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Bond behaviour of fibre reinforced polymer (FRP) rebars in concrete Quayyum, Shahriar 2010

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BOND BEHAVIOUR OF FIBRE REINFORCED POLYMER (FRP) REBARS IN CONCRETE by  Shahriar Quayyum  B.Sc. Bangladesh University of Engineering & Technology, Bangladesh, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in  The College of Graduate Studies (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)  June 2010  © Shahriar Quayyum, 2010  Abstract Recently, fibre reinforced polymer (FRP) rebars have been extensively used in construction instead of steel rebars due to their non-corrosive nature and high tensile strength. Bond between FRP rebars and concrete is a critical design parameter that controls the performance of reinforced concrete members at serviceability and ultimate limit states. In order to prevent a bond failure, an adequate anchorage length should be provided. The anchorage length is derived using a bond stress-slip ( τ − s ) constitutive law. The objective of this study is to investigate the effect of different parameters such as the type of fibre, the rebar surface and the confinement provided by the transverse reinforcement on the bond behaviour of FRP rebars in concrete. Based on the analysis, a generalized bond stressslip relationship will be developed and a new design equation for the required anchorage length of FRP rebar in concrete will be derived. A database was created on the bond stress-slip behaviour of FRP rebars in concrete from the available literature up to 2009. The data was statistically analyzed to investigate the effect of the different parameters on the bond performance of FRP rebars. It was observed that an increase in the confinement provided by the transverse reinforcement increased the bond strength of FRP rebars in concrete. This signifies that the presence of transverse reinforcement affects the bond behaviour of FRP rebars in concrete and hence, it should be taken into consideration while developing design equations for FRP rebars. Type of fibre and rebar surface does not affect the bond stress, but the latter affects the slip corresponding to the peak bond stress. Based on the results, a nonlinear regression analysis was performed to develop the bond stress-slip model for splitting mode of failure and a design equation for determining the development length of the FRP rebars in concrete was derived. The proposed development length equation can save about 10%-15% of the development length than that required by different code equations. This can save a considerable amount of FRP materials, which will eventually reduce the overall cost of construction and thereby, encourage the use of FRP reinforcing bars in the construction of concrete structures.  ii  Table of Contents Abstract ....................................................................................................................................................... ii Table of Contents....................................................................................................................................... iii List of Tables.............................................................................................................................................. vi List of Figures ........................................................................................................................................... vii List of Symbols.............................................................................................................................................x Acknowledgements.................................................................................................................................... xi Dedication.................................................................................................................................................. xii Chapter 1 : Introduction............................................................................................................................1 1.1 Problem Statement ..............................................................................................................................1 1.2 Thesis Overview..................................................................................................................................2 Chapter 2 : Literature Review and Research Objectives .......................................................................4 2.1 What is FRP.........................................................................................................................................4 2.1.1 FRP in Structural Engineering......................................................................................................4 2.1.2 Properties of FRP .........................................................................................................................6 2.2 Bond Mechanism.................................................................................................................................7 2.2.1 Bond Test Specimens .................................................................................................................11 2.2.2 Bond Behaviour of Steel Rebars ................................................................................................12 2.2.3 Bond Behaviour of FRP Rebars .................................................................................................13 2.3 Factors Affecting Bond Behaviour of FRP Rebar in Concrete .........................................................13 2.3.1 Compressive Strength of Concrete.............................................................................................14 2.3.2 Concrete Cover...........................................................................................................................15 2.3.3 Bar Diameter ..............................................................................................................................15 2.3.4 Embedment Length ....................................................................................................................16 2.3.5 Bar Cast Position ........................................................................................................................16 2.3.6 Type of Fibres.............................................................................................................................17 2.3.7 Type of Rebar Surface................................................................................................................18 2.3.8 Transverse Reinforcement..........................................................................................................18 2.4 Evaluation of Bond Strength .............................................................................................................19 2.5 Bond Strength and Development Length Equations in Design Codes ..............................................20 2.5.1 CSA S806-02..............................................................................................................................20 2.5.2 CSA S6-06..................................................................................................................................21 2.5.3 JSCE Recommendation ..............................................................................................................22 iii  2.5.4 ACI 440.1R-06 ...........................................................................................................................23 2.6 Bond Stress-Slip Relations ................................................................................................................25 2.7 Research Needs .................................................................................................................................30 2.8 Research Objectives ..........................................................................................................................30 Chapter 3 : Description of the Database ................................................................................................32 3.1 General ..............................................................................................................................................32 3.2 Failure Modes....................................................................................................................................32 3.3 Type of Fibre .....................................................................................................................................33 3.4 Type of Rebar Surface.......................................................................................................................33 3.5 Bar Cast Position ...............................................................................................................................33 3.6 Transverse Reinforcement.................................................................................................................34 3.7 Bar Diameter .....................................................................................................................................35 3.8 Compressive Strength of Concrete....................................................................................................35 3.9 Concrete Cover..................................................................................................................................36 3.10 Embedment Length .........................................................................................................................38 3.11 Database for Slip at Peak Bond Stress and Bond Stress-Slip Relationship.....................................39 3.12 Summary .........................................................................................................................................40 Chapter 4 : Analysis of Data and Derivation of Development Length ................................................41 4.1 General ..............................................................................................................................................41 4.2 Data Analysis ....................................................................................................................................41 4.2.1 Type of Fibres.............................................................................................................................41 4.2.2 Type of Rebar Surface................................................................................................................44 4.2.3 Compressive Strength of Concrete.............................................................................................48 4.2.4 Concrete Cover...........................................................................................................................50 4.2.5 Embedment Length ....................................................................................................................52 4.2.6 Effect of Confinement ................................................................................................................54 4.3 Derivation of Equations for the Peak Bond Stress and the Corresponding Slip................................55 4.3.1 Peak Bond Stress ........................................................................................................................55 4.3.2 Slip Corresponding to Peak Bond Stress....................................................................................64 4.4 Development Length .........................................................................................................................68 4.4.1 Beam Tests with Splitting Failures.............................................................................................68 4.4.2 Beam Tests with Pullout Failures...............................................................................................69 4.4.3 Effect of Bar Cast Position .........................................................................................................71 iv  4.5 Summary ...........................................................................................................................................72 Chapter 5 : Modeling of Bond Stress-Slip Relationship and Finite Element Analysis ......................73 5.1 General ..............................................................................................................................................73 5.2 Derivation of Bond Stress-Slip Relationship.....................................................................................73 5.2.1 Bond Stress-Slip Relationship Based on Splitting Mode of Failure...........................................76 5.3 Finite Element Analysis (FEA) .........................................................................................................80 5.3.1 Finite Element Modeling............................................................................................................82 5.3.2 FEA Results and Discussion ......................................................................................................88 5.4 Sensivity Analysis .............................................................................................................................91 5.5 Summary ...........................................................................................................................................93 Chapter 6 : Conclusions...........................................................................................................................95 6.1 General ..............................................................................................................................................95 6.2 Limitations of the Study ....................................................................................................................97 6.3 Future Recommendations..................................................................................................................98 Appendices .................................................................................................................................................99 Appendix A .............................................................................................................................................100 Appendix B..............................................................................................................................................121 Appendix C .............................................................................................................................................157 Appendix D .............................................................................................................................................161 Appendix E..............................................................................................................................................165 Biblography..............................................................................................................................................169  v  List of Tables Table 2.1 Typical properties of commercially available FRP reinforcing bars (Bank, 2006).......................7 Table 2.2 Typical properties of commercially available FRP strengthening strips (Bank, 2006).................7 Table 2.3 Typical properties of commercially available FRP strengthening sheets (Bank, 2006)................8 Table 4.1Standard errors for the coefficients of Equation 4.1.....................................................................60 Table 4.2 Regression statistics for Equation 4.1 .........................................................................................60 Table 4.3 ANOVA of the 50 unconfined bottom bar specimens having splitting failure ...........................60 Table 4.4 Regression statistics for Equation 4.3 .........................................................................................63 Table 4.5 ANOVA of the 105 confined bottom bar specimens having splitting failure .............................63 Table 4.6 Standard errors for the coefficients of Equation 4.4....................................................................66 Table 4.7 Regression statistics for Equation 4.4 .........................................................................................66 Table 4.8 ANOVA of 61 specimens having helical lugged FRP rebars .....................................................66 Table A.1 Consolidated database of beam-type specimens for evaluating peak bond stress of FRP rebars in concrete .................................................................................................................................................100 Table B.1 Database of beam-type specimens failed by concrete splitting for deriving bond stress-slip relationship of FRP rebars in concrete ......................................................................................................121 Table B.2 Database of beam-type specimens failed by rebar pullout for deriving bond stress-slip relationship of FRP rebars in concrete ......................................................................................................130 Table C.1 Database of beam-type specimens for deriving slip corresponding to peak bond stress of FRP rebars in concrete.......................................................................................................................................157 Table E.1 Values of Ct from the finite element analysis of the 105 confined beam specimens failed by splitting of concrete ...................................................................................................................................165  vi  List of Figures Figure 2.1 Glass, carbon and aramid fibres...................................................................................................4 Figure 2.2 Different types of commercially available FRP rebar..................................................................5 Figure 2.3 Stress-strain plots of FRP (ACI 440R-96). ..................................................................................6 Figure 2.4 Bond force transfer mechanism. ..................................................................................................8 Figure 2.5 Bond and radial forces. ................................................................................................................9 Figure 2.6 Cracking and damage mechanisms in bond. ..............................................................................10 Figure 2.7 Bond stress versus slip (Harajli, Hamad and Rteil, 2004). ........................................................11 Figure 2.8 Schematic of bond test specimens..............................................................................................12 Figure 2.9 Transfer of force through bond. .................................................................................................20 Figure 2.10 BEP model for pullout failures of steel rebars (Eligehausen et al., 1983)...............................27 Figure 2.11 Modified BEP model (Cosenza et al., 1997). ..........................................................................28 Figure 3.1 Classification of the specimens with respect to type of fibre and rebar surface. .......................34 Figure 3.2 Classification of the specimens with respect to concrete confinement, bar location and failure mode. ...........................................................................................................................................................35 Figure 3.3 Variation of bar diameter for all specimens failing by concrete splitting and rebar pullout......36 Figure 3.4 Compressive strength of concrete for all the specimens failing by concrete splitting and rebar pullout..........................................................................................................................................................37 Figure 3.5 Concrete cover to bar diameter ratio for all the specimens failing by concrete splitting and rebar pullout. ...............................................................................................................................................37 Figure 3.6 Embedment length-bar diameter ratio for all the specimens failing by concrete splitting and rebar pullout. ...............................................................................................................................................38 Figure 4.1 Normalized average bond stress of the specimens for different types of FRP with different concrete cover to bar diameter ratio. ...........................................................................................................42 Figure 4.2 Normalized slip corresponding to peak bond stress plotted against normalized cover for different types of FRP. ................................................................................................................................43 Figure 4.3 Types of FRP rebars considered in the analysis.........................................................................44 Figure 4.4 Normalized average bond stress of the specimens for different surface texture of the rebars with different concrete cover to bar diameter ratio. ....................................................................................46 Figure 4.5 Normalized slip at peak bond stress of the specimens with different rebar surface. .................47 Figure 4.6 Variation of peak bond stress with square root of concrete strength. ........................................49 Figure 4.7 Variation of normalized slip corresponding to peak bond stress with square root of concrete strength for different types of failure...........................................................................................................50 Figure 4.8 Variation of normalized average bond stress with concrete cover to bar diameter ratio. ..........51 vii  Figure 4.9 Variation of normalized slip corresponding to peak bond stress with different concrete cover to bar diameter ratio for different types of failure. ..........................................................................................52 Figure 4.10 Variation of normalized average bond stress with normalized embedment length for bottom bar specimens. .............................................................................................................................................53 Figure 4.11 Slip corresponding to peak bond stress plotted against embedment length of the specimens for pullout and splitting failures........................................................................................................................54 Figure 4.12 Normalized average bond stress plotted against normalized embedment length for bottom bar specimens. ...................................................................................................................................................56 Figure 4.13 Effect of transverse reinforcement on the normalized average bond stress of bottom bar specimens. ...................................................................................................................................................57 Figure 4.14 Effect of transverse reinforcement on the normalized slip corresponding to peak bond stress for the bottom bar specimens. .....................................................................................................................58 Figure 4.15 Normalized average bond stress plotted against normalized embedment length for unconfined bottom bar specimens failed by concrete splitting. .....................................................................................59 Figure 4.16 Comparison of the proposed equation with the ACI 440.1R-06 equation for unconfined bottom bar specimens having splitting failure.............................................................................................61 Figure 4.17 Effect of transverse reinforcement for confined tests with splitting failures. ..........................62 Figure 4.18 Comparison of the proposed equation with the ACI 440.1R-06 equation for confined bottom bar specimens having splitting failure.........................................................................................................63 Figure 4.19 Comparison of normalized slip corresponding to peak bond stress for FRP bars having different surface texture...............................................................................................................................67 Figure 4.20 Test vs. predicted normalized slip corresponding to peak bond stress for all specimens. .......68 Figure 4.21 Normalized average bond stresses of confined specimens for both pullout and splitting mode of failure. .....................................................................................................................................................70 Figure 4.22 Comparison of normalized average bond stress of unconfined top and bottom bar specimens having splitting failure.................................................................................................................................72 Figure 5.1 Bond stress-slip curves for bottom bar specimens having splitting failures. .............................74 Figure 5.2 Bond stress-slip curves for bottom bar specimens having pullout failures................................75 Figure 5.3 A schematic of the proposed bond stress-slip relationship. .......................................................76 Figure 5.4 Nonlinear regression of the experimental data of the bond stress-slip curves for specimens with helical lugged FRP rebars failed by splitting of concrete............................................................................78 Figure 5.5 Nonlinear regression of the experimental data of the bond stress-slip curves for specimens with spiral wrapped FRP rebars failed by splitting of concrete...........................................................................79  viii  Figure 5.6 Comparison of the predicted vs. the experimental results for specimens with helical lugged FRP bars having splitting failure.................................................................................................................81 Figure 5.7 Comparison of the predicted vs. the experimental results for specimens with spiral wrapped FRP bars having splitting failure.................................................................................................................82 Figure 5.8 Hinged beam specimen. .............................................................................................................83 Figure 5.9 Splice beam specimen................................................................................................................84 Figure 5.10 Concrete compressive stress-strain model (Thorenfeldt et al. 1987).......................................86 Figure 5.11 Behaviour of concrete under tension........................................................................................87 Figure 5.12 Constitutive relations for FRP reinforcements.........................................................................87 Figure 5.13 Flow chart of the iterations performed in FEA. .......................................................................89 Figure 5.14 Comparison of experimental and finite element analysis results.............................................90 Figure 5.15 Comparison of the required development length for different cover to bar diameter ratio .....92 Figure D.1 Predicted vs. experimental bond stress-slip curves for specimens with helical lugged FRP bars having splitting mode of failure. ...............................................................................................................162 Figure D.2 Predicted vs. experimental bond stress-slip curves for specimens with spiral wrapped FRP bars having splitting mode of failure.........................................................................................................164  ix  List of Symbols A f ,bar  Area of longitudinal reinforcement, mm2  Atr  Area of transverse reinforcement, mm2  c  Concrete cover, mm  db  Bar diameter, mm  f c′  Compressive strength of concrete, MPa  fF  Maximum stress in reinforcing bar, MPa  l embed  Embedment length of reinforcing bar, mm  ld  Embedment length required to develop a tensile stress of f F , mm  n  Number of bars being developed along the plane of splitting  s  Spacing of transverse reinforcement, mm  τm  Peak bond stress of reinforcing bar in concrete, MPa  τ tr  Transverse reinforcement contribution to peak bond stress, MPa  sm  Slip corresponding to peak bond stress, mm  α η  Rebar surface modification factor for bond stress-slip curve Rebar surface modification factor for slip corresponding to peak bond stress  χ  Bar location modification factor  x  Acknowledgements  The author wishes to convey his profound gratitude to the almighty for allowing him to bring this effort to fruition. The study was undertaken under the supervision of Dr. Ahmad Rteil, Assistant Professor, School of Engineering, The University of British Columbia, Kelowna, BC, Canada. His systematic guidance and constant persuasion has immensely helped the author throughout this work. The author sincerely acknowledges his heartiest gratitude and indebtedness to him for his superior technical expertise and solutions to many projects and computer-related problems.  