Effect of beam size and FRP thickness on interfacial shear stress concentration and failure mode of FRP strengthened beams

EFFECT OF BEAM SIZE AND FRP THICKNESS ON INTERFACIAL SHEAR STRESS CONCENTRATION AND FAILURE MODE IN FRP-STRENGTHENED BEAMS LEONG KOK SANG NATIONAL UNIVERSITY OF SINGAPORE 2003 Founded 1905 EFFECT OF BEAM SIZE AND FRP THICKNESS ON INTERFACIAL SHEAR STRESS CONCENTRATION AND FAILURE MODE IN FRP-STRENGTHENED BEAMS LEONG KOK SANG (B.Eng. (Hons.). UTM) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGEMENTS I would like to express my heartfelt gratitude and thanks to my supervisor, Assistant Professor Mohamed Maalej, for his invaluable guidance, encouragement and support throughout the research years. I wish to thank the National University of Singapore for providing the financial support and facilities to carry out the present research work. Special thanks are extended to my family, and friends especially Ms. S.C. Lee and Mr. Y.S. Liew for their continuous support and encouragement. Furthermore, I would like to acknowledge the assistance of Mr. Michael Chen, a third year MIT student, with the laboratory work during his three-month attachment with National University of Singapore. Finally I would like to thank the technical staff of the Concrete Technology and Structural Engineering Laboratory of the National University of Singapore, for their kind help with the experimental work. January, 2004 Leong Kok Sang i TABLE OF CONTENTS ACKNOWLEDGEMENTS .............................................................................................. i TABLE OF CONTENTS ................................................................................................. ii SUMMARY ...................................................................................................................... iv NOMENCLATURE......................................................................................................... vi LIST OF FIGURES ......................................................................................................... ix LIST OF TABLES ......................................................................................................... xiii CHAPTER ONE: Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Objective and Scopes of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Outline of Thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 CHAPTER TWO: LITERATURE REVIEW 2.1 2.2 2.3 2.4 Failure Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Flexural Failure by FRP Rupture and Concrete crushing. . . . . . . . . . 2.1.2 Shear Failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Concrete Cover Separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Plate-End Interfacial Debonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Intermediate Flexural Crack-Induced Debonding . . . . . . . . . . . . . . . . . 2.1.6 Intermediate Flexural Shear Crack-Induced Debonding… … . . Interfacial Shear Stress Concentration ………………………………..… 2.2.1 Taljsten’s Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Smith and Teng’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Measurement of Interfacial Shear Stresses. . . . . . . . . . . . . . . . . Strength Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Plate-End Interfacial Debonding ………………... . . . . . . . . . . . . . . . . 2.4.1.1 Ziraba et al.’s Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1.2 Varastehpour and Hamelin’s Model. . . . . . . . . . . . . . . . . . . . . . 2.4.2 Concrete Cover Separation ……………….. . . . . . . . . . . . . . . . . . . . . . . 2.4.2.1 Saadatmanesh and Malek’s Model. . . . . . . . . . . . . . . . . . . . . . 2.4.2.2 Jansze’s Model.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Intermediate Flexural Crack-Induced Debonding… … … … … . . 2.4.4 Intermediate Flexural Shear Crack-Induced Debonding… . . … . . 4 5 5 5 5 6 6 7 7 9 11 12 13 13 14 16 16 16 17 18 ii CHAPTER THREE: EXPERIMENTAL INVESTIGATION 3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Specimen Reinforcing Details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Casting Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 CFRP Application. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Testing Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.81 Effects of Strengthening. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.82 Failure Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.83 Interfacial Shear Stresses … . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 23 24 24 25 25 25 26 26 28 30 31 CHAPTER FOUR: FINITE ELEMENT ANALYSIS 4.1 4.2 4.3 4.4 4.5 4.6 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elements Designation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis Procedures… … … … … … . . … … . … . . … … … … … … . … . Material Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of Series A, B and C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Load-Deflection Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 CFRP Strain Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Interfacial Shear Stresses… . … … … . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.4 Effect of Cracking on Interfacial Shear Stress Distribution in the Adhesive Layer… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 51 51 52 53 53 54 54 55 57 CHAPTER FIVE: STRENGTHENING OF RC BEAMS INCORPARATING A DUCTILE LAYER OF ENGINEERED CEMENTITIUOS COMPOSITE 5.1 5.2 5.3 5.4 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Test Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Element Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Load-Deflection Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 CFRP Strain Distribution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Interfacial Shear Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 83 84 85 86 86 87 87 CHAPTER SIX: CONCLUSIONS AND RECOMMENDATIONS Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recommendations for Further Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 101 REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.1 6.2 iii SUMMARY Epoxy-bonding of fibre reinforced polymers (FRP) has emerged as a new structural strengthening technology in response to the increasing need for repair and strengthening of reinforced concrete structures. Because of its excellent strength- and stiffness-to-weight properties, corrosion resistance, and the benefit of minimal labor and downtime, FRP has become a very attractive construction material and has been shown to be quite promising for the strengthening of concrete structures. Although epoxy bonding of FRP has many advantages, most of the failure modes of FRPstrengthened beams occur in a brittle manner with little or no indication given of failure. The most commonly reported failure modes include ripping of the concrete cover and interfacial debonding. These failure modes occur mainly due to interfacial shear and normal stress concentrations at FRP-cut off points and at flexural cracks along the beam. Although there are various analytical solutions proposed to evaluate the state of stress at and near the FRP cut-off points as well as the maximum carbon fibre reinforced polymer (CFRP) tensile stress for intermediate crack-induced debonding, there is a lack of definite laboratory tests and numerical analyses supporting the validity of the proposed model. The main objective of this study is, therefore, to investigate the interfacial shear stress concentration at the CFRP cut-off regions as well as the failure mode of CFRP-strengthened beams as a function of beam size and FRP thickness. Because most structures tested in the laboratory are often scaled-down versions of actual structures (for practical handling), it would be interesting to know whether the results obtained in the laboratory are influenced by the difference in scale. iv The scope of the research work is divided into three parts: 1) a laboratory investigation involving seventeen simply-supported RC beams to study the interfacial shear stress concentration at the CFRP cut-off regions as well as the failure mode of CFRP-strengthened beams; 2) a finite element investigation to verify the experimental results; and 3) an investigation of the performance of FRP-strengthened beams incorporating Engineered Cementitious Composites (ECC) as a ductile layer around the main flexural reinforcement. The studies showed that increasing the size of the beam and/or the thickness of the CFRP leads to increased interfacial shear stress concentration in CFRPstrengthened beams as well as reduced CFRP failure strain. The non-linear FE analysis was found to predict the response of the beam fairly well. Finally, the results showed that ECC can indeed delay debonding of the FRP and result in the effective use of the FRP materials Keywords: CFRP; strengthened beams; interfacial shear stress; failure mode; debonding; ECC. v NOMENCLATURE a Distance from support to CFRP cut-off point A, B Coefficients of curve fitting of ε=A×(1-e-Bx); Ac Cross sectional area of concrete Afrp Cross sectional area of FRP b Distance from CFRP cut-off point to loading point bc Width of concrete beam bfrp Width of FRP sheet Bm Modified shear span C Coefficient of friction d Effective depth of concrete beam dfrp Distance from top of beam to centre of FRP dmax Maximum aggregate size Ea Elastic modulus of adhesive Ec Elastic modulus of concrete Eelastic Elastic energy of beam Efrp Elastic modulus of FRP Etol Total energy of beam f c' Cylinder strength of concrete fcu Cube strength of concrete fct Tensile strength of concrete Ga Shear modulus of adhesive hc Depth of beam I Second moment of area Itr Second moment of area of transformed cracked FRP section vi Itr,conc Second moment of area of transformed cracked concrete section Kn Normal stiffness Ks Shear stiffness l Distance from middle of FRP-beam to CFRP cut-off point L Span of beam Lbd Bond length Le Effectives stress transfer (bond) length Mo Bending moment P Point load Pult Ultimate load; R2 Correlation coefficient of curve fitting; ta Thickness of adhesive tfrp Thickness of FRP Vo Shear force xtr,frp Neutral axis of transformed cracked FRP section xtr,conc Neutral axis of transformed cracked concrete section yc, yfrp Distance from the bottom of concrete and top of FRP to their respective centroid Zc Section modulus of concrete ε Strain in the FRP plate; εs Maximum tensile strain εpfail Strain in the FRP at midspan at failure; εpu FRP tensile rupture strain; εu Limiting strain of concrete α Effective shear area multiplier vii τ Shear stress σy Normal stress σdb Debonding stress φ Friction angle σ1 Principal stress σx Longitudinal stress caused by bending moment βp Ratio of bonded plate width to the concrete member ρp CFRP reinforcement ratio, Ap/Ac ∆ Deflection of the beam at midspan; ∆y Deflection of the beam at midspan at the yielding of steel reinforcement ∆fail Deflection of the beam at midspan at failure load ψ Dilantancy angle of concrete in Drucker-Prager plasticity model µ∆ Deflection ductility index µe Energy ductility index viii LIST OF FIGURES Page Figure 2.1(a) Failure mode in FRP-strengthened beams i. FRP rupture ii. Concrete crushing iii. Shear failure iv. Concrete cover ripping v. Plate-end interfacial debonding 19 (After Teng et al. 2002a) Figure 2.1(b) Failure mode in FRP-strengthened beams vi. Intermediate flexural crack-induced debonding v. Intermediate flexural shear crack-induced debonding (After Teng et al. 2002a) Figure 2.2 Type A partial cover separation (After Garden and Hollaway 1998) Figure 2.3 20 20 Type B partial cover separation (After Garden and Hollaway 1998) 21 Figure 2.4 FRP-strengthened beam 21 Figure 2.5 Load cases 22 Figure 3.1 Specimen reinforcing details 38 Figure 3.2 Section details for Series A, B and C beams 39 Figure 3.3 Reinforcement of Series A, B and C 39 Figure 3.4 Series A, B and C beams 40 Figure 3.5 Typical Series A beams test setup 40 Figure 3.6 Typical Series B beams test setup 41 Figure 3.7 Typical Series C beams test setup 41 Figure 3.8 Notched beam specimen 42 Figure 3.9 Load-midspan deflection for Series A beams 43 Figure 3.10 Load-midspan deflection for Series B beams 43 Figure 3.11 Load-midspan deflection for Series C beams 44 ix Figure 3.12 Approximate calculation of equivalent elastic energy release at failure Figure 3.13 Comparison of measured and predicted CFRP debonding strains Figure 3.14(a) 50 Typical finite element idealization of the (a) RC beams (b) FRP-strengthened beams Figure 4.2 49 Variation of peak interfacial shear stress with respect to beam depth for Group 1 and 2 beams at peak load Figure 4.1 48 Experimentally-measured interfacial shear stress distributions in Series C Figure 3.19 47 Experimentally-measured interfacial shear stress distributions of Series B Figure 3.18 46 Experimentally-measured interfacial shear stress distributions of Series A Figure 3.17 45 Load versus CFRP strain at midspan for Group 2 (ρρ=0.212%) beams Figure 3.16 45 Nominal bending stress at peak load as a function of beam depth Figure 3.15 45 Nominal bending moment at peak load as a function of beam depth Figure 3.14(b) 44 61 Modified Hognestad compressive stress-strain curve of concrete 62 Figure 4.3 Material properties 62 Figure 4.4 Load-deflection response of control beams in Series A iff 63 Figure 4.5 Load-deflection response of control beams in Series B 63 Figure 4.6 Load-deflection response of control beams in Series C 64 Figure 4.7 Load-deflection response of FRP-strengthened beams in Series A 65 x Figure 4.8 Figure 4.9 Load-deflection