flexure governs the overall failure mode of all beams tested even for shear spans as short as the depth of the beam irrespective of the fiber architecture of the tube. Current method of shear analysis of CFFT beams relies on Bernoulli beam theory, which utilizes the basic assumption of linear strain distribution across the depth. In case of deep beams, strain distribution may be nonlinear and the load transfer mechanism could also be significantly different from traditional beam theory. Hence, the well-known strut-tie-model approach is formulated to predict the shear strength of deep CFFT beams. The model was compared with test results. A summary of the state-of-the art on flexural and shear of CFFT is presented in the next section. 2.2 LITERATURE REVIEW Over the last decade, three major studies have dealt with flexural behavior of CFFT beams. Tests by Mirmiran et al. (2000) involved beams with shear-span-to-depth (a/d o ) ratios of about 2, with two different reinforcement ratios ρ of 7.2% and 43.2%, characterized as under- and over-reinforced beams, respectively. The beams were made of off-the-shelf FRP tubes with no direct means of shear transfer. Under-reinforced beams consisted of asymmetric ±55 o glass fiber angle plies, while the over-reinforced beams comprised of symmetric glass fiber plies with 0 o and ±45 o orientations, where all angles are measured with respect to the axis of the tube. As 6

28 Chapter 2 Shear Response of CFFT expected, over-reinforced beams failed in compression while under-reinforced beams failed by tensile rupture of the tube. Davol et al. (2001) tested four carbon CFFT beams with a/d o ratios of 4.7 and 7.7. The shorter beams had two different reinforcement ratio of 6% and 12%, while the longer beams had a reinforcement ratio of 10%. The tube had longitudinal and hoop fibers, e.g., 0 o and 90 o, respectively. All beams failed in flexure, as designed, and by compression. Fam (2000) and Fam and Rizkalla (2002) tested twenty glass CFFT beams with a/d o ratios ranging between 2.67 and 7.4, reinforcement ratios from 3.8% to 12.3%, and a wide range of fiber architecture. All beams failed in flexure, except for one with 0 o degree fibers, which failed by splitting due to horizontal shear. Mirmiran et al. (1998) initiated the pilot monotonic shear test of CFFT. Rectangular cross sections filled with concrete were tested at a constant shear-span-to-depth a/d o ratio of Tubes were fabricated with or without shear connectors to examine the effect of mechanical bond on the shear transfer between the tube and concrete. The FRP tubes consisted of seven angle-plies of polyester resin with unidirectional E-glass fibers wound at ±75 o. Some of the specimens had internal steel reinforcement to increase their flexural capacity, making them more susceptible to shear failure. However, flexural failure mode was precipitated regardless of the interfacial bond and the reinforcement ratio. An analytical truss model was presented to estimate the ultimate shear strength of CFFT as uncoupled sum of the contributions of concrete and FRP tube. The shear strength equation of the jacket was derived based on netting analysis that relates tube properties with the shear failure plane. Sieble et al. (2000) proposed a similar approach for monotonic shear strength taking into account different fiber orientations. No experimental verification was reported at that time. Davol et al. (2001) proposed an approach based on beam theory to estimate shear strain response throughout the loading history. Their approach neglected the contribution of concrete core in flexural tension and flexure/shear interaction with the tube. On the basis of load transfer mechanism and mode of failure, reinforced concrete (RC) beams have been classified into four groups (ASCE-ACI Task Committee 1973), as deep (a/d o 1); short (1< a/d o 2.5); slender (2.5 < a/d o 6); and very slender (6 < a/d o ). Generally speaking, very slender beams fail in flexure, while slender beams without any stirrups experience diagonal tension failure. Short beams without any stirrups fail in either shear-tension or shearcompression, before their flexural capacity is reached. On the other hand, in deep beams without web reinforcement, load transfer is made by tied-arch action. Beam develops inclined cracks 7

29 Chapter 2 Shear Response of CFFT joining the load and the support. The most common mode of failure in such a beam is an anchorage failure at the ends of tension tie combined with dowel splitting. Other modes of failure are crushing at the support, crushing along the inclined crack, and tensile failure of the arch-rib. It seems natural to classify the CFFT beams in a similar manner. On the other hand, based on test data of recent studies (Mirmiran et al. 2000), even for the shortest CFFT beam with an a/d o ratio of 1.93, failure was governed by flexure. Therefore, it is important to determine the criticality of shear in CFFT beams without any internal shear reinforcement, and to further extend the experimental database to what is considered a deep CFFT beam. 2.3 RESEARCH SIGNIFICANCE The present study evaluates typical behavior and failure mode of deep CFFT beams, and compares them with their short and slender counterparts. It also examines the criticality of shear failure across the full spectrum of the shear-span-to-depth ratios and for different reinforcement indices, fiber architecture, and diameter-to-thickness ratios of the tube. The significance of the research lies not only on extending the experimental database for CFFT beams to the lowest practical range of application, but also on the fundamental question as to whether or not a CFFT beam is at all shear-critical, based on traditional classifications of RC beams. 2.4 EXPERIMENTAL PROGRAM This project is a culmination of three major studies of the last decade on CFFT beams. Using a total of four glass FRP tubes, the test program presented here augments previous test data (Mirmiran et al. 2000, Fam 2000, and Fam and Rizkalla 2002) with additional experiments on the same type of tubes to help assess the behavior of CFFT beams over a wide spectrum of a/d o ratios, elastic modulus E, reinforcement index ω, fiber architecture, and D o /t j ratio. The reinforcement index is defined as the reinforcement ratio of the FRP tube multiplied by the ratio of the tensile strength of the FRP tube in the longitudinal direction to the unconfined compressive strength of concrete core. Table 2.1 shows the details of tube properties used in the test program. Tubes I and IV have the lowest and highest tensile modulus, respectively, whereas tube II has the highest tensile strength. Table 2.2 shows the details of the beam specimens in the test program, using tube types I- IV. Three and four point bending tests were conducted to monitor the behavior of the beams. 8

30 Chapter 2 Shear Response of CFFT Mirmiran et al. (2000) conducted flexure tests on short beams using tubes of type I and II, as illustrated in Table 2.2. CFFT beams S-4 and S-6 tested using tubes of type I and II had an a/d o ratio of 1.93 and 2.04, respectively. Fam (2000) investigated flexural behavior of slender CFFT beams, namely S-8 and S-10 with tubes of type III and IV, a/d o ratios in excess of 6. In fact, the deep beam S-7 was cut from those beams cast earlier by Fam (2000). Irrespective of the tube types and a/d o ratios, all beams tested previously had failed in flexure, even at the lowest a/d o ratio of Hence, the a/d o ratio of 1 was selected in this test program as the lowest practical limit to identify the shear criticality and failure modes of the beams made using tubes of types I- IV. In addition to beam S-7, five CFFT beams were cast for this test program. Specimens were air cured for at least 28 days in the laboratory prior to testing. Table 2.2 shows the compressive strengths of companion 4 in 8 in cylinders tested at the same day as their respective beam. An overview of the typical shear test setup and instrumentation are shown in Figure 2.1. The beams were simply supported on conventional hinge-roller system. Strain rosettes were created by placing three electrical strain gages at mid-height of the beam in the center of the shear span. Each beam was further instrumented with a linear potentiometer (pot) to measure mid-span deflection. Relative slippage between concrete and the tube was measured by placing linear pots at each end on top and bottom. Tests were carried out using a 440-kip closed-loop MTS actuator at a constant displacement rate of in/min. A high-speed Optim megadac data acquisition system was used to record the data. 2.5 TEST RESULTS AND DISCUSSION General Behavior of Deep CFFT Beams Figure 2.2 shows the typical load-deflection (total load) response for a CFFT deep beam (S-1). The load-deflection response is linear, until flexural cracking is experienced by the specimen. This is often characterized by an audible noise, a noticeable reduction in the beam stiffness, and the initiation of relative slippage between the FRP tube and the concrete core. After cracking, the response becomes non-linear. The degree of non-linearity depends on the fiber architecture of the tube and the material properties of the matrix. Beams fabricated with angle ply laminates where majority of fibers oriented off-axis more prone to exhibit non-linear behavior. Stresses produced by off-axis tensile loading below neutral axis at the mid-span induce 9

31 Chapter 2 Shear Response of CFFT transverse tension and shear in the material s principal direction of lamina and trigger lamina shear, which is non-linear in nature. Beams S-1, S-2, and S-4, all from tube type I, and S-9, from tube type IV, exhibited quite a non-linear response after flexural cracking of concrete. On the other hand, beams S-5 and S-8, of tube types II and III, respectively, showed nearly linear elastic behavior. Beam S-5 showed a tri-linear response in its overall load-deflection history. This may be attributed to the lack of shear resistance at the weak interface between the inside resin layer and the structural laminate of the tube. The same pattern was noted in the tension coupons of this tube. Nonetheless, 50% of the total fibers in this tube are along the loading axis that generated piecewise linear elastic behavior of beam S-8. Figure 2.2 shows separation between concrete and the tube at the support at about 25% of the ultimate capacity. The separation continued to grow and propagate towards the compression side of the section. Figure 2.2 also shows bulging out of the tube at 80% of the capacity, a characteristic of thick tubes with high D o /t j ratios. For example, beam S-5 with its lower D o /t j ratio did not show this phenomenon, even with the apparent separation between the tube and the core. Another interesting feature was the contraction or necking of the specimen at the bottom of the section at mid-span for beams fabricated with tube type I. This phenomenon, which occurred close to failure was attributed to the Poisson s effect in the FRP tube. All deep CFFT beams were tested to failure, except for S-5, which was loaded up to only 60% of its predicted capacity due to the limitation of the testing frame. Beams S-1, S-2, S-4, S-8 and S-10 all failed by tube rupture in the extreme tension fiber, which is a typical flexural failure rather than a shear failure. Figure 2.2 shows the failure mode of beam S-1. Crack patterns of the concrete core were examined by removing the tube after failure. Figure 2.3 shows a comparison of crack patterns for beams with low and high reinforcement indices. Beams S-1, S-2, S-4, S-8 and S-10 had low reinforcement index ranging from 0.11 to 0.53, whereas beam S-5 had the highest reinforcement index of In general, two major flexural cracks were formed under the load point in beams with low reinforcement index (Figure 2.3a). These cracks did not extend beyond the loading area. On the other hand, beams with high reinforcement index showed web-shear and flexure-shear cracks as well, while flexural cracks were seemingly wider and more dominant (Figure 2.3b). Observation of web-shear crack indicates the formation of compression strut that allows direct shear transfer to the support. Matrix cracks along the compressive stress trajectories were also seen in the inside of the tube in 10

32 Chapter 2 Shear Response of CFFT beam S-5. Figure 2.4 shows crack patterns of beam S-1 and S-2 with D o /t j ratios of 63.4 and 49.5, respectively. Well distributed flexural cracks were observed with lower D o /t j ratios, signifying greater tendency of flexural failure. Lateral contraction or necking, which is quite visible for beam S-1, is due to the combined effect of large longitudinal strains with localized flexural cracks. Comparing beams S-2 and S-4 with a/d o of 1 and 1.89, respectively, reveals that flexural cracks are distributed well along the entire span in short beams, while remain localized under the load point in deep beams. Observing the cracking and sequence of events leading to failure in short and deep CFFT beams reveals yet another important consideration. Once flexural cracks develop, they tend to rapidly run through the entire depth of concrete core, effectively splitting it in half. Thereafter, one can consider the system to be non-composite for all practical purposes. The role of cracked concrete core will then be essentially to stiffen up the tube against inward deflection. Whereas the cracked concrete core may help transfer the shear forces to the support, it falls short of contributing to the flexural resistance of the section. Therefore, one may speculate that shear may never become more critical than flexure in short and deep CFFT beams, unless perhaps relative slippage between FRP and concrete is completely prevented. The effect of end restraints in short and deep CFFT beams is not only very hard to investigate experimentally, but also is not expected to produce tangible results for practical applications. Finally, even with end restraints, failure is expected by horizontal shear and splitting of the tube, rather than diagonal tension Experimental Indication of Failure Mode To examine the sensitivity of the beam failure in shear or flexure, principal tensile strains were calculated based on measured strains at locations where shear force and bending moment have their maximum respective effects. For shear, it is the diagonal tension at the mid-height of the beam in the middle of the shear span, while for bending, it is the flexural tensile strain at the bottom of the beam at mid-span. Figure 2.5 shows a typical load-strain response for the strain rosette with its calculated principal tensile strain. The principal tensile strain almost coincides with the 45 o directional strain. Figure 2.6 depicts the load-strain responses for beams S-1 and S-4 with both the principal tensile strain in the middle of the shear span and the flexural tensile strain at the bottom in the mid-span. The loads are normalized in terms of M/ ' fc D 3 i, where M is the 11