The author also pays his deepest homage to his parents, whom he believes to be cardinal source of inspiration for all his achievement.  xi  Dedication To my wife who has given me support at every step of my life!  xii  Chapter 1: Introduction  1.1 Problem Statement In presence of corrosive environments, reinforcing steel bars in concrete structures may suffer severe deterioration due to corrosion. Therefore, it has been a primary concern for researchers and engineers to control the corrosion of steel reinforcing bars or substitute steel rebars with some alternative reinforcement which will be able to provide the desirable characteristics of steel rebars as well as to prevent corrosion. It has been found that fibre reinforced polymer (FRP) rebars have a great potential to fill such a need (Neale and Labossiére, 1992; Nanni, 1993; Nanni and Dolan, 1993; Tighiouart et al., 1998). FRP reinforcing bars have several advantages over conventional reinforcing steel, namely non-corrosiveness, high tensile strength, light weight, fatigue resistance, nonmagnetic electrical insulation, small creep deformation and specific gravity (Hao et al., 2006). As a result, FRP reinforcing bars have been introduced as reinforcement for different concrete structures subjected to aggressive environments such as chemical and wastewater treatment plants, sea walls, floating docks, and under water structures (Benmokrane and Rahman, 1998; Saadatmanesh and Ehsani, 1998; Dolan et al., 1999; Razaqpur, 2000). In spite of the advantages of FRP reinforcement over conventional steel reinforcement, a direct substitution between FRP and steel rebar is not possible due to various differences in the mechanical and physical properties between the two materials. The main problems that prevent the use of FRP rebars on a wide scale as a reinforcing materials for concrete structures are, •  When subjected to tensile force in the direction of fibres, FRP exhibits linear elastic behaviour up to failure. Therefore, it does not have any yield point which means it exhibits no ductility;  •  The modulus of elasticity for some types of FRP, namely aramid fibre reinforced polymer (AFRP) and glass fibre reinforced polymer (GFRP) is much lower than steel, hence deflection and crack widths may control the design of reinforced concrete structures;  1  •  The bond behaviour of FRP rebars with concrete is different than that of steel rebars due to the non-isotropic material properties and the different surface texture of the FRP rebars (ACI 440.1R-06).  •  Higher cost of FRP compared to steel, lack of familiarity with the new technology and limited availability of literature contributed to the slow adaptation of FRP as concrete reinforcement (Okelo and Yuan, 2005).  The performance of a reinforced concrete member, both at the ultimate limit state (strength) and the serviceability limit state (crack and deflection), depends on the transfer of forces between the concrete and the reinforcement, which, in turn, depends on the quality of bond between the two materials. The resistance of a reinforced concrete member under flexure, shear and torsion forces is directly related to the force developed in the reinforcement. Moreover, many serviceability checks (e.g., crack width and member deflections) require evaluation of the effects of tension stiffening, which directly arises from the bond behaviour. Therefore, the development of adequate bond (or force transfer mechanism) is always a critical aspect of the structural design, regardless of the type of reinforcement (Chaallal and Benmokrane, 1993; Benmokrane et  al., 1996; Tighiouart et al., 1998; Pecce et al., 2001). As a result, considerable experimental research has been conducted to understand the bond behaviour of FRP rebars in concrete environment. Despite the numerous experimental investigations, the bond behaviour of FRP rebars with concrete is not fully understood yet. This is attributed to the complexity of the parameters influencing the bond behaviour (e.g., diameter of the rebar, concrete cover, embedment length, concrete confinement and the concrete compressive strength), and the different types and properties of the currently commercially available FRP rebars (Okelo and Yuan, 2005). Design equations have been developed for designing concrete structures reinforced with FRP rebars based on the available experimental data up to 2002. Since then considerable research has been conducted and therefore, it has become essential to assess the effects of different parameters on the bond performance of FRP rebars to update the guidelines for the design of concrete structures reinforced with FRP rebars. 1.2 Thesis Overview This thesis is organized in six chapters. Chapter 1 gives an overview of the research. Chapter 2 reviews the available literature on the bond between concrete and FRP. This chapter discusses 2  the effect of different parameters on the bond behaviour of FRP rebars in concrete, the available code equations to predict the peak bond stress (bond strength) and also, the existing formulations of bond stress-slip relationship for FRP rebars in concrete. It highlights the gaps in the available literature on the bond behaviour of FRP rebars in concrete and thereby, sets the research objectives. A brief description of the accumulated database is presented in Chapter 3. Chapter 4 presents the results of the statistical analysis of the accumulated database, along with the analytical modeling of the peak bond stress and the corresponding slip equations. The comparisons of the predicted models with the experimental results are also presented in Chapter 4. Based on these models, an equation to calculate the development length of FRP rebars is proposed to be used in design codes. Chapter 5 presents an analytical modeling of the bond stress-slip relationship based on the available database. It also presents the results from a finite element analysis for studying the effect of confinement. Chapter 6 furnishes the conclusions and the limitations of this study and recommends some future research.  3  Chapter 2: Literature Review and Research Objectives  2.1 What is FRP Fibre reinforced polymers (FRP) are composite materials that typically consist of strong fibres embedded in a resin matrix. The fibres provide strength and stiffness to the composite and generally carry most of the applied loads. The thermosetting matrix - typically epoxies, polyesters and vinylesters - acts to bond and protect the fibres and to provide for transfer of forces from fibre to fibre through shear stresses (ACI 440R-07). Generally, there are three types of fibres used in structural engineering applications (Figure 2.1)-glass (GFRP), carbon (CFRP) and aramid (AFRP). FRP used in construction have fibre concentration greater than 30% by volume. AFRP GFRP rebar CFRP tendon CFRP sheet CFRP rebar  Figure 2.1 Glass, carbon and aramid fibres. 2.1.1 FRP in Structural Engineering  In the last 20 years, composite materials have developed into economically and structurally viable construction material for buildings and bridges. Today, FRP are used in structural engineering in a variety of forms: reinforcement material for new concrete construction, strengthening material for existing structures, and structural members for new construction. The FRP material can be used in new construction as internal rebars, prestressing tendons, and stay-in-place formwork. The surface of the FRP rebars are either sand coated, helically 4  wound spiral outer surface, indented, braided, or with ribs. Figure 2.2 shows some commercially available FRP rebar with different surface textures. Extensive research has been conducted since the mid 1990s to study the behaviour of beams and slabs reinforced with various FRP rebars (ACI 440.1R-06).  Steel rebar  CFRP Tendon  Sand coated  Plain rebar  Spiral wound  Ribbed  Figure 2.2 Different types of commercially available FRP rebar.  FRP prestressing tendons were first used in Europe in the 1980s primarily to eliminate corrosion. The use of FRP prestressing is still hindered by the fact that the conventional steel anchor could not be used due to the low transverse strength of the FRP tendons (Erki and Rizkallak, 1993; Nanni et al., 1995; Soudki, 1998). FRP stay-in-place formwork has been explored for some years (Dieter et al., 2002; Ringelstetter et al., 2006; Ozbakkaloglu and Saatcioglu, 2007). Columns and beams made from FRP tubular shapes and filled with concrete has been gaining popularity lately (Mirmiran et al., 2000; Fam and Rizkalla, 2002; Zhu, 2004; Fam et al., 2005). FRP has been used on concrete, steel, masonry and timber structures to increase their existing flexural, shear, or confinement strength. Materials used are either prestressing tendons, pre-manufactured rigid FRP strips adhesively bonded to the surface of the structure, or hand layup sheets that consists of in situ forming of FRP composite on the surface of the structural member using flexible, dry FRP sheets and a polymer resin (Figure 2.1). In the last few years, near surface mounted (NSM) method has been explored, where an FRP tendon or strip 5  (prestressed or non-prestressed) is inserted and then bonded adhesively into a machined groove at the surface of the concrete member. 2.1.2  Properties of FRP  The properties of the currently available FRP systems vary significantly depending on their specific formulation, constituents, and manufacturing method. They are highly directionally dependent. The properties of the FRP composite materials are usually obtained by experimental testing of the FRP material and products. Experimental procedures are given in CSA S806, ACI 440.3 and different ASTM standards. In general, FRP has some special characteristics that make them suitable to be used in the construction industry.  Figure 2.3 Stress-strain plots of FRP (ACI 440R-96).  These characteristics include-high strength, non-corrosive nature, light weight, fatigue resistant, non-magnetic, electrical insulation and small creep deformation. All FRP systems exhibit linear elastic tensile stress-strain behaviour (in the direction of the fibres). From the typical stress-strain curve shown in Figure 2.3, it is noted that FRP systems have no yielding, and except for some carbon fibre reinforced polymers (CFRP) systems, they have lower modulus of elasticity compared to steel. In Table 2.1, Table 2.2 and Table 2.3, typical properties of the FRP rebars, strips and sheets are listed respectively. 6  Table 2.1 Typical properties of commercially available FRP reinforcing bars (Bank, 2006) GFRP-  CFRP-  vinylester  vinylester  Fibre volume (%)  50-60  50-60  50-60  Fibre architecture  unidirectional  unidirectional  unidirectional  Tensile strength, longitudinal (MPa)  500-700  2070  2255  Tensile modulus, longitudinal (MPa)  41-42  124  145  Shear strength, out of plane (MPa)  22-27  --  --  1.7  9  --  6.7-8.8  -7.2-0  0.7  22.0-33.7  73.8-104.4  --  2.1  --  1.6  Bond strength (MPa) -6  -1  Coefficient of thermal expansion, longitudinal (10 °C ) -6  -1  Coefficient of thermal expansion, transverse (10 °C ) 3  Density (g/cm )  CFRP-epoxy  Table 2.2 Typical properties of commercially available FRP strengthening strips (Bank, 2006) Standard  High modulus  modulus  CFRP epoxy  GFRP epoxy  CFRP vinylester  CFRP epoxy Fibre volume (%)  65-70  65-70  65-70  60  Fibre architecture  Unidirectional  unidirectional  unidirectional  unidirectional  Nominal thickness (mm)  1.2-2.9  1.2  1.4-1.9  2.0  Width (mm)  50-100  50-100  50-100  16  Tensile strength, longitudinal (MPa)  2690-2800  1290  900  2070  Tensile strain (max), longitudinal (%)  1.8  --  2.2  1.7  Tensile modulus, longitudinal (MPa)  155-165  300  41  131  2.2 Bond Mechanism For an optimal design of reinforced concrete structures, the force between the reinforcement and the concrete should be transferred efficiently and reliably through the bond between the two materials. In reinforced concrete members, the transfer of forces between a reinforcing bar and concrete occurs by three mechanisms: (1) chemical adhesion between the bar and the concrete, (2) frictional forces arising from the roughness of the interface between the bar and the surrounding concrete, and (3) mechanical interlocking arising from the textures on the rebar 7  surface (Figure 2.4). The addition of these forces can be resolved into an outward component (radial splitting force) and a shear component, parallel to the bar that is the effective bond force (Figure 2.5). Table 2.3 Typical properties of commercially available FRP strengthening sheets (Bank, 2006) Standard modulus  High modulus  GFRP epoxy  CFRP 0.165-0.33  CFRP 0.165  0.35  600  600  1200  Unidirectional  Unidirectional  Unidirectional  Tensile strength, longitudinal (MPa)  3790  3520  1520-3240  Tensile strain (max), longitudinal (%)  1.67-1.7  0.94  2.1-2.45  Tensile modulus, longitudinal (MPa)  230  370  72  Thickness (mm) Width (mm) Fibre architecture  Figure 2.4 Bond force transfer mechanism.  To prevent bond failure, the rebar must be anchored long enough in the concrete or should have enough confinement (concrete cover or transverse reinforcement). In this case, the radial and tangential stresses developed along the bar length will be less than the concrete capacity and the bar can achieve its design tensile strength. In such cases, the failure is initiated by different failure mode (concrete crushing, shear, bar rupture). If adequate anchorage length of the rebar or sufficient confinement to the concrete is not provided, then radial and shear forces may be higher than the concrete capacity which can lead to bond failure (ACI 408R-03).  8  Figure 2.5 Bond and radial forces.  Bond failures are divided into either pullout failure or splitting failure: Splitting Failure: This type of failure occurs when the concrete surrounding the reinforcing bar splits without reinforcing bar rupturing (Figure 2.6a). As reinforcing bars are loaded, the bars exert radial pressure on the surrounding concrete. If the surrounding concrete and/or the transverse reinforcement are not enough to resist this pressure, a splitting crack initiates at the concrete-rebar interface, and propagates towards the surface leading to the failure of the concrete by concrete cover splitting. Splitting failure results in cracking in plane that are both perpendicular and parallel to the reinforcement (Figure 2.6a). Pullout Failure: This type of failure occurs when the bar pulls out of the concrete without concrete splitting or without bar rupturing (Figure 2.6b). This happens when the radial forces from the bar being loaded are lower than what the surrounding concrete and/or transverse reinforcement can resist, but tangential forces are higher compared to the resistance of the concrete. Pullout failure results in shearing along a surface at the top of the ribs around the bars (Figure 2.6b). 9  (a) Cross-sectional view of a concrete member showing splitting cracks between bars and through the concrete cover  (b) Side view of a member showing shear crack and/or local concrete crushing due to bar pullout Figure 2.6 Cracking and damage mechanisms in bond.  Both bond failures are associated with slip of the rebar relative to the concrete. However, pullout failure occurs at higher bond strength than the splitting failure as the concrete is well confined and therefore, the radial splitting cracks need more energy to reach the outer surface of the concrete. Bond stress-slip relationship can be a good way to represent the bond behaviour of reinforcing bar with the concrete. It also helps in determining the required anchorage length to achieve the desired strength of the reinforcing bar. Figure 2.7 shows the bond stress-slip envelope for the pull out and the splitting failure for steel rebar. Both the splitting failure and pullout failure envelopes consist of four phases that explain the bond behaviour during static loading. As loads are applied, the initial stiffness of the bond in a splitting bond failure is similar to that of a pullout failure. The first phase of the bond in a splitting failure ends when an increase in the residual stress component of the bond force results in the development of splitting tensile cracks. Once a splitting crack develops the behaviour of the bond stress-slip relation deviates from the pull out behaviour due to the decrease in the bond stiffness as the crack propagates in the concrete cover. The second phase of the bond in a splitting failure ends when the crack has 10  expanded to the surface and the splitting of the concrete cover takes place. This indicates a complete deterioration of the bond (smax, umax). On the other hand, the second phase of the bond in a pullout failure is a constant bond following the peak bond stress (u1). The third phase of the bond behaviour for both splitting and pullout failures shows a significant drop in the bond stress (Figure 2.7). The fourth phase of the bond in a pullout failure is a constant bond and in a splitting failure, it is a decreasing branch which ends at zero bond due to the expansion of the splitting cracks in the concrete (Harajli et al., 2004). However, while both the bond failures are brittle and should be avoided, splitting failure is more common for the development length ( ld > 30d b ) and the concrete cover ( d b ≤ c ≤ 3d b ) used in practice.  Figure 2.7 Bond stress versus slip (Harajli, Hamad and Rteil, 2004). 2.2.1 Bond Test Specimens  Two types of tests are conducted to measure the bond strength of reinforcing bars: pullout tests (Figure 2.8a) and beam tests (Figure 2.8b, c, d), both of which give different values. Bond strength from beam tests is typically found to be lower than from pullout tests (ACI 408R-03). This is because in the pullout tests, the splitting of the concrete is avoided due to the absence of local bending on the bar, a higher thickness of the concrete cover and the confining action of the reaction plate on the concrete specimen (i.e. the concrete surrounding the reinforcing bars is in compression). Alternatively, in the beam tests, the concrete surrounding the reinforcing bars is in 11  tension, which varies along the span length and leads to cracking under low stresses and reduction in the bond strength. Thus, the pullout tests give an unrealistic bond stress values which can be considered as an upper-bound value for the bond stress-slip performance of FRP bars. That is why beam tests are more realistic than the pullout tests in simulating the real behaviour of concrete members in flexure (Tighiouart et al., 1998).  Figure 2.8 Schematic of bond test specimens. 2.2.2 Bond Behaviour of Steel Rebars  When the surface adhesion is lost, the steel reinforcing bar moves with respect to the surrounding concrete, while bearing forces on the ribs and friction forces on the ribs and the barrel of the bar are mobilized. It has been observed that after initial slip of the bar, most of the force is transferred by bearing. The compressive bearing forces on the ribs increase the value of the friction forces. As the slip increases, friction on the barrel of the reinforcing bar is reduced, leaving the forces at the contact faces between the ribs and the surrounding concrete as the principal mechanism of force transfer (ACI 408R-03). Friction, however, especially between the concrete and the bar ribs plays a significant role in the force transfer. Friction also plays an important role for plain bars (that is, with no ribs), with slip-induced friction resulting from 12  transverse stresses at the bar surface caused by small variations in bar shape and minor, though significant, surface roughness. 2.2.3 Bond Behaviour of FRP Rebars  Bond behaviour of FRP bars with concrete is not the same as that of steel bars because of marked differences in force transfer and failure mechanisms of steel and FRP bars (Faza and GangaRao, 1990; Faza, 1991). This is attributed to the difference in the material properties and the interaction mechanisms of concrete and reinforcement (Chaallal and Benmokrane, 1993). The most fundamental difference is that steel is an isotropic, homogeneous, and elasto-plastic material, whereas FRP is anisotropic, non-homogeneous and linear elastic material. The anisotropy of the FRP bar results from the fact that its shear and transverse properties are dependent on both the resin and the fibre type and direction, even though the longitudinal properties are dominated by fibres (Cosenza et al., 1997). Since material anisotropy leads to different physical and mechanical properties in both longitudinal and transverse directions, the anisotropic nature of the FRP materials need to be accounted for in the development of design equations and in the understanding of failure mechanisms (GangaRao et al., 2001). The mechanical properties of the steel and the FRP reinforcing bars are qualitatively and quantitatively different from each other (JSCE, 1997). Also, FRP bars produced by different manufacturers are different in that they involve different manufacturing process for the outer surface and significant differences in material properties in the longitudinal and transverse directions. Moreover, the outer surface texture of the FRP rebars are created by using either epoxy, fibres or sand coating which make the rebars non-homogeneous and reduces the bond performance. Therefore, it has been observed that for FRP rebars, chemical adhesion and friction are the primary bond mechanisms (Daniali, 1992; Ehsani et al., 1993; Larralde and SilvaRodriguez, 1993; Benmokrane et al., 1996). Figure 2.2 shows different types of commercially available FRP rebars along with a steel rebar. 2.3 Factors Affecting Bond Behaviour of FRP Rebar in Concrete Considerable experimental research has been conducted to understand the bond behaviour of FRP rebars in concrete. This includes tests on beam and pullout specimens with different types and sizes of rebars (Daniali, 1990; Faza, 1991; Ehsani et al., 1993, 1996; Kanakubo et al., 1993; Makitani et al., 1993; Benmokrane et al., 1996; Cosenza et al., 1996, 1997, 1999; Tepfers et al., 13  1998; Tighiouart et al., 1998, 1999; Shield et al., 1997, 1999; Mosley, 2000; Pecce et al., 2001; Defreese and Wollmann, 2002; Aly et al., 2005, 2006, 2007; Okelo, 2007; Rafi et al., 2007; Baena et al., 2009). Research indicates that the bond behaviour of FRP rebars in concrete is influenced by several factors. Some of the important parameters that seem to affect the bond performance of FRP rebars in concrete are explained in the following sections. 2.3.1 Compressive Strength of Concrete  As discussed in section 2.2, both splitting and pullout mode of failures are dependent on the tensile and shear strength of the concrete, which in turn, is dependent on the compressive strength of concrete. It has been reported that the tensile strength of concrete is approximately proportional to the square root of the compressive strength of concrete ( 408, 1992). Hence, bond strength should be related to  f c′ ) (ACI Committee  f c′ . Regression analysis on different  experimental results showed that for bond failure of FRP rebars in concrete, a better correlation exists between the bond strength and  f c′ (Pleimannn, 1987, 1991; Faza and GangaRao, 1990;  Ehsani et al., 1996; Okelo and Yuan, 2005; ACI 440.1R-06; Okelo, 2007). Ehsani et al. (1995) performed investigation to determine the effect of concrete strength on the bond behaviour of FRP rebars in concrete. It was observed that with an increase in the concrete strength, the bond stress of FRP bars increased slightly. Also, the initial stiffness of the bond stress-slip curve increased and the slip decreased. Hattori et al. (1995) tested the bond performance of AFRP bars and noticed that the maximum bond stress is dependent on the compressive strength of concrete. Makitani et al. (1993), Benmokrane et al. (1996) and Tighiouart et al. (1998) investigated the effect of concrete strength on the bond behaviour of FRP rebars in concrete based on beam bond tests and it was concluded that the bond strength increase is proportional to the square root of the compressive strength of concrete. Results from pullout tests also indicated that the mode of failure during bar pullout depends on the compressive strength of concrete. For concrete strength, f c′ > 30 MPa, bond strength of FRP rebars do not depend on the compressive strength of concrete, since in such cases the failure interface occurs at the surface of the FRP rebar. On the contrary, for low strength concrete (around 15 MPa), the compressive strength of the concrete directly influences the bond 14  performance of FRP rebars, because in such cases the failure interface takes place in the concrete matrix (Karlsson, 1997; Tepfers et al., 1998; Achillides and Pilakoutas, 2004; Baena et al., 2009). 2.3.2 Concrete Cover  Concrete cover provides confinement to the rebars which increases the bond strength (Ehsani et  al., 1993; Kanakubo et al., 1993; Defreese and Wollmann, 2002; Aly and Benmokrane, 2005). Therefore, the bond failure mechanism of FRP bars in concrete is influenced by the concrete cover around the reinforcing bar by virtue of its confining effect. ACI 440.1R-06 stated that bond failure occurs through splitting of the concrete when the member does not have adequate concrete cover. On the other hand, when sufficient concrete cover is provided, splitting failure is prevented or delayed. Then the system usually fails by shearing along a surface at the top of the ribs around the bars, resulting in a pullout failure. This indicates that the bond failure mode of a reinforced concrete member depends on the concrete cover. Ehsani et al. (1996) carried out an investigation on 48 beam specimens with GFRP rebars. It was observed that when the specimen had concrete cover of one bar diameter ( c = 1d b ), splitting failure occurred, whereas pullout failure or rebar fracture occurred when the specimens had concrete cover of two bar diameters or more ( c > 2d b ). It is worth mentioning here that the side concrete cover is more effective in increasing the bond strength than the bottom concrete cover and it is recommended not to increase the bottom concrete cover such that it exceeds the side concrete cover (Aly et al., 2006). Aly et al. (2006) performed an investigation on six full-scale beams to study the effect of concrete cover on the bond strength of tensile lap splicing of GFRP rebars. In this study, the concrete cover was varied between one and four bar diameters ( d b ≤ c ≤ 4d b ) and it was observed that the bond strength increased by 27% as the concrete cover increased from one to four bar diameters. Moreover, it was noted that the effect of concrete cover on bond strength was nonlinear. 