response of FRP-strengthened beams in Series B 66 Load-deflection response of FRP-strengthened beams in 67 Series C Figure 4.10 CFRP strain distribution in Series A at peak load 68 Figure 4.11 CFRP strain distribution in Series B at peak load 69 Figure 4.12 CFRP strain distribution in Series C at peak load Load-d 70 Figure 4.13 Interfacial shear stress distribution in the CFRP cut-off region for Series A at peak load Figure 4.14 Interfacial shear stress distribution in the CFRP cut-off region for Series B at peak load Figure 4.15 72 Interfacial shear stress distribution in the CFRP cut-off region for Series C at peak load Figure 4.16 71 73 Variation of peak shear stresses with respect to beam depth for group 1 and 2 beams 74 Figure 4.17 Location of elements with lower tensile strength 75 Figure 4.18 Interfacial shear stress distribution in the adhesive layer in the CFRP cut-off region Figure 4.19 Shear stress distribution in FRP strengthened RC flexural members (After Buyukozturk et. al 2004) Figure 4.20 77 Numerical crack symbols and interfacial shear stress distribution in the adhesive layer at load P=32 and 40 kN Figure 4.22 76 Numerical crack symbols and interfacial shear stress distribution in the adhesive layer at load P= 8, 16 and 24 kN Figure 4.21 75 78 Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=32, 40 and 48 kN 79 xi Figure 4.23 Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=56, 64 and 72 kN Figure 4.24 80 Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=80 and 86 kN 81 Figure 5.1 Specimen reinforcing details 93 Figure 5.2 Tensile stress-strain curve of ECC test 93 Figure 5.3 Load-deflection responses of beams ECC-1, ECC-2, A1 and 94 A3 Figure 5.4 Debonding of CFRP sheets in beam ECC-2 (a) Debonding of CFRP (b) CFRP sheets after debonding (c) Bottom surface of beam ECC-2 after debonding Figure 5.5 Middle section cracking behaviour of control beams ECC-1 and A1, respectively MiA1-A2 control beams Figure 5.6 95 96 Cracking patterns of beams ECC-2 and A3 (a) Cracking patterns of beam ECC-2 around the loading point.(b) Cracking patterns of beam A3 around the loading point Figure 5.7 96 Simplified multi-linear tension softening curve for numerical modelling 97 Figure 5.8 Load-deflection response of control beams 97 Figure 5.9 Load-deflection response of CFRP strengthened beams 98 Figure 5.10 CFRP strain distribution of beam ECC-2 at peak load 98 Figure 5.11 Interfacial shear stress distribution in the CFRP cut-off Figure 5.12 region at peak load of beam ECC-2Ll beams 99 Flexural-shear crack at CFRP cut-off point of beam ECC-2L 99 xii LIST OF TABLE Page Table 3.1 Description of specimens 33 Table 3.2 Material properties 33 Table 3.3 Material properties of CFRP provided by manufacturer 33 Table 3.4 Location of strain gauges on the CFRP sheets along half of the beam 34 Table 3.5 Summary of results 35 Table 3.6 Ductility index of FRP-strengthened beam 36 Table 3.7 Curve fitting results 37 Table 4.1 Material model for concrete in Series A and B 59 Table 4.2 Material model for concrete in Series C 60 Table 4.3 Material model for CFRP, adhesive and steel reinforcement 60 Table 5.1 ECC and concrete mix proportions 89 Table 5.2 Material properties of ECC and concrete 89 Table 5.3 Summary of test results 89 Table 5.4 Material model for concrete 90 Table 5.5 Material model for ECC 91 Table 5.6 Material model for CFRP, adhesive and steel reinforcement 92 xiii CHAPTER ONE INTRODUCTION Statistics have shown that a great number of structures may need to be strengthened or rehabilitated due to changes in utilization, damages (e.g. fire, accident), deterioration (e.g. corrosion of steel) or even construction defects. For instance, in the United States, Canada and United Kingdom, it is estimated that about 243,000 infrastructures are in need of remedial action at a cost of at least $ 296 billion (Bonacci and Maalej 2001). The increasing demand for structural strengthening has pointed to the need to develop a cost-effective structural strengthening technology. The emergence of plate/sheet bonding technique using fibre reinforced polymers (FRP) is in response to this challenge. FRP bonding technique has been established as a simple and economically viable way of strengthening and repairing concrete structures. The use of fibre-reinforced polymer presents a labor saving, aesthetically pleasing and rapid field application of plate bonding. Moreover, FRP does not corrode and creep, thereby offering long-term benefits. The application of FRP involves buildings, bridges, chimneys, culverts and many others. Although epoxy bonding of FRP has many advantages, most of the failure modes of FRP-strengthened beams occur in a brittle manner with little or no indication given of failure. The most commonly reported failure modes include ripping of the concrete cover and interfacial debonding. These failure modes occur mainly due to interfacial shear and normal stresses concentrations at FRP-cut off points and at flexural cracks along the beam. Even though researchers have shown that an anchorage system can be used to prevent plate debonding, the design is still mainly based on intuition (Mukhopadhyaya and Swamy 2001). Moreover, the 1 inability to determine the optimum way of utilizing the FRP will only come at a significant increase in cost. 1.1 Objective and Scopes of Research Numerous researchers have studied interfacial stresses intensively over the past few years. Several analytical models have been proposed to quantify these stresses in order to predict the failure mode of FRP-strengthened beam. However, there is a lack of definite laboratory tests and numerical analyses to support the validity of the proposed models. The main objective of this study is, therefore, to investigate the interfacial shear stress concentration at the carbon fibre reinforced polymer (CFRP) cut-off regions as well as the failure mode of CFRP-strengthened beams as a function of beam size and FRP thickness. Because most structures tested in the laboratory are often scaled-down versions of actual structures (for practical handling), it would be interesting to know whether the results obtained in the laboratory are influenced by the difference in scale. The scope of the research work is divided into three parts: 1) A laboratory investigation of the interfacial shear stress concentration at the CFRP cut-off regions as well as the failure mode of CFRP-strengthened beams as a function of beam size and FRP thickness 2) A finite element investigation to verify the experimental results. 3) An investigation of the performance of FRP-strengthened beams incorporating Engineered Cementitious Composites (ECC) as a ductile layer around the main flexural reinforcement. 2 1.2 Outline of Thesis The present thesis is divided into six chapters. Chapter one introduces the background, research scope and objectives of this study. Chapter Two gives an introduction to previous and latest studies dealing with interfacial shear stress concentration as well as failure mode of FRP-strengthened beams. In particular, this chapter describes the various analytical interfacial stresses and strength models available in the literature to date. Chapter Three presents a detailed description of the experimental setup and procedure. Analysis and discussion of the experimental results are also included. Chapter Four presents the results of numerical simulations carried out to verify the experiment results. Chapter Five presents the results of an investigation where a ductile ECC layer is used to replace the ordinary concrete around the main flexural reinforcement to delay the debonding failure mode and increase the deflection capacity of the FRP-strengthened beam. Chapter Six summarizes the main findings of the study and provides some recommendation for future works. 3 CHAPTER TWO LITERATURE REVIEW 2.1 Failure Modes Over the years, extensive research works have been carried out to study the various failure modes of FRP-strengthened beams. This has given rise to many classifications of failure modes (Chajes et al. 1994, Meier, 1995 Buyukozturk and Hearing 1998, Chaallal et al. 1998, Garden and Hollaway 1998, Taljsten 2001 and Teng et al. 2003). Overall, Teng et al. (2003) appear to provide the latest and most comprehensive classification of failure modes. In their paper, they identified seven types of failure modes in FRP-strengthened beams (Figure 2.1): a) Flexural failure by FRP rupture b) Flexural failure by concrete crushing c) Shear failure d) Concrete cover separation e) Plate-end interfacial debonding f) Intermediate flexural crack-induced interfacial debonding g) Intermediate flexural shear crack-induced interfacial debonding Of all these failures, failure mode (d) and (e) were classified as plate-end debonding while failure mode (f) and (g) were classified as intermediate crackinduced interfacial debonding. A mixture between these failure modes are also possible such as concrete cover separation combined with plate-end interfacial debonding and plate debonding at a shear crack section with extensive yielding of the tension reinforcement (Taljsten 2001). 4 2.1.1 Flexural Failure by FRP Rupture and Concrete Crushing FRP-strengthened beams can fail by tensile rupture or concrete crushing. This type of failure was less ductile compared to flexural failure of reinforced concrete beam due to the brittleness of the bonded FRP (Teng et al. 2002a). 2.1.2 Shear Failure Shear failure of FRP-strengthened beams can occur in a brittle manner. In many FRP-strengthened structures, this failure can frequently be made critical by flexural strengthening. Furthermore, research has shown that the addition of FRP at the bottom of beam did not contribute much to an increase in shear strength (Buyukozturk and Hearing 1998). This has called for great care and attention in the design of FRP-strengthened beams to guard against possible shear failure. 2.1.3 Concrete Cover Separation This type of failure mode had been widely reported by researchers (Sharif et al. 1994, Nguyen et al. 2001, Maalej and Bian 2001). It occurs due to high interfacial shear and normal stress concentrations at the cutoff point of the FRP plate/sheet. These high stresses cause cracks to form in concrete near the FRP cut-off point and subsequently along the level of the tension steel reinforcement before gradually leading to separation of concrete cover (Teng et al. 2002a). 2.1.4 Plate-End Interfacial Debonding Plate-end interfacial debonding refers to debonding between adhesive and concrete that propagate from the end of plate towards the inner part of the beam. Upon debonding, a thin layer of concrete generally remains attached to the plate. 5 Researchers related this type of failure to the high interfacial shear and normal stresses near the end of plate. The debonding normally occurred at the layer of concrete, which was the weakest element compared to adhesive (Teng et al. 2002a). 2.1.5 Intermediate Flexural Crack-Induced Debonding This type of failure mode occurs when a major crack forms in the concrete. The crack causes tensile stresses to transfer from the cracked concrete to the FRP. As a result, high local interfacial stresses are induced near the crack between the FRP and concrete. Upon subsequent loading, stresses at this crack increases and debonding of FRP will take place once these stresses exceed a critical value. The debonding process generally occurs in the concrete, adjacent to the adhesive-to-concrete interface and it propagates from the crack towards one of the plate ends (Teng et al. 2002a). 2.1.6 Intermediate Flexural Shear Crack-Induced Debonding This failure mode initiates when the peeling stresses due to relative vertical displacement between the two faces of a crack is high enough (Meier 1995, Swamy and Mukhopadhyaya 1999, Rahimi and Hutchinson 2001). Garden et al. (1998) categorized this type of failure into two distinct modes, depending on their shear span/depth ratio: partial cover separation of type A and partial cover separation of type B. Type A failure mode was initiated by the vertical step between A and B as shown in Figure 2.2 while Type B failure mode was initiated by the rotation of a “triangular” piece of concrete near the loading position that causes displacement of the plate (Figure 2.3). According to Teng et al. (2002a), the debonding propagation is strongly influenced by the widening of the crack, as in the case of intermediate 6 flexural crack-induced debonding, rather than the relative movement of crack faces, which is of only secondary importance. 2.2 Interfacial Shear Stress Concentration Many researchers had come up with approximate analytical models to predict interfacial stresses (Jones et al.,1998; Roberts 1989, Taljsten 1997, Malek et al. 1998 and Smith and Teng 2001). The model by Smith and Teng (2001) is the most recent and performs relatively well. However, the model proposed by Taljsten (1997) appears to be more simple and easy to apply. In this literature review, only the approximate interfacial shear stress models of Taljsten (1997) and Smith and Teng (2001) were presented. 