33 Chapter 2 Shear Response of CFFT mid-span moment, ' f c is the unconfined compressive strength of concrete core, and D i is the diameter of concrete core. For beam S-1, strains at both critical locations are nearly the same before the first cracking. At the onset of the first crack, the flexural strain becomes significantly larger than the diagonal tensile strain. This indicates that cracking corresponds primarily to flexural strains. From cracking to the ultimate failure, flexural strain at mid-span remains significantly higher than the diagonal tensile strain at shear span. This indicates vulnerability of the beam to flexural failure rather than shear failure. As will be discussed in the next section, laminate analysis of elements that simulate the fiber architecture of the two critical locations with applied tension load was carried out to support the experimental findings. Analysis reproduced the same conclusion as experiments for fiber architecture of beam S-1. Figure 2.6 also shows the effect of a/d o ratio on the relative values of flexural strain and diagonal tensile strain. Beams S-1 and S-4 with a/d o ratios of 0.9 and 1.89, respectively, were both flexure-critical rather shear-critical, as both showed higher mid-span flexural strains than the diagonal tensile strain. The difference between the two critical strains, however, tends to be greater for the beam with a larger a/d o ratio. This indicates that a lower a/d o ratio may potentially lead to a case where the two strain indicators approach the same value. Referring back to Figure 2.6, one can make an important conclusion regarding the criticality of shear failure in CFFT beams. It is obvious that for a beam with similar flexural and shear capacities, the principal tensile strain for diagonal shear is expected to coincide with the mid-span longitudinal strain. The corresponding a/d o ratio will be a critical threshold, below which the beam will be more susceptible to shear failure than flexural failure. Therefore, one may conclude from all beams tested in this program that the critical a/d o ratio for CFFT beams should very well be much lower than 1, implying that shear is not a critical mode of failure for CFFT beams in most practical range of applications. 2.6 COMPARISON OF SLENDER, SHORT AND DEEP BEAMS Figures 2.7 and 2.8 show the normalized load-deflection and the normalized load-slippage for all beams tested. The deflection and average slippage are both normalized with respect to the span length. The loads are normalized, as described for Figure 2.6. A careful examination of the figures reveals that the response of CFFT beams depends on the a/d o ratio. In general, as the a/d o ratio becomes smaller, the beam shows a higher bending 12

34 Chapter 2 Shear Response of CFFT capacity with a lower ductility. It is well known that concrete core enhances the flexural capacity and ductility of an otherwise hollow FRP tube by preventing its buckling. The enhancement depends on the interfacial shear transfer mechanism. Considering the Bernoulli beam theory, the bending capacity of the CFFT beam should remain the same as long as the interfacial shear transfer capability is sufficient to generate composite action. In the beams tested, no special mechanical bond was provided. Theoretically, a large reduction in a/d o ratio affects shear transfer capacity due to reduced development length. Figure 2.8 shows a higher slippage and lower horizontal shear resistance for deep beams (a/d o ratio of 1) with respect to their short or slender counterparts (a/d o ratios of 2 and 6). Subsequently, deep beams should exhibit lower bending capacity than their slender counterparts, if they conformed to the Bernoulli beam theory. However, all deep beams tested as part of this program resulted in higher flexural capacity, confirming that the Bernoulli beam theory is no longer valid for deep beams. It can be concluded that direct shear transfer to support takes place by forming compression struts (see Figure 2.3b) between the load point and the support. Therefore, a strut and tie model approach would be more appropriate to analyze deep CFFT beams. 2.7 STRUT-AND-TIE MODEL FOR DEEP CFFT BEAMS Although significant modeling efforts have been reported on the axial and flexural behavior of CFFT members, none is directly applicable to deep CFFT beams. Bhide (2002) and Burgueno and Bhide (2004) recently augmented the modified compression field theory (MCFT) with the classical lamination theory (CLT) to model shear response of CFFT beams. The approach is based on a sectional layered analysis with an iterative algorithm to achieve equilibrium and compatibility conditions of the composite system, including the cracked behavior of the FRPconfined concrete, until first-ply-failure of the FRP tube. The model assumes linear strain distribution across the depth, and resolves the shear stress distribution from the first order mechanics. However, it is applicable only to the B-region, where Bernoulli s beam theory applies. In the disturbed or D-region, such as CFFT beams with a/d o ratio of 1, inherent assumptions in the model do not apply, since the behavior is dominated by the arching action rather than the beam action. Hence, the model tends to provide lower bound strengths for short and deep CFFT beams. 13

35 Chapter 2 Shear Response of CFFT Previous attempts at estimating shear capacity of CFFT beams include modifications by Sieble et al. (2000) of the UCSD shear strength model of the University of California, San Diego (Priestley et al. 1993) for RC members. In their model, shear strength V n consists of two components, similar to the shear equation of the ACI (2002), as given by V = V + V (2.1) n c j where V c is concrete s contribution, which is based on member s ductility, and is expressed by V = γ 0. 8 Α (2.2) ' c f c g where γ accounts for the reduced shear resisting mechanism of concrete with increased higher ductility, and ranges between 0.1 and 0.29, and A g is the gross area of concrete section. The truss component V j was developed for a 45 o angle between the compression diagonal and the axis of the member, taking into account the effect of multiple angle plies as given by V j n w π = Do t j f o (2.3) 45 ± θ i i = 1 2 where n w is the total number of winding angles, D o is the outer diameter of the tube, t j is the lamina thickness for each winding angle, and f α is the ultimate tensile strength at the winding angle α. Since the equation adopts 45 o crack angle, it implies that compressive stress trajectories are uniform, and thereby assumes the entire length of the member as a B-region. However, the actual internal flow of forces in a disturbed or D-region could be significantly different. It is therefore necessary to use a procedure that more closely represents the actual flow of forces. Strut-and-tie truss model or load path method (Schlaich et al. 1987) can closely model internal force flow in a D-region for a deep RC beam. Furthermore, the empirical Equation (2.2) or the comparable ACI equation may underestimate the shear contribution of concrete, V c in deep beams by as much as 2-3 times. Also, Equation (2.3) does not take into account the interaction between the lamina layers and the principal stress components. Therefore, the prediction of V j would be higher than that an angle ply laminate can actually resist. According to St. Venant s principle (Schlaich et al. 1987), D-regions are generally located within a length equal to the beam depth D o from the support and the load point. For a deep CFFT 14

36 Chapter 2 Shear Response of CFFT beam with a/d o of 1, the entire beam can be regarded as highly disturbed with overlapping D- regions and non-linear strain distribution. As shown in Figure 2.9, a rigorous strut and tie model was developed in lieu of a simple truss. The model comprises of multiple struts and a connecting tie. Tests data (Rogowsky and Macgregor 1986) have shown that shear strength of a deep RC beam increases with lower shear-span-to-depth ratio because of the direct compression strut between the load and the support. Subsequently, the slope of the major compression diagonal strut is an important parameter, and is better defined by the a/d o ratio. Following a similar format of the ACI shear equation, the shear force in a deep CFFT beam is proposed to consist of two components of V c and V j, where the former accounts for the direct shear transfer in the major compression strut between the load and the support, and the latter stems from truss mechanism of the compression fan like struts of concrete and FRP. These struts at the load and reaction points provide stability to the tube under lateral buckling. Figures 2.9b and 2.9c show details of the layout with internal force flow of the truss model. The proposed truss model is highly indeterminate in nature. Geometry of the compressive struts is established by keeping the strut angles between 25 o and 65 o. Number of the struts varies depending on the length of the shear span. Two or three iterations may be required before the geometry of the truss is finalized. The following assumptions are made for the analysis: 1) Failure of the tube takes place at 45 o angle, which is on the plane joining the load and the support for a beam with a/d o ratio of 1. This is confirmed by test observations that the principal tensile strain at mid-depth coincides with strain reading at 45 o (see Figure 2.5). 2) Effective length of the tube for resisting shear is the length between the compression fans like struts that contribute V j to the total shear force (see Figure 2.9a). 3) Vertical component of FRP diagonal shear is equally distributed to the nodes of the truss that consists of compression fan struts and the tube. This assumption is similar to the yielding of all stirrups in an RC deep beam. 4) Perfect bond and full composite action are assumed between concrete and FRP tube, so that there will be no slippage. End plate of the tension tie simulates the embedment of FRP tube in adjacent members, which is the case in structural applications. Figure 2.9c illustrates the force equilibrium of the truss system and the nodes. It is assumed that the horizontal force in concrete at the support node 15

37 Chapter 2 Shear Response of CFFT is fully transferred to the tube by mechanical friction. For partial composite action, the strut force induced in concrete depends on the friction force imparted by the interface. Once the bond resistance is estimated, concrete strut force can be calculated by force transformation. Irrespective of composite action, reaction at the support will significantly enhance the frictional resistance by bearing on the support. Several reasonable assumptions were made to allow for sizing of the compressive struts and tension tie, and determining their stresses. Flexural analyses of CFFT beam suggest that that the neutral axis is located within a region of D o. Depth of the C-C-C node that is subjected to compressive force is therefore assumed to be 0.3D o. Unlike an RC beam, reinforcement in CFFT beams is distributed throughout the depth. Observation of failure modes of deep CFFT beams indicates that cracks propagated up to mid-depth of the member at failure. Therefore, the bottom half of the tube is considered effective in resisting tension at mid-span. Tensile and compressive stress distributions are assumed linear above and below the CCC node. An equivalent rectangular stress block is assumed for concrete compressive stress at mid-span. Equilibrium of forces can be written as C + C = T (2.4) h fh f where T f is the tensile force in the bottom half of FRP, C h is the horizontal component of compressive strut in concrete, and C fh is the induced compressive force in the FRP tube due to compression fan like struts radiating from the load point. Based on the strut and tie model, three types of failure mode can be identified, as follows: (a) shear failure (rupture of the FRP tube under diagonal tension, or crushing of any compression strut, or combined failure of FRP and any compression strut), (b) flexural failure (rupture of tension tie at the bottom in mid-span) or (c) bearing failure at the C-C-C node (load point) or C-C-T node (reaction point) under excessive bearing stress. The truss element that has the weakest capacity in the induced loading direction will govern the overall failure mode of the beam. From the free body diagram, failure load is the smaller of the shear and flexural resistance, as given by u ( V V ) P = 2 + (2.5) P u C j 2 α D o T f = (2.6) a 16

38 Chapter 2 Shear Response of CFFT where αd o is the lever arm between compression and tension forces, and T f is tie force given by T f t j 1.29 f ft = π ( Do t j ) (2.7) 2 2 where f ft is the ultimate tensile strength of FRP. T f is acting at the centroid of the bottom half of the tube. Figure 9d depicts the qualitative shape of the compressive strut. ACI (2002) and AASHTO LRFD (1998) suggest the effective width of a circular section to be D o for calculation of V c. Here a conservative width of 0.65D o, which is equal to the effective length of the bearing plate l dl at load point, is taken as the effective width of the strut. Once the load bearing plate dimensions are known, strut width can be established. Effective compressive strength f ce in concrete strut is adopted from Macgregor (1997) as given by f ce = ν ν f (2.8) ' 1 2 c where v 1 and v 2 are the efficiency factors, with ν 1 selected as 0.8 for CFFT beams based on the values given for deep RC beams in the same reference, and ν 2 is given as 15 ν 2 = ( f ' c ' f c in psi) (2.9) The required strut thickness is calculated once the effective compressive strength f ce is known. Recommended stresses in C-C-C and C-C-T nodal zones are 0.85 f ' c and 0.75 respectively, as per the ASCE-ACI committee (1998) on shear and torsion. Typical verification of the above model is discussed here for beam S-9. In a typical RC beam, about 25%-40% of the shear force is carried by stirrups to ensure ductile mode of failure (1997). However, in majority of CFFT beams the effective amount of shear reinforcement is much greater than RC beams due to the continuous form of shear reinforcement over the shear span. Therefore, it may be reasonable to start with a value of 50% of the total shear transferred through truss mechanism. Tables 2.3 and 2.4 show the lamina thickness and properties of the GFRP tube used to fabricate beam S-9. Laminate analysis was performed to obtain the strength of the laminate, f fu perpendicular to the failure plane. Progressive laminate failure analysis f ' c, 17