2.3.3 Bar Diameter  The effect of bar diameter on the bond resistance of FRP rebars in concrete have been investigated experimentally by Faza and GangaRao (1990), Larrard et al. (1993), Larralde and Silva-Rodriguez (1993), Nanni et al. (1995), Benmokrane et al. (1996), Tighiouart et al. (1998), Defreese and Wollmann (2002), Achillides and Pilakoutas (2004), Aly et al. (2006), Okelo 15  (2007) and Baena et al. (2009). The experimental investigations revealed the same results obtained for steel rebar i.e. the bond strength of FRP bars is increased with decrease in the bar diameter. It has been reported that larger diameter bars loose their adhesive bond earlier (Achillides and Pilakoutas, 2004). Tighiouart et al. (1998) and Hao et al. (2006) explained the cause of this decrease in bond strength with increased bar diameter. They stated that when the diameter of the bar is larger, more bleeding water is trapped beneath the rebar. As a result, there is a greater possibility of creating voids around the rebar which will eventually decrease the contact surface between the concrete and the rebar and thereby, reduces the bond strength. 2.3.4 Embedment Length  The effect of the embedment length on the maximum average bond stress of FRP bars in concrete was studied by Makitani et al. (1993), Nanni et al. (1995), Benmokrane et al. (1996), Shield et al. (1997), Tighiouart et al. (1998, 1999), Cosenza et al. (1999), Pecce et al. (2001) and Aly et al. (2006). It was reported that the maximum average bond stress value decreased with an increase in the embedment length. Steel bars showed the same results. This was explained due to the non-linear distribution of the bond stress along the length of the reinforcing bar. As the embedment length increases, the stress is distributed over a longer length and hence, the bond strength decreases. It was also noticed that the initial bond stiffness of the FRP bars was also influenced by the embedment length. Ehsani et al. (1995) reported that with an increase in the embedment length, there is an increase in the tensile load and the initial stiffness of the bond stress-slip curve. Moreover, it was found that the rate of bond stress increase is greater for smaller embedment lengths than for longer lengths and this was attributed to the non-linear distribution of bond stresses on the bar (Achillides and Pilakoutas, 2004). Okelo (2007) carried out an investigation on the bond behaviour of GFRP and CFRP bars and it was observed that the actual pullout of the rebar occurs when the embedment length is short, compressive strength of concrete is low and the rebar size is small. On the contrary, when the embedment length is long and compressive strength of concrete is high, the failure takes place by rebar fracture, concrete cover splitting or shear compression failure of the concrete. 2.3.5 Bar Cast Position  The effect of bar casting position on the bond behaviour of FRP rebars in concrete was investigated by Chaallal and Benmokrane (1993), Ehsani et al. (1993), Rossetti et al. (1995), 16  Benmokrane and Masmoudi (1996), Tighiouart et al. (1998) and Wambeke (2003). It was observed that during the placement of concrete, air, water and fine particles migrate upward through the poured concrete and get trapped under the rebar. This phenomenon decreases the contact surface between concrete and rebar and thus causes a significant drop in the bond strength under the horizontal reinforcement placed near the top of the pour. Tests have shown that the bond strength of top cast bars is about 66% of that of the bottom cast bars (Ehsani et al., 1993). A decrease in the bond strength will increase the required development length of the FRP bars and hence, a modification factor is needed for calculating the required development length for top rebars. Chaallal and Benmokrane (1993) proposed a modification factor of 1.1 for top bars from pullout tests. A modification factor of 1.3 was recommended by the ACI guide (ACI 440.1R-03) based on the recommendations of Tighiouart et al. (1999). However, this modification factor was refined with more experimental data by Wambeke and Shield (2006) and ACI 440.1R-06 recommended a top bar modification factor of 1.5. CSA S806-02 also recommended a top bar modification factor of 1.3. 2.3.6 Type of Fibres  Tighiouart et al. (1998) found that GFRP bars show less bond strength compared to the steel rebars and this is attributed to the difference in the surface deformations of the two types of bars. This was in agreement with the study of Benmokrane et al. (1996) who found that bond strength of GFRP reinforcing bars was 60-90% of that of the steel reinforcing bars depending on the bar diameter. Rafi et al. (2007) and Okelo (2007) carried out an investigation on CFRP bars by using beam bond specimens and found that bond strength of CFRP bars was about 85% of that of the deformed steel bars. Similar results were also obtained from pullout tests in normal strength concrete, where, the bond strengths of GFRP reinforcing bars varied from 73-96% of that of the steel reinforcing bars, depending on the bar diameter and the embedment length (Larralde and Silva-Rodriguez, 1993). This was also confirmed by Achillides and Pilakoutas (2004), who found that GFRP and CFRP bars developed 72% of the steel’s bond strength. It was also observed from their experimental results that GFRP and CFRP bar exhibited the same bond strength. Wambeke and Shield (2006) gathered all the bond test data up to 2002 and after a comprehensive analysis of the database, it was concluded that the type of fibres does not seem to affect the bond strength of FRP rebars in concrete. According to CSA S806-02, CFRP and GFRP gives the same bond strength, but AFRP shows lower bond strength in comparison to CFRP and 17  GFRP. Based on that, CSA S806-02 specifies factors (1.0 for CFRP and GFRP; 1.25 for AFRP) to account for the effect of type of fibres during the calculation of the development length. 2.3.7 Type of Rebar Surface  FRP reinforcing bars are produced with different types of surface deformations such as sand coated, spiral wrapped, helical lugged/ribbed and indented (Figure 2.2). It was observed that deformed bars produce much better bond performance than plain bars due to the mechanical interlocking between the surface texture and the concrete (Faoro, 1992; Makitani et al., 1993; Al-Zahrani, 1995; Nanni et al., 1995; Rossetti et al., 1995; Cosenza et al., 1997). CSA S806-02 specifies different factors for different rebar surfaces for evaluating the development length of FRP rebars (1.0 for surface roughened or sand coated or braided surfaces; 1.05 for spiral pattern surfaces or ribbed surfaces; 1.8 for indented surfaces). However, Wambeke and Shield (2006) concluded based on the analysis of a database of 269 beam-type specimens, that rebar surface does not appear to affect the bond strength of FRP rebars in concrete. This was confirmed by Mosley et al. (2008), who performed investigation on the bond behaviour of AFRP and GFRP bars by using beam splice tests and concluded that the surface texture does not significantly affect the bond strength or crack width of the beams. However, Baena et al. (2009) carried out 88 pullout tests on FRP bars and concluded that when the failure is not occurring at the concrete matrix, rebar surface treatment has significant influence on the bond strength. From the above discussion, it can be concluded that no definite trend has been established for the effect of rebar surface on bond strength. 2.3.8 Transverse Reinforcement  Transverse reinforcements confine the concrete and thereby, should increase the bond strength of the reinforcing bars in concrete. Studies on bond behaviour of steel reinforcement have demonstrated that the presence of transverse reinforcement confines the developed and spliced bars by limiting the progression of splitting cracks and, thus, increasing the bond force required to cause failure (Tepfers, 1973; Orangun et al., 1977; Darwin and Graham, 1993a, b). An additional increase in the transverse reinforcement results in an increase in the bond force that eventually converts a splitting failure to a pullout failure. Additional transverse reinforcement, above that needed to cause the transition from a splitting to a pullout failure, becomes progressively less effective, eventually providing no increase in the bond strength (Orangun et 18  al., 1977). However, little research has been done so far, on the effect of confinement for the transverse reinforcements on the bond behaviour of FRP rebars in concrete. In Wambeke and Shield’s (2006) study, only 19 beam-type specimens (out of 269 specimens) had transverse reinforcements and the analysis of the database showed that the transverse reinforcement does not affect the bond strength of FRP rebars in concrete. Darwin et al. (1996) found that confining steel bars with a high relative rib area had more of a beneficial increase in the bond force over the same-size steel bars with moderate relative rib area. The counterargument was proposed in Wambeke and Shield’s (2006) study. The GFRP bars have a very low relative rib area and, therefore, the presence of confinement may not increase the average bond stress. However, it was recommended to investigate the effect of confinement on bond strength of FRP rebar in concrete upon availability of more data. 2.4 Evaluation of Bond Strength Bond strength is defined as the maximum local horizontal shear force per unit area of the bar perimeter. For a rebar embedded in concrete with a length lembed , equilibrium condition can be established. Assuming a uniform distribution of stress, the force on the rebar is resisted by an average bond stress, τ f , acting on the surface of the rebar (Figure 2.9). Hence, the following relationship can be derived:  τ f πd blembed + A f ,barf f F = A f ,bar ( f F + ∆f F )  Equation 2.1  where, τ f = average bond stress (MPa); d b = diameter of the rebar (mm); lembed = embedment length of the rebar (mm); f F = tensile stress of the rebar (MPa); A f ,bar = area of one rebar (mm2). From Equation 2.1, the bond strength can be expressed as  τf =  A f ,bar ∆f F  πd b lembed  =  d b ∆f F 4lembed  Equation 2.2  19  Figure 2.9 Transfer of force through bond.  2.5 Bond Strength and Development Length Equations in Design Codes The embedment length required to prevent bond failure is referred to as the development length of the reinforcing bars. Design codes always specify the development length required to develop the design stress in the rebar because it is easier to implement by engineers. However, development length can be related to the bond strength by using Equation 2.2. 2.5.1 CSA S806-02  Canadian Standards Association (CSA S806-02) recommends the use of the following equation to determine the development length for the FRP rebars  ld = 1.15  K1 K 2 K 3 K 4 K 5 f F A f ,bar d cs f c′  Equation 2.3  where, l d = development length of FRP bar (mm); A f ,bar = rebar cross-sectional area (mm2); d cs = smallest of the distance from the closest concrete surface to the center of the bar being developed or two-thirds the c-c spacing of the bars being developed (mm)  d cs ≤ 2.5d b ; f F = required tensile stress in the rebar (MPa); f c′ = compressive strength of concrete (MPa); K1 = bar location factor (1.3 for horizontal reinforcement placed so that more than 300 mm of fresh concrete is cast below the bar; 1.0 for all other cases); K 2 = concrete density factor (1.3 for structural low-density concrete; 1.2 for structural semi-low-density 20  concrete; 1.0 for normal density concrete); K 3 = bar size factor (0.8 for Ab ≤ 300 mm2; 1.0 for  A b > 300 mm2); K 4 = bar fibre factor (1.0 for CFRP and GFRP; 1.25 for AFRP); K 5 = bar surface profile factor (1.0 for surface roughened or sand coated or braided surfaces; 1.05 for spiral pattern surfaces or ribbed surfaces; 1.8 for indented surfaces). Substitution of Equation 2.3 into Equation 2.2 yields the following expression for the average bond strength  τf =  d cs f c′ 1.15( K1 K 2 K 3 K 4 K 5 )πd b  Equation 2.4  From Equation 2.4, it is seen that according to CSA S806 (2002), bond strength is a function of the concrete cover, the concrete strength, the bar diameter, the bar surface profile, the fibre type, bar location and concrete density. 2.5.2 CSA S6-06  According to the Canadian Highway Bridge Design Code (CSA S6-06), the expression for the development length of steel rebar was modified for FRP rebar and it is expressed as follows:  ld = 0.45   fF    A f ,bar  E FRP   f cr  d cs + K tr  Es   k1k 4  Equation 2.5  where, l d = development length of FRP bar (mm); A f ,bar = rebar cross-sectional area (mm2); d cs = smallest of the distance from the closest concrete surface to the center of the bar being developed or two-thirds the c-c spacing of the bars being developed (mm); k1 = bar location factor; k 4 = bar surface factor; K tr = transverse reinforcement index (mm) =  Atr f y 10.5sn  ; Atr = area of transverse  reinforcement normal to the plane of splitting through the bars (mm²); f y = yield strength of transverse reinforcement (MPa); s = center to center spacing of the transverse reinforcement (mm); n = number of bars being developed along the plane of splitting; E FRP = modulus of  21  elasticity of FRP bar (MPa); E s = modulus of elasticity of steel (MPa); f F = specified tensile strength of FRP bar (MPa); f cr = cracking strength of concrete (MPa). Substitution of Equation 2.5 into Equation 2.2 gives expression for average bond strength as  E f cr  d cs + K tr FRP Es τf =  0.45πd b k1k 4      Equation 2.6  Thus, in CSA S6-06, the equation to determine the development length for FRP bars has been obtained by simply multiplying the transverse reinforcement index for steel bars ( K tr ) with  E  the modular ratio  FRP  . However, Equation 2.6 shows that CSA S6-06 considered bond  Es  strength as a function of the concrete strength, the concrete cover, the concrete confinement provided by transverse reinforcement, the bar surface and the bar diameter. 2.5.3 JSCE Recommendation  The Japanese Design Code (JSCE, 1997) modified the expression for the development length of steel rebar and recommended the following equation for evaluating the required development length ( l d ) of FRP rebars in concrete for splitting mode of failure, provided that l d can not be less than 20d b . ld = α1κ  fd db 4 f bod  Equation 2.7  where, f d is the design tensile strength of the reinforcement; κ is a top bar modification factor that takes a value of 1 if there is less than 300 mm (12 in.) of concrete cast below the bar; d b is the bar diameter (mm); and f bod is the design bond strength of concrete which is given by the following expression  f bod  0.28α 2 f c′ 2 / 3 = ≤ 3.2 N/mm2 1.3  Equation 2.8  22  where, f c′ is the compressive strength of concrete (MPa); and α 2 is the modification factor for bond strength ( α 2 = 1 when the bond strength is equal to or greater than that of deformed steel bar, otherwise α 2 shall be reduced according to the test results). The factor α 1 is a confinement modification factor determined as follows:  α1 = 1.0 (where kc ≤ 1.0 ); α1 = 0.9 (where 1.0 < kc ≤ 1.5 ); α1 = 0.8 (where 1.5 < kc ≤ 2.0 ); α1 = 0.7 (where 2.0 < k c ≤ 2.5 ); α1 = 0.6 (where k c > 2.5 ); where k c=  c 15 At Et + ⋅ d b sd b Es  Equation 2.9  where, c is the smaller of the bottom clear cover of main reinforcement or half of the clear space between reinforcement being developed; At is the area of transverse reinforcement; s is the spacing of transverse reinforcement; Et is the Young’s modulus of elasticity for the transverse reinforcement; and Es is the Young’s modulus of elasticity for steel. It can be observed that according to the Japanese design recommendation, the design bond strength or development length of the FRP rebar in concrete is a function of the concrete strength, the concrete cover, the bar location and the concrete confinement provided by the transverse reinforcement. 2.5.4 ACI 440.1R-06  The bond strength equation of FRP rebars to concrete available in ACI 440.1R-06 is as follows (in SI units):  τ fc  ′  = 0.33 + 0.025  d c + 8.3 b db lembed  Equation 2.10  23  where, τ is the FRP rebar-concrete bond strength; f c′ is the compressive strength of concrete; c is the lesser of the cover to the center of the bar or one-half of the center-to-center spacing of the bars being developed; d b is the bar diameter; and l embed is the embedment length of the bar in concrete. This equation was developed from the study by Wambeke and Shield (2006) in which a consolidated database of 269 beam bond tests was created from the published literature up to 2002. The database was limited to beam end tests, notch-beam tests, and splice tests with the majority of the bars represented in the database composed of GFRP (240 out of 269). Three types of rebar surfaces were considered-sand coated, spiral wrap of fibres and helical lug pattern. The diameter of the bars ranged between 13 mm to 29 mm. The compressive strength of concrete ranged from 28 to 45 MPa. Of the 240 beam bond specimens with GFRP bars, 75 failed by splitting of concrete, 94 by rebar pullout and 71 had tensile failure (rebar fracture). For developing Equation 2.10, only splitting failure mode was considered. All of the bond tests, resulting in splitting failures (48 unconfined and 19 confined bottom bars, 8 unconfined top bars) were performed using a clear cover of between one and three bar diameters ( d b ≤ c ≤ 3d b ). As a result of the lack of effect of transverse reinforcement on average bond stress, the full set of data for splitting failures were considered and a linear regression was performed following the same approach as was done by Orangun et al. (1975) to develop Equation 2.10. The relation of Equation 2.10 was then used to determine an expression for the required development length to avoid splitting failure which resulted in (SI units)  l d ,splitting    f fu   db  − 100   0.28 f ′  c  ≥ d b f fu =  c ′ 4.0 + 0.3 2.54 f c db  The term  d b f fu 2.54 f c  ′  Equation 2.11  is the required development length to avoid pullout failure and it was  proposed after the analysis of 81 beam tests that resulted in pullout failures in Wambeke and Shield’s (2006) database. Based on their data, Wambeke and Shield (2006) proposed a bar location modification factor of 1.5 for bars with more than 300 mm (12 in) of concrete cast below. 24  The equation of ACI 440.1R-06 was developed almost based on GFRP rebars. Also, there were very few bond test specimens in which transverse reinforcement was present. In the last decade, a large number of experimental studies were reported in the literature on the bond behaviour of FRP rebars. Therefore, it is necessary to re-evaluate the ACI reported equations with different types of fibres and with the presence of transverse reinforcement. 2.6 Bond Stress-Slip Relations Bond is a critical design parameter for reinforced concrete structures which controls the performance of structural members both at serviceability limit state (crack width and deflection) and ultimate limit state (strength). To prevent bond failure in reinforced concrete members and to ensure complete transfer of forces between the reinforcement and the concrete, the reinforcement should be adequately anchored in the concrete. To determine the required anchorage length of the rebar, bond stress-slip ( τ − s ) law is needed. Although many formulations for bond stressslip law were proposed for steel rebars, for FRP rebars an extensive research effort is still needed. Moreover, the formulations of bond stress-slip relationship proposed so far for FRP rebars have to be validated by experimental investigation and curve fitting of the experimental data. Therefore, a generalized bond stress-slip law, which can be applied to different types of FRP rebars has not been established (Cosenza et al., 1997). The following discussion will present an overview of the available bond stress-slip relationship of the FRP rebar in concrete in the literature. Malvar (1994) proposed the first bond stress-slip ( τ − s ) relationship for GFRP rebars. Malvar (1994) performed an extensive experimental investigation of the bond behaviour of GFRP rebars in concrete with different types of rebar surfaces and different confinement pressures. Based on the experimental results, Malvar (1994) proposed a model to predict the bond stress-slip law for FRP rebars in concrete, represented by the following relationship:  τ = τm   s F   sm    s  + (G − 1)   sm   s 1 + (F − 2)  sm        s  + G   sm  2      2  Equation 2.12  25  where, τ m = peak bond stress; sm = slip at peak bond stress; and F, G = empirical constants determined by curve fitting of the experimental data for each bar type. Malvar (1994) also provided two other relationships to predict bond stress-slip for a given value of confinement pressure which are expressed as follows:   Cσ = A + B 1 − exp − ft  ft   τm      sm = D + Eσ  Equation 2.13  Equation 2.14  where, σ = confining axisymmetric radial pressure; f t = tensile concrete strength; and A, B, C, D, E = empirical constants determined for each type of rebar. The well known bond stress-slip law, known as BEP model, for deformed steel bars failing by rebar pullout was proposed by Eligehausen et al. (1983). According to this model, the bond stress-slip of steel rebars shows four distinct branches (Figure 2.10): initial ascending branch up to the peak bond stress (τ 1 ) for s ≤ s1 , a second branch with constant bond (τ = τ 1 ) up to slip s = s2 , a linearly descending branch from ( s2 , τ 1 ) to ( s3 , τ 3 ) and a horizontal branch for s > s3 , with a value of τ due to the development of friction ( τ = τ 3 ). The BEP model expresses the ascending branch of bond-slip relationship as follows: α  τ s =  τ 1  s1   Equation 2.15  where, τ 1 = maximum bond strength; and s1 = slip corresponding to maximum bond strength. Values of s2 , s3 and τ 3 have to be calibrated based on the experimental results. In Equation 2.15, α is a curve-fitting parameter that must not be greater than 1, to be physically meaningful. The value of α proposed by Eligehausen et al. (1983) in the case of steel bars is equal to 0.4.  26  Figure 2.10 BEP model for pullout failures of steel rebars (Eligehausen et al., 1983).  The BEP model was applied to FRP rebars by Faoro (1992), Alunno Rossetti (1995), Focacci et al. (2000), Pecce et al. (2001). When the BEP model was applied to FRP rebars, it was observed that there were some differences between the experimental curves and the curves obtained by applying the BEP model. Cosenza et al. (1996) investigated the bond stress-slip behaviour of GFRP rebars in concrete and based on the results, it was concluded that the bond stress-slip curves for GFRP rebars lack the second branch with constant bond as was found in the BEP model and hence, it was recommended not to consider this second branch in case of GFRP rebars (Figure 2.11). Based on their experimental results, Cosenza et al. (1996) modified the BEP model and proposed an alternative bond stress-slip relationship for GFRP rebars. According to the modified BEP model, the bond stress-slip curves have three distinct branches (Figure 2.11): initial ascending branch up to the peak bond stress ( τ 1 ) for s ≤ s1 which is the same as was used in Equation 2.15, a softening branch, having slope p  τ = 1− τ1  s  p − 1  s1   τ1 s1  from ( s1 , τ 1 ) to ( s3 , τ 3 ) given by  Equation 2.16  where, p is an empirical parameter that needs to be determined based on the curve fitting of the experimental results; and a horizontal branch for s > s3 , with a value of τ due to the development of friction ( τ = τ 3 ). 27  It has been observed that a refined model of the bond stress-slip is needed for the ascending branch only, since most structural problems are to be dealt with at this stress level. As a result, Cosenza et al. (1997) refined the BEP model and proposed another model for the ascending branch of the bond stress-slip curve up to the peak bond stress. This relationship is also known as CMR model and is defined by the following expression: − τ  = 1− e s τ m   s r       β  Equation 2.17  where, τ m = peak bond stress; and s r and β = parameters based on curve-fitting of the actual data.  Figure 2.11 Modified BEP model (Cosenza et al., 1997).  Tighiouart et al. (1998) performed experimental investigation on the bond behaviour of GFRP rebars in concrete by varying the bar diameter and the embedment length. Based on the experimental results, Tighiouart et al. (1998) suggested values for s r and β of the CMR model 1 ( S r = − and β = 0.5 ). 4  A numerical method was proposed by Focacci et al. (2000) to calibrate the parameters of a given local bond stress-slip relationship using experimental results of pullout tests. The proposed method aimed to determine the parameters of a given bond stress-slip relationship in such a way 28  that it can predict the results of a pullout test in terms of the applied pullout force and the consequent slip at the loaded end and the slip at the free end. The BEP and the CMR bond stressslip models were selected for the application of the proposed method. However, the proposed method could be applied to any analytical expression. The expressions for the BEP and the CMR models proposed by Focacci et al. (2000) are presented in Equations 2.18 and 2.19. α   s   s τ (s ) = τ m   1 −   sm   s   τ (s ) =  τ msβ  sr  β  βs 1 −  2 sr  Equation 2.18      Equation 2.19  where, τ m = peak bond stress, s m = slip corresponding to peak bond stress, and α , s , β , sr are curve fitting parameters. Baena et al. (2009) calibrated the modified BEP (Equation 2.15 and 2.16) and the CMR model (Equation 2.17) of the bond stress-slip relationship based on the results of 88 pullout tests specimens. From the experimental results, it was noted that the bar diameter should be incorporated into the bond stress-slip relationship for high strength concrete. Therefore, based on the experimental data, the following expressions were proposed for predicting the parameters of modified BEP and CMR model substitutingτ m for τ 1 and s m for s1 :  τ m = τ 0 + τ 1d b For BEP model: sm = m0 e (m1db )  α = α 0 d bα  Equation 2.20  1  where, τ 0 , τ 1 , m0 , m1 and α 0 , α 1 are curve fitting parameters.  β = β 0e(β d  1 b  For CMR model:  )  sr = r0 e (r1db )  Equation 2.21  where, β 0 , β1 and r0 , r1 are curve fitting parameters.  29  From the bond stress-slip relationships presented in Equations 2.12 to 2.21, it became evident that no specific formulations (proposed so far) for bond stress-slip relationship can predict the bond behaviour of different types of FRP rebars. Moreover, all of the proposed formulations need to be validated by comparison with the experimental investigation. In addition, these equations were developed from pullout test specimens (with only GFRP rebars), which do not represent the realistic behaviour of structural members. Therefore, it is necessary to develop a generalized bond stress-slip relationship from beam-type specimens which can be applied to different types of FRP rebars and be able to capture the real bond stress-slip behaviour. 2.7 Research Needs From the presented literature, it is evident that there are some gaps in the available literature on the bond behaviour of FRP rebars in concrete. The research needs that are identified from the previous discussion are presented below: •  There is a need to re-evaluate the effect of different parameters, especially the effect of transverse reinforcement, on the bond behaviour of FRP rebars in concrete due to an increase in the experimental data produced during the last decade.  •  Based on the new data, a new design equation should be proposed for determining the development length of FRP rebars in concrete.  •  A general bond stress-slip law needs to be derived for pullout and splitting mode of failure. This relationship should be able to predict the bond behaviour of different types of FRP rebar with different surface textures. Moreover, the proposed relationship should take into account all the parameters that affect the bond performance of FRP rebars i.e. type of fibres, rebar surface, concrete strength, bar diameter, concrete cover, embedment length and concrete confinement.  2.8 Research Objectives This study presents investigation on the bond behaviour of the FRP reinforcing bars in concrete environment and thereby, proposes design guidelines to alleviate the design of reinforced  30  concrete structures using FRP reinforcing bars. The objectives set for the study are summarized below: •  Develop a consolidated database on the bond behaviour of FRP rebars in concrete by accumulating all the beam-type bond test data from the available literature up to 2009.  •  Perform an analysis to evaluate the effect of different parameters on the bond behaviour of FRP rebars in concrete.  •  Propose equations to predict the peak bond stress and the corresponding slip of FRP rebars in concrete, and derive a design equation to determine the development length of the FRP rebars that incorporates all the influential bond parameters.  •  Establish a generalized bond stress-slip relationship for FRP rebars in concrete, which can be applied to any type of FRP rebar with any type of surface texture by taking into consideration all the parameters that influence the bond behaviour of FRP rebars in concrete i.e. fibre type, rebar surface, bar diameter, concrete strength, concrete cover, embedment length and confinement provided by the transverse reinforcement.  •  Validate the proposed bond stress-slip relationship and the effect of transverse reinforcement on the bond behaviour of FRP rebars in concrete by using finite element analysis.  31  Chapter 3: Description of the Database  3.1 General The first step of the present study was to create a database of different bond tests available in the literature up to 2009. The bond tests were usually categorized into two major groups-pullout tests and beam tests. In pullout tests, the concrete surrounding the reinforcement is in compression and hence, it does not represent the actual behaviour of reinforced concrete members, where the concrete and the reinforcement are in tension. On the contrary, in beam tests, the concrete surrounding the reinforcement is in tension and therefore, it represents a more realistic behaviour of reinforced concrete members. In this study, only beam bond tests were considered and a database of 541 beam-type specimen consisted of beam end specimens, beam anchorage specimens, and splice specimens was created from the available literature (Daniali, 1990; Faza and GangaRao, 1990; Faza, 1991; Ehsani et al., 1993, 1996; Kanakubo et al., 1993; Makitani et al., 1993; Benmokrane et al., 1996; Shield et al., 1997, 1999; Tepfers et al., 1998; Tighiouart et al., 1998, 1999; Cosenza et al., 1997, 1999; Mosley, 2000; Pecce et al., 2001; DeFreese and Wollmann, 2002; Wambeke, 2003; Aly and Benmokrane, 2005; Maji and Orozco, 2005; Aly et al., 2006; Wambeke and Shield, 2006; Aly, 2007; Okelo, 2007; Rafi et al., 2007; Thamrin and Kaku, 2007; Mosley et al., 2008). The detail of the database is presented in Appendix A. The beam-type specimens of the database had different concrete strengths, concrete covers, embedment lengths and confinements. In addition, the failure mode was different for different specimens. The following sections describe the parameters considered in the database. 3.2 Failure Modes The beam-type specimens considered in the study failed by four different modes: flexural failure, shear failure, bond splitting failure and bond pullout failure. Of the 541 specimens, 161 had flexural or shear failure. These specimens were excluded from the analysis as the bars achieved their ultimate strength, i.e. they did not fail through bond. Of the remaining 380 specimens, 177 had bond failure through splitting of concrete cover and 203 had bond failure through rebar pullout. These will be used to analyze the bond behaviour of FRP rebars in concrete.  32  3.3 Type of Fibre The available equations for predicting maximum bond stress and bond stress-slip relationship were based on only glass FRP rebars (GFRP). The objective of this study was to derive design equations for FRP rebars which will hold for different types of FRP. Hence, all types of FRP rebars – glass, aramid and carbon- were considered in this study. Of the 380 beam-type specimens of the database that failed in bond, 275 had glass FRP rebars (72%), 90 had carbon FRP rebars (24%) and 15 had aramid FRP rebars (4%). It is observed that the number of specimens with AFRP was very small in comparison to specimens with GFRP and CFRP. However, since AFRP bars are rarely used in the construction of reinforced concrete structures, the data can be thought to be sufficient for representing bond behaviour of FRP rebars in concrete made from different fibres. 3.4 Type of Rebar Surface The bond test specimens considered in the database consisted of three types of rebar surface – sand coated, spiral wrapped and helical lugged/ribbed. In few of the specimens, sand coating and spiral wrapping were applied simultaneously. Of the 380 beam-type specimens which failed in bond, 155 specimens had spiral wrapped FRP bars (41%), 163 had helical lugged FRP bars (43%) and 62 had sand coated FRP bars (16%). Of the 62 sand coated bars, 22 were GFRP, 37 were CFRP and 3 were AFRP. Of the 155 spiral wrapped bars, 113 were GFRP, 33 were CFRP and 9 were AFRP. Of the 163 helical lugged bars, 140 were GFRP, 20 were CFRP and 3 were AFRP. Figure 3.1 shows the breakdown of the database with respect to different types of fibre and their surface geometries. 3.5 Bar Cast Position Bar cast position has significant effect on the bond behaviour of FRP rebars in concrete as described in section 2.3.5. It has been observed that the top reinforcing bars usually have lower bond strength than the bottom bars. Therefore, in this study the database was splitted based on the bar cast positions. Of the 380 beam-type specimens which failed in bond, 332 specimens tested were cast as bottom bars and 48 were cast as top bars, which indicate that about 87% of specimens were tested with bottom bars. For evaluating bond behaviour of FRP rebars in concrete, only the bottom bar specimens were considered and the top bar specimens were used to develop a modification factor for top bar cast positions. 33  Sand Coated AFRP, 3  Sand Coated CFRP, 37 Sand Coated GFRP, 22 Spiral Wrapped AFRP, 9  Helical Lugged GFRP, 140  Spiral Wrapped CFRP, 33  Helical Lugged CFRP, 20 Spiral Wrapped GFRP, 113 Helical Lugged AFRP, 3  Figure 3.1 Classification of the specimens with respect to type of fibre and rebar surface.  3.6 Transverse Reinforcement Transverse reinforcement confines concrete and thereby, increases the bond performance of reinforcing bars in concrete. For FRP rebars, there is still no evidence of the effect of transverse reinforcement on the bond behaviour due to the limited availability of the experimental data in the literature. Therefore, in this study, all the experimental data on the confined and the unconfined beam-type specimens were considered to assess the effect of concrete confinement provided by the transverse reinforcement on the bond performance of FRP rebars in concrete. There were 105 beam tests which resulted in a splitting failure that contained transverse reinforcement. For all the specimens, the transverse reinforcements were made of steel. The nominal diameter of the steel stirrups used in the specimens varied between 8 mm (0.32 in) to 11.3 mm (0.44 in) with a spacing of between 78 mm (3.1 in) and 150 mm (5.9 in) and all of the tests were performed on bottom bars. There were 127 beam tests that resulted in a pullout failure and contained transverse reinforcement. In all of these tests, the nominal diameter of the steel stirrups was 10 mm (0.4 in) with a spacing of between 50 mm (2 in) and 153 mm (6 in) and all of these tests were performed on bottom bars. Figure 3.2 shows the breakdown of the database with respect to failure modes, bar cast positions and confinement. 34  Unconfined Top Bars with Splitting Failure, 22  Confined Bottom Bars with Pullout Failure, 127  Unconfined Bottom Bars with Pullout Failure, 50  Unconfined Top Bars with Pullout Failure, 26  Unconfined Bottom Bars with Splitting Failure, 50  Confined Bottom Bars with Splitting Failure, 105  Figure 3.2 Classification of the specimens with respect to concrete confinement, bar location and failure mode.  3.7 Bar Diameter In the database, the bar diameter of the FRP rebars varied widely. Bar diameter of the specimens having splitting mode of failure varied from 8 mm to 28.58 mm, whereas the bar diameter varied from 6.35 mm to 28.58 mm for specimens having pullout mode of failure. For sand coated bars, the bar diameter varied between 8 mm to 19.1 mm irrespective of the mode of failure. On the other hand, the diameters of the spiral wrapped bars and helical lugged bars ranged between 6.35 mm to 27.4 mm and 8 mm to 28.58 mm respectively. Figure 3.3 shows the variation of the bar diameters considered in the database of all the specimens which failed by rebar pullout and concrete splitting. It can be observed that the number of specimens with small diameter FRP bars were very diminutive. 3.8 Compressive Strength of Concrete The database contained a fairly wide range of compressive strength of concrete. The compressive strength of concrete, for the specimens which failed by splitting of concrete, varied between 27 MPa and 49 MPa. 35  40  No. of Specimens  35 30  Unconfined Splitting Confined Splitting Unconfined Pullout Confined Pullout  25 20 15 10 5 0 6M  8M  10M  12M  15M  20M  25M  Bar Diameter (mm)  Figure 3.3 Variation of bar diameter for all specimens failing by concrete splitting and rebar pullout.  Only two specimens were tested with 65 MPa concrete strength. On the other hand, most of the specimens which failed by rebar pullout had compressive strength of concrete between 23 MPa and 47 MPa. Only four specimens were tested with concrete strength greater than 50 MPatwo of them had 51 MPa concrete strengths and the other two had 65 MPa. Figure 3.4 shows the variation of compressive strengths of concrete in all the specimens failing by rebar pullout and splitting of concrete. It can be observed that about 51% of all the specimens had normal strength concrete ( f c′ = 20-35 MPa), 48% had medium high strength concrete ( f c′ = 35-50 MPa) and only 1% had high strength concrete ( f c′ >50 MPa). Therefore, it is concluded that the findings of this study is only limited for f c′ < 50 MPa. More tests are required with f c′ > 50 to arrive at definite conclusion about the bond behaviour of FRP rebars in high strength concrete. 3.9 Concrete Cover In the database, concrete cover also varied between wide ranges. Figure 3.5 shows the variation of concrete cover normalized by bar diameter (  c ) for all the specimens which failed by db  concrete splitting and rebar pullout. It was observed that most of the specimens which failed by splitting of the concrete cover had a concrete cover to bar diameter ratio between 1 and 3 36  ( d b ≤ c ≤ 3d b ), whereas most of the specimens which failed by rebar pullout had a concrete cover to bar diameter ratio greater than 3 ( c ≥ 3d b ).  80  Unconfined Splitting Confined Splitting  No. of Specimens  70  Unconfined Pullout 60  Confined Pullout  50 40 30 20 10 0 20-30  31-40  41-50  >50  Concrete Compressive Strength (MPa)  Figure 3.4 Compressive strength of concrete for all the specimens failing by concrete splitting and rebar pullout.  90  No. of Specimens  80 70  Unconfined Splitting Confined Splitting Unconfined Pullout Confined Pullout  60 50 40 30 20 10 0 1-2  2-3 Concrete Cover to Bar Diameter Ratio  c db  >3  Figure 3.5 Concrete cover to bar diameter ratio for all the specimens failing by concrete splitting and rebar pullout.  37  It was observed that of the 177 specimens which failed by splitting of concrete, 45% and 42% had concrete cover to bar diameter ratio between 1-2 and 2-3 respectively. This includes both top and bottom bar specimens. If only bottom bar specimens were considered, 93% of the specimens failing by concrete splitting had concrete cover to bar diameter ratio of less than 3. Of the 203 specimens which failed by rebar pullout, 57% had concrete cover to bar diameter ratio greater than 3. This includes both top and bottom bar specimens. If top bar specimens were excluded, about 70% of the specimens failing by rebar pullout had concrete cover to bar diameter ratio of greater than 3 and the remaining 30% had concrete cover to bar diameter ratio of between 1 and 3. 3.10 Embedment Length Embedment length may be defined as the anchorage length of the reinforcement (or the length of a splice in a splice test) to the concrete. In the database, there was a significant variation in the embedment lengths of the FRP rebars. Figure 3.6 shows the variation of the embedment length normalized by the bar diameter (  lembed ) of FRP rebars for all the specimens failing by splitting of db  concrete and rebar pullout. 80  Unconfined Splitting Confined Splitting  No. of Specimens  70  Unconfined Pullout  60  Confined Pullout  50 40 30 20 10 0 0-15  16-30  31-60  61-90  >90  l embed Embedment Length-Bar Diameter Ratio db  Figure 3.6 Embedment length-bar diameter ratio for all the specimens failing by concrete splitting and rebar pullout. 38  The embedment length of the specimens which failed by concrete splitting were much longer than those of the specimens which failed by rebar pullout. The embedment length of the specimens which failed by concrete splitting, ranged between 4 to 116 bar diameters ( 4d b ≤ lembed ≤ 116d b ). On the contrary, the embedment length of specimens having pullout failure ranged between 3 to 60 bar diameters ( 3d b ≤ lembed ≤ 60d b ). Of the specimens which failed by splitting of the concrete, over 56% had embedment length of less than or equal to 30 bar diameters ( lembed ≤ 30d b ) and 44% had embedment length greater than 30 bar diameters ( lembed > 30d b ). On the other hand, 94% of the specimens which failed by rebar pullout had embedment length of less than or equal to 30 bar diameters and only 6% had embedment length greater than 30 bar diameters ( lembed > 30d b ). 3.11 Database for Slip at Peak Bond Stress and Bond Stress-Slip Relationship The 380 beam bond tests (failed in bond) considered in this study reported the peak bond stress of the specimens, but bond stress-slip curves and the slip corresponding to the peak bond stress were not reported for each of the 380 beam tests. Therefore, for developing bond stress-slip relationship and an equation for determining the slip corresponding to the peak bond stress, only bond tests where these values were reported were considered. The database used for developing bond stress-slip relationship and slip corresponding peak stress is presented in Appendix B and Appendix C respectively. There were 97 specimens for which slip corresponding to peak bond stress was reported. Of the 97 specimens, 40 failed by concrete splitting and 57 failed by rebar pullout. The 97 specimens consisted of 7 AFRP bars, 31 CFRP bars and 59 GFRP bars. Of the 97 specimens, 61 had helical lugged bars, 5 had sand coated bars and 31 had spiral wrapped bars. There were 91 beam-type specimens in the database for which bond stress-slip data were reported along with the bond stress-slip curves. Of these 91 specimens, 23 specimens failed by concrete splitting and 68 specimens failed by rebar pullout. Of the 23 beam-type specimens that failed by splitting of concrete, 11 had helical lugged FRP rebars and 12 had spiral wrapped FRP rebars. There was no reported specimen with sand coated rebars which failed by concrete splitting. All of bars were cast as bottom bars. Of the 23 beam specimens, 6 were unconfined and 39  17 were confined. The 23 specimens consisted of 7 AFRP rebars, 11 CFRP rebars and 5 GFRP rebars. On the other hand, of the 68 beam-type specimens that failed by rebar pullout, 40 had helical lugged FRP rebars, 26 had spiral wrapped FRP rebars and 2 had sand coated FRP rebars. All of bars were cast as bottom bars. Of the 68 beam-type specimens, 6 were unconfined and 62 were confined. The 68 specimens consisted of 9 AFRP rebars, 22 CFRP rebars and 37 GFRP rebars. 3.12 Summary The database contains adequate information about all the parameters that appear to influence the bond behaviour of FRP rebars in concrete and it takes into account a wide range of values for all the parameters. Further analysis using MS Excel and a statistical analysis program, JMP8, revealed that only 5% correlation exists between the individual parameters. Hence, it was concluded that there was no correlation between any two independent parameters. Therefore, the data can be thought to be sufficient to perform statistical analysis to evaluate the effects of different parameters that seem to affect the bond performance of FRP rebars in concrete. The next chapters concentrate on the statistical and the numerical analysis of the database.  40  Chapter 4: Analysis of Data and Derivation of Development Length  4.1 General In this chapter, a statistical analysis of the database will be performed to identify the parameters that influence the bond stress of FRP rebars and the corresponding slip. Based on the results of the analysis these parameters will be incorporated in the equations that will be derived to predict the peak bond stress (bond strength) and the corresponding slip. Also, an equation will be proposed to determine the required development length of FRP rebars. 4.2 Data Analysis The database was analysed based on the two types of failure modes-splitting failure and pullout failure. For analysing the data, the bond stress was normalized by the square root of the compressive strength of concrete to reduce the variability of the bond stress data with respect to the compressive strength of concrete. Moreover, the embedment length and concrete cover were normalized by the bar diameter to reduce the variability with respect to bar diameter. The following sections discuss the effects of different parameters on the bond stress of FRP rebars in concrete. 4.2.1 Type of Fibres  The 380 specimens of the database, which failed in bond, included 275 glass FRP rebars, 90 carbon FRP rebars and 15 aramid FRP rebars which indicates that the number of specimens with GFRP rebars is much higher compared to the specimens with CFRP and AFRP rebars. Data analysis was performed for different types of fibres by splitting the database with respect to the concrete cover to bar diameter ratio (Figure 4.1). It was observed that irrespective of the failure mode and  c ratio, the type of fibre does not have any noticeable effect on the bond behaviour of db  FRP rebars to concrete. This is in agreement with CSA S806-02 which recommended the same modification factor for CFRP and GFRP when calculating the required development length of FRP rebars in concrete. However, it should be mentioned here that there was no correlation between any two individual parameters as discussed in section 3.12. 41  6 CFRP  GFRP  CFRP  GFRP  5  4  1≤ τm f c′  3  c ≤2 db  2  1  0 0  20  40  60  80  l embed db  100  120  2.5 CFRP  GFRP  AFRP  CFRP  GFRP  AFRP  2  1.5  τm  2<  f c′  c ≤3 db  1  0.5  0 0  20  40  60  80  l embed db  100  120  6 CFRP  GFRP  AFRP  CFRP  GFRP  AFRP  5  4  τm f c′  3  c >3 db  2  1  0 0  20  40  60  l embed db  80  100  120  140  Figure 4.1 Normalized average bond stress of the specimens for different types of FRP with different concrete cover to bar diameter ratio. 42  There were 97 specimens for which slip corresponding to peak bond stress was reported. Of the 97 specimens, 40 failed by concrete splitting and 57 failed by rebar pullout. On the other hand, of the 97 specimens, 7 had AFRP bars, 31 had CFRP bars and 59 had GFRP bars. Figure 4.2 shows the variation of the normalized slip (  sm lembed  ) corresponding to peak bond stress ( τ m )  with respect to the normalized cover for splitting and pullout modes of failure. 0.025 AFRP  CFRP  GFRP  0.02  0.015  sm l embed 0.01  0.005  0 0  0.5  1  1.5  2  c 2.5 db  3  3.5  4  4.5  (a) Splitting Failure  0.025 AFRP  CFRP  GFRP  0.02  0.015  sm l embed 0.01  0.005  0 0  1  2  3  c db  4  5  6  7  (b) Pullout Failure Figure 4.2 Normalized slip corresponding to peak bond stress plotted against normalized cover for different types of FRP. 43  It was observed that for a splitting mode of failure, no definite trend was found for the variation of the normalized s m with the type of the FRP due to lack of enough data. On the contrary, for pullout failure mode, CFRP bars tend to show higher normalized s m values than GFRP and AFRP bars. Still any definite conclusion could not be made since the number of CFRP specimens was very small compared to the GFRP specimens for pullout mode of failure. Therefore, it is recommended that more tests are required to arrive at a definite conclusion about the effect of the type of fibres on the normalized s m . In this study, it will be assumed that type of fibre does not have any effect on the bond performance of FRP rebars in concrete. 4.2.2 Type of Rebar Surface  Three types of bar surfaces were observed during the analysis of the data and they are: helical lugged/ribbed, sand coated and spiral wrapped bars (Figure 4.3). Of the 380 beam-type specimens which failed in bond, 155 specimens had spiral wrapped FRP bars, 163 had helical lugged FRP bars and 62 had sand coated FRP bars.  Sand Coated  Spiral Wrapped  Helical Lugged/Ribbed  Figure 4.3 Types of FRP rebars considered in the analysis.  Figure 4.4 shows the normalized average bond stresses (  against the normalized embedment lengths (  τm f c′  ) of the specimens plotted  l embed c ) for different cover to bar diameter ( ) db db  ratios. The following observations were made from Figure 4.4. 44  •  1≤  c ≤ 2 : For small embedment lengths ( ld ≤ 15d b ), bars with spiral wraps had db  larger bond strength than the bars with helical lugs/sand coating, but for large embedment lengths ( ld > 15d b ), bars with helical lugs had larger bond strength than the other two. •  2≤  c ≤ 3 : For small embedment lengths ( ld ≤ 15d b ), bars with sand coating had db  the largest bond strength compared to bars with helical lugs/spiral wraps and helical lugged bars had greater bond strength than spiral wrapped bars. On the other hand, for large embedment lengths ( ld > 15d b ), bars with spiral wraps and sand coating had almost similar bond strength which is larger than the helical lugged bars. •  c > 3 : For small embedment lengths ( l d ≤ 15d b ), all the bars have similar bond db  strength, but for large embedment lengths ( l d > 15d b ), bars with sand coating have larger bond strength than the other two and helical lugged and spiral wrapped bars have almost the same bond strength. From the above discussion, it is clear that the effect of rebar surface has no definite trend on the bond strength irrespective of the failure mode and hence, it is recommended that more tests to be performed to arrive at any definite conclusion about the effect of rebar surface on bond strength of FRP bar with concrete. It should be mentioned here that CSA S806-02 proposed the same bar surface modification factors for spiral wrapped, helical lugged and sand coated FRP rebars. Of the 97 specimens, for which s m was reported, 61 had helical lugged bars, 5 had sand coated bars and 31 had spiral wrapped bars. Of the 61 specimens with helical lugged bars, 46 failed by rebar pullout and 15 failed by concrete splitting. On the other hand, of the 31 specimens with spiral wrapped bars, 9 failed by rebar pullout and 22 failed by concrete splitting. For the 5 specimens with sand coated bars, 2 failed by rebar pullout and 3 failed by concrete splitting.  45  6 Helical Lug  Spiral Wrap  Sand Coated  Helical Lug  Spiral Wrap  Sand Coated  5  4  τm f c′  3  1≤ 2  c ≤2 db  1  0 0  20  40  60  80  l embed db  100  120  2.5 Helical Lug  Spiral Wrap  Sand Coated  Helical Lug  Spiral Wrap  Sand Coated  2  1.5  τm  2≤  f c′  c ≤3 db  1  0.5  0 0  20  7  40  60  80  l embed db  Helical Lug Helical Lug  100  Spiral Wrap Spiral Wrap  120  Sand Coated Sand Coated  6  5  τm f c′  4  c >3 db  3  2 1 0 0  20  40  60  l embed db  80  100  120  140  Figure 4.4 Normalized average bond stress of the specimens for different surface texture of the rebars with different concrete cover to bar diameter ratio.  46  0.025 Helical Lugged  Sand Coated  Spiral Wrapped  0.02  0.015  sm lembed 0.01  0.005  0 0  0.5  1  1.5  2  c 2.5 db  3  3.5  4  4.5  (a) Splitting Failure  0.025 Helical Lugged  Sand Coated  Spiral Wrapped  0.02  0.015  sm lembed 0.01  0.005  0 0  1  2  3  c db  4  5  6  7  (b) Pullout Failure Figure 4.5 Normalized slip at peak bond stress of the specimens with different rebar surface.  47  Figure 4.5 clearly shows that helical lugged bars had higher values of the normalized slip corresponding to peak bond stress than sand coated and spiral wrapped bars for both type of failure modes. Sand coated and spiral wrapped bars showed almost the same normalized s m values. Based on the results, it was concluded that rebar surface affects the slip corresponding to the peak bond stress and it should be taken into consideration when developing an equation for slip corresponding to peak bond stress. 4.2.3 Compressive Strength of Concrete  From the reported literature, it was observed that the average bond stress of FRP rebars in concrete is a function of square root of concrete strength (Faza and GangaRao, 1990; Pleiman, 1991; Ehsani et al., 1996; Esfahani et al., 2005; Okelo and Yuan, 2005). Therefore, the peak bond stresses of the 380 beam-type specimens which failed in bond were plotted against the square root of the corresponding concrete strength (  f c′ ). Figure 4.6(a) and Figure 4.6(b) show  the peak bond stresses of the specimens of the database with respect to square root of concrete strength for splitting and pullout mode of failures respectively. It was observed that for splitting mode of failure, peak bond stress increased with an increase in the square root of concrete strength (Figure 4.6a). A higher concrete strength provided a higher confinement to the embedded reinforcement (FRP rebar) and hence, a larger force is needed to crack the concrete cover. Therefore, the bond strength increased. On the other hand, Figure 4.6b indicates that the pullout bond strength is not affected by the compressive strength of the concrete. This could be explained by the fact that pullout failure occurs when there is enough confinement provided to the concrete and hence, there is no splitting crack in the concrete. In such case, the rebar surface and the concrete surrounding the rebar surface shears off due to friction and the rebar starts to slip. Therefore, the failure mode is not dependent on the strength of concrete. Figure 4.7 shows the variation of the normalized slip corresponding to peak bond stress with the square root of concrete strength for both splitting and pullout modes of failure. It was observed that the slip corresponding to peak bond stress decreased with the increase in concrete strength for both types of failure mode. Therefore, it is evident that the compressive strength of 48  concrete affects the bond behaviour of FRP rebars in concrete and hence, it must be taken into account while determining a bond stress-slip relationship.  