2.2.1 Taljsten’s Model (1997) Taljsten (1997) proposed an analytical model to calculate the interfacial stresses in the adhesive layer. The model was based on the following assumptions: bending stiffness of the strengthening plate was negligible as the bending stiffness of beam was much greater than the stiffness of plate; stresses were constant across the adhesive thickness; load is applied at a single point (Figure 2.4). The model for a single point load can be applied to two point loads by superimposing the shear stresses obtained from first and second point loads. The equation for the shear stresses in the adhesive layer was given by: τ = C1 cosh(λx) + C 2 sinh(λx) + Ga P (2l + a − b) l+a 2λ t a E c Z c 2 2.1 7 where λ2 = Ga b frp ⎛ y c 1 1 ⎜ + + ⎜ t a ⎝ E c Z c E c Ac E frp A frp ⎞ ⎟ ⎟ ⎠ Ga Shear modulus of adhesive P Point load ta Thickness of adhesive Ec Elastic modulus of concrete Zc Section modulus of concrete l Distance from middle of FRP-beam to CFRP cut-off point a Distance from support to CFRP cut-off point b Distance from CFRP cut-off point to loading point 2.2 C1,C2 Constants Ac Cross sectional area of concrete Afrp Cross sectional area of FRP yc Distance from bottom of concrete beam to its centroid Equation 2.1 was valid for a distance from cut-off point to loading point ( 0 ≤ x ≤ b ) since singularity exists under the point load. By considering only the case where λb is greater than 5 and with appropriate boundary condition, Taljsten (1997) comes out with a final expression for the shear stress: τ max = Ga P (2l + a − b) (aλe − λx + 1) 2t a E c Z c l+a λ2 2.3 However, this equation should be used only when close to the end, x = 0, to reduce the simplification error. Then, the maximum shear stress at the cut-off point was given by: 8 τ max = Ga P (2l + a − b) (aλ + 1) 2t a E c Z c l+a λ2 2.4 If there were two point loads, P1 and P2, the total peak shear stresses were calculated by adding the peak shear stresses caused by both of the point loads as follows: τ max 1 = Ga P1 (2l + a − b1 ) (aλ + 1) 2t a E c Z c l+a λ2 τ max 2 = Ga P2 (2l + a − b2 ) (aλ + 1) 2t a E c Z c l+a λ2 2.5 2.6 and the total peak shear stress is equal to : τ total = τ max 1 + τ max 2 2.2.2 2.7 Smith and Teng’s Model (2001) Many of the available interfacial stress models did not consider the effects of axial deformation or bending deformation of bonded plate which can be critical when the bonded plate has significant flexural rigidity. Furthermore, some of the analytical models suffered from limited loading conditions. To overcome these limitations, Smith and Teng (2001) proposed a new model to determine interfacial shear and normal stress concentrations of FRP-strengthened beams with the inclusion of axial deformation and several load cases. Smith and Teng’s solution was applicable for beams made with all kinds of bonded thin plate materials. In their model, they assumed: linear elastic behaviour of concrete, FRP and adhesive; deformations were due to bending, axial and shear; adhesive layer was subjected to constant stresses across its thickness; no slip at the interface. The derivation below was expressed in terms of adherends 1 and 2, where adherend 1 refers to the concrete beam and 9 adherend 2 refers to the FRP composite (Figure 2.4). There are a total of three load cases being considered, namely uniformly distributed load, single point load and two symmetric point loads as shown in Figure 2.5. Uniformly distributed load ⎡ m2 a ⎤ qe − λx ⎛L ⎞ + m1 q⎜ − a − x ⎟ ( L − a ) − m1 ⎥ ⎝2 ⎠ ⎣ 2 ⎦ λ τ ( x) = ⎢ 2.8 Single point load a< b ' : τ (x) ⎛ b' ⎞ ⎛ b' ⎞ Pa⎜1 − ⎟e −λx + m1 P⎜1 − ⎟ − m1 cosh(λx)e − k for 0 ≤ x ≤ (b'− a ) λ ⎝ L⎠ ⎝ L⎠ m2 = b' ⎛ b' ⎞ Pa⎜1 − ⎟e −λx − m1 P − m1 P sinh(k )e −λk λ L ⎝ L⎠ m2 or = 2.9 for (b'− a ) ≤ x ≤ L p a> b ' : τ (x) b' ⎛ a⎞ Pb' ⎜1 − ⎟e −λx − m1 P λ L ⎝ L⎠ m2 = for 0 ≤ x ≤ L p 2.10 Two symmetric point loads a< b ' : τ ( x) = or = m2 λ m2 λ Pae −λx + m1 P − m1 P cosh(λx)e − k for 0 ≤ x ≤ (b'−a) 2.11 Pae −λx + m1 P sinh(k )e −λk for (b'−a) ≤ x ≤ L p / 2 a> b ' : τ ( x) = m2 λ Pb' e −λx for 0 ≤ x ≤ L p 2.12 where 10 λ2 = G a b frp ⎛ ( y c + y frp )( y c + y frp +t a ) 1 1 ⎜ + + ⎜ ta ⎝ E c I c + E frp I frp E c Ac E frp A frp m1 = Ga 1 ⎛⎜ y c + y frp t a λ2 ⎜⎝ E c I c + E frp I frp m2 = ⎞ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠ Ga y c t a Ec I c k = λ (b'− a ) 2.13 2.14 2.15 2.16 and Ec,Ea Elastic modulus of concrete and adhesive, respectively Ga Shear modulus Ic,,Ifrp Second moment of area of concrete and FRP, respectively bfrp Width of the FRP Ac,Afrp Area of concrete and FRP, respectively α Effective shear area multiplier, 5/6 for rectangular section yc,yfrp Distance from the bottom of concrete and the top of FRP plate to their respective centroid b' 2.3 Distance from support to loading point Experimental Measurement of Interfacial Shear Stresses Maalej and Bian (2001) proposed an experimental procedure for measuring the interfacial shear stress concentration at the FRP cut-off point. The procedure requires measurement of the strain in the FRP at closely-spaced points along the FRP sheet in the cut-off region. The shear stress distributions are obtained by curve fitting the strain readings from the experiment to the distance from cut-off point (Equation 2.17) and then relating the shear stress to the rate of change of strain as follows (Equation 2.18). 11 ε ( x, ∆) = A(1 − e − Bx ) τ ( x) = t frp E frp dε dx 2.17 2.18 where A and B are constants that need to be determined from the curve fitting procedure; x is the distance from the cut-off point and ∆ is the mid-span deflection. The shear stress distribution and maximum shear stress are then obtained from the following equations: τ ( x, ∆ ) = t frp E frp AB(e − Bx ) τ max (∆) = t frp E frp AB 2.4 2.19 2.20 Strength Models Many researchers had proposed strength models to predict plate-end debonding, concrete cover ripping and intermediate crack-induced debonding. Among them are Ziraba et al. (1994), Varastehpour and Hamelin (1997), Saadatmanesh and Malek (1998), Jansze (1997) and Teng et al. (2002a). In particular, the models of Ziraba et al.(1994) and Varastehpour and Hamelin (1997) were developed for plateend debonding failure, while the models of Saadatmanesh and Malek (1998) and Jansze (1997) were for concrete cover separation. Teng et al. (2002a) proposed a simple modification to the Chen and Teng model (2001) to predict intermediate crackinduced debonding. 12 2.4.1 Plate-End Interfacial Debonding 2.4.1.1 Ziraba et al.’s Model (1994) Ziraba et el. (1994) proposed a debonding strength model to predict plate-end interfacial debonding. They assumed that debonding will take place once the combined shear stress and normal stress reaches an ultimate value. This value was determined using the Mohr-Coulomb law, as follows: τ + σ y tan φ ≤ C 2.21 where τ , σ y ,C and φ are the peak interfacial shear stress, peak interfacial normal stress, coefficient of cohesion and internal friction angle, respectively. The peak interfacial shear and normal stresses were given by: ⎛C V ⎞ τ = α 1 f ct ⎜⎜ R1 ' o ⎟⎟ ⎝ fc ⎠ 5/ 4 2.22 σ y = α 2 C R 2τ 2.23 where C R1 ⎛ ⎜ ⎛ Ks = ⎜1 + ⎜ ⎜ ⎜ ⎝ E frp b frp t frp ⎝ CR2 1 ⎞ ⎞ 2 M 0 ⎟ b frp t frp ⎟ (d frp − xtr , frp ) ⎟ V ⎟I 0 ⎟ tr , frp f frp ba ⎠ ⎠ ⎛ Kn = t frp ⎜ ⎜ 4E I frp frp ⎝ 2.24 1 ⎞4 ⎟ ⎟ ⎠ 2.25 Ks = G a ba ta 2.26 Kn = E a ba ta 2.27 13 Ks, Kn, Mo and Vo are the shear stiffness, normal stiffness, bending moment and shear force, respectively. dfrp is the distance from the top of beam to the centre of FRP. f c' and f cu are the cylinder strength and cube strength of concrete, respectively. The parameters α1 and α2 (having values of 35 and 1.1, respectively) are empirical regression coefficients determined from the steel-concrete bonding parametric studies by Ziraba et al. (1994). The equation for CR1 and CR2 are obtained from Robert’s model (1989) and φ is assumed as 28 º. The value of C should be between 4.8 MPa and 9.50 MPa according to Ziraba et al. (1995). However, it should be noted that the suggested values for the parameters α1 and α2 are valid only for: a ≤ 3.0 hc 2.28 where a is the distance from the support to the CFRP cut-off point and hc is the beam depth. Finally, Itr,frp and xtr,frp are the second moment of area of transformed cracked FRP section and neutral axis of the transformed cracked FRP section, respectively. 2.4.1.2 Varastehpour and Hamelin’s Model (1997) Varastehpour and Hamelin (1997) also developed a strength model based on Mohr-Coulomb failure criterion to predict plate end interfacial debonding failure. The differences between the models’ of Ziraba et al. (1994) and Varastehpour and Hamelin (1997) lie in the coefficient of cohesion and internal friction values of the Mohr-Coulomb failure criterion. In Varestehpour and Hamelin’s model, an average value of 5.4 MPa for C and 33º for φ were adopted. In addition, the shear stress in the Mohr-Coulomb equation was determined using a different approach as follows: τ= 3 1 β (λV0 ) 2 2 2.29 14 where λ is the flexural rigidity given by : λ= t frp E frp I tr ,conc E c (d frp − xtr ,conc ) 2.30 Itr,conc is the second moment of area of the transformed cracked concrete section and xtr,conc is the neutral axis of the transformed cracked concrete section. The parameter β is a factor introduced to take into account the various variables that may affect the distribution of shear stresses such as the thickness of the plate, the cross-sectional geometry and the loading condition: β= 1.26 x10 5 b ' 0.7 hc t frp E frp 2.31 where b' distance from support to loading point hc Beam depth With these values, the shear force that causes debonding can be determined by 2 Vdbd = 1.6τ max 3 1 λβ 3 2.32 5.4 1 + C R 2 tan 33° 2.33 and τmax is given by τ max = CR2 is given by equation 2.25. 15 2.4.2 Concrete Cover Separation 2.4.2.1 Saadatmanesh and Malek’s Model (1998) The strength model proposed by Saadatmanesh and Malek (1998) for concrete cover ripping was expressed by: ⎛σ +σ y σ 1 = ⎜⎜ x 2 ⎝ ⎞ ⎟⎟ + ⎠ ⎛σ x −σ y ⎜⎜ 2 ⎝ 2 ⎞ ⎟⎟ + τ 2 ⎠ 2.34 There were four components of stresses in equation 2.35, namely σ1 ,σx, σy and τ. σ1 is the principal stress while σx is the longitudinal stresses cause by bending moment, mo, at the cut-off point. In addition, the bending moment (mo) had to be increased by an amount of Minc to account for the peak interfacial shear stress: M inc = 0.5hc ab frpτ 2.35 Finally σy and τ are the normal and shear stresses, respectively. Then, a biaxial failure mode of concrete under tension-tension state of stress was assumed for local failure. 2 σ 2 = f ct = 0.295( f cu ) 3 2.36 where σ2 is the splitting tensile strength of concrete. Once σ1 exceeds σ2, concrete cover failure is expected to occur. 2.4.2.2 Jansze’s Model (1997) Jansze (1997) developed a strength model to predict concrete cover ripping for steel-plated beams. The model was developed based on the shear capacity of concrete alone, without the contribution of shear reinforcement. The failure is assumed to occur when the external shear acting on the beam at the plate ends exceeds a certain 16 critical value. The shear force at the plate end required to cause concrete cover ripping is given by: Vmax = τ bc d where τ = 0.183 3 Bm = 4 d Bm 2.37 ⎛ 200 ⎞3 ⎟ 100 ρ s f c' ⎜1 + ⎜ d ⎟⎠ ⎝ (1 − ρs ) 2.38 2 ρs da 3 2.39 ρ s = As / bc d 2.40 Bm is the modified shear span which if greater than the actual shear span of the beam, would become (Bm+ b ' )/2. d and bc are the effective depth and width of concrete beam, respectively. It should be noted that Jansze’s model is not valid for cut-off point located at the support. 2.4.3 Intermediate Flexural Crack-Induced Debonding Teng et al. (2002a) proposed a simple modification to Chen and Teng’s (2001) model to predict intermediate flexural crack-induced debonding with the introduction of an additional parameter, αc, to the original equation as follows: σ db = α c β p β L E frp f cu t frp 2.41 where βp = 2− b frp bc 1+ b frp bc βL =1 if Lbd ≥ Le β L = sin (πL / 2 Le ) if Lbd < Le 2.42 2.43 2.44 17 Le = E frp t frp f c' 2.45 αc is a coefficient obtained from calibration against experimental data. In the case of beams, an average value of 1.1 is obtained, which correspond to a 50% exceedence in terms of the stresses in the plate (Teng et al. 2002a). For design, Teng et al. (2002a) adopted a value of 0.4 for αc which correspond to 5.7% of exceedence for the case of combined beam and slab. Lbd and fcu are the bond length (distance from CFRP cut-off point to nearest loading point for beam under two symmetric point loads) of FRP and the cube strength of concrete, respectively. 2.4.4 Intermediate Flexural Shear Crack-Induced Debonding According to Teng et al. (2003), the peak stress caused by flexural shear crack-induced debonding would not significantly differ from that of the flexural crack-induced debonding. They found that the Teng et al. model (2002a) gave equally conservative predictions to the intermediate flexural shear crack-induced debonding. For this reason, they recommended that the Teng et al. model (2002a) to be used to design against intermediate flexural shear crack-induced debonding until further studies are carried out. 18 i. FRP rupture ii. Concrete crushing iii. Shear crack iv. Concrete cover ripping v. Crack propagation Plate end interfacial debonding Figure 2.1(a) : Failure modes in FRP-strengthened beams i. FRP rupture ii. Concrete crushing iii. Shear failure iv. Concrete cover ripping v. Plate-end interfacial debonding (After Teng et al. 2002a) 19 vi. Crack propagation Intermediate flexural crack-induced debonding vii. Crack propagation Intermediate flexural shear crack-induced debonding Figure 2.1(b) : Failure mode in FRP-strengthened beams vi. Intermediate flexural crack-induced debonding v. Intermediate flexural shear crack-induced debonding (After Teng et al. 2002a) Shear crack To end of beam Level of internal tensile reinforcement v A B CFRP composites w Shear crack displacement components in Type A partial cover separation Figure 2.2 : Type A partial cover separation (After Garden and Hollaway 1998) 20 To end of beam Flexural shear crack Flexural shear crack CFRP plate Stage 1: Shear crack formation Stage 2: Tributary crack formation To end of beam Flexural shear crack Level of internal rebars CFRP plate Stage 3: Relative vertical movement Stage 4: After collapse of beam Profile of Separated Concrete Thin layer of separated concrete Figure 2.3 : Type B partial cover separation (After Garden and Hollaway 1998) b’ b p A Lp a Section A-A A l l L Figure 2.4: FRP-strengthened beam 21 (a) Uniformly distributed load (b) Single point load (b) Two symmetric point loads Figure 2.5 : Load cases 22 CHAPTER THREE EXPERIMENTAL INVESTIGATION 3.1 Introduction The main objective of this experimental study is to investigate the interfacial shear stress concentration at the CFRP cut-off regions as well as the failure mode of CFRP-strengthened beams as a function of beam size and FRP thickness and to compare the test results with theoretical predictions. Because most structures tested in the laboratory are often scaled-down versions of actual structures (for practical handling), it would be interesting to know whether the results obtained in the laboratory are influenced by the difference in scale. 