39 Chapter 2 Shear Response of CFFT (Daniel and Ishai 1994) was carried out with Tsai-Wu failure criteria (Daniel and Ishai 1994) for laminate, and strength was found to be ksi for tube type IV. Failure plane was assumed at 45 o angle, as confirmed by the tests. After finalizing the truss geometry, ultimate load P u was found to be 178 kips and 202 kips to fail the beam S-9 in flexure and shear, respectively. This indicates that flexure governs the mode of failure, as confirmed by the tests. The predicted failure load also agrees favorably with the experimental load of 190 kips. The analysis showed that shear failure, if critical, would occur by crushing of the struts BH and AB (see Figure 2.9b) rather than diagonal tension failure of the tube. Stresses in nodes C-C-C and C-C-T were both below the respective limiting stresses Parametric Studies on Shear Criticality The above strut-and-tie model was used to evaluate the shear criticality of CFFT beams in a parametric study with the following four key factors: (a) fiber architecture, (b) a/d o ratio, (c) D o /t j ratio, and (d) concrete strength, ' f c. For simplicity and practicality, all material and geometric properties were selected to vary around those of beam S-9, unless otherwise noted. Figure 2.10a shows the effect of fiber architecture on the ratio of the ultimate load P u for shear to its value under flexure. The load ratio indicates shear criticality, if less than 1. The fiber architecture is taken as a parameter, since it also reflects the effect of jacket strength, f j in the axial and hoop directions and the fiber volume fraction of the laminate. Three types of laminate architecture were used to study the effect of this factor on shear criticality. Types of axial and hoop represent two extreme cases of 0 o and 90 o angles, respectively. Type of angle ply has the same lay-up, thickness, and materials as tube type IV and can be regarded as the intermediate case. Type of axial and hoop fiber architecture simulate the least shear and flexural capacity, respectively. They both fail by splitting of the tube parallel to the fiber direction. The figure clearly shows that axial fiber orientation, such as in pultruded shapes, is vulnerable to horizontal shear failure. On the other hand, angle plies are generally better in terms of shear and flexural capacity, and can be optimized for a balanced design. Figure 2.10b depicts the effect of a/d o ratio on shear criticality of CFFT beams. As the a/d o ratio approaches 0.5, the number of struts consolidates to only on major diagonal strut. However, for a/d o of 0.75, the number of compression fan like struts reduces to two. Due to lack of any experimental evidence, a 45 o angle can be assumed for all cases, even though it is 18

40 Chapter 2 Shear Response of CFFT believed that it may be somewhat higher for the a/d o ratio of Analysis reveals that for the a/d o ratio of 0.5, shear contribution of concrete is about 100% of the total capacity due to the increase in major compression strut angle and a decrease in the effective length of the tube. For higher values of a/d o ratio, if a beam is sufficiently slender so that compression fan regions at the load and reaction points do not overlap, no major compression strut will exist. Instead, a uniform compression stress field will develop, which means that the method proposed by Burgueno and Bhide (2004) would be appropriate. However, a truss model can also be developed to predict the shear capacity of slender CFFT beam. It can be seen from the figure that critical a/d o ratio is about 0.9 for this particular set of parameters. Figures 2.10c and 2.10d show the effects of D o /t j ratio and concrete strength, respectively, on shear criticality of CFFT beams. The D o /t j ratio is varied by changing the thickness of lamina layers of tube type IV. Both parameters show similar trends as that for the a/d o ratio. Shear tends to be critical for very low values of each parameter. Flexural capacity is more sensitive to the D o /t j ratio, while shear capacity is more sensitive to concrete strength. A careful observation of the effect of concrete strength reveals important aspects of shear design of CFFT beam. At lower levels of concrete strength a brittle shear failure may occur in one or more concrete struts, while at higher levels of concrete strength, a combined failure of concrete struts and FRP tube may take place with some ductility imparted from the FRP tube. Therefore, a higher concrete strength is generally more desirable. A judicious selection of concrete strength and fiber architecture with different proportions of shear and flexural capacities of the tube can help optimize the use of materials. 2.8 SUMMARY AND CONCLUSIONS An analytical and experimental study was undertaken to investigate the behavior of slender, short and deep beams made of concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) under three and four point transverse loading. A total of ten beams were tested to study the effect of fiber architecture, shear-span-to-depth ratio, reinforcement index, and diameter-to-thickness ratio of the tube. Test results reveal that flexure governs the overall failure mode of all beams tested even for shear spans as short as the depth of the beam irrespective of the fiber architecture of the tube. As shear span decreases, bending capacity of the beam increases, mainly due to the formation of direct compression strut between the load and the support. Bond between concrete 19

41 Chapter 2 Shear Response of CFFT and tube is more critical for deep CFFT beams, as the degree of composite action affects the capacity of such members. A strut-and-tie model approach was adopted to predict the shear strength of deep CFFT beams. Prediction shows good agreement with test results. A parametric study is carried out to assess the shear criticality of CFFT beams. It was concluded that shear failure is only critical for beams with shear span less than their depth. High strength concrete is found to improve capacity of CFFT beams. However, a judicious selection of concrete strength and fiber architecture with different proportions of shear and flexural capacities of the tube can help optimize the use of materials. 20

42 Chapter 2 Shear Response of CFFT Table 2.1 Mechanical properties of GFRP tubes used in CFFT beam shear tests Tube type (Designated surface color) I (Yellow) II (White) III (Grey) IV (Red) Fiber architecture [±55 o ] 17 layers V f = 75.5% [0 o /0 o /+45 o /-45 o ] layers V f = 51.2% [±34 o +80 o ±34 o ] 5 layers V f = 51% [{-88 o +3 o -88 o } 2 {+3 o } 1 {-88 o +3 o -88 o } 1 ] 10 layers V f = 51% Tensile strength (ksi) Tensile elastic modulus (ksi) Compressive strength (ksi) Compressive elastic modulus (ksi) Hoop strength (ksi) Hoop elastic modulus (ksi) N/A N/A * N/A 19.0* 1305* * N/A 58.3* 2857* * Predicted by laminate theory; Tube I bending strength = 23 ksi, bending modulus = 1460 ksi; Tube II bending strength = 81 ksi, bending modulus = 3564 ksi Coupon testing by Fam & Rizkalla (2002) Table 2.1 Test matrix for slender, short and deep CFFT beams Outer dia., Thickness Span Span-to-depth Tube Beam type No. D o t j length, L ratio, (in) (in) (in) a/d o Concrete strength, (ksi) ' f c Beam type I II S Deep 5.9 S Deep S Short S Short S Deep S Short S Deep III S Slender S Deep IV S Slender four point loading Beam S-3 and S-6 : Mirmiran et al. (2000); Beam S-8 and S-10 : Fam and Rizkalla (2002) 21

43 Chapter 2 Shear Response of CFFT Table 2.3 Details of laminate architecture Properties Tube type IV Ply lay-up Thickness (in) Table 2.4 Lamina properties for parametric study Properties* E 1 E 2 G 12 v 12 F 1t F 1c F 2t F 2c F 6 Values 5,511 ksi 1,131 ksi 507 ksi ksi 77.3 ksi 5.66 ksi ksi ksi *Parameters described in list of symbols 22

44 Chapter 2 Shear Response of CFFT L = 1.8D o 2D o Strain rosette l d = 6 l d = 4 D o /2 C L D o /2 ½ a a Strain gage PI gage Potentiometer l dl = 8 Side elevation Figure 2.1 (a): Schematics of deep beam test setup and instrumentation Figure 2.1(b) : A view of test setup 23

45 Chapter 2 Shear Response of CFFT Failure mode 80% of capacity 45% of capacity 25% of capacity Deep beam S Mid-span deflection (in) Figure 2.2: Typical load-deflection behavior of deep CFFT beam 24 Applied load (kip) 24

46 Chapter 2 Shear Response of CFFT Top Bottom FRP rupture at failure Figure 2.3(a) : Typical cracking pattern of deep beam with low reinforcement index Web shear crack Flexure-shear crack Top Bottom Matrix crack along compression stress trajectories Figure 2.3 (b) : Cracking pattern of deep beam with high reinforcement index 25

47 Chapter 2 Shear Response of CFFT Top a) Beam S-2 D o /t j = 49.5 a/d o = 1.0 Bottom FRP rupture at failure Top Bottom Poisson effect b) Beam S-1 D o /t j = 63.4 a/d o = 0.9 c) Beam S-4; D o /t j = 63.4 a/d o = 1.89 Figure 2.4 : Cracking patterns comparison of short and deep beams with variable D o /t j and a/d o ratios 26

48 Chapter 2 Shear Response of CFFT Applied load (kip) S-1 : SG - 0 degree S-1 : SG-45 degree 20 S-1 : SG-90 degree S-1 : Principal tensile strain Strain rosette at mid depth (me) Figure 2.5 : Typical load vs. strain rosette response of a deep CFFT beam S-4 a/d o = 1.89 M ' 3 f c Di S-1 a/d o = S-1 : Flexural strain S-1 : Diagonal tensile strain 0.02 S-4 : Flexural Strain S-4 : Diagonal tensile strain Strain (me) Figure 2.6 : Effect of a/d o ratio on diagonal tension and flexural strains 27

49 28 ' 3 c D i f M S-5; not tested to failure S-7 S-1 S-6 S-2 Deep beam S-1 Deep beam S-2 Short beam S-3 Short beam S-4 Deep beam S-5 Short beam S-6 Deep beam S-7 Slender beam S-8 Deep beam S-9 Slender beam S δ L Figure 2.7 : Comparison of load vs. deflection responses of deep, short and slender CFFT beams S-9 S-8 S-10 S-3 S-4 Chapter 2 Shear Response of CFFT 29

50 Chapter 2 Shear Response of CFFT 29 ' 3 c D i f M S-4 S-4 S-7 S-10 S-2 S-5; Not tested to failure Deep beam S-1 Deep beam S-2 Short beam S-4 Deep beam S-5 Deep beam S-7 Slender beam S-8 Deep beam S-9 Slender beam S u L Figure 2.8 : Comparison of load-slip responses of deep, short and slender CFFT beams S-1 S-9 Chapter 2 Shear Response of CFFT 30

51 Chapter 2 Shear Response of CFFT Effective length of tube resisting shear l d D o D o C L l d 2D o Figure 2.9 (a) : Strut-and-tie model for deep CFFT beam D E F G V c V V j B αd o C h + C fh F fu θ F fu Cosθ A V j V c θ H I J K T f l ah θ = 45 o l hk l bg V Figure 2.9 (b) : Details of strut-and-tie model 30

52 Chapter 2 Shear Response of CFFT F fu Cosθ/N s V c V j C fh C h 0.3D o αd o T f 0.18D o V j V c V Figure 2.9(c) : Equilibrium of truss model with internal force flow Effective width l d l dl Node B Major compression strut Node A D o 2 l d Figure 2.9(d) : Qualitative shape of major compression strut 31

53 Chapter 2 Shear Response of CFFT Fiber architeture a Do = 1 ; D o = t ' f c = 5.9 ksi j P P u shear u flexure Flexure governs Shear governs 0.0 axial angle ply hoop Figure 2.10(a) : Effect of fiber architecture on shear criticality of CFFT beam D Angle ply ; o = t ' f c = 5.9 ksi j P P u shear u flexure Flexure governs Shear governs a Shear span D o Figure 2.10(b) : Effect of a/d o ratio on shear criticality of CFFT beam 32

54 Chapter 2 Shear Response of CFFT a Angle ply ; = 1 Do ' f c = 5.9 ksi P P u shear u flexure Flexure governs Shear governs Reinforcement ratio D o Figure 2.10(c) : Effect of D o /t j ratio on shear criticality of CFFT beam t a Angle ply ; = 1 Do D o = 50.9 t j P P u shear u flexure Flexure governs Shear governs Concrete strength ' f c (ksi) Figure 2.10(d) : Effect of concrete strength ' f c on shear criticality of CFFT beam 33