10 9 8  τm  (MPa)  7 6 5 4 3 2 1 0 5  5.5  6  6.5  7  7.5  8  8.5  f c′  (a) Splitting Failure  20 18 16  τ m (MPa)  14 12 10 8 6 4 2 0 5  5.5  6  6.5  7  7.5  8  8.5  f c′  (b) Pullout Failure  Figure 4.6 Variation of peak bond stress with square root of concrete strength. 49  0.025 Splitting Failures Pullout Failures Pullout Failure Splitting Failure  0.02  0.015  sm lembed 0.01  0.005  0 4  4.5  5  5.5  6  6.5  7  7.5  f c′  Figure 4.7 Variation of normalized slip corresponding to peak bond stress with square root of concrete strength for different types of failure. 4.2.4 Concrete Cover  The more the concrete cover, the more the concrete is confined which will increase the bond strength of the reinforcing bars. Figure 4.8(a) and Figure 4.8(b) shows the variation of the normalized average bond stress for different concrete cover to bar diameter ratios for the beamtype specimens of the database for splitting and pullout modes of failure respectively. It is quite evident from these figures that the bond strength increases with an increase in the concrete cover due to the increased confining effect and that the bond strength for pullout mode of failure is higher than that for splitting mode of failure for same  c . db  Figure 4.9 shows the variation of the normalized slip (  sm lembed  ) corresponding to the peak  bond stress for different concrete cover to bar diameter ratio for both splitting and pullout modes of failure. It was observed that the normalized slip decreased with an increase in the concrete cover. This was attributed to the confining action of the concrete cover which resulted in the peak bond stress to occur at a relatively smaller slip.  50  1.4  1.2  1  τm f c′  0.8  0.6  0.4  0.2  0 0  1  2  3  4  5  6  7  c db  (a) Splitting Failure  5  4  3  τm f c′ 2  1  0 0  1  2  3  4  5  6  7  8  9  10  c db  (b) Pullout Failure  Figure 4.8 Variation of normalized average bond stress with concrete cover to bar diameter ratio.  51  0.025 Splitting Failures  Pullout Failures  0.02  0.015  sm l embed 0.01  0.005  0 0  1  2  3  c db  4  5  6  7  Figure 4.9 Variation of normalized slip corresponding to peak bond stress with different concrete cover to bar diameter ratio for different types of failure. 4.2.5 Embedment Length  From the reported literature, it was shown that the embedment length of FRP rebars is inversely proportional to its bond strength (Achillides and Pilakoutas, 2004; Aly et al., 2006). Figure 4.10 shows the variation of the normalized average bond stress plotted against the normalized embedment length for splitting and pullout failures. It was observed that the bond strength decreased with an increase in the embedment length of the FRP rebars. This was attributed to the nonlinear distribution of the bond stress on the bar. In general, the tensile stress in the rebar attenuates rapidly from the loaded end (high tensile stress in the rebar) towards the free end (low tensile stress in the rebar) referring to a nonlinear distribution of the bond stress. As the embedment length increased, the applied load approached the tensile strength of the rebar and the average bond strength diminishes and hence, specimens with shorter development length develop higher bond strength. Figure 4.11 shows the variation of the slip corresponding to the peak bond stress with respect to the embedment length for both pullout and splitting failures. With an increase in the embedment length of the bar, the slip corresponding to the peak bond stress increased. This was attributed to the nonlinear distribution of the bond stress on the bar. As the embedment length  52  increases, the stress is distributed over a longer length and hence, bond failure occurs at a relatively higher slip.  (a) Splitting Failure  (c) Pullout Failure Figure 4.10 Variation of normalized average bond stress with normalized embedment length for bottom bar specimens. 53  3 Splitting Failures  Pullout Failures  2.5  s m (mm)  2  1.5  1  0.5  0 0  100  200  300  400  500  600  700  800  900  l embed (mm)  Figure 4.11 Slip corresponding to peak bond stress plotted against embedment length of the specimens for pullout and splitting failures. 4.2.6 Effect of Confinement  In theory, the presence of transverse reinforcement should confine the concrete and thereby, limit the progression of splitting cracks, thus, increasing the bond strength. However, due to the limited availability of experimental data in the literature, the theory has not been proven in case of FRP rebars in concrete. In the database, there were 177 and 203 specimens which failed by concrete splitting and rebar pullout respectively. Of the 177 specimens that failed by concrete splitting, 105 had transverse reinforcement and of the 203 specimens that failed by rebar pullout, 127 had transverse reinforcement. Figure 4.12(a) and Figure 4.12(b) present the normalized bond strength of the unconfined and confined bottom bar specimens which failed by concrete splitting and rebar pullout respectively. It was observed that for both types of failure modes, confined specimens had higher bond strength than the unconfined specimens which signifies that confinement affects the bond behaviour of FRP rebars in concrete. Figure 4.13 shows the effect of transverse reinforcement on the bond strength of FRP rebars in concrete for both splitting and pullout modes of failure. The parameter that was selected to  54  represent the effect of transverse reinforcement was  Atr , where, Atr is the area of transverse snd b  reinforcement normal to the plane of splitting through the bars, s is the center to center spacing of the transverse reinforcement, n is the number of bars being developed along the plane of splitting and d b is the bar diameter. This parameter was selected as it has been observed that for steel rebars, the effectiveness of a transverse reinforcement is proportional to the area of transverse reinforcement and inversely proportional to the spacing of the transverse reinforcement, the rebar diameter and the number of bars being developed (Orangun et al., 1975). It was found from Figure 4.13(a) that for splitting mode of failure, as  Atr increased by snd b  10%, the normalized average bond stress increased by10%-15% on an average. On the other hand, for pullout mode of failure (Figure 4.13b), there was no increase in the normalized average bond stress with increase in  Atr . This was expected, as for pullout failure there is enough snd b  confinement provided to the concrete and failure takes place through shearing off the rebar surface and the concrete surrounding the rebar surface due to friction and there is no splitting crack in the concrete. Hence, increasing concrete confinement by providing transverse reinforcement does not increase the average bond stress. Figure 4.14 shows the effect of transverse reinforcement on the normalized slip corresponding to the peak bond stress for both splitting and pullout modes of failure. It was observed that with an increase in the amount of the transverse reinforcement, the normalized slip values decreased due to the confining action provided by the transverse reinforcements. Therefore, the presence of transverse reinforcement should be taken into consideration when developing an equation for slip corresponding to peak bond stress. 4.3 Derivation of Equations for the Peak Bond Stress and the Corresponding Slip 4.3.1 Peak Bond Stress  Peak bond stress values were reported for all 380 beam-type specimens of the database which failed in bond. Of these 380 beam-type specimens, 177 failed by concrete splitting. These 177 data were used to generate an equation to predict the peak bond stress of FRP rebars in concrete. 55  3 Unconfined Confined  2.5  Unconfined Confined  2  τm 1.5 f c′ 1  0.5  0 0  20  40  60  l embed db  80  100  120  140  (a) Splitting Failure 5 Unconfined Confined  4  Unconfined Confined  3  τm f c′ 2  1  0 0  10  20  30  40  l embed db  50  60  70  80  90  (b) Pullout Failure Figure 4.12 Normalized average bond stress plotted against normalized embedment length for bottom bar specimens.  56  2 1.8 1.6 1.4 1.2  τm  1  f c′ 0.8 0.6 0.4 0.2 0 0  0.02  0.04  0.06  0.08  Atr snd b  0.1  0.12  (a) Splitting Failure 4  3.5  3  2.5  τm  2  f c′ 1.5  1  0.5  0 0  0.05  0.1  0.15  0.2  0.25  0.3  0.35  0.4  Atr snd b  (b) Pullout Failure Figure 4.13 Effect of transverse reinforcement on the normalized average bond stress of bottom bar specimens.  57  0.02 Splitting Failures Pullout Failures Pullout Failure Splitting Failure 0.015  s m 0.01 lembed  0.005  0 0.001  0.021  0.041  0.061  0.081  0.101  0.121  0.141  0.161  0.181  Atr snd b  Figure 4.14 Effect of transverse reinforcement on the normalized slip corresponding to peak bond stress for the bottom bar specimens.  However, from sections 4.2.1 and 4.2.2, it was evident that the type of fibre and the rebar surface do not affect the peak bond stress of FRP rebars in concrete. On the other hand, from section 4.2.6, it was observed that the presence of transverse reinforcement affects the peak bond stress. Therefore, the 177 data points were divided based on whether the bond region was confined with transverse reinforcement or not (72 unconfined, 105 confined). In addition, the 203 specimens which failed by rebar pullout were used to set a limit for the development length to avoid pullout failure. Peak Bond Stress Based on Unconfined Beam Tests with Splitting Failure  There were 72 unconfined beam tests that failed by splitting of the concrete. Of these 72 tests, 22 tests were performed on specimens where the bars were cast as top bars. These 22 tests were not used to develop the peak bond stress equation. The normalized average bond stresses (  the remaining 50 beam tests were plotted against the normalized embedment lengths (  τc f c′  ) of  l embed ) in db  Figure 4.15.  58  It was observed that as the normalized embedment length increased, the peak bond stress decreased because the stress was distributed over a longer length. Using the same approach as Orangun et al. (1975), a linear regression analysis on the normalized cover (cover to the center of the bar divided by the nominal bar diameter) and the inverse of the normalized embedment length was used to develop Equation 4.1 in SI units.  τc f c′  = 0.03 + 0.14  d c + 9.0 b db l embed  Equation 4.1  Figure 4.15 Normalized average bond stress plotted against normalized embedment length for unconfined bottom bar specimens failed by concrete splitting.  where, τ c is the peak bond stress of unconfined FRP rebar to concrete (i.e. due to concrete cover only). The standard errors for each of the coefficients of Equation 4.1 are presented in Table 4.1. The regression statistics of the linear regression performed to develop Equation 4.1 showed that the proposed equation presented a high adjusted determination coefficient (adjusted R square) value of 0.903 explaining 90.3% of the variability of the response and standard error of 0.142 (Table 4.2). This indicates a good correlation of the proposed equation with the experimental data. The statistical significance of the model (Equation 4.1) has been evaluated by  59  the F-test analysis of variance (ANOVA) which has revealed that this regression is statistically significant (Table 4.3). Table 4.1Standard errors for the coefficients of Equation 4.1 Coefficients  Standard Error  Intercept  0.03  0.0477  c db  0.14  0.0173  9.0  0.4172  db l embed  Table 4.2 Regression statistics for Equation 4.1 Regression Statistics Multiple R 0.952405 R Square 0.907075 Adjusted R Square 0.903121 Standard Error 0.142632 Observations 50  Table 4.3 ANOVA of the 50 unconfined bottom bar specimens having splitting failure  Regression Residual Total  Degrees of Freedom 2 47 49  Sum of Squares 9.333487 0.956166 10.28965  Mean Squares 4.666743 0.020344  F 229.3922  Significance F 5.63784E-25  When the predicted values from Equation 4.1 were plotted against the experimental values and the values obtained from the ACI 440.1R-06 equation (Figure 4.16), it was found that the bond strength values obtained from the proposed equation are very close to the actual test results and the values predicted by the ACI 440.1R-06 equation. The average of the ratio of the experimental to the predicted values using Equation 4.1 was found to be 0.998 with a standard deviation of 0.123. This indicates that any significant parameter was not left out from the  60  proposed equation. Thus, Equation 4.1 can provide an adequate estimate of the peak bond stress of the FRP rebars to concrete when failure is initiated by concrete splitting. Peak Bond Stress Based on Confined Beam Tests with Splitting Failure  In this study, there were 105 beam-type specimens which had transverse reinforcement and failed by concrete splitting. From the analysis of the database, it was evident that the presence of the transverse reinforcement increased the overall bond strength of the FRP rebars to concrete and hence, the presence of transverse reinforcement should be taken into consideration when calculating the peak bond stress and the development length of the FRP rebars (section 4.2.6). The peak bond stress of a confined rebar can be regarded as the linear addition of the strength of an unconfined rebar and the strength contributed by the transverse reinforcement (Orangun et al. 1975). 15  Experimental Peak Bond Stress (MPa)  Eq. 4.1 ACI 440.1R-06  12  Eq. 4.1 ACI 440.1R-06  9  6  3  0 0  3  6  9  12  15  Predicted Peak Bond Stress (MPa)  Figure 4.16 Comparison of the proposed equation with the ACI 440.1R-06 equation for unconfined bottom bar specimens having splitting failure.  The transverse reinforcement contribution to bond stress ( τ tr ) was calculated by subtracting τ c , as determined from Equation 4.1, from the total bond stress achieved in a confined beam test, τ confined i.e. τ tr = τ confined − τ c . The value of  τ tr f c′  was plotted against  Atr for snd b  the bars considered in Figure 4.17. The straight line fit proposed led to the following equation: 61  τ tr f c′  = 2.9  Atr sndb  Equation 4.2  Therefore, the peak bond stress of an FRP bar with transverse reinforcement was determined by combining Equations 4.1 and 4.2 as follows:  τm f c′  =  τc f c′  +  τ tr f c′  = 0.03 + 0.14  d A c + 9.0 b + 2.9 tr db lembed snd b  Equation 4.3  Figure 4.17 Effect of transverse reinforcement for confined tests with splitting failures.  Equation 4.3 provides the peak bond stress values for FRP rebars to concrete for splitting mode of failure. The regression statistics of Equation 4.3 showed that the proposed equation presented a moderate adjusted determination coefficient (adjusted R square) value of 0.671 explaining 67.1% of the variability of the response and standard error of 0.116 (Table 4.4). This indicates a reasonable correlation of the proposed equation with the experimental data. The statistical significance of the model (Equation 4.3) has been evaluated by the F-test analysis of variance (ANOVA) which has revealed that this regression is statistically significant (Table 4.5). Figure 4.18 shows the comparison of the normalized average bond stress for the proposed equation (Equation 4.3) against the experimental data and ACI 440.1R-06 equation respectively. 62  Table 4.4 Regression statistics for Equation 4.3 Regression Statistics Multiple R 0.824899 R Square 0.680458 Adjusted R Square 0.670967 Standard Error 0.116191 Observations 105  Table 4.5 ANOVA of the 105 confined bottom bar specimens having splitting failure Degrees of Freedom 3 101 104  Regression Residual Total  Sum of Squares 2.903607 1.363526 4.267133  Mean Squares 0.967869 0.0135  F 71.6926  Significance F 6.37242E-25  8 Eq. 4.3 Experimental Peak Bond Stress (MPa)  ACI 440.1R-06 Eq. 4.3 6  ACI 440.1R-06  4  2  0 0  2  4  6  8  Predicted Peak Bond Stress (MPa)  Figure 4.18 Comparison of the proposed equation with the ACI 440.1R-06 equation for confined bottom bar specimens having splitting failure.  It can be observed that the ACI equation underestimates the bond strength in presence of transverse reinforcement. This manifests the inadequacy of ACI equation in calculating the bond strength of FRP rebars to concrete in presence of transverse reinforcement. On the other hand, the proposed equation takes into account the effect of the presence of transverse reinforcement and it shows good agreement with the test results. The average of the ratio of experimental to 63  predicted values using Equation 4.3 was found to be 0.94 with a standard deviation of 0.21, while the average of the ratio of the experimental to the predicted values using ACI equation was found to be 1.05 with a standard deviation of 0.33. It can be observed that the ACI equation underestimated the bond strength by 5%, whereas the proposed equation overestimated the bond strength by 6%. Although the ACI equation is showing conservativeness over the experimental results, it is missing one of the important parameters i.e. the effect of the transverse reinforcement. But the proposed equation was able to capture all the important parameters although it overestimated the bond strength by 6%. However, the proposed equation will result in shorter development length than the ACI equation because it takes advantage of the presence of confinement provided by the transverse reinforcement. 4.3.2 Slip Corresponding to Peak Bond Stress  From section 4.2.2, it was observed that the normalized slip corresponding to the peak bond stress (  sm lembed  ) is influenced by the type of the rebar surface and so, all the data were splitted  based on the type of the rebar surface. Of the 97 specimens, for which s m was reported, 61 had helical lugged bars, 5 had sand coated bars and 31 had spiral wrapped bars. Moreover, from sections 4.2.3 to 4.2.6, it was noted that the normalized s m is affected by the concrete strength, the concrete cover, the embedment length and the confinement. Therefore, these parameters were considered when developing a model for s m . Linear regression was performed to develop an equation to predict the slip corresponding to the peak bond stress. The response parameter was chosen as the slip corresponding to the peak bond stress normalized by embedment length ( (  sm lembed  ) and the variable parameters were chosen as the square root of the concrete strength  f c′ ), the concrete cover to bar diameter ratio (  c A ) and tr . Linear regression analysis was db snd b  performed on the data of the specimens having helical lugged bars and bar surface modification factor was proposed based on the data of specimens having sand coated and spiral wrapped bars. The helical lugged bars were chosen for regression because it had the highest number of specimens in the database.  64  There were 61 specimens that had helical lugged FRP rebars. Of the 61 specimens, 6 had AFRP bars, 11 had CFRP bars and the remaining 44 had GFRP bars. However, it was found from section 4.2.1 that the type of FRP does not affect  sm lembed  and hence, all types of FRP data  were combined for the analysis. The 61 specimens had compressive strength of the concrete ranging between 23 to 48 MPa, the concrete cover ranging between 1 to 6 bar diameters ( d b ≤ c ≤ 6d b ) and the embedment length ranging between 3 to 28 bar diameters ( 3d b ≤ lembed ≤ 28d b ). Figure 4.7, Figure 4.9 and Figure 4.14 show the plot of the normalized slip corresponding to the peak bond stress with respect to the different parameters for the specimens for different types of FRP rebars. It was observed that with an increase in the compressive strength of concrete, the concrete cover and the transverse reinforcement, the normalized slip decreased due to their confining action. The regression resulted in the following equation in SI units. sm lembed  =  A  1  c  20.8 − 1.3 f c′ − 2.1 − 3.8 tr  1000  db snd b   Equation 4.4  Equation 4.4 provides the slip corresponding to the peak bond stress for helical lugged FRP bars. Table 4.6 shows the standard errors for the coefficients of Equation 4.4. The regression statistics of the linear regression performed to develop Equation 4.4 showed that the proposed equation presented an adjusted determination coefficient value of 0.428 explaining 42.8% of the variability of the response (Table 4.7). The statistical significance of the model predicted in Equation 4.4 has been evaluated by the F-test analysis of variance (ANOVA) which has revealed that this regression is statistically significant (Table 4.8). It was found that the average normalized slip (  sm lembed  ) of the sand coated and spiral wrapped bars were less than the values  obtained from the Equation 4.4 by 50%-60% (Figure 4.19). Therefore, rebar surface modification factor should be proposed for Equation 4.4 based on the available data.  65  Table 4.6 Standard errors for the coefficients of Equation 4.4 Coefficients  Standard Error  Intercept  0.0208  0.0043  f c′  0.0013  0.0007  c db  0.0021  0.0003  Atr snd b  0.0038  0.0258  Table 4.7 Regression statistics for Equation 4.4 Regression Statistics Multiple R 0.65427 R Square 0.42806 Adjusted R Square 0.39796 Standard Error 0.00346 Observations 61  Table 4.8 ANOVA of 61 specimens having helical lugged FRP rebars  Regression Residual Total  Degrees of Freedom 3 57 60  Sum of Squares 0.000512 0.000684 0.001195  Mean Squares 0.000171 1.2E-05  F 14.2205  The average ratio of test/predicted normalized slip (  sm lembed  Significance F 4.95683E-07  ) for helical lugged and spiral  wrapped specimens was 1.08 and 0.46 respectively. A modification factor of 0.43 was recommended based on the ratio of the spiral wrapped FRP bar specimens to that of the helical lugged FRP bar specimens. Similarly, the average ratio of test/predicted normalized slip (  sm lembed  )  for helical lugged and sand coated specimens was 1.08 and 0.41 respectively. A modification factor of 0.38 was recommended based on the ratio of the sand coated FRP bar specimens to that 66  of the helical lugged FRP bar specimens. Therefore, by incorporating the bar surface modification factor, Equation 4.4 can be rewritten as sm lembed  =  η   A  c  20.8 − 1.3 f c′ − 2.1 − 3.8 tr  1000  db snd b   Equation 4.5  where, η is the bar surface modification factor, which equals to 1 if the bar surface is helical lugged, 0.43 if it is spiral wrapped and 0.38 if it is sand coated. Figure 4.20 shows the comparison of the predicted normalized slip (  sm lembed  ) obtained by using Equation 4.5 with the  experimental data. 0.018 Helical Lugged Sand Coated Spiral Wrapped Helical Lugged Spiral Wrapped Sand Coated  0.015  0.012  S max 0.009 l embed 0.006  0.003  0 0  1  2  3  c db  4  5  6  7  Figure 4.19 Comparison of normalized slip corresponding to peak bond stress for FRP bars having different surface texture.  It was observed that predicted values were reasonably close to the actual test results. The average of the ratio of the predicted to the experimental values for the normalized slip (  sm lembed  )  was 1.04 with a standard deviation of 0.18, which indicates a good correlation between the experimental and predicted values. Therefore, based on the analysis and the comparison with the experimental results, it can be concluded that the proposed equation (Equation 4.5) is adequate in predicting the slip corresponding to the peak bond stress for different types of FRP rebars with 67  different rebar surface. However, due to lack of enough data, specimens having pullout and splitting failure were combined together for developing Equation 4.5. Therefore, more tests are required to split the data according to the mode of failure and thus, Equation 4.5 can be modified with availability of more experimental data. 0.025  Predicted  sm l embed  0.02  0.015  0.01  0.005  0 0  0.005  0.01  0.015 Actual  0.02  0.025  sm l embed  Figure 4.20 Test vs. predicted normalized slip corresponding to peak bond stress for all specimens.  4.4 Development Length 4.4.1 Beam Tests with Splitting Failures  Equation 4.3 can be used to generate an equation to determine the development length required to achieve the full tensile strength of the FRP rebar. The average bond stress τ can be written in terms of the stress in the reinforcing bar as:  τ=  f F Ab f d = F b πd b lembed 4lembed  Equation 4.6  where, f F is the maximum stress in the FRP bar. By combining Equations 4.3 and 4.6 and rearranging, a relationship between the embedment length required to achieve a stress f F in the rebar can be determined as follows:  68   ff   ff  db  db  − 9.0  − 9.0  4 f′  4 f′  c c     ld = = Atr c  c A 0.03 + 0.14 + 2.9 0.03 + 0.14 + 20.7 tr db snd b snd b  db      Equation 4.7  where, l d is the embedment length required to develop a tensile stress of f F in the rebar. The embedment length is the bonded length of the rebar provided in the member, whereas, the development length is the embedment length of the rebar required to achieve the desired tensile strength. Equation 4.7 gives an expression for the development length required to avoid splitting mode of failure. This equation will give shorter development length than that required by ACI 440.1R-06 and CSA S806-02 equations since the effect of confinement was taken into consideration. This can save a considerable amount of FRP materials and thereby, reduce the cost of construction. For example, for a beam reinforced with 2-16 mm GFRP bars ( f Fu = 650 MPa) with 10 mm diameter steel stirrups placed at 100 mm spacing, with a compressive strength of concrete, f c′ = 30 MPa, and  c = 1.5 , Equation 4.7 provides 995 mm db  development length. On the contrary, ACI 440.1R-06, CSA S806-02, CSA S6-06 and JSCE equations require 1310, 2500, 1465 and 1059 mm development length respectively, which are 32%, 152%, 47% and 7% higher than that required by the proposed equation (Equation 4.7). 4.4.2 Beam Tests with Pullout Failures  In the database, there were 203 beam tests that resulted in pullout failures; 26 of these had FRP bars cast as top bars. Of the remaining 177 beam tests, 127 tests were confined and 50 were unconfined. The normalized average bond stresses of all the specimens having pullout and  c A splitting failures were plotted against  + 20.7 tr snd b  db    in Figure 4.21.   69  5 Splitting Failure  Pullout Failure  4  3  τm f c′ 2  1  0 0  1  2  3  4  5  6  7  8  9  10  11  12  13  A c + 20.7 tr db snd b  Figure 4.21 Normalized average bond stresses of confined specimens for both pullout and splitting mode of failure.   c A The term  + 20.7 tr snd b  db    was chosen because it indicates the total amount of confinement    c A provided to the concrete. When  + 20.7 tr snd b  db    is large, there will be enough confinement   provided to the concrete and hence, pullout failure will occur. On the contrary, when  c A  + 20.7 tr snd b  db    is not sufficient enough, then the specimen will fail by splitting of concrete due   to  of  the  lack   c A for  + 20.7 tr snd b  db  concrete  confinement.  From  Figure  4.21,  it  was  noticed  that    > 3.5 , almost all the specimens failed by rebar pullout. This indicates that    c A when  + 20.7 tr snd b  db    is greater than 3.5, there will be enough confinement to the concrete and   the specimen will fail by rebar pullout. This sets an upper limit to avoid pullout mode of failure  c A for  + 20.7 tr snd b  db    in Equation 4.7 as 3.5.   