3.2 Specimen Reinforcing Details Three sizes of beams (breadth x depth x length = 115x146x1500mm, 230x292x3000mm and 368x467x4800mm) were considered in this study. The beams were designated as Series A, B and C and had size ratios of 1:2:3.2. For the sizeeffect investigation, two groups of beams were considered. The first group consisted of beams A3-A4; B3-B4 and C3-C4 and had a CFRP reinforcement ratio (ρp=Ap/Ac) equal to 0.106% of the gross concrete cross-sectional area (i.e. Ap = 107.8x0.165mm, 215.6x0.330mm and 368x0.495mm, respectively). The second group consisted of beams A5-A6; B5-B6 and C5 and had a CFRP reinforcement ratio equal to 0.212% of the gross concrete cross sectional area. Beams in each group were geometrically similar but of different sizes. The CFRP cut-off length for Series A, B and C were 25, 50 and 80 mm, respectively. A clear concrete cover of 15, 30 and 51.2 mm was used 23 for specimens in Series A, B and C, respectively. Further details on the specimens are provided in Figure 3.1-3.3 and Table 3.1. 3.3 Materials Ready-mix concrete with 9 mm maximum coarse aggregate size was used to fabricate all the specimens, as reported by the supplier. The concrete fracture energy determined by means of three-point bend tests on notched beams and the tensile splitting strength at test-day for both Series A and B were 133 N/m and 3.41 MPa, respectively, while those for Series C were 128 N/m and 3.24 MPa, respectively. A summary of other related material properties is given in Table 3.2 and 3.3. 3.4 Casting Scheme Series A and series B were cast simultaneously while series C were cast separately due to the limitation of the volume of concrete a truck can carry. During casting, concrete were placed horizontally and compacted by means of power-driven vibrators. After casting, these beams were covered with plastic sheet and wet burlap for about one week before demoulding of the formwork. For each batch, cubes, cylinders and notch beams were cast and cured. The cube and cylinder specimens were then tested for the 28-day compressive strength, tensile strength and elastic modulus while four notched beams were tested for fracture energy. A photograph of the concrete specimens showing Series A, B and C is given in Figure 3.4. 24 3.5 CFRP Application The tension surface of concrete beams was roughened using a disk grinder and cleaned with water to remove unwanted dust and dirt. The concrete surface was then left to dry for about one day before a two part epoxy, composed of primer and saturant, was applied on the concrete surface, followed by CFRP sheets application. Finally, an over coating resin was applied onto the CFRP sheets. The strengthened beams were left to cure for about two weeks before testing. During the curing period, strain gauges were installed on the surface of the CFRP sheets. 3.6 Instrumentation Four and five strain gauges were installed on the transverse and longitudinal reinforcements, respectively, and one strain gauge was installed on the top of the concrete specimen at midspan. To measure the interfacial shear stress distribution following the method proposed by Maalej and Bian (2001), the CFRP sheets were instrumented with 27, 29 and 31 electrical strain gauges distributed along the length of the sheet for Series A, B and C, respectively. The detail position of the strain gauges is shown in Table 3.4. A total of 10 strain gauges spaced at 20mm were placed near the cutoff point to measure the steep variation of strain. 3.6 Testing Procedure The beams were tested in third-point bending using an MTS universal testing machine with a maximum capacity of 1000-kN for Series A and 2000-kN for both Series B and C. The beams were simply-supported on a pivot bearing on one side and a roller bearing on the other. A total of four LVDTs (Series A) and three LVDTs (Series B and C) were used to measure the displacements of the beams at the 25 supporting points, the loading points and at midspan during testing. Typical beam setup for Series A, B and C are shown in Figure 3.5-3.7 in addition to that of the notched beam specimens (Figure 3.8) 3.8 Results and Discussion Load-deflection curves for all specimens are plotted and summarized in Table 3.5. It can be seen that all CFRP-strengthened beams performed significantly better than the control beams with respect to load-carrying capacity. However, the observed strength increases were associated with reductions in the deflection capacity of the respective beams. The CFRP-strengthened beams failed prematurely with no concrete crushing occurring at ultimate load and only one type of failure mode— intermediate flexural crack-induced interfacial debonding—was observed. 3.8.1 Effects of Strengthening Figure 3.9-3.11 shows the load-deflection curves for beam Series A, B and C. The average strengthened capacity for beams strengthened with 0.106% CFRP (Group 1) was 27.0%, 29.0% and 27.5% higher than the control for Series A, B and C, respectively. For beams strengthened with 0.212% CFRP (Group 2) the average strengthened capacity was 43.0% and 43.5% higher than the control for Series A and B, respectively. The figures also show that beams with higher CFRP reinforcement ratio have lower deflection capacities but higher stiffness based on the measured load-deflection curves. The average midspan deflection capacity for Group 1 beams (ρp = 0.106%) was 51.5%, 63.5% and 72% lower than that of the control beams for Series A, B and C, respectively. For Group 2 beams (ρp = 0.212%) the average midspan deflection 26 capacity was 49%, 57.0% and 52% lower than the control for Series A,B and C respectively. It can also be seen that up to a load of approximately 60kN, 200kN and 400kN for Series A, B, and C, respectively, a linear load-deflection response is exhibited by all the beams. As the strengthened beams approached yielding, the strain in the CFRP sheets was still larger than that in the reinforcing bars, suggesting satisfactory bond transfer between the CFRP sheets and the beams. The results shown in Table 3.5 (except for Beam C5) indicate that the strengthening ratios SR (defined as the strength of beams with CFRP reinforcement divided by the strength of control beams) for beams with same CFRP reinforcement ratios ρp but different sizes are similar, suggesting that the beam size does not significantly influence the extent to which a RC beam can be strengthened (provided that the beams are not shear-critical). However, the deflection capacity, expressed as a fraction of total span length seems to be different for the different Series of beams, with larger beams showing smaller (relative) deflection capacity. Beam C5 (ρp=0.212%) did not reach the expected strengthening ratio of about 1.4 because it failed prematurely due to CFRP debonding and will be discussed later. To examine the ductility of the strengthened beams, two ductility criteria were used, namely the deflection ductility and the energy ductility. i. Deflection ductility: µ∆ = ∆u fail 3.1 ∆y where ∆ fail is the midspan deflection at failure load and ∆ y is the midspan deflection at yielding of tension steel reinforcement (Spadea et al. 2001). 27 3.2 ii. Energy ductility: µe = ⎤ 1 ⎡ E tot + 1⎥ ⎢ 2 ⎣ E elastic ⎦ where Etot and E elastic are the total energy up to failure load (area under the loaddeflection curve) and elastic energy, respectively (Naaman and Jeong 1995). The elastic energy was estimated using an equivalent triangular area formed at failure load with the unloading slope determined by the following equation, as shown in Figure 3.12: S= P1 S 1 + ( P2 − P1 ) S 2 P2 3.3 P1 and P2 are loads shown in Figure 3.12 and S1 and S2 are the corresponding slopes. If one looks at the deflection ductility and energy ductility index of the CFRPstrengthened beams, there seems to be no significant difference among the values for the different Series of beams, except for beam C5 which had particularly low ductility index, as shown in Table 3.6. The data suggest that geometry scaling of the beams does not affect the deflection ductility of the beams significantly. 3.8.2 Failure Modes All control beams failed in the conventional mode of steel yielding followed by concrete crushing. The failure mode for all CFRP-strengthened beams was intermediate flexural crack-induced interfacial debonding. Upon debonding, a very thin layer of concrete and aggregate generally remained attached to the CFRP sheet. A comparison was made between the experimental strain values at midspan and the analytical results using the Teng et al. (2002a) model for the ultimate strain in the CFRP for intermediate flexural crack-induced interfacial debonding. An average 28 value of 1.1 for αc (calibration factor, refer to equation 2.41) was used in the model and the results are shown in Figure 3.13. It can be seen that the Teng et al.’s model (2002a) predicted fairly well the CFRP strain at failure with the experimental results being within 15% of the predicted results. From Figure 3.13, it can be seen that when the beam size increases, the CFRP failure strain decreases. As stated earlier, beam C5 fails prematurely at a load lower than expected because the strain in the CFRP sheets of beam C5 has already reached the debonding strain, which caused it to fail prematurely. Although the CFRP failure strain decreased with increasing beam size, the strengthening ratio did not seem to be affected, except for beam C5. It seems that the reduced contribution of the CFRP (in terms of the maximum CFRP tensile strain that the beams were able to develop) to the strength increase in large-size beams is offset by the reduced nominal load capacity of the unstrengthened beam (Ozbolt and Bruckner 1999, see Figure 3.14) leading to almost similar strengthening ratios among the different beams. To further illustrate this, the nominal bending moment (Mn) corresponding to the peak load (plotted as a function of the beam depth) for the control specimens is shown in Figure 3.14a. The bending moment is normalized to My, the lowest possible bending (yielding) moment calculated according to My = fyAs(0.9hc), where 0.9hc = effective beam depth, ignoring the contribution of concrete to the peak load (Ozbolt and Bruckner 1999). It can be seen that Series A generally have higher nominal bending moment capacity compared to Series B and C. A similar pattern can also be observed from the plot of nominal stress at ultimate load (defined as σn=Pu/bcd) versus beam depth shown in Figure 3.14b. Beam C5 failed at an ultimate load of 649 kN and achieving a SR of only 25%. The low strengthening ratio of beam C5 may be explained by referring to the plots of 29 load-midspan CFRP strain for Group 2 beams as shown in Figure 3.15. The loads were computed from section analysis according to the procedure outlined by Teng et al. (2002a). It can be seen that the plots consist of two successive portions: a nonlinear portion with gradually decreasing slope for εfrp up to about 0.005 and a final almost linear portion. In the nonlinear portion, the load decreases rapidly with a decrease in CFRP strain; this was the case of beam C5 where the ICID debonding strain was below 0.005 ( ε predicted = 0.0042 and ε exp erimental = 0.0037 ) due to the thick layer of CFRP sheets. This may explain why beam C5 failed at a lower load and did not achieve the expected strengthening ratio. On the other hand, the other groups of beams did not show significant difference in strengthening ratio mainly because the CFRP debonding strains were greater than 0.005. 