55 Chapter 3 Flexural Fatigue : Experimental Work CHAPTER 3 FLEXURAL FATIGUE : EXPERIMENTAL WORK 3.1 INTRODUCTION A thorough experimental program was undertaken to study the structural response and performance of concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) under fatigue loading in four point bending. Flexural response is evaluated by four basic criteria, namely; damage accumulation, stiffness degradation, fatigue life, and finally reserve strength, if failure does not occur after a predetermined number of load cycles. Parameters investigated in this study include reinforcement index, fiber architecture, load range, and boundary conditions. A total of eight beams were tested. Test results suggest that fatigue behavior of the CFFT beams is dominated by the material properties of FRP. Hence to address fatigue modeling of CFFT beams, material level creep and fatigue tests of FRP coupons were carried out on a total of eighteen specimens. Test data was used to calibrate creep model parameters of Findley (1960) and fatigue model parameters of Ogin et al. (1985) for the types of FRP tubes used in this study. 3.2 LITERATURE REVIEW Fatigue study of concrete began in the early 1900 s with the development of reinforced concrete (RC) railroad bridges. These bridges were expected to resist millions of cycles of repeated axle loads from trains during their intended service lives. The primary role of concrete in any typical RC structure is to resist compression forces. For this reason, the interest in fatigue of concrete has traditionally been directed toward its compressive properties. A number of studies (Hilsdorf and Kesler 1966, Bennet and Raju 1971) have shown that fatigue strength of concrete at 10 million cycles may be taken to be about 55 percent of its static strength, when the minimum value of the fluctuating load is near zero and there are no prolonged rest periods. No endurance limit has yet been found for concrete. This implies that no stress level is known, 34

56 Chapter 3 Flexural Fatigue : Experimental Work below which the fatigue life of concrete will be infinite. Traditionally, the relationship between fatigue strength of concrete, S and the number of cycles of repeated loading, N is plotted as a socalled S-N curve or Wohler curve to represent the true vulnerability of concrete to fatigue loading. When the Wohler curve is being determined, it is typical for the minimum value of repeated stress to be constant and for the maximum stress to be varied. It has been suggested that susceptibility of concrete fatigue is independent of its static strength. Therefore, the stress coordinate of the Wohler curve is often given in a non-dimensional format of S = f ' max / f c ratio of the maximum stress to the static strength. When N is plotted in a logarithmic scale, the fatigue curves for concrete turn out to be approximately linear (Murdock and Kesler 1958). However, the S-N curve may also be plotted for a constant stress amplitude, taking into account the effect of stress ratio, R = f min / f max, the, where f min and f max are minimum and maximum stresses applied. Aas-Jakobsen (1970) showed that the relationship between ' max / f c f and ' min / f c f is linear for a fatigue life of 2 million cycles. Combining this linear relationship with Wohler curve, Aas-Jakobsen (1970) proposed a formula for predicting fatigue life or strength of concrete as ( 1 R) log N S = 1 β 10 (3.1) where β = The above equation can be used for 0 R 1 but not for stresses which alternate between compression and tension. Tsu (1981) extended Equation (3.1) to a more general four-variable f-n-t-r relationship for predicting the fatigue strength of concrete. The relationship incorporates the new dimension, T, which is the period of repetitive loading. This four parameter relationship simultaneously accounts for the time effect and the effect of loading rate. The effect of loading frequency has been studied by many investigators (ACI Committee 215, 1974). It is generally believed that frequency of loading between 1Hz to 15Hz has little or no effect on fatigue strength, provided that the maximum stress level is less than 75% of the static strength. Zhang et al. (1996) incorporated the effects of stress reversals and loading frequency by modifying the above equation. Zhang et al. (1998) further extended the modified equation to take into account the effect of sustained loads. Kim et al. (1996) studied the fatigue behavior of high-strength 35

57 Chapter 3 Flexural Fatigue : Experimental Work concrete. Test results showed that fatigue life would decrease with increasing concrete strength. Although fatigue life of concrete has been investigated extensively, its deformation characteristics are addressed in a rather limited manner. A review of those deformation characteristics is provided in Chapter 4. Even though fatigue life of concrete under compression is studiedly primarily under uniaxial compression, there are many structures such as foundation of rotating machines where fatigue could act triaxially. Taleirco and Gobbi (1996 and 1998) experimentally investigated the triaxial fatigue behavior of plain concrete under a varying axial load and a constant active confining pressure. It was concluded that fatigue life increases as the mean confinement pressure increases. In recent years, retrofitting of concrete columns with FRP has become increasingly popular. This has lead to the development of a new construction concept (Mirmiran and Shahawy 1995 and 1997) of concrete-filled FRP tubes. The concept is also implemented in several real applications as bridge columns and piles (Seible et al. 1999, Mirmiran 2003a), where concrete core would be placed in a passive state of confinement. Vechicular traffic and pile driving impact may induce axial fatigue of concrete under confinement. Harmon et al. (1998) and Hooi (2000) have studied the behavior of confined concrete under low and high cycle fatigue loading in uniaxial compression. Results showed that lateral confinement improves the fatigue properties of concrete. The classical model of Aas-Jakobsen (1970) was modified by Hooi (2000) to include the effect of passive confinement. Unlike compressive fatigue loading, relatively few studies have focused on tensile fatigue of concrete. This is perhaps due to difficulties associated with testing methods, and to a lesser extent on scarce application of concrete to carry tension fatigue in the field. Tepfers and Kutti (1979) and Saito and Imai (1982) investigated tension-tension fatigue behavior of concrete. Test results showed that plain concrete exhibits no fatigue limit in tension, and that fatigue strength for concrete at 2 million cycles is 73% of its static tensile strength. Since FRP has been widely used in the aerospace industry, and also because fatigue failure under service conditions is of grave concern in those applications, fatigue testing of different types of FRPs has drawn tremendous appeal over the last four decades. Fatigue life of composite materials is evaluated in terms of two specific properties; strength and stiffness. Strength degradation is usually evaluated by finding the residual strength from a static test after fatigue 36

58 Chapter 3 Flexural Fatigue : Experimental Work cycling. Therefore, a series of tests are required to determine a single strength degradation curve. On the other hand, stiffness degradation can be evaluated by measuring the elastic modulus of the material using a much smaller number of specimens. Therefore, damage models for composite materials are usually stiffness-based rather than strength-based. Curtis (1989) reviewed the fatigue behavior and performance of FRP laminates made with carbon, glass or aramid, and demonstrated that the matrix composition has a greater influence on the fatigue performance than the type of fibers used. Comparing the S-N curve for the three types of composites under tension-tension fatigue, it was stated that the stress ratio at high fatigue life is smallest for the glass laminates and greatest for the carbon laminates. Talreja (1981) and Curtis (1989) concluded that the slope of the S-N curve is determined primarily by the strain in matrix. In addition to the S-N curve for composite materials, their damage mechanisms in tensiontension fatigue loading history are also well addressed (Reifsnider et al. 1983). Stiffness change is a well defined engineering property that directly relates to crack formation and stress redistribution during fatigue or cyclic loading. Three distinct regions of damage mechanism are identified: I) matrix cracks, II) crack propagation and delaminations or debonding, and III) fiber rupture and global failure of laminate. Cracks develop at larger spacing in early life, and thereafter quickly stabilize into a uniform pattern in the transition of regions I and II. This event is comparable to crack formation in tension stiffening of reinforced concrete, except for the fact that stiffness change is more gradual. Simultaneously, the rate of stiffness change or damage growth is quite rapid at early life, and gradually stabilizes with uniform crack pattern. In region I, matrix cracks form parallel to fibers and perpendicular to the dominant load axis. The damage mechanism in region I is merely a laminate property and independent of loading history, whether static or quasi-static or fatigue. Therefore, it can be completely defined by the properties of individual plies, thickness of plies, stacking sequence and fiber architecture. In region II, coupling of early matrix cracks and their growth especially along the interfaces of laminae can be observed. Interface separation namely local delamination or debonding is the dominant damage mechanism in region II. A rapid increase in damage development happens near the end of fatigue life of composites as failure occurs by fiber rupture. Other than studies on damage mechanisms, effects of stress ratio and frequency on fatigue behavior of composite materials were studied by Kadi and Ellyin (1994) and Barron et al. (2001), respectively. Frequency effects were found to profoundly influence the fatigue behavior 37

59 Chapter 3 Flexural Fatigue : Experimental Work of cross-ply and angle ply laminates. Effect of biaxial loading (Ellyten and Martens 2001), twostage axial loading (Found and Quaresimin 2003), variable amplitude loading (Paepegem and Degrieck 2001), multi-stage loading (Clark et al. 1999), compression-compression fatigue loading (Ratwani and Kan 1980, Soutis et al. 1991, Choi et al 2002), and tension-compression fatigue loading (Rotem and Nelson 1989, Gamstedt and Sjogren 1999) have also been investigated for different types of composite materials. An excellent review of fatigue behavior under different loading conditions is compiled by Gamstedt and Anderson (2001) as well as Harris (2003). To date, only one study has been reported in the literature on fatigue behavior of CFFT. Karbhari et al. (2000) designed and tested a prototype FRP deck and CFFT beam assembly by subjecting them to 2 million cycles of fatigue loading at 20% of the ultimate moment capacity. The bridge superstructure withstood the 2 million cycles without any noticeable stiffness degradation. In another related study, Deskovic et al. (1995) developed a new hybrid system consisting of a glass FRP box beam combined with a concrete layer cast on to the top flange, and a thin carbon-fiber-reinforced-polymer (CFRP) laminate bonded to its tension face. Fatigue performance of the hybrid system was evaluated experimentally under service load conditions. Beams survived 3-4 million cycles, and the eventual failure was initiated by tensile fracture of the carbon FRP laminate. Analytical models were also developed based on the laminate theory and the semi-empirical material models for FRP, as discussed in Chapter 4. Relatively more studies are available on FRP-retrofitted concrete beams. Barnes and Mays (1999) examined the fatigue performance of RC beams strengthened with CFRP laminates. Three loading options were used to compare the performances of different beams; a) applying the same loads to both strengthened and control beams, b) applying the same stress range in the rebars in both beams, and c) applying the same fraction of the ultimate capacity to each beam. Fatigue fracture of steel appears to be the dominant factor governing failure in retrofitted beams. Shahawy and Beitleman (1999) also conducted similar tests on CFRP- strengthened T-beams. Comparisons were made for the standard section and equivalent sections with different number of layers of CFRP in regards to fatigue behavior, stiffness and strength. The results from the fatigue study indicated that fatigue life of RC beams may be significantly improved using externally bonded CFRP laminates. Papakonstantinou et al. (2002) and Hwan et al. (2003) studied the fatigue behavior of GFRP-strengthened and steel-strengthened RC beams and 38

60 Chapter 3 Flexural Fatigue : Experimental Work reported similar findings. An equation was proposed by Papakonstantinou et al. (2002) for the S- N curve based on a regression analysis. Most recently, Heffernan and Erki (2004) reported the test results of CFRP strengthened RC beams. Failure modes included rupture of tensile steel followed by debonding or rupture of CFRP. 3.3 EXPERIMENTAL PROGRAM The experimental program consisted of two phases. The first phase dealt with testing of CFFT beams under flexural fatigue. To determine the level of applied fatigue load, static capacities of the members were needed before proceeding with fatigue tests. Static capacities were obtained either directly from the tests pertinent to Chapter 2, or from previous research by Mirmiran et al. (2000) and Fam and Rizkalla (2002). The second phase dealt with especially the long-term material properties characterization of FRP materials. Static tests were conducted to determine the level of creep and fatigue loads. Parameters of creep model (Findley 1960) and fatigue model (Ogin et al. 1985) were established through coupon prepared from the tubes used to fabricate the CFFT beams. The main objective of the first phase was to characterize the flexural fatigue behavior of CFFT beams with different tube properties. Test parameters included reinforcement index, laminate architecture, load or stress range, end restraint and multistage loading (Figure 3.1). Four different types of tubes namely types I, II, III and V were used to fabricate the test specimen. Table 3.1 describes the details of the tube types with their material properties. Note that fatigue tests were part of a larger test program, which included a tube type IV that was not studied under fatigue loading. Type I tube was made using the filament winding process with 17 layers of E-glass fibers at ±55 o angle and a thermosetting epoxy resin. Outer diameter of the tube used for fabricating the beams was in. The winding angle was optimized for pipe flow applications with 2:1 pressure loading in the hoop direction versus longitudinal direction. Structural thickness of the tube was 0.2 in with a volume fraction of 75.5% and no internal lining. Type II tube was manufactured by the centrifuge or spin casting method using E-glass fibers and epoxy resin. The tube had an outside diameter of 12 in and a wall thickness of 0.74 in. The wall thickness, however, was not entirely made of a structural laminate, but consisted of two 39