70  4.4.3 Effect of Bar Cast Position  The casting position has been shown to significantly influence the peak bond stress under monotonic static loading (Ehsani et al., 1996). The Canadian and American design codes define top bar reinforcement as the horizontal reinforcement with more than 300 mm (12 in) of concrete below it at the time of casting. In cases of top bar reinforcement, air, water and fine particles migrate upward through the poured concrete during the placement of concrete, thus decreasing the contact area between the rebar and the concrete. This phenomenon can cause a significant drop in the peak bond stress. In the current ACI and CSA codes, the top bar effect is accounted for by multiplying the development length of FRP reinforcement by a top bar modification factor. ACI 440.1R-06 recommended the use of a bar location modification factor of 1.5 for top bars based on the study by Wambeke and Shield (2006), whereas CSA S806-02 recommended 1.3 as the top bar modification factor. In the present study, there were 22 specimens with top bar which failed by concrete splitting. Figure 4.22 shows a comparison of the normalized average bond stress of unconfined top and bottom bar specimens which failed by concrete splitting. It was found that the average peak bond stress of the top bars was less than the values obtained from the bottom bars by 40-50%. Therefore, bar location modification factor should be proposed based on the available data. The average ratio of test/predicted normalized bond stress for bottom bar and top bar specimen was 0.92 and 0.65 respectively for splitting mode of failure. A modification factor of 1.5 was recommended based on the ratio of the bottom bar specimens to that of the top bar specimens which is the same as the one recommended by ACI 440.1R-06. Therefore, by incorporating the bar location modification factor, Equation 4.7 can be rewritten as  f  d b  f − 9.0  χ 4 f′  c   ld =  c A  0.03 + 0.14 + 20.7 tr  sndb   db  Equation 4.8  where χ is the bar location modification factor, which equals to 1.5 if there is more than 300 mm (12 in) of concrete cast below the bar, otherwise χ equals 1.  71  1.6 Top Bar Specimens Top Bar Specimens  Bottom Bar Specimens Bottom Bar Specimens  f c′  Test/P redicted  τm  1.4  1.2  1  0.8  0.6  0.4 0  5  10  15  20  25  30  35  lembed db  Figure 4.22 Comparison of normalized average bond stress of unconfined top and bottom bar specimens having splitting failure.  4.5 Summary This chapter presented the analysis results of the accumulated database which identified the parameters that affect the bond behaviour of FRP rebars in concrete. Linear regression was performed to develop equations for predicting the peak bond stress and the corresponding slip by taking into account all the parameters that affect the bond behaviour of FRP rebars. Modification factors were proposed for rebar surface and bar cast position. It was found that the proposed equations were in good agreement with the experimental results. Based on the peak bond stress equation, design equation for determining the development length of FRP rebars in concrete was derived and a limit was recommended for avoiding a more brittle pullout mode of failure. The most significant contribution of this chapter is that it underlines the effect of confinement provided by the transverse reinforcement on the bond behaviour of FRP rebars in concrete which was either ignored in the formulations proposed for predicting the bond behaviour or modified from the equations available for steel rebars.  72  Chapter 5: Modeling of Bond Stress-Slip Relationship and Finite Element Analysis  5.1 General In the previous chapter, it has been observed that the confinement provided by the transverse reinforcement affects the peak bond stress of the FRP rebars in concrete and therefore, a design equation for the peak bond stress was proposed taking into account the effect of the transverse reinforcement. In this chapter, a generalized bond stress-slip relationship will be proposed based on the experimental data and by using the peak bond stress and the corresponding slip equations derived in Chapter 4. In addition, a finite element analysis (FEA) will be performed on the 105 beam-type specimens of the accumulated database, which had transverse reinforcements and failed by splitting of concrete. The purpose of the finite element analysis is to further investigate the effect of the transverse reinforcement on the peak bond stress of FRP rebar in concrete. 5.2 Derivation of Bond Stress-Slip Relationship There were 91 beam-type specimens in the database for which bond stress-slip data were reported along with the bond stress-slip curves. Of these 91 specimens (all the bars were cast as bottom bars), 23 specimens failed by concrete splitting and 68 specimens failed by rebar pullout. Figure 5.1 and Figure 5.2 show typical bond stress-slip curves of the specimens which failed by splitting of concrete and rebar pullout respectively. It can be observed that for pullout mode of failure, the bond stress-slip curves consist of two distinct branches-one initial ascending branch up to the peak bond stress and the other one is a descending post-peak branch (Figure 5.2). On the contrary, for splitting mode of failure, bond stress-slip curves of FRP rebars consist of three distinct branches (Figure 5.1)-two ascending pre-peak branches and one descending post-peak branch. However, in this study, for simplicity and due to the lack of enough experimental data (only 23 specimens failed by splitting of concrete), only one pre-peak branch and one post-peak branch was considered for splitting mode of failure. Therefore, the bond stress-slip data were splitted into two parts-one for the ascending branch of the bond stress-slip curve up to the peak bond stress and the other one is for the descending post-peak branch of the bond stress-slip curve (Figure 5.3). In addition, the data were splitted based on the surface type of the FRP rebars (sand 73  coated, spiral wrapped and helical lugged) which affected the slip corresponding to the peak bond stress. 5 Beam1 Beam 3 Beam 5 Beam 7 Beam 9 Beam 11  4.5  Bond Stress (MPa)  4 3.5  Beam Beam Beam Beam Beam  2 4 6 8 10  3 2.5 2 1.5 1 0.5 0 0  2  4  6  8  10  12  Slip (mm)  (a) Helical Lugged Bars 5 Beam1 Beam 3 Beam 5 Beam 7 Beam 9 Beam 11  4.5  Bond Stress (MPa)  4 3.5  Beam 2 Beam 4 Beam 6 Beam 8 Beam 10 Beam 12  3 2.5 2 1.5 1 0.5 0 0  1  2  3  4  5  6  7  8  9  Slip (mm)  (b) Spiral Wrapped Bars Figure 5.1 Bond stress-slip curves for bottom bar specimens having splitting failures. 74  20 Beam 1  18  Beam 2 Beam 5  16  Beam 13 Beam 31  Bond Stress (MPa)  14 12 10 8 6 4 2 0 0  5  10  15  20  25  Slip (mm)  (a) Helical Lugged Bars  12 Beam Beam Beam Beam Beam  Bond Stress (MPa)  10  1 2 3 4 7  8  6  4  2  0 0  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  Slip (mm)  (b) Spiral Wrapped Bars Figure 5.2 Bond stress-slip curves for bottom bar specimens having pullout failures.  Nonlinear regression analysis was performed on the bond stress-slip data to develop two equations for the ascending and the descending branches of the bond stress-slip curve. It is noted 75  from Figure 5.3 that to predict the bond stress-slip relationship of FRP rebar in concrete, it is necessary to know the peak bond stress ( τ m ) and the corresponding slip ( s m ), because the ascending part ends at that point ( s m , τ m ) and the descending part starts from the same point. Therefore, in the derivation of the bond stress-slip, Equation 4.3 and Equation 4.5 were used to define the peak bond stress and the corresponding slip respectively.  Figure 5.3 A schematic of the proposed bond stress-slip relationship. 5.2.1 Bond Stress-Slip Relationship Based on Splitting Mode of Failure  Of the 23 beam-type specimens that failed by splitting of concrete, 11 had helical lugged FRP rebars and 12 had spiral wrapped FRP rebars. There was no reported specimen with sand coated rebars which failed by concrete splitting. All of the bars were cast as bottom bars. The data was divided for the ascending part and the descending part of the curves for different surface of the rebar. Of the 23 beam specimens, 6 were unconfined and 17 were confined. However, the effect of confinement would be accounted for in the bond stress-slip relationship through the use of the peak bond stress and the corresponding slip equations. Of the 23 specimens, 7 had AFRP rebars, 11 had CFRP rebars and 5 had GFRP rebars. Since it was observed (section 4.2.1) that the type of FRP does not affect the bond stress-slip of FRP rebars in concrete, it was only important to split the data according to the type of the rebar surface and perform a statistical analysis to develop the bond stress-slip relation for FRP bars with different rebar surface. 76  Nonlinear regression analysis was performed on the normalized bond stress ( normalized slip (  τ ) and the τm  s ) to develop a generalized bond stress-slip relationship for the 23 beam-type sm  specimens which failed by concrete splitting. Figure 5.4 and Figure 5.5 present the experimental data along with the nonlinear regression results for all specimens having helical lugged FRP bars and spiral wrapped FRP bars respectively. It was observed that the ascending part of the bond stress-slip curve, for both helical lugged and spiral wrapped FRP bars, showed the same behaviour and therefore, the following equation was proposed for the ascending part of the bond stress-slip relationship (0 ≤ s ≤ sm ) : τ   s    =    τ m   sm   0.45  Equation 5.1  On the other hand, for the descending part of the bond stress-slip curves (s > s m ) , there was a slight difference in the behaviour of helical lugged and spiral wrapped FRP bars (Figure 5.4b and Figure 5.5b). It was also noted that the bond stress-slip behaviour of the FRP bars for the descending part of the bond stress-slip curve was nonlinear. Therefore, one generalized equation was proposed for the descending part of the bond stress-slip relationship based on a nonlinear regression analysis of the experimental data and it is expressed as: τ   s    =    τ m   sm   α  Equation 5.2  where, α is dependent on the rebar surface (-0.56 for helical lugged FRP bars and -0.60 for spiral wrapped FRP bars). Therefore, based on the experimental data and the nonlinear regression results, the proposed generalized bond stress-slip relationship of FRP rebars in concrete is:  77  (a) Ascending Branch  (b) Descending Branch Figure 5.4 Nonlinear regression of the experimental data of the bond stress-slip curves for specimens with helical lugged FRP rebars failed by splitting of concrete.  78  (a) Ascending Branch  (b) Descending Branch Figure 5.5 Nonlinear regression of the experimental data of the bond stress-slip curves for specimens with spiral wrapped FRP rebars failed by splitting of concrete.  79   s  0.45 When 0 ≤ s ≤ sm   s  τ   m    =  α  τ m   s  When s > sm  s   m   Equation 5.3  where, τ m and sm are calculated from Equation 4.3 and 4.5 respectively, and − 0.56 for helical lugged/ribbed bars − 0.60 for spiral wrapped bars  α =  Figure 5.6 and Figure 5.7 show a comparison of the predicted bond stress-slip curves with the experimental results for four beam-type specimens. The comparison of the predicted and the experimental bond stress-slip curves for all 23 specimens is presented in Appendix D (Figure D.1 and Figure D.2) and the reference of each of the experimental beam specimens are presented in Appendix B (Table B.1). It was observed that the predicted values showed good agreement with the experimental data, especially for the ascending part of the bond stress-slip curve up to the peak bond stress and the proposed relationship could capture the peak bond stress in each case. The proposed equation for the ascending part of the bond stress-slip relationship showed a high adjusted determination coefficient (adjusted R-square) value of 0.963 explaining 96.3% of the variability of the response. On the contrary, the proposed equation for the descending part of the bond stress-slip relation showed a moderate adjusted determination coefficient (adjusted Rsquare) value of 0.663 explaining 66.3% of the variability of the response. Therefore, it can be concluded based on the results of the analysis that the proposed generalized bond stress-slip relationship can give a good prediction of the bond stress-slip behaviour of FRP rebars in concrete when the failure is initiated by splitting of concrete. 5.3 Finite Element Analysis (FEA) During the statistical analysis of the database, it was noted that the confinement provided by the transverse reinforcement increased the peak bond stress and hence, Equation 4.3 was proposed for predicting the peak bond stress of FRP rebars in concrete by taking into account the effect of transverse reinforcement. This conclusion was based on 105 confined beam specimens which failed by splitting of concrete. The data had large scatter and therefore, it was necessary to 80  investigate more. In this section, finite element analysis will be performed to further investigate the effect of concrete confinement provided by the transverse reinforcement on the peak bond stress of FRP rebars in concrete. 4.5 Experimental Beam 1 (Appendix B)  4  Predicted  Bond Stress (MPa)  3.5 3 2.5 2 1.5 1 0.5 0 0  1  2  3  4  5  6  7  8  Slip (mm)  4.5 Experimental Beam 2 (Appendix B)  4  Predicted  Bond Stress (MPa)  3.5 3 2.5 2 1.5 1 0.5 0 0  1  2  3  4  5  6  7  8  Slip (mm)  Figure 5.6 Comparison of the predicted vs. the experimental results for specimens with helical lugged FRP bars having splitting failure.  81  5 4.5 Experimental Beam 1 (Appendix B) 4  Predicted  Bond Stress (MPa)  3.5 3 2.5 2 1.5 1 0.5 0 0  1  2  3  4  5  6  7  8  Slip (mm)  4 Experimental Beam 2 (Appendix B)  3.5  Predicted  Bond Stress (MPa)  3  2.5  2  1.5  1  0.5  0 0  1  2  3  4  5  6  7  8  9  Slip (mm)  Figure 5.7 Comparison of the predicted vs. the experimental results for specimens with spiral wrapped FRP bars having splitting failure. 5.3.1 Finite Element Modeling  For the finite element analysis of the beam specimens, a commerical finite element package “ABAQUS” was used, since it provides the facility of modeling concrete as a smeared-crack material in 2-dimensional models. In addition, it is regarded as offering a better nonlinear solution procedure for approaching the initiation of cracking in the model. There were 105 confined beam-type specimens which failed by concrete splitting. These included hinged beam 82  specimens and splice beam specimens and all of the specimens were confined with transverse reinforcement. In the FE modeling of the specimens, a half beam model was considered to simulate the hinged beam specimens and a full beam model was considered to simulate the splice beam specimens (Figure 5.8 and Figure 5.9).  (a) Experimental hinged beam specimen used by Makitani et al. (1993)  (b) Half beam model considered in the FE analysis  (c) Finite element mesh Figure 5.8 Hinged beam specimen.  83  (a) Experimental splice beam specimen used by Tighiouart et al. (1999)  (b) Full beam model considered in the FE analysis  (c) Finite element mesh Figure 5.9 Splice beam specimen. Modeling the Interaction between Concrete and FRP Rebar  Shell elements were used to establish connection between the concrete and the FRP bar. These connecting elements are referred to as “bond element”. The main role of the bond elements in this model was to simulate the bond interaction between the bar and the surrounding concrete. The required input data that defined the behaviour of the bond element was the bond stress-slip properties of the bar and the surrounding concrete. In order to define the input bond stress-slip 84  curve, the proposed bond stress-slip relationship for splitting mode of failure was used (Equation 5.3). The values of the peak bond stress ( τ m ) and the corresponding slip ( sm ) in Equation 5.3 was determined by using the following equations that were derived in Chapter 4.  τm f c′  sm =  = 0.03 + 0.14  d A c + 9.0 b + 2.9 tr db lembed sndb  ηlembed   A  c  20.8 − 1.3 f c′ − 2.1 − 3.8 tr  db snd b  1000   Equation 4.3  Equation 4.5  where, f c′ is the compressive strength of concrete; c is the lesser of the cover to the center of the bar or one-half of the center-to-center spacing of the bars being developed; d b is the bar diameter; l embed is the embedment length of the bar in concrete; Atr is the area of the transverse reinforcement normal to the plane of splitting through the bars; s is the center to center spacing of the transverse reinforcement; n is the number of bars being developed along the plane of splitting; and η is a surface dependent factor, which equals to 1 if the bar surface is helical lugged, 0.43 if it is spiral wrapped and 0.38 if it is sand coated. It can be noted that the bond elements are not continued all through the length of the beam to simulate the experimental set up. Materials Model  The following sections will describe the material models that have been used to represent the behaviour of the concrete and the FRP bars in this study. Concrete  Concrete was modeled by using shell element. Since the concrete is mostly used to resist compressive stresses, the behaviour of concrete in compression is of prime importance. In this study, a constitutive model for the concrete in compression suggested by Popovics (1973) and later modified by Thorenfeldth (1987), has been used to describe the compressive behaviour of concrete in the direction of the principal compressive strain. The uniaxial stress-strain relation is expressed by Equation 5.4.  85  σ f c′  =  ε × ε0   n  ε  n − 1 +     ε0   nk  Equation 5.4      where, n is the curve fitting parameter and k is the post-peak decay term and is taken as 1 for  ε < 1 . Collins and Mitchell (1991) suggested expressions for n and k, which are given in ε0 Equation 5.5. It is to be noted that f c′ is taken in the metric system of units in Equation 5.5. A typical stress-strain relation according to Equation 5.4 is shown Figure 5.10. n = 0.8 +  f c′ 17  k = 0.67 +  f c′ 62  Equation 5.5  Figure 5.10 Concrete compressive stress-strain model (Thorenfeldt et al. 1987).  Concrete is a weak material in tension and its tensile strength is of very little significance in any direct application. However, it plays a key role in the development of cracks in the concrete, which can influence its behaviour at the structure level and also in bond. In this study, the stressstrain relation for the uncracked concrete in the direction of the maximum principal tensile strain has been assumed linear up to the tensile strength ( f ct ) and its post-peak behaviour comprise of a tension softening branch as shown in Figure 5.11. Equations 5.4 and 5.5 were used to calculate 86  the stress and the plastic strain for concrete and these were used as material properties for concrete.  f ct = 0.6 f c′  ε ct =  f ct Ec  Figure 5.11 Behaviour of concrete under tension. FRP Reinforcement  Shell element was used to model the FRP rebar. FRP reinforcements were modeled as a linear elastic material with a brittle fracture in tension (Figure 5.12). The ultimate tensile strength of the material is represented by f Fu , while the corresponding strain at failure is ε Fu .  Figure 5.12 Constitutive relations for FRP reinforcements.  87  Finite Element Mesh  The different parts of the beam was meshed by using the module “mesh” in ABAQUS/CAE. The top down meshing technique (free meshing), a more flexible method, was used in this study. A 3-node linear plane strain triangle element (CPE3) was defined for the concrete, the FRP reinforcing bar, and the bond element. Finer meshing was used near the bond element. Figure 5.8(c) and Figure 5.9(c) show the finite element mesh for the half beam and the full beam specimens considered in the study respectively. The models of the beam specimens were run with different mesh densities and it was observed that the modeling procedure used was insensitive to the mesh size. 5.3.2 FEA Results and Discussion  The objective of the finite element analysis was to model the experimental beams of the database and investigate whether the presence of transverse reinforcement affects the peak bond stress of the FRP rebars in concrete. The proposed equation to predict the peak bond stress obtained from the experimental data can be expressed as follows  τm f c′  = 0.03 + 0.14  d A c + 9.0 b + Ct tr db lembed sndb  Equation 5.6  where, Ct is a constant that was determined from the experimental statistical analysis as 2.9. The approach for the finite element analysis was to model each of the 105 confined beam specimens of the database that failed by concrete splitting and the bond stress-slip relationship for each of the specimens was assigned as the input parameter on the bond element. The bond stress-slip relationship for each of the specimens was obtained by using Equation 5.3. The peak bond stress was determined from Equation 5.6 by using a different value for Ct . Static load was applied on the specimens until each of the specimens failed in bond. The failure loads obtained from the finite element analysis were then compared with the experimental failure loads. If the failure load obtained from the FE analysis was not equal or very close to the experimental failure load, the coefficient Ct of the transverse reinforcement effect (  Atr ) in peak bond stress snd b  equation (Equation 5.6) was modified and the model was executed again. Figure 5.13 shows a 88  flow chart for the iterations performed during the finite element analysis. Thus, several iterations were performed on each beam specimen by changing the coefficient Ct . Hence, 105 values of the coefficient Ct were obtained for each of the 105 confined beam specimens which are shown in Appendix E (Table E.1). Assume  Ct  Use Eq. 5.6 in the FE model to calculate the peak bond stress  Get the failure load P from FEA  No  If PFEA= Pexp  Yes Finish  Figure 5.13 Flow chart of the iterations performed in FEA.  By using the 105 values of Ct , the peak bond stress of the 105 specimens were obtained. The contribution of the transverse reinforcement in the peak bond stress (τ tr )FEA was calculated by deducting the peak bond stress of the unconfined specimen, τ c calculated by using Equation 4.1, from the peak bond stress obtained from FEA i.e. (τ tr )FEA = τ FEA − τ c . Figure 5.14 shows the normalized peak bond stress contribution of the transverse reinforcement (  against  τ tr f c′  ) plotted  Atr from both the experimental and the finite element analysis results along with the snd b  regression line of the plotted values.  89  It was observed that the regression model of the plotted values obtained from the FE analysis gave the value of the coefficient Ct as 2.45, whereas, from the experimental results it was obtained as 2.93. A positive value of the coefficient Ct indicates that the confinement provided by the transverse reinforcement increased the peak bond stress and hence, the presence of transverse reinforcement should be considered in determining the peak bond stress. The results also indicated that the proposed equation (Equation 5.6) for predicting the peak bond stress may be unconservative in some cases. 0.5 Experimental 0.4  FEA Experimental FEA  0.3  τ tr f c′  0.2  y = 2.9328x y = 2.4772x  0.1  0 0  0.01  0.02  0.03  0.04  0.05  0.06  0.07  Atr snd b  Figure 5.14 Comparison of experimental and finite element analysis results.  Therefore, based on the results of the finite element analysis, a value of 2.0 was recommended as the coefficient Ct of the effect of transverse reinforcement (  Atr ) in Equation snd b  5.6 to be on the conservative side. Then the equation for the peak bond stress takes the following form  τm f c′  = 0.03 + 0.14  d A c + 9.0 b + 2.0 tr db lembed sndb  Equation 5.7  Using Equation 5.7, the following development length equation was derived for FRP rebars in concrete 90   f  d b  f − 9.0  χ 4 f′  c   ld =  c A  0.03 + 0.14 + 14.3 tr  snd b   db  Equation 5.8  5.4 Sensivity Analysis Figure 5.15 shows the comparison of the required development length obtained from the proposed equation (Equation 5.8) against ACI 440.1R-06, CSA S806-02, CSA S6-06 and JSCE equations for different cover to bar diameter (  c ) ratio for a beam reinforced with 2-16 mm db  FRP bars with 10 mm diameter steel stirrups placed at 100 mm spacing. It was observed that for all cover to bar diameter (  c ) ratios, ACI 440.1R-06 and CSA S806-02 equations overestimate db  the development length required to achieve the full tensile strength of the rebar compared to the proposed equation (Equation 5.8). For 1 ≤  c ≤ 2 , the development length required by the ACI db  440.1R-06 equation is 15%-20% higher than that required by the proposed equation, whereas the development length required by the CSA S806-02 equation is more than twice the length required by the proposed equation. For 2 ≤  c ≤ 3.5 , the development length required by the ACI db  440.1R-06 equation is 50%-60% higher than that required by the proposed equation, whereas the development length required by the CSA S806-02 equation is still almost twice the length required by the proposed equation. It was observed that as the concrete strength is increased or the ultimate tensile strength of the bar is decreased, the proposed equation can save more of the development length compared to the ACI 440.1R-06 or the CSA S806-02 equations. CSA S6-06 also overestimates the development length compared to the proposed equation. For FRP rebars with low ultimate tensile strength, the development length required by the CSA S6-06 equation is 20% (on an average) higher than that required by the proposed equation. On the other hand, for FRP rebars with high ultimate tensile strength and  c ≤ 2.5 , the development db  length required by the CSA S6-06 equation is 10% (on an average) higher than that required by 91  ffu = 650 MPa  ffu = 1650 MPa 700  250  ACI 440.1R-06  ACI 440.1R-06 CSA S806  CSA S806  600  CSA S6-00  CSA S6-00  JSCE  JSCE  500  Eq. 5.8 150  ld db  ld db 100  fc΄=25 MPa  200  Eq. 5.8  400  300  200 50  100  0  0 1  1.5  2  c db  2.5  3  3.5  200  1  1.5  2  c db  2.5  3  3.5  500 ACI 440.1R-06  ACI 440.1R-06 450  CSA S806 CSA S6-00  160  CSA S806 CSA S6-00  400  JSCE 140  fc΄=40 MPa  180  JSCE  Eq. 5.8  350  120  300  ld 100 db  ld 250 db  80  200  60  150  40  100  20  50  0  Eq. 5.8  0 1  1.5  2  c db  2.5  3  3.5  160  1  1.5  2  c db  2.5  3  3.5  450 ACI 440.1R-06  ACI 440.1R-06 400  CSA S806  CSA S806  CSA S6-00  CSA S6-00 350  JSCE  120  Eq. 5.8  fc΄=60 MPa  140  JSCE Eq. 5.8  300  100  ld db  l d 250 db  80  200  60 150 40  100  20  50 0  0 1  1.5  2  c db  2.5  3  3.5  1  1.5  2  c db  2.5  3  3.5  Figure 5.15 Comparison of the required development length for different cover to bar diameter ratio 92  the proposed equation, but for  c > 2.5 , CSA S6-06 and the proposed equation calculate almost db  the same development length. The development length required by the JSCE equation was very close to the proposed equation. For FRP rebars with low ultimate tensile strength and  c ≤ 1.5 , the proposed equation db  gives a conservative estimate of the development length compared to the JSCE equation, which is 10% higher than that required by the JSCE equation, but for  c > 1.5 , the proposed equation db  gives a development length that is 30%-40%% lower than that required by the JSCE equation.. For FRP rebars with high ultimate tensile strength and  c ≤ 2 , the proposed equation gives a db  conservative estimate of the development length compared to the JSCE equation, which is 20% higher than that required by the JSCE equation, but for  c > 2 , the proposed equation gives a db  development length that is 20-25% lower than that required by the JSCE equation. Based on the analysis, it can be concluded that the proposed equation can save on an average 10%-15% of the required development length compared to the code equations. This will reduce the cost of materials, which will eventually reduce the cost of construction. Therefore, the proposed equation can be a reasonable and a cost-effective option to estimate the development length required for FRP rebar in the design of RC structures. 