3.83 Interfacial Shear Stresses The interfacial shear stress distributions along the CFRP interface at the CFRP curtailment region were computed according to the procedure proposed by Maalej and Bian (2001). The peak shear stresses were plotted in Figure 3.16-3.18 at different load levels and the curve fitting results are shown in Table 3.7. The results show that the interfacial shear stresses vary significantly along the CFRP sheet in the curtailment region with the peak stress occurring at the FRP cut-off point. However, the interfacial shear stresses for all beams are generally low enough not to cause failure by end-plate debonding or ripping of the concrete cover. The results also indicate that the interfacial shear stresses increase with increasing load, and the peak shear stress values at ultimate load for both beam Groups 1 and 2 (ρp = 0.106% and 0.212%, respectively) increase with increasing size of the beam and CFRP thickness. The increase in peak shear stress with beam size can be explained by 30 the fact that peak shear stress increased with decreasing thickness of the adhesive layer (Teng 2001b and Talstjen 1997) and this was the case of Group 1 and Group 2 specimens where the thickness of adhesive layer was not scaled in accordance to the beam size, causing larger beams to have relatively thinner layer of adhesive and therefore higher peak shear stress. Figure 3.19 shows the analytical peak shear stress computed using Smith and Teng’s model (2001) along with the experimentally-obtained values. In the analytical model, the second moment of area is the gross uncracked concrete section along the centroidal axis, ignoring the small increase in the moment of inertia due to the reinforcement. It can be seen from this figure that for both Group 1 and 2 the peak interfacial shear stresses seem to increase with increasing beam size as well as with increasing CFRP reinforcement ratio. The peak shear stresses predicted by Smith and Teng’s model (2001) seems to be in reasonable agreement with the experimental results for group 1 beams. For group 2 beams, however, Smith and Teng’s model (2001) seems to underestimate the interfacial shear stresses at FRP cut-off point particularly for beam C5 To further support the experimental results, nonlinear finite element modelling was carried out. The finite element software package “DIANA” (Version 8) was used to analyse the CFRP-strengthened beams because of its ability to model the nonlinear behaviour of both steel and concrete, including cracking. The results of the finite element will be discussed in Chapter 4. 3.9 Conclusions Tests in this study showed that increasing the size of the beam and/or the thickness of the CFRP leads to increased interfacial shear stress concentration in 31 CFRP-strengthened beams as well as reduced CFRP failure strain. The work has also led to the following conclusions: (a) The beam size does not significantly influence the strengthening ratio, nor does it significantly affect the deflection and energy ductility of CFRP-strengthened beams. (b) The model by Teng et al. (2002a) to predict intermediate flexural crack-induced debonding was found to agree reasonably well with observed test data. (c) The model by Smith and Teng (2001) to predict interfacial shear stresses in the adhesive layer at FRP cut-off points was found to agree reasonably well with observed test data for group 1 beams. For group 2 beams, however, Smith and Teng’s model (2001) seems to underestimate the interfacial shear stresses at FRP cut-off point particularly for beam C5. 32 Table 3.1: Description of specimens Dimension (mm) d L Series Beam A A1, A2 A3, A4 A5, A6 B1, B2 B3, B4 B5, B6 C1, C2 C3, C4 C5 B C 120 120 120 240 240 240 384 384 384 1500 1500 1500 3000 3000 3000 4800 4800 4800 External reinforcements (CFRP sheets) No. of Sheet layers thickness 0 0 1 0.165 2 0.330 0 0 2 0.330 4 0.660 0 0 3 0.495 6 0.990 Internal reinforcements Tensile Comp. As/bd As/bd (%) (%) 1.71 1.14 1.71 1.14 1.71 1.14 1.71 1.14 1.71 1.14 1.71 1.14 1.71 1.14 1.71 1.14 1.71 1.14 Shear Av/bws (%) 0.82 0.82 0.82 0.82 0.82 0.82 0.82 0.82 0.82 Table 3.2: Material properties Series A Series B Property/Materials R6 T10 Conc. R12 T20 Conc. Yield stress (MPa) 348 547 324 544 Yield strain (%) 0.17 0.35 0.17 0.35 a 488 644 39.8a Ultimate stress 460 584 39.8 42.8b 42.8b (MPa) Modulus (GPa) 237 180 27 199 183 27 a 28-Day cylinder strength bTest-Day cylinder strength R16 324 0.20 492 188 Series C T32 Conc. 552 0.45 650 41.0a 42.4b 181 25 Table 3.3: Material properties of CFRP provided by manufacturer Property Value Ea(MPa) Ga(MPa) ta(mm) Ep(GPa) 1824 622 0.636 235 fpu(MPa) 3550 εpu(mm/mm) 0.015 33 Table 3.4: Location of strain gauges on the CFRP sheets along half of the beam Series A Strain gauge 1-10 11 12 13 14 (Ctr. of beam) Distance from cut-off point (mm) 200 (Spacing of 20mm from ctr. to ctr.) 240 320 480 725 Series B Strain gauge 1-10 11 12 13 14 15 (Ctr. of beam) Distance from cut-off point (mm) 200 (Spacing of 20mm from ctr. to ctr.) 240 320 480 800 1450 Series C Strain gauge 1-10 11 12 13 14 15 16 (Ctr. of beam) Distance from cut-off point (mm) 200 (Spacing of 20mm from ctr. to ctr.) 240 320 480 800 1440 2320 34 Table 3.5: Summary of results Series A B C Beam Load at failure Deflection at failure ∆fail/L εpfail Failure mode ∆fail % of ctrl. (%) - 38.6 - 2.57 - CC 60.7 - 46.4 - 3.09 - CC A3 77.5 128 22.0 52 1.47 9910 ICID A4 75.5 125 21.8 51 1.45 8213 ICID A5 87.4 144 21.0 49 1.40 6745 ICID A6 85.8 142 20.9 49 1.39 6273 ICID B1 (ctrl) 203.9 - 59.5 - 1.98 - CC B2 (ctrl) 200.3 - 50.6 - 1.69 - CC B3 263.5 130 35.0 64 1.17 7463 ICID B4 260.3 129 34.9 63 1.16 7995 ICID B5 294.7 146 32.2 59 1.07 5761 ICID B6 284.3 141 30.4 55 1.01 4691 ICID C1 (ctrl) 520.0 - 76.2 - 1.59 - CC C2 (ctrl) 519.1 - 74.3 - 1.55 - CC C3 652.9 126 52.4 70 1.09 5824 ICID C4 669.3 129 56.4 74 1.17 6725 ICID C5 650.1 125 39.5 52 0.82 3665 ICID Pfail (kN) % of ctrl. A1 (ctrl) 60.4 A2 (ctrl) (mm) CC = concrete crushing; ICID = Intermediate flexural crack-induced interfacial debonding 35 Table 3.6: Ductility index of FRP-strengthened beam Group Series Yield load (kN) Deflection ductility index ( µ∆ ) Energy ductility index ( µe ) 1 A B C 64 202 529 1.65 1.74 1.66 1.39 1.42 1.38 2 A B C 72 234 582 1.42 1.41 1.20 1.32 1.22 1.15 36 Table 3.7: Curve fitting results τmax % of control beam load Coefficients Beam R2 (MPa) A B 33 A3-A4 0.05 125 0.0109 0.99 66 A3-A4 0.13 1389 0.0071 0.94 100 A3-A4 0.63 2975 0.0054 0.92 Ultimate load A3-A4 0.71 5752 0.0032 0.80 33 A5-A6 0.12 278 0.0058 0.98 66 A5-A6 0.53 1009 0.0068 0.92 100 A5-A6 1.20 2380 0.0065 0.93 Ultimate load A5-A6 1.32 2476 0.0069 0.95 33 B3-B4 0.07 72 0.0118 0.97 66 B3-B4 0.24 103 0.0303 0.99 100 B3-B4 0.47 687 0.0089 0.88 Ultimate load B3-B4 0.72 1366 0.0073 0.85 33 B5-B6 0.22 57 0.0246 0.93 66 B5-B6 0.73 126 0.0375 0.95 100 B5-B6 1.01 1254 0.0052 0.78 Ultimate load B5-B6 1.46 6515 0.0015 0.76 33 C3-C4 0.22 57 0.0246 0.93 66 C3-C4 0.87 99 0.0564 0.85 100 C3-C4 1.18 1667 0.004 0.80 Ultimate load C3-C4 1.17 2092 0.0036 0.77 33 C5 0.31 56 0.0236 0.99 66 C5 1.10 126 0.0375 0.95 100 C5 1.23 1586 0.0033 0.92 Ultimate load C5 1.87 1277 0.0063 0.78 37 75 25 3T10 A CFRP 1500 146 500 P/2 500 P/2 500 R6-60 2T10 A 25 75 SERIES A P/2 1000 2T20 P/2 B 1000 292 1000 R12-120 CFRP 50 150 3T20 3000 50 150 B SERIES B P/2 1600 1600 C 2T32 467.2 R16-133 P/2 1600 80 240 CFRP 3T32 4800 C 80 240 SERIES C NOTE: ALL UNITS IN MM Figure 3.1: Specimen reinforcing details 38 368 mm 51.2 mm 230 mm 30 mm 467.2 mm 115 mm 15 mm 292 mm 146 mm Section A-A Section B-B Section C-C Figure 3.2: Section details for Series A, B and C beams Figure 3.3: Reinforcement of Series A, B and C 39 Figure 3.4: Series A, B and C beams Figure 3.5 : Typical Series A beams test setup 40 Figure 3.6 : Typical Series B beams test setup Figure 3.7 : Typical Series C beams test setup 41 Figure 3.8 : Notched beam specimen 42 100 A5 A6 Load (kN) 80 A3 A4 60 A1-ctrl. A2-ctrl. 40 20 0 0 10 20 30 40 Midspan displacement (mm) 50 Figure 3.9 : Load-midspan deflection for Series A beams 350 B5 300 B6 Load (kN) 250 B3 B4 200 150 B1-ctrl B2-ctrl 100 50 0 0 10 20 30 40 50 60 Midspan displacement (mm) Figure 3.10 : Load-midspan deflection for Series B beams 43 800 700 C4 C5 C3 Load (kN) 600 C1-ctrl 500 400 C2-ctrl 300 200 100 0 0 20 40 60 Midspan displacement (mm) 80 Figure 3.11 : Load-midspan deflection for Series C beams P3 P2 Load (kN) S3 S2 S Inelastic energy Elastic energy P1 S1 Deflection (mm) Figure 3.12 : Approximate calculation of equivalent elastic energy release at failure 44 Failure strain in CFRP (microstrain) 14000 12000 10000 Group 1 8000 6000 Group 2 4000 Exp. values ♦ Predicted (Teng et al. 2002a) ■ Avg. exp. values ▲ 2000 0 0 100 200 300 Beam depth (mm) 400 500 Figure 3.13 : Comparison of measured and predicted CFRP debonding strains 5.0 1.2 A1-A2 Mn/My 0.8 Strength limit M y = f y A s ( 0.9h c ) B1-B2 0.6 4.0 C1-C2 A1-A2 B1-B2 3.0 C1-C2 Pu/bd 1.0 2.0 0.4 1.0 Ctrl. specimen (average) 0.2 0.0 0 200 400 Beam depth (mm) Ctrl. specimen (average) 0.0 600 Figure 3.14 (a): Nominal bending moment at peak load as a function of beam depth 0 200 400 Beam depth (mm) 600 Figure 3.14 (b): Nominal bending stress at peak load as a function of beam depth 45 100 B5-B6 (ρρ =0.212%) 300 60 Almost linear portion 40 Load (kN) 80 Load (kN) 400 A5-A6 (ρρ =0.212%) Almost linear portion 200 100 20 0 0 0 0.002 0.004 0.006 Midspan CFRP strain 1000 0 0.002 0.004 0.006 Midspan CFRP strain 0.008 C5 (ρρ =0.212%) 800 Load (kN) 0.008 600 Almost linear portion 400 200 0 0 0.002 0.004 0.006 Midspan CFRP strain 0.008 Figure 3.15: Load versus CFRP strain at midspan for Group 2 (ρρ=0.212%) beams 46 2.0 1.6 Shear stress (MPa) 33% of ctrl. 66% of ctrl. 100% of ctrl. Ultimate load A3-A4 (ρρ=0.106%) 1.2 0.8 0.4 0.0 0 25 50 75 100 Distance from cut-off point (mm) Shear stress (MPa) 2.0 33% of ctrl. 66% of ctrl. 100% of ctrl. Ultimate load A5-A6 (ρρ=0.212%) 1.6 1.2 0.8 0.4 0.0 0 25 50 75 100 Distance from cut-off point (mm) Figure 3.16: Experimentally-measured interfacial shear stress distributions of Series A 47 2.0 1.6 Shear stress (MPa) 33% of ctrl. 66% of ctrl. 100% of ctrl. Ultimate load B3-B4 (ρρ=0.106%) 1.2 0.8 0.4 0.0 0 25 50 75 100 Distance from cut-off point (mm) 2.0 B5-B6 (ρρ=0.212%) Shear stress (MPa) 1.6 33% of ctrl. 66% of ctrl. 100% of ctrl. Ultimate load 1.2 0.8 0.4 0.0 0 25 50 75 Distance from cut-off point (mm) 100 Figure 3.17: Experimentally-measured interfacial shear stress distributions of Series B 48 2.0 1.6 Shear stress (MPa) 33% of ctrl. 66% of ctrl. 100% of ctrl. Ultimate load C3-C4 (ρρ=0.106%) 1.2 0.8 0.4 0.0 0 25 50 75 100 Distance from cut-off point (mm) 2.0 1.6 Shear stress (MPa) 33% of ctrl. 66% of ctrl. 100% of ctrl. Ultimate load C5 (ρρ=0.212%) 1.2 0.8 0.4 0.0 0 25 50 75 100 Distance from cut-off point (mm) Figure 3.18: Experimentally-measured interfacial shear stress distributions in Series C 49 3.0 Smith and Teng (2001) Shear stress (MPa) 2.5 Experimental Group 1 (ρρ=0.106%) 2.0 1.5 1.0 A3-A4 C3-C4 B3-B4 0.5 0.0 0 100 200 300 Beam depth (mm) 3.0 Smith and Teng (2001) Shear stress (MPa) 2.5 Experimental 400 500 Group 2 (ρρ=0.212%) C5 2.0 A5-A6 1.5 B5-B6 1.0 0.5 0.0 0 100 200 300 Beam depth (mm) 400 500 Figure 3.19: Variation of peak interfacial shear stress with respect to beam depth for Group 1 and 2 beams at peak load 50 CHAPTER FOUR FINITE ELEMENT ANALYSIS 4.1 Introduction Finite element analyses (FEA) have been carried out to study the effect of beam size and FRP thickness on interfacial shear stress concentration of FRPstrengthened beams and to verify the experimental results. A non-linear FEA was conducted to study the response of the FRP-strengthened beam taking into consideration cracking and the nonlinear behaviour of both steel and concrete material. In this study, the finite element software DIANA was used. 4.2 Elements Designation Two-dimensional three-node plane stress triangle and four-node plane stress quadrilateral elements (T6MEM and Q8MEM respectively) were used to model the concrete while four-node plane stress quadrilateral elements (Q8MEM) were used to model the adhesive and CFRP layers. Due to symmetry, only half of the beam was modeled. For the tension, compression and shear reinforcement, embedded reinforcement elements (BAR) were used. The details of the mesh division are shown in Figure 4.1. Refined mesh was used near to the cut-off point of CFRP in order to capture the steep variation of stresses. The element size for the refined mesh and coarse mesh was 5 mm and 25mm, respectively. 4.3 Analysis Procedures In this study, the smeared crack model was used (De Whitte and Feenstra 1998) to simulate the cracking in DIANA. The analysis was terminated once the 51 midspan deflection of the beam reached the experimentally-measured ultimate value. In the analyses, the self weights of the beams were also considered. 4.4 Material Models The plasticity behaviour of concrete in the compressive regime was modeled using Drugker-Prager yield criteria (De Whitte et al. 1998). Table 4.1 and 4.2 present the material model for concrete in Series A, B and C. For concrete, both values of friction φ and dilantancy ψ angles used in this simulation were 10°, as suggestion by DIANA (De Whitte et al. 1998). An analytical uniaxial stress-strain curve proposed by Hognestad (1951) was used to model the nonlinear behaviour of concrete. The stress-strain diagram is shown in Figure 4.2. The limiting strain, εcu, was taken as 0.0038. In DIANA, the uniaxial stress-strain diagram was then translated into an equivalent cohesion-equivalent plastic strain, the ( c − k ) relationship, according to Drucker-Prager yield criterion with constant friction ( φ (k ) = φ ) and dilation angle (ψ (k ) = ψ ) and a strain hardening hypothesis (De Whitte et al. 1998). The expression for c and k are given by c = f c' where 1 − sin φ 2 cos φ k= 1 + 2α g εc 1−α g αg = 2 sin ψ ( k ) 3 − sin ψ ( k ) 4.1 4.2 4.3 In the input file of DIANA, the c − k relationship is specified by entering the values of c follow by k as shown in Table 4.1 and 4.2. 