61 Chapter 3 Flexural Fatigue : Experimental Work 0.14 in resin rich layers on the inside and in between the two laminates, and a 0.02 in exterior white gel coating for ultraviolate ray protection. The middle and inner rich resin layers were inherent to the manufacturing process, as the excess resin was used to ensure proper wetting of the fabric. The tube consisted of 40 plies, with a symmetric fiber architecture of (0 o /0 o /+45 o /-45 o ) starting from the outside of the tube. Out of 40 layers, 20 layers were along the longitudinal direction and 10 layers each were at +45 o and -45 o, respectively. Burnout tests conducted by the manufacturer determined the glass content of the tubes to be 51.2%. Tube type III had an overall thickness of 0.29 in with a structural thickness of in. Outer diameter of the tube was in. The tube consisted 5 plies with a laminate architecture of {(±34 o ) 2 /80 o /(±34 o ) 2 }. It was manufactured with E-glass fibers and polyester resin using the filament winding technique. The fiber volume fraction of the tube was 51%, with 70% of the glass fibers oriented at ±34 o and the remaining at 80 o with respect to the axis of the tube. Tube type V had the lowest thickness and volume fraction among all the tubes considered for this study. Fiber architecture composed of 14 angle plies of ±75 o fiber orientation with respect to the longitudinal axis. The outer diameter of the tube was 12 in with an overall thickness of 0.16 in and a fiber volume fraction of 44%. Table 3.1 shows the mechanical properties of tubes used for this study. Two batches of concrete were used in order to cast the beam specimens. Beams F-5, F-6, F- 8 and F-8S (companion beam for static test) were cast in the first batch. Beams F-1, F-2, F-3 and F-4 were cast in the second batch. The mix designs for both batches were similar and designed for a target strength of 4 ksi at 28 days. Type I Portland cement was used for mixing with water reducing admixture. The target slump for both batches of concrete was 4 inch. Actual concrete strengths at the time of testing of the beams were found to be 4.5 ksi for the first batch and 5.2 ksi for the second batch, respectively. All beams were prepared with no end restraint, except for beam F-3. In field practice (Zhao et al. 2000), CFFT beams are usually constructed with their ends embedded into the adjacent structural members to provide structural integrity for the entire system. Hence, beam F-3 was designed with end blocks to achieve full composite action between FRP and concrete by preventing end slippage. The 24 in 24 in 16 in concrete end blocks were cast for beam F-3 with a designed concrete strength of 5 ksi. Continuity between the end blocks and the CFFT beam was maintained by eight No. 4 dowel bars at each end with steel of Grade 60 ksi. Dowel bars were embedded 8 in into the CFFT beam. As mentioned earlier in Chapter 2, a 40

62 Chapter 3 Flexural Fatigue : Experimental Work beam cast as part of the experimental program of Fam and Rizkalla (2002), was cut to prepare the desired span length of beam F-7. A total of eight beams were tested in fatigue under four point bending to impart a constant bending moment region at mid-span. Table 3.2 shows the details of the beams with some of the test results. Figure 3.2 depicts the schematics of the test setup and the instrumentation plan. All specimens had flexural spans of 6 ft with loads applied at third points of the span length. Beams were simply supported on neoprene pads at both ends, as shown in Figure 3.1. Since fatigue is dynamic in nature, it induces significant vibration during the test. Neoprene pads were selected as supports to reduce the vibration, thus providing stability to the specimen during the test. At higher load ranges, it was initially experienced that the actuator loading plane and the geometric centroidal plane of the circular beam deviated from each other beyond the tolerance, thus causing instability. To alleviate this problem, elaborate lateral restraints were designed and mounted at the mid-span of the beams to guide the actuator movement only in the vertical direction. Figures 3.3 and 3.4 illustrate the typical test setup with or without lateral restraint. Figure 3.5 shows beam F-3 with end blocks during testing. The primary interest in the instrumentation of the CFFT beam was concerned with the strain distribution and deflection at the mid-span section, which is in the region of pure flexure without any shear force. Each beam was instrumented with six longitudinal strain gages at midspan as shown in Figure 3.2. Five longitudinal linear pots were placed at 45 o angles around one side of the section to monitor longitudinal strains across depth (Figure 3.2). Linear pots were used as a back up to strain gages, in case the strain gages failed before the specimen reached fatigue life. Two strain gages were used at the top and bottom of the mid-span section to measure hoop strains. Deflections were monitored at every 1/6 th point of the span length including the mid-span. Relative end slippages were measured at both ends on top and bottom of the section continuously throughout the test. In addition, support displacements and end rotations were both monitored. Data was recorded automatically using a high speed megadac data acquisition system, at a regular interval of 50,000 cycles, once the deflections were stabilized. Within the first 25,000 cycles, data was collected more frequently to capture the initial rapid degradation of specimens. Deflections were generally stabilized after the first 25,000 cycles, regardless of the type of beam specimen. Data was recorded at a sample frequency of 200 scans per second. 41

63 Chapter 3 Flexural Fatigue : Experimental Work The basic evaluation criteria and objectives of the fatigue tests were fourfold; a) damage accumulation, b) stiffness degradation, b) number of cycles to failure and c) reserve strength after the completion of fatigue test at a predetermined number of cycles. The main goal was to continue testing at a frequency of 2 Hz until 1 million cycles, unless the specimen failed earlier. If the specimen did not fail after 1 million cycles, test would continue into a second stage at a higher stress level. Details of the load levels, stages of loading, failure modes, and number of cycles to failure are provided in Table 3.2. The load range was varied from as low as 5% of P static, where P static is the total ultimate static load on the beam, to 75% of P static. Majority of the beams were tested at or below 50% of P static, which is the upper bound of service level load. As stated earlier the list of test parameters considered for this study is shown in Figure 3.1. Two different levels of P min, 5% and 12.5% of P static, were selected as the representative range of dead loads in an actual structure. P max was varied to simulate the transient live load. Depending on the capacity of the specimen, the tests were carried out using either the 220 kip or 110 kip MTS actuators. The 110 kip actuator was mainly used for the higher load range, since it included a high capacity dual servo valve (90 gpm) that allowed testing of specimen to undergo larger displacement amplitude in each cycle. Static tests were conducted up to the maximum fatigue level at the beginning of each stage of loading to obtain the initial and residual static stiffness of each beam. Dynamic stiffnesses of each beam for the entire period of loading history were obtained from the recorded data. Static tests were done in displacement control at a displacement rate of in/min, while fatigue tests were carried out in load control with a sine wave between the minimum and maximum load levels. A safety threshold was set to force the hydraulic system to shut down, if the stroke exceeded the static ultimate deflection of the respective specimen. Specimens were periodically examined to identify any sign of visual distress or cracking. 3.4 STATIC TESTS RESULTS AND DISCUSSION Static test results for tube types I, II, and III were obtained either from the parallel study on behavior of CFFT beams (see Chapter 2) or as part of the previous research program undertaken by Mirmiran et al. (2002) and Fam and Rizkalla (2002). Table 2.2 in Chapter 2 shows test results for the companion beams S-3 and S-4 for tube type I, S-6 for tube type II, and S-8 for tube type III. It may be noted that section and beam geometries were slightly different for beam S-4, S-6, 42

64 Chapter 3 Flexural Fatigue : Experimental Work S-8 from the fatigue tests. Additionally, a 6 ft long beam (F-8S) made of tube type V was tested to obtain its moment capacity. Figure 3.6 illustrates the normalized moment-deflection responses of CFFT beams with four different tube types. As expected, CFFT beam made with tube type II, which may be considered as an over-reinforced section, had the highest capacity. CFFT beam made with tube type V, on the other hand, had the lowest capacity. This may be regarded as the practical lower bound reinforcement index possible, since the ultimate capacity of the beam was approximately 33 percent higher than its cracking moment. Static moment capacities of all beams are provided in Table 3.1. Figure 3.7 shows the typical strain distribution and the neutral axis at various stages of pre-cracking, post-cracking and the ultimate load level. Strain distribution remains linear after cracking. However, in the post cracking region, CFFT beams begin to exhibit non-linear strain distribution. 3.5 FATIGUE TESTS Test Observations and Failure Modes Table 3.2 summarizes the results of the flexural fatigue test program. Figures show the typical response of one of the CFFT beams (beam F-7) under flexural fatigue loading. The beam was subjected to two stages of loading. In the first stage, the applied load level was between 12.5% and 25% of P static. Since the beam did not fail after one million cycles, the upper load level was increased to 50% P static, while the lower load level was kept the same as before. Both stages of loading cycled around the flexural cracking load of the beam. In the first stage of loading, the beam experienced only 29% deflection of δ static before stabilizing at 25,000 cycles, where δ static is the static deflection at failure. During the same period, the beam showed only 10% dynamic stiffness degradation with respect to its initial dynamic stiffness. Stiffnesses were calculated as the slope of the lines connecting the peak and valley points of the loading and unloading curve, and therefore is in fact the secant stiffnesses of the member. After 25,000 cycles, the specimen showed nominal deflection accumulation and stiffness degradation until 1 million cycles. Figure 3.9 describes the deflection evolution of beam F-7 at 1/6 th points along the span. Beam F-7 had fibers at ±34 o with great influence on the longitudinal stiffness of the tube. Lower initial deflection resulted in less relative slippage, thereby maintaining a higher degree of composite action between the FRP tube and concrete core. Figure 3.10 confirms this point by depicting the growth of flexural strains in the FRP tube during the fatigue loading. Figure

65 Chapter 3 Flexural Fatigue : Experimental Work shows the strain distribution across the depth of the beam at its mid-span, confirming the general assumption of plane sections remaining plane throughout the first stage of loading. No visible matrix cracking was observed on the outer layer of the FRP tube in the first 1 million cycles. At the beginning of the second stage of loading, the specimen experienced a sudden jump in deflection, strain, and slippage and a sudden drop in stiffness, all of which again stabilized after only 25,000 cycles. By that time, the beam had lost a total of 35% of its stiffness, or an additional 21% in only 25,000 cycles. After the first 1 million cycles, strain distribution had become substantially non-linear. Test was stopped at 1.7 million cycles with little or no further stiffness degradation. Only minimal matrix cracking and slippage were observed at that time (see Figure 3.13). It is also important to note that only 57% of the longitudinal strain capacity of the tube was utilized after 1.7 million cycles of fatigue loading. The neutral axis had moved down from 4.1 in to 4.6 in as a result of stiffness degradation in the tube. Following termination of the fatigue loading, the specimen was subjected to a static reserve strength test. Figure 3.12 compares the response of the corresponding virgin specimen and that of beam F-7 after the 1.7 million cycles of fatigue loading. It is clear that fatigue loading had softened the response to the level of a post-cracked specimen, but had not significantly affected the strength. Failure of the beam in the reserve strength test was triggered by the rupture of FRP tube at the bottom of the mid-span section, as shown in Figure Figure 3.15 depicts typical growth of mid-span deflections and stiffness degradations of CFFT beams (beams F-5 and F-4) fabricated with tube type I having different modes of failure. Beam F-5 was subjected to a single stage of loading at the same initial loading level of beam F-7, i.e., 12.5% to 25% of P static. It is important to note that the selected load range for this beam also fluctuated around its flexural cracking load. Beam F-5 with fiber orientation of ±55 o showed significant deflection in its very early stage of fatigue loading. It reached 3 in of deflection, i.e., 70% of its δ static, within only 1,500 cycles or 0.3% of its fatigue life N f. Deflection continued to grow rapidly, with some stabilizations at various short intervals. On the other hand, the beam lost almost ½ of its initial dynamic stiffness in the first 1,500 cycles, with majority of degradation occurring in the first 10 cycles of loading. This significant loss of stiffness at the very early stage may be attributed largely to the slippage of the concrete core that occurred as a result of the dynamic nature of the loading. Furthermore, matrix cracking of FRP was noticeable at the bottom of the beam in the mid-span region from very early on. Hairline cracks were seen parallel 44