5.5 Summary In this chapter, a generalized bond stress-slip relationship of FRP rebars in concrete has been developed by performing nonlinear regression of the experimental data. Modification factors were proposed so that the derived bond stress-slip relationship can be applied to any type of FRP rebar with different surface textures. It was observed that the proposed bond stress-slip relationship was in good agreement with the experimental data. Based on the data analysis and the comparison with the experimental data, it was concluded that the proposed bond stress-slip relationship can be a reasonable mean to predict the bond behaviour of FRP rebars in concrete with acceptable accuracy. Moreover, the finite element analysis results of the confined beam 93  specimens have been presented in this chapter which indicated that confinement provided by the transverse reinforcement increased the bond strength of FRP rebars in concrete and based on the FEA results, the proposed peak bond stress and the development length equations have been modified. The proposed development length equation was compared with the available code equations and it was noted that the proposed development length equation can save 10%-15% of the development length required by the code equations and thereby, reduce the overall cost of construction.  94  Chapter 6: Conclusions  6.1 General The objective of the present study was to investigate the effect of different parameters on the bond behaviour of FRP rebars in concrete and thereby, to propose equations for predicting the peak bond stress and the corresponding slip, to establish a general bond stress-slip law, to derive a design equation for determining the development length which can be applied to different types of FRP rebars. For this purpose, all the experimental data on beam bond test was accumulated from the literature up to 2009 and the database was analysed statistically. Based on the analysis of the experimental data, expressions were derived for the peak bond stress and the corresponding slip, the development length and a general bond stress-slip law. In addition, a finite element analysis was performed to validate the proposed expressions. The results of the statistical and the finite element analyses lead to the following conclusions; •  Type of fibres does not affect the peak bond stress and the corresponding slip of FRP rebars in concrete. Rebar surface does not influence the peak bond stress, but it affects the slip corresponding to the peak bond stress. Helical lugged/ribbed bars show larger slip before attaining the peak bond stress than spiral wrapped or sand coated bars. Spiral wrapped and sand coated bars show almost the same slip at the peak bond stress. This means initial stiffness of the bond stress-slip curves of spiral wrapped and sand coated bars are larger than that of the helical lugged/ribbed bars.  •  Compressive strength of concrete, concrete cover, embedment length and bar diameter affect the peak bond stress and the corresponding slip of FRP rebars in concrete significantly. With increase in concrete strength and concrete cover, the peak bond stress increases, whereas slip at peak bond stress decreases. This indicates that there is an increase in the initial stiffness of the bond stress-slip curve with increase in concrete strength and concrete cover. On the contrary, with increase in the bar diameter and the embedment length, the peak bond stress decreases, whereas slip at peak bond stress increases i.e. there is a decrease in the initial stiffness of the bond stress-slip curve. 95  •  Bar cast position has a significant effect on the peak bond stress of FRP rebars in concrete. When there is more than 300 mm of concrete cast below the reinforcing bars (known as top bars), the bars usually show 50% decrease in the peak bond stress than the bottom bars.  •  Confinement provided by the transverse reinforcement influences the peak bond stress and the corresponding slip. Peak bond stress increases with increase in the amount of transverse reinforcement, whereas slip at peak bond stress decreases due to the confining action of the transverse reinforcements. It has been observed from the experimental data that there is 10%-15% increase in the peak bond stress in presence of transverse reinforcement. This indicates a decrease in the required development length of FRP rebars in concrete due to the confinement provided by the transverse reinforcement.  •  By considering all the parameters that influence the peak bond stress and the corresponding slip, relationships have been derived to evaluate the peak bond stress and the corresponding slip by using linear regression analysis. The confining effect of transverse reinforcement has been taken into consideration for deriving the equations. Rebar surface modification factors have been proposed for the slip at the peak bond stress equation. It has been observed that the proposed equations are in good agreement with the experimental results and they can predict the peak bond stress and the corresponding slip with acceptable accuracy. The proposed peak bond stress equation has also been compared with the ACI 440.1R-06 equation and it has been observed that the ACI equation underestimates the peak bond stress in presence of transverse reinforcements, whereas the proposed equation shows good correlation with the experimental results since it takes into account the confinement provided by the transverse reinforcements.  •  Based on the peak bond stress equation, a design equation has been derived to determine the development length required to achieve the design tensile strength of FRP rebars in concrete.  •  After defining relations for the peak bond stress and the corresponding slip, a general bond stress-slip relationship has been developed for splitting mode of failure. It has been observed that all types of FRP bars show similar behaviour for the initial ascending part 96  of the bond stress-slip curves, but for the softening post-peak branch, the behaviour varied for different rebar surfaces and hence, rebar surface modification factors have been proposed. It has also been noted that the proposed bond stress-slip relationship shows good agreement with the experimental results, and it provides a reasonable means of predicting the bond behaviour of FRP rebars in concrete. •  Finite element analysis has been performed to validate the proposed bond stress-slip relationship and the effect of transverse reinforcement on the bond strength of FRP rebars in concrete. Based on the finite element analysis results, the equations for the peak bond stress and the development length were modified.  •  Sensitivity analysis of the proposed development length equation with the ACI 440.1R06, CSA S806-02, CSA S6-06 and JSCE equations reveals that the proposed development length can save about 10%-15% of the development length required by the code equations on an average, since it takes the advantage of the confining action provided by the transverse reinforcement. A reduction in the development length leads to a reduction in the cost of materials which will eventually decrease the overall cost of construction and encourage the use of FRP in the construction of reinforced concrete structures.  6.2 Limitations of the Study There are some limitations which need to be acknowledged and addressed regarding the present study. The limitations of the study are summarized below: •  The effect of transverse reinforcement was accounted for in the development of the proposed design equations and this was based on 105 confined beam specimens which failed by splitting of concrete. Also, no comprehensive and systematic study was performed on the effect of transverse reinforcement on the bond behaviour of FRP rebars in concrete. Hence, more experiments are required to modify the proposed design equations.  •  The equation proposed for the slip corresponding to the peak bond stress was based on 97 beam bond tests. The data was not splitted based on the failure mode due to the lack of 97  sufficient data. Moreover, there was no specimen with sand coated bars for splitting mode of failure and hence, no conclusion could be made for sand coated bars having splitting failures. •  The bond stress-slip curves of the specimens failed by splitting of concrete showed three branches-two pre-peak and one post-peak. For simplicity and due to the lack of enough experimental data, one pre-peak and one post-peak branches were considered.  •  There was no bond stress-slip curve for specimens with sand coated FRP bars having splitting failure and hence, no equation was proposed for sand coated bars.  •  The number of bond tests with f c′ > 50 MPa was very small and hence, more tests are needed with high strength concrete.  6.3 Future Recommendations This study can be further improved with the availability of more literature. However, following are some recommendations for future investigation: •  More experimental works are needed on AFRP and CFRP reinforcing bars to verify whether there is any effect of the type of fibre on the bond behaviour of FRP rebars in concrete.  •  Studies are required to determine particularly the effect of rebar surface on the bond behaviour of FRP rebars in concrete.  •  Extensive experimental investigation is necessary for confined beam specimens to assure the effect of concrete confinement provided by the transverse reinforcement. Effect of transverse reinforcements made of FRP bars should also be investigated.  •  Bond behaviour of FRP rebars in high strength concrete should be investigated by using beam bond tests.  •  More bond stress-slip measurements are required to validate and modify the proposed bond stress-slip model. 98  Appendices  99  Appendix A Table A.1 Consolidated database of beam-type specimens for evaluating peak bond stress of FRP rebars in concrete SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  1  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  16.00  nr  nr  Tensile  2  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  16.00  nr  nr  Tensile  3  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  16.00  nr  nr  Tensile  4  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  24.00  nr  nr  Tensile  5  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  24.00  nr  nr  Tensile  6  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  24.00  nr  nr  Tensile  7  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  32.00  nr  nr  Tensile  8  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  32.00  nr  nr  Tensile  9  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  12.7  5.56  3.00  32.00  nr  nr  Tensile  10  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  16.00  nr  nr  Pullout  11  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  16.00  nr  nr  Pullout  12  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  16.00  nr  nr  Pullout  13  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  24.00  nr  nr  Splitting  14  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  24.00  nr  nr  Splitting  15  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  24.00  nr  nr  Splitting  16  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  32.00  nr  nr  Tensile  17  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  32.00  nr  nr  Tensile  18  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  19.05  5.56  3.00  32.00  nr  nr  Tensile  19  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  20.00  nr  nr  Pullout  20  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  20.00  nr  nr  Pullout  21  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  20.00  nr  nr  Pullout  22  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  25.00  nr  nr  Pullout  23  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  25.00  nr  nr  Pullout  100  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  24  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  25.00  nr  nr  Pullout  25  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  30.00  nr  nr  Pullout  26  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  30.00  nr  nr  Splitting  27  Daniali (1990)  NB  GFRP  Confined  Bottom  SW  25.4  5.56  3.00  30.00  nr  nr  Splitting  28  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  64.00  0.079  0.498  Tensile  29  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  64.00  0.079  0.494  Tensile  30  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  32.00  0.079  0.743  Tensile  31  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  32.00  0.079  0.734  Tensile  32  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  21.33  0.079  1.277  Tensile  33  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  21.33  0.079  1.087  Tensile  34  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  25.4  5.38  1.00  16.00  0.029  0.572  Pullout  35  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  25.4  5.38  1.00  16.00  0.029  0.611  Pullout  36  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  25.4  5.38  1.00  24.00  0.029  0.493  Pullout  37  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  25.4  5.38  1.00  24.00  0.029  0.510  Pullout  38  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  42.67  0.079  nr  Grip Failure  39  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  nr  9.525  5.38  2.67  42.67  0.079  nr  Grip Failure  40  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.00  16.00  0.029  0.590  Splitting  41  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.00  16.00  0.029  0.630  Splitting  42  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.00  24.00  0.029  0.508  Splitting  43  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.00  24.00  0.029  0.525  Splitting  44  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  5.25  2.67  42.67  0.079  na  Grip  45  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  5.25  2.67  42.67  0.079  na  Grip  46  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  5.25  2.67  64.00  0.079  0.510  Tensile  47  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  5.25  2.67  64.00  0.079  0.510  Tensile  48  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  7.18  2.67  32.00  0.079  0.556  Tensile  49  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  7.18  2.67  32.00  0.079  0.549  Tensile  101  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  50  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  7.18  2.67  21.33  0.079  0.955  Tensile  51  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  7.18  2.67  21.33  0.079  0.813  Tensile  52  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  12.7  7.18  6.00  8.00  0.059  1.253  Slip  53  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  12.7  7.18  6.00  8.00  0.059  1.423  Slip  54  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  6.35  7.18  12.00  24.00  0.118  1.676  Tensile  55  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  6.35  7.18  12.00  24.00  0.118  1.737  Tensile  56  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  12.7  8.08  6.00  16.00  0.059  1.137  Splitting  57  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  12.7  8.08  6.00  16.00  0.059  0.970  Splitting  58  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  8.08  8.00  10.67  0.079  1.739  Pullout  59  Faza & GangaRao (1990)  IHB  GFRP  Confined  Bottom  SW  9.525  8.08  8.00  10.67  0.079  1.217  Pullout  60  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  16.00  nr  nr  Tensile  61  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  16.00  nr  nr  Tensile  62  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  16.00  nr  nr  Tensile  63  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  24.00  nr  nr  Tensile  64  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  24.00  nr  nr  Tensile  65  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  24.00  nr  nr  Tensile  66  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  24.00  nr  nr  Tensile  67  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  32.00  nr  nr  Tensile  68  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  32.00  nr  nr  Tensile  69  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  32.00  nr  nr  Tensile  70  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  12.7  5.25  3.00  32.00  nr  nr  Tensile  71  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  16.00  nr  nr  Pullout  72  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  16.00  nr  nr  Pullout  73  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  16.00  nr  nr  Pullout  74  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  24.00  nr  nr  Splitting  75  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  24.00  nr  nr  Splitting  102  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  76  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  19.05  5.25  2.00  32.00  nr  nr  Pullout  77  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  20.00  nr  nr  Pullout  78  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  20.00  nr  nr  Pullout  79  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  20.00  nr  nr  Pullout  80  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  25.00  nr  nr  Pullout  81  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  25.00  nr  nr  Pullout  82  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  25.00  nr  nr  Pullout  83  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  30.00  nr  nr  Pullout  84  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  30.00  nr  nr  Splitting  85  Daniali (1991)  IHB  GFRP  Confined  Bottom  SW  25.4  5.25  1.75  30.00  nr  nr  Splitting  86  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  9.6774  5.46  2.00  10.50  0.000  2.028  Tensile  87  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  9.6774  5.91  4.00  15.75  0.000  1.621  Tensile  88  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  9.6774  5.91  6.00  21.00  0.000  1.277  Tensile  89  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  9.6774  6.99  2.00  10.50  0.000  1.728  Tensile  90  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  9.6774  6.99  4.00  15.75  0.000  1.330  Tensile  91  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  9.6774  6.99  6.00  21.00  0.000  0.885  Tensile  92  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  5.25  1.00  3.94  0.000  3.723  Splitting  93  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  5.25  2.00  3.94  0.000  4.671  Pullout  94  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  5.25  2.00  7.87  0.000  2.518  Pullout  95  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  5.46  2.00  10.50  0.000  2.186  Tensile  96  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  5.91  4.00  15.75  0.000  1.443  Tensile  97  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  5.91  6.00  21.00  0.000  1.070  Tensile  98  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  6.99  2.00  10.50  0.000  1.851  Tensile  99  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  6.99  4.00  15.75  0.000  1.166  Tensile  100  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  9.6774  6.99  6.00  21.00  0.000  0.998  Splitting  101  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  5.25  1.00  4.13  0.000  2.624  Splitting  103  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  102  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  5.25  2.00  4.13  0.000  3.352  Pullout  103  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  5.25  2.00  8.26  0.000  1.820  Pullout  104  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  6.25  2.00  16.53  0.000  0.925  Pullout  105  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  6.25  4.00  22.04  0.000  0.899  Pullout  106  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  6.25  6.00  24.79  0.000  0.842  Tensile  107  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  6.90  2.00  16.53  0.000  0.849  Pullout  108  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  6.90  4.00  22.04  0.000  0.776  Pullout  109  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  18.44  6.90  6.00  24.79  0.000  0.809  Tensile  110  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  5.25  1.00  4.13  0.000  2.107  Pullout  111  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  5.25  2.00  4.13  0.000  2.796  Pullout  112  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  5.25  2.00  8.26  0.000  1.484  Pullout  113  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  6.25  2.00  16.53  0.000  0.865  Pullout  114  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  6.25  4.00  22.04  0.000  0.845  Pullout  115  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  6.25  6.00  24.79  0.000  0.856  Tensile  116  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  6.90  2.00  16.53  0.000  0.824  Pullout  117  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  6.90  4.00  22.04  0.000  0.744  Pullout  118  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  18.44  6.90  6.00  24.79  0.000  0.719  Tensile  119  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  5.25  1.00  3.71  0.000  2.175  Splitting  120  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  5.25  2.00  3.71  0.000  3.093  Pullout  121  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  5.25  2.00  7.41  0.000  1.720  Pullout  122  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  6.30  2.00  20.39  0.000  0.708  Pullout  123  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  6.30  4.00  24.10  0.000  0.653  Pullout  124  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  6.30  6.00  27.80  0.000  0.602  Tensile  125  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  6.68  2.00  20.39  0.000  0.620  Pullout  126  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  6.68  4.00  24.10  0.000  0.567  Pullout  127  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Bottom  SW  27.407  6.68  6.00  27.80  0.000  0.513  Tensile  104  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  128  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  27.407  6.30  2.00  20.39  0.000  0.694  Pullout  129  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  27.407  6.30  4.00  24.10  0.000  0.625  Pullout  130  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  27.407  6.30  6.00  27.80  0.000  0.610  Tensile  131  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  27.407  6.68  2.00  20.39  0.000  0.594  Pullout  132  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  27.407  6.68  4.00  24.10  0.000  0.546  Pullout  133  Ehsani et al. (1993)  IHB  GFRP  Unconfined  Top  SW  27.407  6.68  6.00  27.80  0.000  0.534  Tensile  134  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  8  7.01  3.13  15.00  0.000  0.120  Slip  135  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  8  7.01  3.13  15.00  0.000  0.823  Splitting  136  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  10  7.01  2.50  15.00  0.000  1.326  Splitting  137  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  13  7.01  1.92  15.00  0.000  0.707  Splitting  138  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  10  7.01  2.50  15.00  0.000  1.112  Splitting  139  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  11  7.01  2.27  15.00  0.000  1.065  Tensile  140  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  12.5  7.01  2.00  15.00  0.000  0.850  Splitting  141  Kanakubo et al. (1993)  IHB  CFRP  Unconfined  Top  SC  8  7.01  3.13  15.00  0.000  1.195  Splitting  142  Kanakubo et al. (1993)  IHB  AFRP  Unconfined  Top  SC  12  7.01  2.08  15.00  0.000  1.076  Splitting  143  Kanakubo et al. (1993)  IHB  AFRP  Unconfined  Top  SC  12  7.01  2.08  15.00  0.000  1.004  Break of Coupler  144  Kanakubo et al. (1993)  IHB  AFRP  Unconfined  Top  SC  10  7.01  2.50  15.00  0.000  1.206  Splitting  145  Kanakubo et al. (1993)  IHB  GFRP  Unconfined  Top  SC  10  7.01  2.50  15.00  0.000  1.051  Splitting  146  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.10  4.00  40.00  0.314  na  Tensile  147  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.81  4.00  40.00  0.314  na  Tensile  148  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.42  4.00  40.00  0.314  0.941  Pullout  149  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.89  4.00  40.00  0.314  na  Tensile  150  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.16  4.00  20.00  0.314  2.210  Pullout  151  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.38  4.00  20.00  0.314  1.972  Pullout  152  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.28  4.00  20.00  0.314  1.060  Pullout  153  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.76  4.00  20.00  0.314  1.840  Pullout  105  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  154  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.37  4.00  10.00  0.314  2.497  Pullout  155  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.16  4.00  10.00  0.314  2.637  Pullout  156  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.19  4.00  10.00  0.314  0.791  Pullout  157  Makitani et al. (1993)  HB  CFRP  Confined  Bottom  SW  10  5.48  4.00  10.00  0.314  2.903  Pullout  158  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.38  4.00  40.00  0.314  na  Tensile  159  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.49  4.00  40.00  0.314  na  Tensile  160  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.22  4.00  40.00  0.314  1.340  Pullout  161  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.59  4.00  20.00  0.314  1.680  Pullout  162  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.64  4.00  20.00  0.314  2.181  Pullout  163  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.49  4.00  20.00  0.314  1.640  Pullout  164  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.01  4.00  10.00  0.314  3.194  Pullout  165  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.41  4.00  10.00  0.314  3.455  Pullout  166  Makitani et al. (1993)  HB  AFRP  Confined  Bottom  SW  10  5.39  4.00  10.00  0.314  2.206  Pullout  167  Makitani et al. (1993)  HB  GFRP  Confined  Bottom  SW  10  5.56  4.00  40.00  0.314  na  Tensile  168  Makitani et al. (1993)  HB  GFRP  Confined  Bottom  SW  10  5.10  4.00  20.00  0.314  na  Tensile  169  Makitani et al. (1993)  HB  GFRP  Confined  Bottom  SW  10  5.43  4.00  10.00  0.314  2.762  Pullout  170  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  10.00  0.393  1.563  Pullout  171  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  15.00  0.393  1.832  Pullout  172  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  20.00  0.393  1.976  Pullout  173  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  25.00  0.393  2.119  Pullout  174  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  30.00  0.393  2.245  Pullout  175  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  40.00  0.393  2.335  Pullout  176  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  50.00  0.393  2.030  Pullout  177  Makitani et al. (1993)  S  CFRP  Confined  Bottom  HL  8  5.57  5.00  60.00  0.393  1.473  Pullout  178  Benmokrane et al. (1996)  HB  GFRP  Confined  Bottom  HL  12.7  5.57  3.44  10.00  0.082  1.904  Pullout  179  Benmokrane et al. (1996)  HB  GFRP  Confined  Bottom  HL  15.9  5.57  2.64  10.00  0.066  1.311  Pullout  106  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  180  Benmokrane et al. (1996)  HB  GFRP  Confined  Bottom  HL  19.1  5.57  2.12  10.00  0.055  1.185  Pullout  181  Benmokrane et al. (1996)  HB  GFRP  Confined  Bottom  HL  25.4  5.57  1.47  10.00  0.041  1.149  Pullout  182  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  5.25  1.00  4.00  0.000  2.551  Splitting  183  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  5.25  2.00  4.00  0.000  3.255  Pullout  184  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  5.25  2.00  8.00  0.000  1.770  Pullout  185  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  6.26  2.00  16.00  0.000  0.894  Pullout  186  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  6.91  2.00  16.00  0.000  0.825  Pullout  187  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  6.26  4.00  21.33  0.000  0.862  Pullout  188  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  6.91  4.00  