52 The behaviour of concrete under tension was characterized by the tensionstiffening model shown in Figure 4.3a. A constant tension cut-off criterion (Figure 4.3b) was selected for the initiation of crack. The maximum tensile strain ε s in the tension-stiffening model (Figure 4.3a) was calculated based on the following equation (De Whitte and Feenstra 1998): εs = fy Es 4.0 fy and Es are the yield stress of the reinforcing steel and Young’s modulus, respectively (Table 4.3). The tensile splitting strength of concrete fct for Series A, B and C are given in Table 4.1 and 4.2. The recommended constant shear retention value of 0.2 ((De Whitte et al., 1998) was adopted to account for the ability of cracks to transfer shear stresses by aggregate interlock. The nonlinear behaviour of steel reinforcement was described by an elasto-plasticity model satisfying the Von Mises yield criterion (Fig. 4.3c and Table 4.3) (De Whitte et al., 1998). Both of the behaviour of CFRP and adhesive were assumed to be linear-elastic (Table 4.3). 4.5 Result of Series A,B and C 4.5.1 Load-Deflection Curves The load-deflection responses of the control beams and the CFRPstrengthened beams from DIANA are presented in Figures 4.4-4.9. The deflections were taken at the midspan of the beam. The measured load-deflection curves are also presented for comparison. It can be seen that for the control beams, the numerical simulation slightly overestimated the peak load of Series B and C while it underestimated the peak load for Series A. On the other hand, it can be seen that the 53 FEA predicted the measured load-deflection of the CFRP-strengthened beams reasonably well. 4.5.2 CFRP Strain Distribution Figures 4.10-4.12 show the tensile strain distribution in the CFRP at peak load predicted by the FE together with the experimentally-measured CFRP strains. On the whole, it can be seen that the FEA satisfactorily predicted the test data. The figures also indicate that CFRP strains in the constant moment region were the highest and almost constant (due to constant bending moment as ε ( x) ∝ M ( x ) ). 4.5.3 Interfacial Shear Stresses The interfacial shear stress distribution in the adhesive layer in the CFRP cut- off region at peak load is shown in Figures 4.13-4.15. The analysis results, including those obtained from the model by Smith and Teng (2001) are presented along with the experimental results. It was observed that the shear stress distributions obtained from the FEA were not smooth especially for Series A beams. An examination on the “crack status” from DIANA at the peak load indicated that cracks had formed extensively over the soffit of the beams, including the cut-off region. The simulation of cracks in concrete is expected to influence the shear stress distributions in the adhesive layer. Similar observation was also noted by Wu and Yin (2003). An investigation had been carried out to gain insight into this phenomenon and it will be discussed later. Overall, the FEA appeared to overestimate the peak shear stress in the adhesive layer. However, if one looks at the shear stress distributions deduced following the method proposed by Maalej and Bian (2001) from the rate of change of CFRP strain as predicted by the 54 FEA, it can be seen from Figure 4.13-4.15 that the shear stress distributions were in much closer agreement with the test data. Figure 4.16 shows plots of peak shear stress for Group 1 and Group 2 beams as a function of beam depth, indicating a close agreement between the measured peak shear stresses and those deduced from FEA. 4.5.4 Effect of Cracking on Interfacial Shear Stress Distribution in the Adhesive Layer To study the effect of cracking on interfacial shear stress distributions in the adhesive layer, the FE solutions for beam A5 (which showed the most irregular shear stress distribution) was obtained for three different cases of cracking: 1) a single crack 2) a row of cracks and 3) overall cracking. In the first case, a concrete element in the refined mesh near the CFRP cut-off region (element 898) was assigned a lower tensile strength (1 MPa) and lower maximum tensile strain ε s (0.0065) than the rest of the concrete elements in order to initiate a crack. The location of the element is shown in Figure 4.17(a). Figure 4.18 shows the shear stress distributions in the adhesive layer in the CFRP cut-off region at different loading levels. At low load, it was seen that the shear stress distribution was rather smooth and the peak shear stress occurred at the cut-off point. However, as the applied load was increased from 8 kN to 16 kN, an oscillation of shear stress was observed to occur across element 898. An examination of the numerical crack output showed that element 898 had partially cracked, i.e. crack for which the normal crack strain is yet to reach the maximum tensile strain but was undergoing tension-stiffening. The formation of partial crack had obviously caused the shear stress to oscillate. When the applied load was increased from 16 kN to 32 kN, the partial crack was seen to develop into a full crack, i.e. crack for which the normal crack strain is beyond the maximum tensile strain, and the shear stresses 55 were noticed to oscillate in greater magnitude. The oscillation of shear stresses due to presence of cracks was noted by Buyukozturk et al. (2003) in their conceptual illustrations as shown in Figure 4.19. Also, Kim and Sebastian (2002) observed a similar behaviour from their plot of shear stress distribution (calculated from the strain data of CFRP plate) across a midspan crack. They attributed the oscillation to the preservation of increase of axial stress in CFRP plate at both sides of the crack. In the subsequent analysis, the number of element with reduced tensile strength was increased from one to seven as shown in Figures 4.17(b). These elements were assigned a tensile strength of 1 MPa and ε s of 0.003, except for the mid element where ε s was assumed to be 0.0065 in order to simulate a full crack. Figures 4.204.21 show plots of the numerical crack patterns and the shear stress distributions at different loading levels for beam A5. At applied load of 16 kN, it was noticed that the shear stress distributions were not much affected by the formation of partial cracks, compared to the previous simulation (single crack), except at about 100 mm away from the CFRP cut-off point where the shear stresses were seen to approach zero. As the applied load was increased from 16 kN to 24 kN, an oscillation of shear stress was noticed to form. With further increase in the applied load (32kN), two elements were seen to unload along with the occurrence of another oscillation. At the applied load of 40 kN, a full crack were seen to form in between the unloaded elements and the shear stresses were seen to exhibit greater oscillation. Finally, the overall cracking behaviour of beam A5 was investigated. Figures 4.22-4.24 show the evolution of numerical crack patterns in beam A5 near the CFRP cut-off region at different load levels together with the corresponding plots of shear stress distributions. It was seen that the cracks were spread all over the soffit of the beam and the cracks propagated towards the CFRP cut-off point as the applied loads 56 were increased. Additionally, the shear stress distributions become more and more uneven as the cracks continued to propagate. Upon reaching the peak load (86 kN), an oscillation of shear stresses occurred in the region of about 80 mm away from the CFRP cut-off region. Closed scrutiny of the crack status (Figure 4.25) revealed that a full crack had formed in between the unloading elements, apparently causing the shear stresses to be oscillating. This agrees with what had been previously demonstrated in the simulation of a row of cracks. The foregoing investigations had shown that the shear stress distributions at the adhesive layer obtained from the FE analyses were significantly affected by the simulation of cracks. In addition, the smeared crack model tends to spread the formation of cracks over the entire beam, thus was unable to predict well the local behaviour (Rots et al. 1985, Rahimi and Hutchinson 2001). Nevertheless, the FEA were able to provide a reasonable prediction of the CFRP strains. This was also noted by Pesic and Pilakoutas (2003). In view of this, the FE predicted CFRP strain distributions in the CFRP layer were used in this study to deduce the shear stress distribution in the CFRP cut-off region. 4.6 Conclusions This study was conducted to predict the behaviour of FRP-strengthened beams and verify the experimental results. The following are the main conclusions: (a) The FE predicted the measured load-deflection and CFRP strains of the FRPstrengthened beams reasonably well. (b) The interfacial shear stress distributions in the adhesive layer of FRPstrengthened beams and the peak shear stress deduced from the FE predicted CFRP strains have been found to compare reasonably well with the test data. 57 (c) The effect of cracking on shear stress distribution in the adhesive layer was investigated and it was verified that the presence of cracks can significantly affect the interfacial shear stress distributions. 58 Table 4.1: Material model for concrete in Series A and B Material Concrete Description Series A Series B Parameter Young modulus (MPa) Value 27300 Poison Density (kg/m3) Drucke-Prager yield criteria • C, sin φ and sinψ • Yield Value, c-k (Refer to equation 4.1 and 4.2) 0.2 2300 Tensile strength of concrete, fct (MPa) Compressive strength of concrete, f c' (MPa) Tension stiffening • Maximum tensile strain (ε s ) Beta (β) 17.98, 0.1736, 0.1736 00 3.3902 0.000324 6.1181 0.000613 10.7274 0.001192 14.2081 0.00177 16.56 0.002349 17.313 0.002638 17.784 0.002927 17.972 0.003216 17.878 0.00351 17.503 0.00380 16.845 0.00408 15.904 0.00437 15.817 0.00440 3.41 42.8 0.003 0.2 59 Table 4.2: Material model for concrete in Series C Material Concrete Description Series C Parameter Young modulus (MPa) Poison Density (kg/m3) Drucke-Prager yield criteria Values 25000 0.2 2300 • C, sin φ and sinψ 17.81, 0.1736, 0.1736 • Yield Value, c-k (Refer to equation 4.1 and 4.2) 00 3.117 0.000324 5.647 0.000613 9.989 0.001192 13.377 0.00177 14.712 0.0020 15.809 0.002349 16.667 0.00264 17.286 0.00293 17.666 0.00322 17.807 0.00351 17.709 0.00380 17.373 0.00408 16.798 0.00437 16.741 0.00440 3.24 Tensile strength of concrete, fct (MPa) Compressive strength of concrete, f c' (MPa) Tension stiffening 42.4 • 0.003 Maximum tensile strain (ε s ) Beta (β) 0.2 Table 4.3: Material model for steel reinforcement Series Property Series A Young modulus, E (GPa) Series B Yield strength, σy (MPa) Young modulus, E (GPa) Series C Yield strength, σy (MPa) Young modulus, E (GPa) Yield strength, σy (MPa) CFRP Adhesive Steel 235 - 1.824 - 180 547 235 - 1.824 - 183 544 235 - 1.824 - 181 552 60 (a) L/20 L/2 150 mm hc CFRP cut-off length, a (b) Figure 4.1: Typical finite element idealization of the (a) RC beams (b) FRPstrengthened beams 61 linear Stress, fc ffc'c˝ ' 0.15 ffcc" f c = ffcc'"[ 2ε c ε0 −( εc 2 ) ] ε0 E c = tan α f cc' " Ec Strain, εc ε 0 = 1. 8 0.0038 Figure 4.2: Modified Hognestad compressive stress-strain curve of concrete σ σ2 fct fct ε=fct/Ec fct ε εs (a) Concrete under tension σ1 b) Constant tension cut-off σ σy ε σy c. Reinforcement Figure 4.3: Material properties 62 80 FEA Experimental 70 Load (kN) 60 50 40 30 20 A1-A2 (Control) 10 0 0 10 20 30 40 Midspan Deflection (mm) 50 60 Figure 4.4: Load-deflection response of control beams in Series A 300 FEA Experimental 250 Load (kN) 200 150 100 50 B1-B2 (Control) 0 0 20 40 60 Midspan Deflection (mm) 80 Figure 4.5: Load-deflection response of control beams in Series B 63 700 FEA Experimental 600 Load (kN) 500 400 300 200 C1-C2 (Control) 100 0 0 20 40 60 80 Midspan Deflection (mm) 100 Figure 4.6: Load-deflection response of control beams in Series C 64 100 FEA Experimental Load (kN) 80 60 40 20 A3-A4 (ρρ=0.106) 0 0 5 10 15 20 Midspan Deflection (mm) 25 100 FEA Experimental Load (kN) 80 60 40 20 A5-A6 (ρρ=0.212) 0 0 5 10 15 20 Midspan Deflection (mm) 25 Figure 4.7: Load-deflection response of FRP-strengthened beams in Series A 65 350 FEA Experimental 300 Load (kN) 250 200 150 100 B3-B4 (ρρ=0.106) 50 0 0 10 20 30 Midspan Deflection (mm) 40 350 FEA Experimental 300 Load (kN) 250 200 150 100 B5-B6 (ρρ=0.212) 50 0 0 10 20 30 Midspan Deflection (mm) 40 Figure 4.8: Load-deflection response of FRP-strengthened beams in Series B 66 800 FEA Experimental 700 Load (kN) 600 500 400 300 200 C3-C4 (ρρ=0.106) 100 0 0 10 20 30 40 Midspan Deflection (mm) 50 60 800 FEA Experimental 700 Load (kN) 600 500 400 300 200 C5 (ρρ=0.212) 100 0 0 10 20 30 Midspan Deflection (mm) 40 50 Figure 4.9: Load-deflection response of FRP-strengthened beams in Series C 67 0.012 FEA Experimental Tensile strain in CFRP 0.010 0.008 0.006 0.004 0.002 A3-A4 (ρρ=0.106%) 0.000 0 200 400 600 Distance from cut-off point (mm) 800 0.012 FEA Experimental Tensile strain in CFRP 0.010 0.008 0.006 0.004 0.002 A5-A6 (ρρ=0.212%) 0.000 0 200 400 600 Distance from cut-off point (mm) 800 Figure 4.10: CFRP strain distribution in Series A at peak load 68 0.012 FEA Experimental Tensile strain in CFRP 0.010 0.008 0.006 0.004 B3-B4 (ρρ=0.106%) 0.002 0.000 0 250 500 750 1000 1250 Distance from cut-off point (mm) 1500 0.012 FEA Experimental Tensile strain in CFRP 0.010 0.008 0.006 0.004 0.002 B5-B6 (ρρ=0.212%) 0.000 0 250 500 750 1000 1250 Distance from cut-off point (mm) 1500 Figure 4.11: CFRP strain distribution in Series B at peak load 69 0.012 FEA Experimental Tensile strain in CFRP 0.010 0.008 0.006 0.004 0.002 C3-C4 (ρρ=0.106%) 0.000 0 500 1000 1500 2000 Distance from cut-off point (mm) 2500 0.012 FEA Experimental Tensile strain in CFRP 0.010 0.008 0.006 0.004 C5 (ρρ=0.212%) 0.002 0.000 0 500 1000 1500 2000 Distance from cut-off point (mm) 2500 Figure 4.12: CFRP strain