66 Chapter 3 Flexural Fatigue : Experimental Work to the fiber direction and perpendicular to beam axis around mid-span bottom zone of the beam. At 425,000 cycles, necking of FRP tube was visible along with matrix delamination at the bottom of the beam in the mid-span region. Sudden failure occurred at 498,800 cycles by tensile rupture of FRP at the mid-span, when mid-span deflection reached 80% of δ static (see Figure 3.16). Stiffness degradation prior to failure was found to be about 49%, which was only 4% larger than that experienced after the first 1,500 cycles. Two types of failure modes were identified as typical for beams made with tube type I. At the low load range, failure occurred by tensile rupture of FRP tube at mid-span (beams F-1 and F-5), whereas in the high load range (beams F-2 and F-4) shear-compression failure took place (see Figure 3.17). Behavior and mechanism of the second type of shear-compression failure is described below. Figure 3.15 depicts the mid-span deflection growth or damage accumulation and stiffness degradation of beam F-4. The load range was between 5% and 25% of P static. The beam showed a similar behavior as that of beam F-5. However, due to the higher load level, the beam was subjected to a larger initial deflection, which in turn activated a significantly larger end slippage of concrete core at a relatively low number of cycles. An equal amount of slippage was noticed at the top and bottom of the end sections. This indicated that the crack was propagated through the entire depth of the concrete core. Eventually, a large localized crack developed with the increased number of cycles. Contraction or necking of the FRP tube due to the Poisson s effect was noted at mid-span and under the two load points. These were attributed to the large crack and separation in the concrete core. With further opening of the concrete crack at the load point, a crack was formed on the compression side of the tube within the influence zone of the load point. Subsequently, the crack propagated to the bottom of the tube along the fiber direction, as shown in Figure Failure may be characterized as combined compression and transverse shear near the load point. Behavior under two stages of loading was also investigated for a beam fabricated with tube type I. Beam F-1 was subjected to 1 million cycles at a load range of 5% to 15% of P static, and subsequently 5% to 20% of P static until failure. The response was similar to beam F-5 with 16% of δ static as deflection growth and 23% stiffness degradation in the first stage of loading. Behavior in the second stage of loading was similar to beam F-6 with total deflection growth of 64% of δ static and stiffness degradation of 56% at failure. Three phases of damage accumulation similar 45

67 Chapter 3 Flexural Fatigue : Experimental Work to that seen in FRP materials were captured from the response. This confirms the relative significance of matrix cracking and delamination, as compared to fiber rupture, which occurs at failure. Failure was recorded at 1,518,235 cycles, which was quite similar to the failure of beam F-5. Detailed responses of this beam and other beams made with tube type I are provided in Appendix B. Beam F-6 showed a generally similar response to that of beams F-7 and F-1 in the two stages of loading (see Figure 3.18). However, it is important to note that the load range for both stages of loading were within the post-cracked region of the specimen. In other words, the minimum load level was higher than the cracking load of the beam. The specimen showed large cracks on its compression side right under the load point at about 1.2 million cycles, and subsequently a compression failure occurred under the load point due high stress concentration (see Figure 3.19). Prior to failure, the overall deflection and stiffness degradation were 70% of δ static and 43% of the initial stiffness, respectively. Unlike other beams in this test program, moment capacity of beam F-8 was quite low, especially relative to its cracking moment. The ultimate moment capacity of the beam was about 1.33M cr, where M cr is the cracking moment of the beam. Noting that the minimum permissible reinforcement ratio in an RC beam is one that results in an ultimate capacity of 1.2M cr, beam F-8 clearly represented the lowest reinforcement ratio of all specimens, with the smallest postcracked region. Since the load range of 12.5%-25% of P static was well below the cracking load, the fatigue behavior of the beam was expected to be dominated by the uncracked concrete section. Theoretically speaking, for any load range below the cracking load, concrete is expected to be fatigue neutral, since the applied stress range is much less than 0.55 f c '. Therefore, beam F- 8 would have shown the best performance among the four beams tested in this program, if tested at the same load level as the other beams. Keeping this in mind, three stages of loading were employed to better understand the behavior of this beam (see Table 3.2). The specimen survived only 28 cycles in the third stage of loading, when the maximum load level reached 75% of P static. Figures 3.20 and 3.21 show the mode of failure and deflection of beam F-8, respectively, under three stages of loading. 46

68 Chapter 3 Flexural Fatigue : Experimental Work Test Results and Discussion Table 3.2 shows types of beams and their reinforcement indices, ω defined as ((Mirmiran et al. 2000, Fam and Rizkalla 2002) 4 t j f ω = (3.2) D f o ft ' c where t j is the thickness of the FRP tube, D o is the outside diameter of the tube, f ft is the ultimate tensile strength of FRP tube in the longitudinal direction, and ' f c is the unconfined strength of concrete core. Since strength of FRP tube is direction dependent, it needs to take into account the fiber architecture of the tube. Figure 3.22 illustrates the fatigue response of beams F-5 and F-6, where the reinforcement index of beam F-6 is 13 times higher than that of beam F-5. The deflection of each beam is normalized with respect to its ultimate static deflection, δ static, whereas the dynamic stiffness is normalized with respect to its initial stiffness, (EI) o. Beams F-5 and F-6 consist of different fiber architecture. Any change in fiber architecture affects stiffness and strength of the tube. However, effect of fiber architecture is more pronounced on strength. In other words, strength increases or decreases at a higher rate than that of stiffness due to changes in fiber architecture. Therefore, the deflection should be normalized with respect to the static deflection to compare performances of beams with different fiber architecture. It can be seen from the figure that the rate of stiffness degradation, deflection or damage accumulation and fatigue life of CFFT beam are all significantly higher for the beam with relatively low reinforcement index. Barnes and Mays (1999), Shahawy and Beitleman (1999) and Papakonstantinou et al. (2001) have all arrived at similar conclusions from the results of un-strengthened and strengthened RC beams with CFRP and GFRP laminates. Beam F-5, which had a lower reinforcement index failed at 498,800 cycles with 49% stiffness degradation. On the other hand, beam F-6 did not fail after 1 million cycles and only had a stiffness degradation of 22%. Significant change in stiffness may be attributed to the early matrix cracking and matrix delamination, which in turn are due to less effective reinforcement in the longitudinal direction. Substantial matrix cracking in the transverse direction and parallel to fiber angle was observed as early as the first 10 cycles for beam F-5. However, beam F-6 showed no visible cracking after 1 million cycles. 47

69 Chapter 3 Flexural Fatigue : Experimental Work Figure 3.22 illustrates the effect of reinforcement index, ω on the mid-span deflection accumulation and dynamic stiffness degradation for a single stage flexural fatigue loading. Level of applied loading was 12.5%-25% of the respective static strength. Deflection at mid-span is normalized with respect to the ultimate static deflection, and dynamic stiffness is normalized with respect to its value at the first loading cycle. Slippage due to fatigue of interface bond is yet another important factor that contributes to the early stiffness degradation. Figure 3.23 shows the normalized average slippage growth of beams F-5, F-6 and F-7. Average of the four slippage measurements at both ends are taken and normalized with respect to half of the span length. Note that beam F-5 with its low reinforcement index experienced a larger rate of slippage growth as compared to beam F-6. The slippage eventually led to the failure of beam F-5. As shown in Figure 3.24, beams F-5 and F-7 were chosen to show the effect of fiber architecture on fatigue behavior, since their reinforcement indices were similar. Performance was compared only for single stage loading with 1 million cycles and an applied load level between 12.5% and 25% of P static. The better performance of beam F-7, as compared to beam F-5, was mainly attributed to its fiber architecture of the tube and to a lesser extent on the compressive strength of concrete core (see Tables 3.1 and Table 3.2). However, the load levels employed resulted in concrete stresses significantly lower than 0.55 f ' c and therefore, fatigue of FRP tube was more critical than that of concrete core. Beam F-7 has longitudinal fibers at ±34 o with much greater influence on the longitudinal stiffness of the tube. Lower initial deflection results in less relative slippage, thereby maintaining a higher degree of composite action between the tube and the concrete core. No matrix cracking was observed on the outer surface of FRP tube in the first one million cycles. Referring back to the literature review, fatigue behavior of FRP can be classified into three phase of damage accumulation; i) matrix cracking, ii) matrix delamination, and iii) fiber fracture. Beam F-5 experienced matrix cracking and matrix delamination within the first 1,500 cycles, whereas beam F-7 did not show any delamination even after one million cycles. This indicates that FRP tube in beam F-7 was still in the first phase of damage accumulation. Visual observation of the three damage processes and failure by FRP rupture in beam F-5 and other beams made with tube type I indicate that behavior of CFFT beam is largely dominated by the behavior of FRP tube. 48

70 Chapter 3 Flexural Fatigue : Experimental Work Figure 3.25 represents the effect of load range on fatigue behavior of CFFT beams, taking into consideration both the deflection accumulation and stiffness degradation. Responses of beams F-1, F-4 and F-5 are plotted together in the figure. Beam F-1 was subjected to a load range of 5%-15% of P static, beam F-4 was subjected to 5%-25% of P static, and beam F-5 was subjected to 12.5% to 25% of P static. As expected, the rates of deflection growth and stiffness degradation are higher for the beam subjected to the higher load range. Beam F-4 with 20% load range failed at much lower number of cycles than the other two beams. In order to verify its fatigue susceptibility, beam F-2 was tested as a duplicate of beam F-4. It also failed at 5,672 cycles. Plots of end slippages for the three beams are shown in Figure Slippage of beam F- 4 at failure is 5 times higher than that of the companion beam F-1 at one million cycles. This confirms that the interface bond is vulnerable to higher range of fatigue loading, and it could dramatically decrease the fatigue life of the specimen. Comparison of beams F-4 and F-5, with the minimum load levels at 5% and 12.5% of P static, respectively, reveals that fatigue behavior and fatigue life do not depend much on the level of minimum load. It can be noted from the figure that beam F-5 exhibited higher deflection at any given number of cycles, which may be attributed to the lower concrete strength of beam F-5. Findings and conclusions of the effect of load range and maximum load are in general similar to those reported in the literature for the material level studies (Do et al. 1993, Harmon et al. 1998, Mahfuz et al. 1995) and member level studies (Barnes and Mays 1999, Shahawy and Beitleman 1999) studies of unconfined and confined concrete, FRP coupons and RC beams. To demonstrate the effect of end restraint in preventing slippage, and thereby maintaining full composite action, static and fatigue responses of beams F-3 and F-4 are compared in Figure Beam F-3 which had end blocks was subjected to 1 million cycles at the same load level as beam F-4 with no end restraints. The two beams behaved quite differently with different degrees of deflection growth at the initial phase as well as the steady state phase. The steady state of deflection growth was achieved at 1,000 and 25,000 cycles for beams F-4 and F-3, respectively. At the end of the steady state phase, beam F-4 reached 57% of δ static, quite similar in relative magnitude to that of Beam F-1. It can be seen that fatigue life of beam F-3 is dramatically higher than that of beam F-4. Beam F-3 with its end restraints is in fact expected to survive 200 times more cycles than beam F-4. This better fatigue performance is mainly attributed to the low rate of slippage growth in beam F-3, as seen in Figure Better fatigue performance may also be 49

71 Chapter 3 Flexural Fatigue : Experimental Work addressed from the point of view of stiffness degradation. A comparison of the stiffness degradation in the two beams reveals that beam F-3 had a much higher initial stiffness at the beginning of the fatigue loading (see Figure 3.27). This is because beam F-3 has a higher postcracking stiffness in its initial static load-deflection response (see Figure 3.27). Beam F-3 showed 83% higher stiffness than its companion beam F-4. Even though the rate of stiffness degradation of both beams are quite similar in the first few cycles (see Figure 3.27), beam F-4 displayed a higher rate of stiffness degradation in later cycles due to lack of resistance against slippage. Failure in beam F-4 occurred when its stiffness degradation reached 50%. However, beam F-3 lost only 25% of its stiffness after 1 million cycles of loading when the test was stopped. Figure 3.29 shows a comparison of stiffness degradation of all four CFFT beams with the same FRP tube but different load ranges and end conditions. The figure serves two purposes. Firstly, it shows the enhancement in stiffness while the end slippage is preserved by end restraints. Secondly, it shows the total amount of stiffness degradation experienced by CFFT beams during their fatigue life regardless of loading history. Beam F-5 had 28% higher initial stiffness than its companion beams, F-1 and F-4, mainly due to different batches of concrete. Stiffness of each beam is normalized with respect to the stiffness of beam F-4. This shows the higher stiffness of beam F-3. It also presents the percent of stiffness degradations of beams F-1, F-4 and F-5. By comparing the stiffness degradation from Figure 3.29 and the growth of slippage from Figures 3.23, 3.26 and 3.28, two important conclusions may be drawn as follows 1) Fatigue life of a CFFT beam without end restraints is related to the amount of stiffness degradation that takes place during its life time irrespective of the variation of the load range and concrete properties. A CFFT beam is expected to fail when its flexural stiffness reaches 40%-50% of its initial stiffness. For beams with end restraint this value may be much lower, since composite action is maintained throughout the loading history. 2) Slippage is probably the single most important factor that dominates the fatigue behavior and fatigue life of CFFT beams. Fatigue life is directly related to the amount of slippage that occurs between the concrete core and the FRP tube. The load range clearly impacts the slippage. The higher the load range, the higher the slippage. Hence, it is important to preserve the composite action between the concrete core and the FRP 50

72 Chapter 3 Flexural Fatigue : Experimental Work tube. This may be achieved using mechanical shear connectors on the inside surface of the FRP tube, or through end restraints to prevent rigid body movement of the concrete core. 3.6 CHARACTERIZATION OF MATERAIL PROPERTIES OF FRP Observation of the behavior and failure modes of tested beams suggests that fatigue life and performance of CFFTs are mainly governed by the properties of FRP tubes. As mentioned in the literature review, concrete survives up to 10 million cycles at compressive stress of 55% of its static strength. However, concrete stress in the present study was well below that level, especially when considering that concrete was confined by the FRP tube, and therefore had a higher compressive strength. As such, creep and fatigue properties of FRP were investigated experimentally to calibrate material models needed for the analytical modeling of CFFT. A test program was devised comprising of eighteen coupons made with different tube types. Table 3.3 shows the details of the test matrix and some of the test results. All coupons were cut from the unused portions of the tubes, and were prepared according to ASTM D3039 (2002). Each specimen was glued to aluminium tabs with high-strength epoxy to facilitate its gripping, and to reduce stress concentration at its ends (Figure 3.30). For each tube type, two static tension tests were conducted to take the average tensile strength, which was subsequently used to determine the level of applied load in creep and fatigue specimens. For tube types I, II, and III, two tension-tension fatigue tests were conducted at two different stress levels whereas only one creep test was carried out for tube types II and III, and two creep tests for tube type I. No fatigue and creep tests were conducted on tube type V due to its low strength and since it was difficult to maintain low load levels in fatigue and creep tests with the universal testing machine available in the laboratory. All uniaxial tension tests and tension-tension fatigue tests followed ASTM D3039 (2002) and ASTM D3479 (2002), respectively. Figure 3.31 shows a typical setup of static and fatigue tension tests. Stress levels for creep and fatigue tests were provided in Table 3.2. Frequency was kept at 2 Hz, the same as beam tests, to eliminate the effect of loading rate on the dynamic stiffness degradation of the materials. Static tests were performed up to the level of creep or fatigue stress levels to measure the static stiffness of each specimen in displacement control before starting the creep or fatigue test. Tests were stopped when either the specimen failed or 51

73 Chapter 3 Flexural Fatigue : Experimental Work sufficient data was collected to calibrate the creep and fatigue models. Fatigue tests were performed in the 220 kip MTS universal testing machine under load control with a sinusoidal loading pattern. High pressure hydraulic wedge grips were used to hold specimens in position. Each specimen was instrumented with a 0.24 in long strain gage in the middle. At times, microcracking in the matrix caused failure of the strain gage. In those cases, the gage was replaced with a new one before continuing with the test. Two 1.5 in linear pots were used to monitor the change in stroke and to calculate the deformations and average strains in each specimen. Data from strain gages and linear pots were compared and found to be in reasonable agreement. Figures represent the virgin stress-strain curves of the coupons for tube types I, II, III and V, respectively, under uniaxail tension. Small load drops accompanied by change in the stiffness were attributed to matrix cracking. Failure of tube type II was in the form of fiber rupture, whereas for tube type I and tube type III failure was governed by the interlaminar shear of resin and pull out of fibers. This may be attributed to the test procedure. Although some researchers have suggested tension test of the entire tube (Joseph and Perreux 1994, Khatibzadeh and Piggot 1998), ASTM standard D3479 was adhered to in this test program using strips of tube sections. Failure of tube V (Figure 3.35) was initiated in the resin and was followed by fiber rupture. The main purpose of the creep and fatigue coupon tests was to calibrate the Findley creep model (1960) and Ogin et al. (1985) tension-tension fatigue model. These models were then used to perform long-term analysis of CFFT beams, as discussed in Chapter 4. Findley creep model for FRP is given by f cr f o n ( 1 + mt c ) ε =ε (3.3) f where ε o represents the instantaneous strain at time t = 0, and m and n c are material constants that need to be obtained from a least square curve fit to the experimental data. Parameter n c represents the gradient of the curve, and parameter m when multiplied with f ε o provides the strain value at one hour after applying the load. Figures 3.36, 3.37, and 3.38 illustrate the creep deformations of tube types I, II, and III for a time duration of hours and the associated values of m and n c for a stress level of 25% of f ft, where f ft is the tensile strength of the 52

74 Chapter 3 Flexural Fatigue : Experimental Work respective FRP coupon in static test. For tube type I, it was expected that nonlinear viscoelasticity may dominate the behavior. Therefore, an additional specimen Y-6 was tested at 50% of f ft. Value of n is higher for the higher stress level, which confirms the activation of nonlinear viscoelasticity at higher stress levels for tube type I. Tube type II had a higher creep deformation due to a greater volume of resin content in its laminate. None of the creep specimens failed after the specified duration. Matrix crack growth is the primary reason for stiffness degradation in almost every laminated composite material system (Tong 2002). Stiffness of FRP falls gradually as the density of the matrix cracks increases during fatigue cycling. Ogin et al. (1985) used an approach assuming linear relationship between the elastic modulus and crack density, and the total crack length as the power function of the stored elastic energy, given by where n f 2 1 de fmax = A Eo dn (3.4) 2 E Eo 1 E o 1 de is the modulus reduction rate at a given value of E/E o, E o is the uncracked E dn o elastic modulus, E is the secant modulus of FRP at a given number of cycles, and n f and A are the material constants, which are obtained from the least square fit of test data. Ogin et al. (1985) also demonstrated that when the right hand side and left hand side of the above equation are plotted as x and y coordinates in a log-log scale for different maximum stress levels, a straight line can be fit for which n f and A represent the slope and intercept with y axis, respectively. Following this procedure, maximum stress levels of tube types I, II, and III were varied to minimize the testing duration while collecting the necessary data to calibrate n f and A. The minimum stress level was kept constant as 12.5% of the static strength of the corresponding laminate, f ft. Two different stress levels were taken for each tube type, as stated in Table 3.3. Figures 3.39, 3.40, and 3.41 show the plots of the above equation in log-log scale at different stress levels for tube types I, II, and III, respectively. n f and A values are extracted from the plots and are shown in the figures. Once n f and A values are known, the relation between the dynamic 53

75 Chapter 3 Flexural Fatigue : Experimental Work modulus and the number of cycles and the stress levels for the three different types of tubes can be expressed as f max E = Eo N Eo for tube type I (3.5) f max E = Eo N Eo for tube type II (3.6) 1.52 f max E = Eo N Eo for tube type III (3.7) The above equations are arrived at by integrating Equation (3.4) and substituting the respective values of n f and A obtained from log-log plots of test data. Figures 3.42, 3.43 and 3.44 show the plots of the above equations with the experimental graphs of dynamic stiffness degradation. Good correlation is noted. A comparison of the predicted stiffness degradations for tube types I, II, and III is provided in Figure It is clear from the figure that tube type I had the highest degradation. The same observation was made for the CFFT beam made of tube type I. On the contrary, tube type II has the lowest degradation. The degradation trend may be correlated to the reinforcement index of the tubes. Table 3.3 shows fatigue life of each specimen under tension-tension loading, if failure occurred. Specimens Y-3 and Y-4 did not fail under fatigue loading. Figure 3.32 shows the reserve strength test of specimen Y-3 after fatigue loading. Stiffness and strength degradations of the coupon are clear from the figure. Coupons of tubes type II and III failed under fatigue loading but in a different mechanism from the static test. In tube type II, cracks first formed in the middle resin layer (see Figure 3.33) after which delamination at the interface of inner resin layer and the laminate occurred. At this stage, only the outer fiber layers resisted the load. Failure of the coupon occurred once the cracks propagated along the width by ripping off the outer fiber layers. The Achilles heel of tube type II undoubtedly lies with the interface of fiber and the middle resin layer. Failure of type III tube happened once the delamination cracks in resin interface were connected and formed a complete separation of the specimen across its width (Figure 3.43). 54

76 Chapter 3 Flexural Fatigue : Experimental Work Table 3.1 Mechanical properties of FRP tubes used in fatigue tests Tube type (Designated surface color) I (Yellow) II (White) III (Grey) V (Green) Fiber architecture [±55 o ] 17 layers V f = 75.5% [0 o /0 o /+45 o /-45 o ] layers V f = 51.2% [±34 o +80 o ±34 o ] 5 layers V f = 51% [±75 o ] 14 layers Tensile strength (ksi) Tensile elastic modulus (ksi) Compressive strength (ksi) Compressive elastic modulus (ksi) Hoop strength (ksi) Hoop elastic modulus (ksi) N/A N/A * N/A 19.0* 1305* * 4115* V f = 44% * Predicted by laminated theory; Tube I bending strength = 23 ksi, bending modulus = 1460 ksi; Tube II bending strength = 81 ksi, bending modulus = 3564 ksi Coupon testing by Fam & Rizkalla (2002) 55

77 Chapter 3 Flexural Fatigue : Experimental Work Table 3.2 Test results of flexural fatigue Beam Concrete strength, ' f c (ksi) Reinforcement index ω = 4t D f ft ' o fc Cracking moment, M cr (P cr ) (kip-in Static capacity, M static (P static ) (kip-in Level and stages of loading No. of cycles Total Cycles in each stage Failure mode and kip) and kip) F (13.3) 1,824 (150) 5% - 15% P static 5% - 20% P static 1.52 million (N f ) 1 million 518,235 Tension F (23.5) 1,824 (150) 5% -25% P static 5,672 (N f ) 5,672 Shear compression *F (15.7) 5% - 25% 1,824 P static (150) 5% - 35% P static million million (N f ) 90,000 Did not fail F (13.6) 1,824 (150) 5% - 25% P static 5,264 (N f ) 5,264 Shear compression F (18.8) 1,824 (150) 12.5% - 25% P static 498,800 (N f ) 498,800 Tension F (7.4) 4,476 (373) 12.5% - 25% P static 37.5% - 50% P static million million (N f ) 0.2 million Compression F (19.5) 1,140 (95) 12.5% -25% P static 12.5% - 50% P static 1.7 million 1 million 0.7 million Did not fail F (8.2) 123 (10.2) 12.5% - 25% P static 12.5% -25% P static 12.5% -75% P static 35,128 (N f ) ,100 P static and P cr are total applied loads; N f is number of cycles to failure; *Only beam with end restraint 28 Tension 56