distribution in Series C at peak load 70 3.0 FEA Shear stress (MPa) Smith and Teng (2001) A3-A4 (ρρ=0.106%) Experimental 2.0 FEA * 1.0 0.0 0 Shear stress (MPa) 3.0 20 40 60 80 Distance from cut-off point (mm) FEA Smith and Teng (2001) Experimental FEA * 2.0 100 A5-A6 (ρρ=0.212%) 1.0 0.0 0 20 40 60 80 Distance from cut-off point (mm) 100 Figure 4.13: Interfacial shear stress distribution in the CFRP cut-off region for Series A at peak load * Deduced from the rate of change of CFRP strain as predicted by FEA and following the method proposed by Maalej and Bian (2001) discussed in section 2.3 71 Shear stress (MPa) 3.0 FEA Smith and Teng (2001) Experimental FEA * 2.0 B3-B4 (ρρ=0.106%) 1.0 0.0 0 Shear stress (MPa) 3.0 20 40 60 80 Distance from cut-off point (mm) FEA Smith and Teng (2001) Experimental FEA * 2.0 100 B5-B6 (ρρ=0.212%) 1.0 0.0 0 20 40 60 80 Distance from cut-off point (mm) 100 Figure 4.14: Interfacial shear stress distribution in the CFRP cut-off region for Series B at peak load 72 Shear stress (MPa) 3.0 FEA Smith and Teng (2001) Experimental FEA * 2.0 C3-C4 (ρρ=0.106%) 1.0 0.0 0 Shear stress (MPa) 3.0 20 40 60 80 Distance from cut-off point (mm) FEA Smith and Teng (2001) Experimental FEA * 2.0 100 C5 (ρρ = 0.212%) 1.0 0.0 0 20 40 60 80 Distance from cut-off point (mm) 100 Figure 4.15: Interfacial shear stress distribution in the CFRP cut-off region for Series C at peak load 73 3 FEA Smith and Teng (2001) Experimental FEA * Shear stress (MPa) Group 1 (ρρ=0.106%) 2 1 0 0 100 200 300 Beam depth (mm) 400 500 (a) 3 FEA Shear stress (MPa) Smith and Teng (2001) Group 2 (ρρ=0.212%) Experimental 2 FEA * 1 0 0 100 200 300 Beam depth (mm) 400 500 (b) Figure 4.16: Variation of peak shear stresses with respect to beam depth for Group 1 and 2 beams 74 80 75 Element (898) with lower tensile strength (a) Single element 35 Elements with lower tensile strength (b) A row of elements Figure 4.17: Location of elements with lower tensile strength Shear stress (MPa) 1.0 0.5 El. 898 0.0 0 -0.5 20 40 60 80 100 120 At P = 8 kN At P = 16 kN At P = 32 kN -1.0 Distance from cut-off point (mm) Figure 4.18: Interfacial shear stress distribution in the adhesive layer in the CFRP cutoff region 75 Shear Stress Stress analysis Actual stress Figure 4.19: Shear stress distribution in FRP strengthened RC flexural members (After Buyukozturk et. al 2004) 76 Shear stress (MPa) 2.0 40 Lower tensile strength 1.5 1.0 0.5 0.0 120 40 60 80 100 120 Distance from cut-off point (mm) At load P = 8 kN Shear stress (MPa) 1.0 40 120 0.5 0.0 40 60 80 100 120 -0.5 -1.0 Distance from cut-off point (mm) At load P = 16 kN 40 120 Shear stress (MPa) 1.0 0.5 0.0 40 60 80 100 120 -0.5 -1.0 Distance from cut-off point (mm) At load P = 24 kN Crack symbols: Partial crack * Partially unloading crack Full crack Figure 4.20: Numerical crack symbols and interfacial shear stress distribution in the adhesive layer at load P= 8, 16 and 24 kN 77 Shear stress (MPa) 1.0 40 120 0.5 0.0 40 60 80 100 120 -0.5 -1.0 Distance from cut-off point (mm) At load P = 32 kN Shear stress (MPa) 1.0 40 0.5 0.0 40 60 80 100 120 -0.5 120 -1.0 Distance from cut-off point (mm) At load P = 40 kN Crack symbols: Partial crack * Partially unloading crack Full crack Figure 4.21: Numerical crack symbols and interfacial shear stress distribution in the adhesive layer at load P=32 and 40 kN 78 Shear stress (MPa) 4.0 FEM 3.0 2.0 1.0 0.0 CFRP cut-off point 0 100mm 20 40 60 80 100 Distance from cut-off point (mm) At load P = 32 kN 4.0 Shear stress (MPa) FEM 3.0 2.0 1.0 0.0 CFRP cut-off point 0 100mm 20 40 60 80 100 Distance from cut-off point (mm) At load P = 40 kN 4.0 Shear stress (MPa) FEM 3.0 2.0 1.0 0.0 CFRP cut-off point 100mm 0 20 40 60 80 100 Distance from cut-off point (mm) At load P = 48 kN Figure 4.22: Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=32, 40 and 48 kN 79 4.0 Shear stress (MPa) FEM 3.0 2.0 1.0 0.0 CFRP cut-off point 0 100mm 20 40 60 80 100 Distance from cut-off point (mm) At 56 kN 4.0 Shear stress (MPa) FEM 3.0 2.0 1.0 0.0 CFRP cut-off point 100mm 0 20 40 60 80 100 Distance from cut-off point (mm) At P = 64 kN 4.0 Shear stress (MPa) FEM 3.0 2.0 1.0 0.0 CFRP cut-off point 100mm 0 20 40 60 80 100 Distance from cut-off point (mm) At P = 72 kN Figure 4.23: Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=56, 64 and 72 kN 80 4.0 Shear stress (MPa) FEM 3.0 2.0 1.0 0.0 CFRP cut-off point 100mm 0 20 40 60 80 100 Distance from cut-off point (mm) At P = 80 kN 4.0 Shear stress (MPa) FEM A CFRP cut-off point 100mm 3.0 2.0 1.0 0.0 0 20 40 60 80 100 Distance from cut-off point (mm) At load P = 86 kN Crack symbols: Partial crack * Partially unloading crack Full crack Crack symbols of beam A5 in the cut-off region at load P= 86 kN 5 mm CFRP cut-off point 100 mm Figure 4.24: Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=80 and 86 kN 81 CHAPTER FIVE STRENGTHENING OF RC BEAMS INCORPARATING A DUCTILE LAYER OF ENGINEERED CEMENTITIUOS COMPOSITE 5.1 Introduction The applications of Fibre Reinforced Polymer (FRP) Composites to concrete structures have been studied intensively over the past few years in view of the many advantages that FRPs possess. While FRP have been shown to be effective in strengthening RC beams, strength increases have generally been associated with reductions in the beam deflection capacity due to premature debonding. Debonding failure modes occur mainly due to interfacial shear and normal stress concentrations at FRP-cut off points and at flexural cracks along the RC beam. In the present study, it is suggested that if the quasi-brittle concrete material which surrounds the main flexural reinforcement is replaced with a ductile engineered cementitious composite (ECC) material, then it would be possible to delay the debonding failure mode and hence increase the deflection capacity of the strengthened beam. This is expected to be the case because when ECC is introduced in a RC member, more but thinner cracks are expected to form on the beam tensile face rather than fewer but wider cracks in the case of an ordinary concrete beam. More frequent but finer cracks are expected to reduce crack-induced stress concentration and result in a more efficient stress distribution in the FRP layer. ECC is a cement-based material designed to exhibit tensile strain hardening by adding to the cement-based matrix a specific amount of short randomly-distributed fibres of proper type and property (Maalej et al. 1995). ECCs are characterized by their high tensile strain capacity, fracture energy and notch insensitivity. Under 82 uniaxial tension, sequentially developed parallel cracks contribute to the inelastic strain at increasing stress level. The ultimate tensile strength and strain capacity can be as high as 5 MPa and 4%, respectively. The latter is two orders of magnitude higher than that of normal or ordinary fibre reinforced concrete. This chapter presents the results of an experimental program designed to evaluate the performance of FRP-strengthened RC beams incorporating ECC as a ductile layer around the main flexural reinforcement (ECC layered beams). The loadcarrying and deflection capacities as well as the maximum FRP strain at failure are used as criteria to evaluate the performance. Further, 2-D numerical simulation is performed to verify the experimental results. 5.2 Experimental Investigation Two series of RC beams were included in the experimental program. One series consists of two ordinary RC beams (beam A1 and A3) from Series A of chapter three and another series consisted of two ECC layered beams (ECC-1 and ECC-2). In each series, one specimen was strengthened using externally-bonded CFRP while the second was kept as a control in order to compare its load-deflection behaviour with the strengthened specimen. The ECC layer was about one third of the total depth of the beam as shown in Figure 5.1 and only one layer of CFRP sheet was used. The beams were tested under third-point loading. The specimen dimensions and reinforcement details of ECC layered beams were similar to those of Series A beams, except the distance between the support and the CFRP was increased from 25mm to 100mm to make the shear stress concentration at the cut-off point more critical. 83 In this investigation, a two percent by volume of fibre was used to produce the ECC material. The reinforcing fibres consist of high modulus steel fibres (0.5%) and polyethylene fibres (1.5%). In addition, Type I portland cement, silica fume and superplasticizer were used to form the cement paste. The concrete used for casting the ECC beams was batched in the laboratory using a drum mixer. The maximum coarse aggregate size was about 10 mm. Further details on the mix constituents of concrete and ECC are given in Table 5.1. The material properties for ECC and concrete at 28day are shown in Table 5.2. A typical tensile stress-strain curve of ECC obtained from a laboratory test is shown in Figure 5.2. 5.2.1 Test Results The load-deflection curves of the control beam as well as the CFRPstrengthened ECC beam (beams ECC-1 and ECC-2, respectively) are presented in Figure 5.3 together with the load-deflection curves of beams A1 and A3 from the previous test. A summary of test results is shown in Table 5.3. The failure mode of the CFRP-strengthened ECC beam was by CFRP sheet debonding. About half of the CFRP sheet (along the longitudinal direction of the beam) was seen to debond followed by complete debonding of the CFRP sheet as shown in Figure 5.4. It can be seen from Figure 5.3 that the ultimate load of ECC-1 was slightly higher (3% more) than that of beam A1. The slight increase in strength may be attributed to the contribution of the ECC material because of its ability to carry tensile stress. As for the strengthened beams, beam ECC-2 depicted higher load-carrying capacity compared to beam A3. If expressed in terms of strengthening ratio, ECC-2 had a strengthening ratio of about 1.43, compared to 1.28 for beam A3. The strengthening ratio of ECC-2 was almost exactly the same as that of A5-A6 beams 84 which had two layers of CFRP sheets (1.43). Also, it can be seen that ECC-2 shows considerable increase in deflection capacity (29.6mm) at peak load compared to that of beam A3 (21.9mm). If one looks at the ductility index, ECC-2 had a deflection ductility and energy ductility of 2.30 and 1.70, respectively, which are about 39% and 22% higher than those of beam A3 respectively. On the cracking behaviour, both ECC-1 and ECC-2 showed considerable number of fine cracks compared to the ordinary RC beams as revealed in Figure 5.5 and 5.6. The crack spacings were consequently much smaller in the former beams, particularly in ECC-2. These multiple but fine cracks play a major role by reducing crack induced stress concentration resulting in more efficient stress distribution in the FRP sheet and a better stress transfer between the FRP and the concrete beam. This delays intermediate crack induced debonding and results in higher strengthening ratio and higher deflection capacity and therefore a more effective use of the FRP material. The use of ECC layer is also expected to delay plate end debonding or peeling of concrete cover due to the high fracture energy of the ECC material (Maalej et al. 1995). In this experiment, despite the large distance between the support and the FRP cut-off point in the FRP-strengthened ECC beam, plate end debonding or concrete cover peeling were not observed. Based on the models by Saadatmanesh and Malek (1998) and Jansze (1997), an ordinary RC beam with a cut-off distance equal to that of ECC-2 would have failed by peeling of the concrete cover. 5.3 Finite Element Investigation A numerical simulation was performed to verify the experimental results such as the load-deflection curves, the CFRP strain distributions and the interfacial shear stresses. The finite element model developed for ECC-2 beam was similar to that of 85 Series A except that the bottom one-third of the beam was modeled with ECC and the cut-off point length was increased from 25 mm to 100 mm. As the ECC material is characterized by its tensile pseudo-strain hardening behaviour, the user defined multilinear tension-softening model in DIANA was used to model the tensile behaviour (Figure 5.7). The tensile stress-strain values were determined based on the direct tension test curve obtained from a laboratory test. On the plasticity behaviour in compression, the Drucker-Prager plasticity model was used for both of the ECC and concrete material. The nonlinear FE analysis was terminated once the midspan deflection reached the experimentally-measured ultimate value. The input values for concrete, ECC, CFRP, adhesive and steel reinforcement are shown in Table 5.4, 5.5 and 5.6, respectively. 5.3.1 Load-Deflection Curves Figure 5.8 and 5.9 show the load-deflection responses of the control beams (beams A1 and ECC-1) as well as the CFRP strengthened beams (beams A3 and ECC-2). Overall, it can be seen that the finite element model predicted the loaddeflection responses with a reasonable accuracy. 