78 Chapter 3 Flexural Fatigue : Experimental Work Table 3.3 Test matrix and results of tension coupon tests Tube type I II III V Specimen No. Gage length, l g (in) Width, b (in) Total thickness, t j (in) Type of test Levels of loading, % of f ft No. of cycles, N or duration, hours Failure cycles Y static - Y static - Y fatigue 12.5% - 65% 430,000 - Y fatigue 12.5% -70% 130,000 - Y creep 25% Y creep 50% 42 W static - 45 W static - W fatigue 12.5% -35% 308, ,930 W fatigue 12.5% - 40% 77,644 77,644 W creep 25% 48 G static - G static - G fatigue 12.5% - 45% 482, ,326 G fatigue 12.5% - 50% 177, ,522 G creep 25% 48 GR static - GR static - N f 57

79 58 F-1 Observation of two-stage loading Tube type I (±55 o ) 17 Outer dia. D o = in *Thickness = 0.2 in Reinforcement index ω = F-2 F-3 Load range *Only structural thickness, excluding protective gel End restraint F-4 F - 5 Load range Test Matrix Tube type II (0 o /0 o /+45 o /-45 o ) 10 Outer dia. D o = 12 in Thickness = 0.46 in Reinforcement index ω = 1.97 Reinforcement index Fiber architecture Figure 3.1 Details of the test parameters Tube type III {(±34 o ) 2 /(80 o ) 1 /(±34 o ) 2 } Outer dia. D o = in Thickness = in Reinforcement index ω = Tube type V (±75 o ) 14 Outer dia. D o = 12 in Thickness = 0.16 in Reinforcement index ω = F - 6 F - 7 F - 8 Minimum reinforcement index Chapter 3 Flexural Fatigue : Experimental Work 58

80 59 Steel I beam L/6 L/3 L/3 L/3 L/6 L = 6 ft 3.5 in Front View Strain gage layout underneath linear pot Concrete block 59 l d = 4 in 45 o 45 o D o /2 D o /2 D o Tube I D o = in, t j = 0.20 in Tube II D o = in, t j = 0.75 in Tube III D o = in, t j = 0.28 in Tube V D o = in, t j = 0.16 in l dl = 8 in Side Elevation Figure 3.2 Schematics of static and fatigue test setup and instrumentation of CFFT beams C L Legend Strain gage in the longitudinal and hoop direction Inclinometer Linear pot Short linear pot to measure strain 1 3/8 in thick steel plate 3 in thick neoprene pad 1 3/8 in thick steel plate Chapter 3 Flexural Fatigue : Experimental Work

81 Chapter 3 Flexural Fatigue : Experimental Work Figure 3.3 CFFT beam F-5 subjected to four point bending fatigue without lateral restraint Lateral restraint Figure 3.4 CFFT beam F- 4 with lateral restraint to guide actuator 60

82 Chapter 3 Flexural Fatigue : Experimental Work Figure 3.5 CFFT beam F-3 with end restraint S-6 Tube type I - beam S-3 Tube type I - beam S-4 Tube type II - beam S-6 Tube type III - beam S-8 Tube type V - beam F-8S ' 3 c D i f M F-8S S S-8 S δ L Figure 3.6 Static responses of tube types used in fatigue study 61

83 Chapter 3 Flexural Fatigue : Experimental Work 12 9 Tension 6 Compression 3 Depth (in) 0-3 *load drop after first crack Typical failure At 25% of P static : before first crack -6 At 50% of P static : before first crack At 80% of P static : before first crack -9 At 40% of P static : after first crack* At 75% of P static : after first crack At ultimate P static Longitudinal strain (me) Figure 3.7 Typical mid-span strain profile of CFFT beam in static test Mid-span deflection (in) Dynamic secant stiffness (kip-in) Beam F-7 : Deflection Beam F-7 : Stiffness No. of cycles (N) Figure 3.8 Fatigue response of beam F-7 under two-stage loading 62

84 Chapter 3 Flexural Fatigue : Experimental Work 0.0 Beam span (in) Deflection (in) C L 1st cycle 100 cycle 5000 cycle cycle cycle cycle cycle cycle cycle cycle cycle Figure 3.9 Progressive growth of deflection in CFFT beam F-7 Longitudinal strain (me) Pot longitudinal top or 0o o Pot longitudinal 45 Pot longitudinal 90 o o Pot longitudinal 135 o Pot longitudinal bottom or Compression Tension No. of cycles (N) Figure 3.10 Evolution of longitudinal strains of CFFT beam for tube type III 63

85 Chapter 3 Flexural Fatigue : Experimental Work 8 Based on linear pot measurement 6 0 o 4 45 o Depth (in) o 90 o 1st cycle 25th cycle 100 cycle cycle cycle cycle cycle cycle cycle cycle cycle o Longitudinal strain (me) Figure 3.11 Mid-span longitudinal strain profile of beam F Virgin response Applied load (kip) Degradation Reserve bending response Deflection (in) Figure 3.12 Comparison of virgin and reserve strength responses of beam F-7 64

86 Chapter 3 Flexural Fatigue : Experimental Work Figure 3.13 End slippage after 1.7 million cycles Figure 3.14 Tensile rupture in reserve strength test Deflection (in) No. of cycles (N) F-4 : Deflection F-5 : Deflection 20 F-4 : Stiffness F-5 : Stiffness 0 Dynamic secant stiffness (kip-in) Figure 3.15 Typical responses of tube type I CFFT beams with two different failure modes 65

87 Chapter 3 Flexural Fatigue : Experimental Work Figure 3.16 Tensile failure mode in CFFT beam of tube type I Figure 3.17 Shear-compression failure mode of tube type I CFFT beam Deflection (in) Dynamic secant stiffness (kip-in) Deflection Stiffness No. of cycles (N) Figure 3.18 Flexural fatigue response of beam F-6 made with tube type II 66

88 Chapter 3 Flexural Fatigue : Experimental Work Figure 3.19 Compression failure mode in CFFT beam of tube type II Figure 3.20 Tensile failure mode in CFFT beam of tube type V % to 75% P static 0.16 Deflection (in) % to 50% P static % to 25% P static Deflection No. of cycles (N) Figure 3.21 Response of CFFT beam F-8 made with tube type II 67

89 Chapter 3 Flexural Fatigue : Experimental Work P max = 25% P static P min = 12.5% P static δ δ static EI ( EI ) o Beam F-6 : Deflection 0.20 Beam F-6 : Dynamic secant stiffness Beam F-5 : Deflection Beam F-5 : Dynamic secant stiffness No. of cycles (N) Figure 3.22 Effect of reinforcement index on fatigue behavior Beam F-5 : End slip Beam F-6 : End slip Beam F-7 : End slip P max = 25% P static P min = 12.5% P static 2u L No. of cycles (N) Figure 3.23 Comparison of slippage of beams F-5, F-6 and F-7 68

90 Chapter 3 Flexural Fatigue : Experimental Work δ δ static EI ( EI ) o P max = 25% P static P min = 12.5% P static Beam F-7 : Deflection Beam F-7 : Dynamic secant stiffness Beam F-5 : Deflection Beam F-5 : Dynamic secant stiffness No. of cycles (N) Figure 3.24 Effect of fiber architecture on fatigue behavior % to 25% P static 0.8 δ δ static % to 25% P static 0.6 EI ( EI ) o F1 : Deflection F-4 : Deflection F-5 : Deflection F-1 : Dynamic secant stiffness F-4 : Dynamic secant stiffness F-5 : Dynamic secant stiffness % to 15% P static No. of cycles (N) 0 Figure 3.25 Effect of load range and minimum applied load on fatigue behavior 69

91 Chapter 3 Flexural Fatigue : Experimental Work Beam F-1 Beam F-4 Beam F-5 5% to 25% P static % to 25% P static 2u L % to 25% P static No. of cycles (N) Figure 3.26 Comparison of slippage of beams F-1, F-4 and F F-3 : Deflection :with end restraint F-4 : Deflection :without end restraint F-3 : Dynamic secant stiffness F-4 : Dynamic secant stiffness Applied load (kip) 50 Beam F-3 40 Beam F Deflection (in) δ δ static P max = 25% P static P min = 5% P static Second stage 1.5 ( EI ) restrained ( EI ) O unrestrain ed Second stage No. of cycles (N) 0 Figure 3.27 Effect of end boundary conditions on fatigue behavior 70

92 Chapter 3 Flexural Fatigue : Experimental Work Beam F-3 : End slip Beam F-4 : End slip P max = 25% P static P min = 5% P static u L No. of cycles (N) Figure 3.28 Comparison of slippage for different end conditions F-1 : Stiffness F-3 : Stiffness F-4 : Stiffness F-5 : Stiffness F-3 : Stage 1 5% to 25% P static F-3 : Stage 2 5% to 35% P static 1.50 ( EI ) restrained ( EI ) O unrestrain ed 1.00 F-5 : Stage % to 15% P static F-1 : Stage 1 5% to 15% P static F-4 : Stage 1 5% to 25% P static No. of cycles (N) F-1 : Stage 2 5% to 20% P static Figure 3.29 Comparison of dynamic stiffness degradation of all CFFT beams of tube type I 71

93 Chapter 3 Flexural Fatigue : Experimental Work Aluminum tabs Strain gage Figure 3.30 : Typical tension coupon specimen Figure 3.31 : Typical static, creep and fatigue test setup 72

94 Chapter 3 Flexural Fatigue : Experimental Work 10 Matrix crack 8 Tensile stress (ksi) 6 4 Test stopped Tension failure 2 0 Tube type I-Tension Tube type I-Reserve tension Strain (in/in) Figure 3.32 Static response and reserve tension response after fatigue of tube type I coupon 60 Tube type II 50 Tensile Stress (ksi) Tension failure 10 Thickness with resin layers Strain (in/in) Figure 3.33 Static tensile response of tube type II coupon 73

95 Chapter 3 Flexural Fatigue : Experimental Work 20 Tube type III 16 Tensile stress (ksi) 12 8 Tension failure Strain (in/in) Figure 3.34 Static tensile response of tube type III coupon 5 Tube type V 4 Tensile stress (ksi) Tension failure Strain (in/in) Figure 3.35 Static tensile response of tube type V coupon 74

96 Chapter 3 Flexural Fatigue : Experimental Work Strain (in/in) m = n = m = n = Experiment- 25% ft Findley model-25% f ft Experiment-50% f ft Findley model-50% Time, t (hours) f f ft Figure 3.36 Tensile creep response at 25% and 50% of ultimate strength of tube type I coupon m = n = Strain (in/in) Experiment : 25% Findley Model Time, t (hours) f ft Figure 3.37 Tensile creep response at 25% of ultimate strength of tube type II coupon 75

97 Chapter 3 Flexural Fatigue : Experimental Work m = n = Strain (in/in) Experiment - 25% Findey Model Time, t (hours) f ft Figure 3.38 Tensile creep response at 25% of ultimate strength of tube type III coupon y = x R 2 = A = = n = 2.83 log 1 E o de dn f max log E 2 o 1 Figure 3.39 Modulus reduction rate of tube type I coupon in log-log scale E E o 65% 70% f f ft ft 76

98 Chapter 3 Flexural Fatigue : Experimental Work Dynamic modulus, E (ksi) Experiment Fatigue model No. of cycles (N) Figure 3.40 Comparison of experimental and fatigue model stiffness degradations of tube type I y = x = R A = = n = 3.39 log 1 E o de dn f max log 2 E E o 1 E o 40% 45% f ft f ft Figure 3.41 Modulus reduction rate of tube type II coupon in log-log scale 77

99 Chapter 3 Flexural Fatigue : Experimental Work Dynamic modulus, E (ksi) Fatigue failure Fatigue failure 200 Experiment Fatigue model No. of cycles (N) Figure 3.42 Comparison of experimental and fatigue model stiffness degradations of tube type II y = x = R A = = n = log 1 E o de dn f max log 2 E E o 1 E o Figure 3.43 Modulus reduction rate of tube type III coupon in log-log scale 45% 50% f f ft ft 78

100 Chapter 3 Flexural Fatigue : Experimental Work Dynamic modulus (ksi) Fatigue failure Fatigue failure Experiment Fatigue model No. of cycles (N) Figure 3.44 Comparison of experimental and fatigue model stiffness degradations of tube type III EI ( EI ) o f max = 5 ksi Tube type I Tube type II Tube type III No. of cycles (N) Figure 3.45 Comparison of stiffness degradations of three different tubes 79