5.3.2 CFRP Strain Distribution The peak load strain distribution in the CFRP for beam ECC-2 at peak load is shown in Figure 5.10. It can be seen that the strain values are in a reasonable agreement with the experimental values, except at the constant moment region where the predicted CFRP strain was somewhat higher than the experimentally-measured values. At high strain values (>10,000 µε), the integrity of the bond between the strain 86 gauge and the CFRP could be seriously affected and hence may not be able to measure the true strain in the CFRP. 5.3.3 Interfacial Shear Stresses Figure 5.11 presents the interfacial shear stress distributions in the adhesive layer in the CFRP cut-off region at peak load of beam ECC-2. As expected, the interfacial shear stress distributions were not smooth due to presence of cracks. The shear stress distributions deduced from the FE CFRP strains were seen to be in closer agreement with the experimental data compared to those directly obtained from FEA. Smith and Teng’s model (2001), on the other hand, appeared to overestimate the peak shear stress. Close examination at the CFRP cut-off region of beam ECC-2 revealed that a flexural-shear crack had formed at the CFRP cut-off point as shown in Figure 5.12. The formation of this crack may be expected to relieve the shear stress and cause the observed reduction in peak shear stress. The occurrence of flexural-shear cracks leading to a decrease in peak shear stress at the cut-off point was also reported by Maalej and Bian (2001). This may explain the overestimation of peak shear stress by Smith and Teng’s model (2001). 5.4 Conclusions The application of an ECC material in a CFRP-strengthened beam was experimentally investigated. The results showed that ECC has indeed delayed debonding of the CFRP and resulted in effective use of the FRP materials. The method of using ECC in combination with FRP can be adopted for repair and strengthening of deteriorating RC structures. 87 Further works could be done to investigate other possible types of failure modes in CFRP-strengthened beams as well as bond strength between FRP laminates and ECC. 88 Table 5.1: ECC and concrete mix proportions Material Cement Coarse/fine aggregate Silica fume Superplasticizer Water ECC 1.00 - 0.1 0.02 0.28 Concrete 1.00 1.22 - 0.02 0.43 Table 5.2: Material properties of ECC and concrete Material Compressive strength (MPa) Tensile strength (MPa) Modulus of elasticity (GPA) ECC 69.6 (cubes) 54.1 (Cylinder) 3.28 (Direct tensile) 18.0 Concrete 53.75(cubes) 43.0 (cylinder) 3.43 (Split cylinder) 29.0 Table 5.3: Summary of test results A1 60.4 - 38.6 - - Μax CFRP strain at failure - A3 77.5 128 21.9 57 1.5 9910 DBD ECC-1 ECC-2 62.4 89.5 143 31.4 29.6 94 2.1 2.0 11370 CC DBD Beam Load at failure Pfail % of (kN) ctrl. Deflection at failure % of ∆fail (mm) ctrl. ∆fail / L (%) Failure mode CC DBD – sheets debonding, CC - concrete crushing 89 Table 5.4: Material model for concrete Material Description Parameter Values Concrete ECC-1 and A1 Young modulus (MPa) 29000 Poison 0.2 Density (kg/m3) 2300 Drucke-Prager yield criteria • C, sin φ and sinψ 18.04, 0.1736, 0.1736 • Yield Value, c-k (Refer to equation 4.1 and 4.2) 00 3.406 0.000324 6.147 0.000613 10.777 0.001192 14.274 0.00177 16.637 0.00235 17.394 0.00264 17.867 0.00298 18.056 0.00322 17.962 0.00351 17.584 0.00380 16.923 0.00408 15.979 0.00408 15.891 0.00437 Tensile strength of Concrete, fct (MPa) Compressive strength of Concrete f c' (MPa) Tension stiffening 42.8 • 0.003 Maximum tensile strain ε s Beta (β) 3.41 0.2 90 Table 5.5: Material model for ECC Material ECC Description ECC-2 Parameter Young modulus Values (MPa) Poison Density 18000 0.2 (kg/m3) 2300 Drucke-Prager yield criteria • C, sin φ and sinψ • Yield Value, c-k (Refer to equation 4.1 and 4.2) 22.7, 0.1736, 0.1736 00 3.92 0.000579 5.79 0.000868 7.6 0.001157 9.34 0.001446 11.01 0.001736 12.60 0.002025 14.11 0.002314 15.53 0.002603 16.87 0.002893 18.12 0.003182 19.27 0.00376 20.32 0.00405 22.11 0.00434 Tensile strength of ECC fct (MPa) Compressive strength of ECC, f c' (MPa) Multi-linear tension curve 3.28 69.6 3.28 0 4.2 0.023 0.8 0.06 0.8 0.1 Beta (β) 0.2 91 Table 5.6: Material model for CFRP, adhesive and steel reinforcement Series Property CFRP Adhesive Steel Series A Young modulus, E (GPa) 235 1.824 180 Yield strength, σy (MPa) - - 547 92 Section A-A Figure 5.1: Specimen reinforcement detail 5.0 Tensile stress (MPa) 4.0 3.0 2.0 1.0 0.0 0.000 0.025 0.050 0.075 Strain Figure 5.2 Tensile stress-strain curve of ECC 93 100 80 ECC-2 ECC- 1 Load (kN) A3 A1 60 40 20 0 0 10 20 30 Midspan Deflection (mm) 40 Figure 5.3 Load-deflection responses of beams ECC-1, ECC-2, A1 and A3 94 Plate debonding and separation (a) (b) (c) Figure 5.4: Debonding of CFRP sheets in beam ECC-2 (a) Debonding of CFRP (b) CFRP sheets after debonding (c) Bottom surface of beam ECC-2 after debonding 95 (a) ECC-1 control beam (b) A1 control RC beam Figure 5.5: Middle section cracking behaviour of control beams ECC-1 and A1, respectively (a) (b) Figure 5.6: Cracking patterns of beams ECC-2 and A3 (a) Cracking patterns of beam ECC-2 around the loading point. (b) Cracking patterns of beam A3 around the loading point. 96 5.0 Multi-linear curve Tensile stress (MPa) 4.0 Uniaxial tension curve 3.0 2.0 1.0 0.0 0.000 0.025 0.050 Strain 0.075 0.100 Figure 5.7: Simplified multi-linear tension softening curve for numerical modelling 100 ECC- l (FEA) Load (kN) 80 ECC-1 A1 60 A1 (FEA) 40 20 0 0 10 20 30 40 Midspan Deflection (mm) 50 Figure 5.8: Load-deflection response of control beams 97 100 ECC-2 (Exp.) Load (kN) 80 ECC-2 (FEA) A3 (FEA) 60 A3 (Exp.) 40 20 0 0 10 20 30 Midspan Deflection (mm) 40 Figure 5.9: Load-deflection response of CFFRP strengthened beams 0.020 Tensile strain in CFRP ECC-2 ECC-2 (FEA) 0.016 0.012 0.008 0.004 0.000 0 200 400 600 Distance from cut-off point (mm) Figure 5.10: CFRP strain distribution of beam ECC-2 at peak load 98 4 FEA Smith and Teng (2001) Experimental Shear stress (MPa) 3 FEA * 2 1 0 0 15 30 45 60 75 Distance from cut-off point (mm) 90 Figure 5.11: Interfacial shear stress distribution in the CFRP cut-off region at peak load of beam ECC-2 * Deduced from the rate of change of CFRP strain as predicted by FEA and following the method proposed by Maalej and Bian (2001) discussed in section 2.3 Flexural-shear crack in front of the CFRP cut-off point Figure 5.12: Flexural-shear crack at CFRP cut-off point of beam ECC-2 99 CHAPTER SIX CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions The main objective of this study is to investigate the interfacial shear stress concentration at CFRP cut-off regions as well as failure modes of CFRP-strengthened beams as a function of beam size and FRP thickness. The study showed that increasing the size of the beam and/or the thickness of the CFRP leads to increased interfacial shear stress concentration in CFRP-strengthened beams as well as reduced CFRP failure strain. The work has also led to the following conclusions: (a) The beam size does not significantly influence the strengthening ratio, nor does it significantly affect the deflection and energy ductility of CFRPstrengthened beams. (b) The model by Teng et al. (2002a) to predict intermediate flexural crackinduced debonding was found to agree reasonably well with observed test data (c) The model by Smith and Teng (2001) to predict interfacial shear stresses in the adhesive layer at FRP cut-off points was found to agree reasonably well with observed test data for group 1 beams. For group 2 beams, however, Smith and Teng’s model (2001) seems to underestimate the interfacial shear stresses at FRP cut-off point particularly for beam C5. (d) The FE predicted the measured load-deflection and CFRP strains of the FRPstrengthened beams reasonably well. (e) The interfacial shear stress distributions in the adhesive layer of FRPstrengthened beams and the peak shear stress deduced from the FE predicted CFRP strains have been found to compare reasonably well with the test data. 100 (f) The effect of cracking on shear stress distribution in the adhesive layer was investigated and it was verified that the presence of cracks can significantly affect the interfacial shear stress distributions. (g) The results have shown that ECC has indeed delayed debonding of the FRP and resulted in effective use of the FRP materials. (h) The potential of using ECC in combination with FRP for the repair and strengthening of deteriorated RC structures may be investigated in future study. 6.2 Recommendations for Further Studies Further studies on FRP externally-strengthened beams are recommended as described next: (a) Further works could be done to investigate other types of failure modes in FRP-strengthened beams as well as FRP-strengthened beams with ECC. (b) Further works could be carried out to investigate other parameters that may affect the interfacial shear stress of FRP-strengthened beams such as concrete strength and FRP type. (c) In order to gain a better understanding of the stress transfer mechanism between the FRP and ECC material, it is suggested that a bond strength test be conducted. 101 REFERENCES Bonacci, J.F. and Maalej, M. Externally Bonded FRP for Service Life, Extension of RC Infrastructure. Journal of Infrastructure Systems, Vol.6, No.1, pp.41-51. 2000. Buyukozturk, O. and Hearing, B. 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Materials and Structures, Vol.28, pp.518-525. 1995. 107 [...]... curve of concrete 62 Figure 4.3 Material properties 62 Figure 4.4 Load-deflection response of control beams in Series A iff 63 Figure 4.5 Load-deflection response of control beams in Series B 63 Figure 4.6 Load-deflection response of control beams in Series C 64 Figure 4.7 Load-deflection response of FRP- strengthened beams in Series A 65 x Figure 4.8 Figure 4.9 Load-deflection response of FRP- strengthened. .. beams 97 Figure 5.9 Load-deflection response of CFRP strengthened beams 98 Figure 5.10 CFRP strain distribution of beam ECC-2 at peak load 98 Figure 5.11 Interfacial shear stress distribution in the CFRP cut-off Figure 5.12 region at peak load of beam ECC-2Ll beams 99 Flexural -shear crack at CFRP cut-off point of beam ECC-2L 99 xii LIST OF TABLE Page Table 3.1 Description of specimens 33 Table 3.2 Material... support the validity of the proposed models The main objective of this study is, therefore, to investigate the interfacial shear stress concentration at the carbon fibre reinforced polymer (CFRP) cut-off regions as well as the failure mode of CFRP -strengthened beams as a function of beam size and FRP thickness Because most structures tested in the laboratory are often scaled-down versions of actual structures... conditions To overcome these limitations, Smith and Teng (2001) proposed a new model to determine interfacial shear and normal stress concentrations of FRP- strengthened beams with the inclusion of axial deformation and several load cases Smith and Teng’s solution was applicable for beams made with all kinds of bonded thin plate materials In their model, they assumed: linear elastic behaviour of concrete,... yielding of the tension reinforcement (Taljsten 2001) 4 2.1.1 Flexural Failure by FRP Rupture and Concrete Crushing FRP- strengthened beams can fail by tensile rupture or concrete crushing This type of failure was less ductile compared to flexural failure of reinforced concrete beam due to the brittleness of the bonded FRP (Teng et al 2002a) 2.1.2 Shear Failure Shear failure of FRP- strengthened beams can... application of plate bonding Moreover, FRP does not corrode and creep, thereby offering long-term benefits The application of FRP involves buildings, bridges, chimneys, culverts and many others Although epoxy bonding of FRP has many advantages, most of the failure modes of FRP- strengthened beams occur in a brittle manner with little or no indication given of failure The most commonly reported failure modes... 8, 16 and 24 kN Figure 4.21 75 78 Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=32, 40 and 48 kN 79 xi Figure 4.23 Evolution of crack patterns and interfacial shear stress distribution in the adhesive layer of beam A5 at load P=56, 64 and 72 kN Figure 4.24 80 Evolution of crack patterns and interfacial shear stress distribution in the... 4.14 Interfacial shear stress distribution in the CFRP cut-off region for Series B at peak load Figure 4.15 72 Interfacial shear stress distribution in the CFRP cut-off region for Series C at peak load Figure 4.16 71 73 Variation of peak shear stresses with respect to beam depth for group 1 and 2 beams 74 Figure 4.17 Location of elements with lower tensile strength 75 Figure 4.18 Interfacial shear stress. .. practical handling), it would be interesting to know whether the results obtained in the laboratory are influenced by the difference in scale The scope of the research work is divided into three parts: 1) A laboratory investigation of the interfacial shear stress concentration at the CFRP cut-off regions as well as the failure mode of CFRP -strengthened beams as a function of beam size and FRP thickness. .. predicted CFRP debonding strains Figure 3.14(a) 50 Typical finite element idealization of the (a) RC beams (b) FRP- strengthened beams Figure 4.2 49 Variation of peak interfacial shear stress with respect to beam depth for Group 1 and 2 beams at peak load Figure 4.1 48 Experimentally-measured interfacial shear stress distributions in Series C Figure 3.19 47 Experimentally-measured interfacial shear stress ...Founded 1905 EFFECT OF BEAM SIZE AND FRP THICKNESS ON INTERFACIAL SHEAR STRESS CONCENTRATION AND FAILURE MODE IN FRP- STRENGTHENED BEAMS LEONG KOK SANG (B.Eng (Hons.) UTM) A THESIS SUBMITTED... the interfacial shear stress concentration at the carbon fibre reinforced polymer (CFRP) cut-off regions as well as the failure mode of CFRP-strengthened beams as a function of beam size and FRP. .. Load-deflection response of control beams in Series C 64 Figure 4.7 Load-deflection response of FRP- strengthened beams in Series A 65 x Figure 4.8 Figure 4.9 Load-deflection response of FRP- strengthened beams