21.33  0.000  0.753  Pullout  189  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  5.25  1.00  3.56  0.000  2.037  Splitting  190  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  5.25  2.00  3.56  0.000  2.893  Pullout  191  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  5.25  2.00  7.11  0.000  1.618  Pullout  192  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  6.30  2.00  19.56  0.000  0.667  Pullout  193  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  6.69  2.00  19.56  0.000  0.598  Pullout  194  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  6.30  4.00  23.11  0.000  0.619  Pullout  195  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  6.88  4.00  23.11  0.000  0.553  Pullout  196  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  5.25  1.00  4.00  0.000  3.921  Splitting  197  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  5.25  2.00  4.00  0.000  4.854  Pullout  198  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  5.25  2.00  8.00  0.000  2.627  Pullout  199  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  5.25  1.00  4.00  0.000  2.037  Splitting  200  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  5.25  2.00  4.00  0.000  2.703  Pullout  201  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  5.25  2.00  8.00  0.000  1.447  Pullout  202  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  6.26  2.00  16.00  0.000  0.831  Pullout  203  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  6.91  2.00  16.00  0.000  0.796  Pullout  204  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  6.26  4.00  21.33  0.000  0.815  Pullout  205  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  6.91  4.00  21.33  0.000  0.724  Pullout  107  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  206  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  28.575  6.30  2.00  19.56  0.000  0.651  Pullout  207  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  28.575  6.69  2.00  19.56  0.000  0.568  Pullout  208  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  28.575  6.30  4.00  23.11  0.000  0.587  Pullout  209  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  28.575  6.88  4.00  23.11  0.000  0.523  Pullout  210  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  9.525  5.46  2.00  10.67  0.000  2.107  Tensile  211  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  9.525  7.00  2.00  10.67  0.000  1.729  Tensile  212  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  9.525  5.92  4.00  16.00  0.000  1.673  Tensile  213  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  9.525  7.00  4.00  16.00  0.000  1.329  Tensile  214  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  9.525  5.92  6.00  21.33  0.000  1.318  Tensile  215  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  9.525  7.00  6.00  21.33  0.000  0.886  Tensile  216  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  5.92  6.00  21.33  0.000  1.116  Tensile  217  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  7.00  6.00  21.33  0.000  1.000  Tensile  218  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  6.26  6.00  24.00  0.000  0.815  Tensile  219  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  6.91  6.00  24.00  0.000  0.709  Tensile  220  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  6.30  6.00  26.67  0.000  0.571  Tensile  221  Ehsani et al. (1996)  HB  GFRP  Unconfined  Bottom  HL  28.575  6.88  6.00  26.67  0.000  0.494  Tensile  222  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  5.46  2.00  10.67  0.000  2.308  Tensile  223  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  7.00  2.00  10.67  0.000  1.871  Tensile  224  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  5.92  4.00  16.00  0.000  1.504  Tensile  225  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  9.525  7.00  4.00  16.00  0.000  1.171  Tensile  226  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  6.26  6.00  24.00  0.000  0.831  Tensile  227  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  19.05  6.91  6.00  24.00  0.000  0.695  Tensile  228  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  28.575  6.30  6.00  26.67  0.000  0.571  Tensile  229  Ehsani et al. (1996)  HB  GFRP  Unconfined  Top  HL  28.575  6.88  6.00  26.67  0.000  0.523  Tensile  230  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  13.462  6.22  2.00  10.38  0.000  1.389  Splitting  231  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  13.462  6.22  2.00  10.38  0.000  1.558  Splitting  108  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  232  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  13.462  6.22  2.00  10.38  0.000  1.268  Splitting  233  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  19.304  6.22  2.00  13.16  0.000  1.084  Splitting  234  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  19.304  6.22  2.00  13.16  0.000  1.038  Splitting  235  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  19.304  6.22  2.00  13.16  0.000  1.014  Splitting  236  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  19.304  6.22  2.00  13.16  0.000  1.149  Splitting  237  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  19.304  6.22  2.00  13.16  0.000  0.903  Splitting  238  Shield and Retika (1996)  IHB  GFRP  Unconfined  Bottom  SW  19.304  6.22  2.00  13.16  0.000  0.982  Splitting  239  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  12.7  5.56  3.40  10.00  0.000  1.900  Pullout  240  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  SW  12.7  5.56  3.40  10.00  0.000  2.206  Pullout  241  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  15.875  5.56  2.60  10.08  0.000  1.309  Pullout  242  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  SW  15.875  5.56  2.60  10.08  0.000  1.936  Pullout  243  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  5.56  2.10  10.00  0.000  1.183  Pullout  244  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  25.4  5.56  1.50  10.00  0.000  1.147  Pullout  245  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  SW  25.4  5.56  1.50  10.00  0.000  1.327  Pullout  246  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  12.7  5.56  3.40  16.00  0.000  1.560  Tensile  247  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  5.56  2.10  16.00  0.000  0.951  Pullout  248  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  25.4  5.56  1.50  16.00  0.000  0.915  Pullout  249  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  12.7  5.56  3.40  6.00  0.000  2.027  Pullout  250  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  15.875  5.56  2.60  6.08  0.000  1.900  Pullout  251  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  19.05  5.56  2.10  6.00  0.000  1.274  Pullout  252  Tighiouart (1996)  HB  GFRP  Unconfined  Bottom  HL  25.4  5.56  1.50  6.00  0.000  1.255  Pullout  253  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  36.94  0.036  0.639  Splitting  254  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  36.94  0.073  0.657  Splitting  255  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  43.47  0.073  0.479  Splitting  256  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  43.47  0.073  0.638  Splitting  257  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  80.41  0.073  0.359  Splitting  109  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  258  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  80.41  0.073  0.359  Splitting  259  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  99.18  0.073  0.301  Splitting  260  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  12.446  5.56  2.40  99.18  0.073  0.298  Splitting  261  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  15.494  5.56  1.90  43.61  0.073  0.573  Splitting  262  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  15.494  5.56  1.90  43.61  0.058  0.578  Splitting  263  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  15.494  5.56  1.90  56.23  0.058  0.454  Splitting  264  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  15.494  5.56  1.90  56.23  0.058  0.491  Splitting  265  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  15.494  5.56  1.90  99.67  0.058  0.407  Splitting  266  Tighiouart et al. (1998)  S  GFRP  Confined  Bottom  HL  15.494  5.56  1.90  99.67  0.058  0.425  Splitting  267  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  12.7  5.57  3.44  6.00  0.058  2.030  Pullout  268  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  15.9  5.57  2.64  6.00  0.071  1.904  Pullout  269  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  19.1  5.57  2.12  6.00  0.057  1.275  Pullout  270  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  25.4  5.57  1.47  6.00  0.047  1.257  Pullout  271  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  12.7  5.57  3.44  10.00  0.036  1.904  Pullout  272  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  12.7  5.57  3.44  10.00  0.071  2.209  Pullout  273  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  15.9  5.57  2.64  10.00  0.071  1.311  Pullout  274  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  15.9  5.57  2.64  10.00  0.057  1.940  Pullout  275  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  19.1  5.57  2.12  10.00  0.057  1.185  Pullout  276  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  25.4  5.57  1.47  10.00  0.047  1.149  Pullout  277  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  25.4  5.57  1.47  10.00  0.036  1.329  Pullout  278  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  12.7  5.57  3.44  16.00  0.036  1.563  Slip  279  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  19.1  5.57  2.12  16.00  0.071  0.952  Pullout  280  Tighiouart et al. (1998)  HB  GFRP  Confined  Bottom  HL  25.4  5.57  1.47  16.00  0.047  0.593  Pullout  281  Tepfers et al. et al. (1998)  S  GFRP  Confined  Bottom  SW+SC  25  5.40  1.20  16.00  nr  0.790  Pullout  282  Tepfers et al. et al. (1998)  S  GFRP  Confined  Bottom  SW+SC  25  5.40  1.20  24.00  nr  0.744  Pullout  283  Tepfers et al. et al. (1998)  S  GFRP  Confined  Bottom  SW+SC  25  5.40  1.20  32.00  nr  0.588  Pullout  110  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  284  Cosenza et al. (1999)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.08  5.41  5.00  0.000  1.858  Pullout  285  Cosenza et al. (1999)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.32  5.41  5.00  0.000  2.609  Pullout  286  Cosenza et al. (1999)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.16  5.41  10.00  0.000  1.995  Tensile  287  Cosenza et al. (1999)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.32  5.41  10.00  0.000  2.293  Pullout  288  Cosenza et al. (1999)  HB  GFRP  Unconfined  Bottom  HL  12.7  7.21  5.41  20.00  0.000  1.040  Tensile  289  Cosenza et al. (1999)  HB  GFRP  Unconfined  Bottom  HL  12.7  7.42  5.41  20.00  0.000  0.998  Tensile  290  Cosenza et al. (1999)  HB  GFRP  Unconfined  Bottom  HL  12.7  7.07  5.41  30.00  0.000  0.651  Tensile  291  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  24.19  0.000  0.647  Tensile Spaghetti  292  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  24.19  0.000  0.668  Tensile Spaghetti  293  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  24.19  0.000  0.665  Tensile Spaghetti  294  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  24.19  0.000  0.644  Tensile Spaghetti  295  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  24.19  0.000  0.697  Tensile Spaghetti  296  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  24.19  0.000  0.711  Tensile Spaghetti  297  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  20.16  0.000  0.840  Splitting  298  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  20.16  0.000  0.747  Splitting  299  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  20.16  0.000  0.772  Splitting  300  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  20.16  0.000  0.751  Tensile  301  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  20.16  0.000  0.836  Splitting  302  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  20.16  0.000  0.879  Splitting  303  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  16.13  0.000  0.849  Splitting  304  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  16.13  0.000  0.897  Tensile Spaghetti  305  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  16.13  0.000  0.923  Tensile Spaghetti  306  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  16.13  0.000  0.891  Tensile Spaghetti  307  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  16.13  0.000  1.103  Tensile Spaghetti  308  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  3.00  16.13  0.000  0.918  Splitting  309  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  75.81  0.000  0.183  Tensile Spaghetti  111  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  310  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  75.81  0.000  0.247  Tensile Spaghetti  311  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  75.81  0.000  0.146  Tensile Spaghetti  312  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  75.81  0.000  0.211  Tensile Spaghetti  313  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  75.81  0.000  0.161  Tensile Spaghetti  314  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  75.81  0.000  0.255  Tensile Spaghetti  315  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  24.19  0.000  0.707  Tensile Spaghetti  316  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  24.19  0.000  0.485  Tensile Spaghetti  317  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  24.19  0.000  0.796  Splitting  318  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  24.19  0.000  0.562  Tensile Spaghetti  319  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  24.19  0.000  0.615  Tensile Spaghetti  320  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  24.19  0.000  0.640  Tensile Spaghetti  321  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  20.16  0.000  0.386  Tensile  322  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  20.16  0.000  0.785  Splitting  323  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  20.16  0.000  0.760  Tensile Spaghetti  324  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  20.16  0.000  0.683  Tensile Spaghetti  325  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  20.16  0.000  0.709  Splitting  326  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.66  2.00  20.16  0.000  0.726  Splitting  327  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.60  2.00  20.16  0.000  0.800  Tensile  328  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.60  2.00  20.16  0.000  0.706  Splitting  329  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  HL  15.748  6.60  2.00  20.16  0.000  0.732  Tensile Spaghetti  330  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  25.84  0.000  0.703  Splitting  331  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  25.84  0.000  0.746  Splitting  332  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  25.84  0.000  0.757  Splitting  333  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  25.84  0.000  0.720  Splitting  334  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  19.38  0.000  0.786  Splitting  335  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  19.38  0.000  0.752  Splitting  112  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  336  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  19.38  0.000  0.729  Splitting  337  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  19.38  0.000  0.954  Splitting  338  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  19.38  0.000  0.912  Splitting  339  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  3.00  19.38  0.000  0.877  Splitting  340  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  60.72  0.000  0.324  Tensile Spaghetti  341  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  32.30  0.000  0.621  Splitting  342  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  32.30  0.000  0.516  Splitting  343  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  32.30  0.000  0.712  Splitting  344  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  32.30  0.000  0.622  Splitting  345  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  25.84  0.000  0.686  Splitting  346  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  25.84  0.000  0.699  Splitting  347  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  25.84  0.000  0.808  Splitting  348  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  25.84  0.000  0.742  Splitting  349  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  25.84  0.000  0.814  Splitting  350  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  19.38  0.000  0.737  Splitting  351  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  19.38  0.000  0.760  Splitting  352  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  19.38  0.000  0.834  Splitting  353  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  19.38  0.000  0.709  Splitting  354  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  19.38  0.000  0.803  Splitting  355  Shield and Hanus (1999)  IHB  GFRP  Unconfined  Bottom  SW  19.66  6.60  2.00  19.38  0.000  0.814  Splitting  356  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  15.875  6.66  2.00  12.50  0.000  1.172  Splitting  357  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  15.875  6.66  2.00  15.00  0.000  1.257  Splitting  358  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  15.875  6.66  2.00  47.00  0.000  0.319  Tensile  359  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  15.875  6.66  3.00  10.00  0.000  1.406  Splitting  360  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  15.875  6.66  3.00  12.50  0.000  1.293  Splitting  361  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  15.875  6.66  3.00  15.00  0.000  1.067  Tensile  113  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  362  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  19.05  6.60  2.00  15.00  0.000  1.069  Splitting  363  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  19.05  6.60  2.00  20.00  0.000  1.032  Splitting  364  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  19.05  6.60  2.00  25.00  0.000  0.849  Splitting  365  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  19.05  6.60  2.00  47.00  0.000  0.482  Tensile  366  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  19.05  6.60  3.00  15.00  0.000  1.148  Splitting  367  Shield et al. (1999)  IHB  GFRP  Unconfined  Top  HL  19.05  6.60  3.00  20.00  0.000  1.006  Splitting  368  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  36.22  0.049  0.670  Splitting  369  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  36.22  0.049  0.688  Splitting  370  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  42.52  0.049  0.453  Splitting  371  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  42.52  0.049  0.602  Splitting  372  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  78.74  0.049  0.352  Splitting  373  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  78.74  0.049  0.352  Splitting  374  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  97.24  0.049  0.296  Splitting  375  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  12.7  5.57  2.36  97.24  0.049  0.293  Splitting  376  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  42.45  0.039  0.559  Splitting  377  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  42.45  0.039  0.564  Splitting  378  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  54.72  0.039  0.438  Splitting  379  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  54.72  0.039  0.474  Splitting  380  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  97.17  0.039  0.397  Splitting  381  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  97.17  0.039  0.415  Splitting  382  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  78.93  0.039  0.498  Compression  383  Tighiouart et al. (1999)  S  GFRP  Confined  Bottom  HL  15.9  5.57  1.89  78.93  0.039  0.535  Compression  384  Mosely (2000)  S  GFRP  Confined  Top  SW  15.875  6.21  2.40  28.80  0.022  0.368  Splitting  385  Mosely (2000)  S  GFRP  Confined  Top  HL  15.875  6.21  2.40  28.80  0.022  0.313  Splitting  386  Mosely (2000)  S  AFRP  Confined  Top  SW  15.875  6.21  2.40  28.80  0.022  0.389  Splitting  387  Mosely (2000)  S  GFRP  Confined  Top  SW  15.875  5.31  2.40  19.20  0.022  0.325  Splitting  114  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  388  Mosely (2000)  S  GFRP  Confined  Top  HL  15.875  5.31  2.40  19.20  0.022  0.332  Splitting  389  Mosely (2000)  S  AFRP  Confined  Top  SW  15.875  5.31  2.40  19.20  0.022  0.350  Splitting  390  Mosely (2000)  S  GFRP  Confined  Top  SW  15.875  6.37  2.40  19.20  0.022  0.462  Splitting  391  Mosely (2000)  S  GFRP  Confined  Top  HL  15.875  6.37  2.40  19.20  0.022  0.437  Splitting  392  Mosely (2000)  S  AFRP  Confined  Top  SW  15.875  6.37  2.40  19.20  0.022  0.485  Splitting  393  Peece (2000)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.32  9.30  5.00  0.000  2.603  Pullout  394  Peece (2000)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.08  9.30  5.00  0.000  1.856  Pullout  395  Peece (2000)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.32  9.30  10.00  0.000  1.939  Tensile  396  Peece (2000)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.08  9.30  10.00  0.000  2.377  Tensile  397  Peece (2000)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.16  9.30  20.00  0.000  1.218  Tensile  398  Peece (2000)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.32  9.30  20.00  0.000  1.165  Tensile  399  Peece (2000)  HB  GFRP  Unconfined  Bottom  HL  12.7  7.20  9.30  30.00  0.000  0.640  Tensile  400  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  12.7  5.38  5.50  5.00  0.018  3.302  Pullout  401  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  12.7  5.38  5.50  5.00  0.018  2.765  Pullout  402  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  12.7  5.38  5.50  5.00  0.018  3.968  Pullout  403  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  12.7  5.38  5.50  5.00  0.018  3.596  Pullout  404  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  12.7  5.38  5.50  7.50  0.018  2.816  Pullout  405  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  12.7  5.38  5.50  7.50  0.018  3.021  Pullout  406  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  15.875  5.38  4.40  5.00  0.015  3.507  Pullout  407  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  15.875  5.38  4.40  5.00  0.015  3.737  Pullout  408  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  15.875  5.38  4.40  7.50  0.015  4.620  Pullout  409  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  15.875  5.38  4.40  7.50  0.015  2.278  Pullout  410  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  19.05  5.38  3.70  5.00  0.012  2.918  Pullout  411  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  19.05  5.38  3.70  5.00  0.012  3.085  Pullout  412  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  19.05  5.38  3.70  7.50  0.012  2.688  Pullout  413  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SW  19.05  5.38  3.70  7.50  0.012  2.726  Pullout  115  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  414  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  12.7  5.38  5.50  5.00  0.018  3.763  Pullout  415  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  12.7  5.38  5.50  5.00  0.018  3.904  Pullout  416  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  12.7  5.38  5.50  5.00  0.018  3.558  Pullout  417  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  12.7  5.38  5.50  5.00  0.018  4.032  Pullout  418  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  12.7  5.38  5.50  7.50  0.018  3.213  Pullout  419  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  12.7  5.38  5.50  7.50  0.018  3.417  Pullout  420  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  15.875  5.38  4.40  5.00  0.015  3.225  Pullout  421  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  15.875  5.38  4.40  5.00  0.015  2.061  Pullout  422  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  15.875  5.38  4.40  7.50  0.015  4.070  Pullout  423  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  15.875  5.38  4.40  7.50  0.015  4.236  Pullout  424  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  19.05  5.38  3.70  5.00  0.012  2.854  Pullout  425  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  19.05  5.38  3.70  5.00  0.012  3.136  Pullout  426  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  19.05  5.38  3.70  7.50  0.012  2.675  Pullout  427  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  HL  19.05  5.38  3.70  7.50  0.012  2.880  Pullout  428  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  12.7  4.84  5.50  5.00  0.018  4.367  Pullout  429  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  12.7  4.84  5.50  5.00  0.018  2.304  Pullout  430  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  12.7  4.84  5.50  7.50  0.018  3.770  Pullout  431  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  12.7  4.84  5.50  7.50  0.018  3.755  Pullout  432  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  15.875  4.84  4.40  5.00  0.015  3.983  Pullout  433  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  15.875  4.84  4.40  5.00  0.015  3.528  Pullout  434  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  15.875  4.84  4.40  7.50  0.015  3.940  Pullout  435  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  15.875  4.84  4.40  7.50  0.015  1.892  Pullout  436  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  19.05  4.84  3.70  5.00  0.012  3.215  Pullout  437  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  19.05  4.84  3.70  5.00  0.012  3.030  Pullout  438  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  19.05  4.84  3.70  7.50  0.012  3.386  Pullout  439  Defreese & Wollmann (2001)  IHB  GFRP  Confined  Bottom  SC  19.05  4.84  3.70  7.50  0.012  3.058  Pullout  116  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  440  Pecce et al. (2001)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.08  9.34  5.00  0.000  1.858  Pullout  441  Pecce et al. (2001)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.32  9.34  5.00  0.000  2.609  Pullout  442  Pecce et al. (2001)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.32  9.34  10.00  0.000  2.293  Pullout  443  Pecce et al. (2001)  HB  GFRP  Unconfined  Bottom  HL  12.7  6.16  9.34  10.00  0.000  1.995  Tensile  444  Pecce et al. (2001)  HB  GFRP  Unconfined  Bottom  HL  12.7  7.21  9.34  20.00  0.000  1.040  Tensile  445  Pecce et al. (2001)  HB  GFRP  Unconfined  Bottom  HL  12.7  7.42  9.34  20.00  0.000  0.998  Tensile  446  Pecce et al. (2001)  HB  GFRP  Unconfined  Bottom  HL  12.7  7.07  9.34  30.00  0.000  0.651  Tensile  447  Maji and Orozco (2005)  HB  CFRP  Unconfined  Bottom  SW  6.35  6.82  3.12  78.00  0.000  0.111  Pullout  448  Maji and Orozco (2005)  HB  CFRP  Unconfined  Bottom  SW  6.35  6.82  3.12  78.00  0.000  0.148  Pullout  449  Maji and Orozco (2005)  HB  CFRP  Unconfined  Bottom  SW  6.35  6.82  3.12  78.00  0.000  0.223  Pullout  450  Maji and Orozco (2005)  HB  CFRP  Unconfined  Bottom  SW  6.35  6.82  3.12  78.00  0.000  0.257  Pullout  451  Maji and Orozco (2005)  HB  CFRP  Unconfined  Bottom  SW  6.35  6.82  3.12  78.00  0.000  0.279  Pullout  452  Maji and Orozco (2005)  HB  CFRP  Unconfined  Bottom  SW  6.35  6.82  3.12  78.00  0.000  0.316  Compression  453  Maji and Orozco (2005)  HB  CFRP  Unconfined  Bottom  SW  6.35  6.82  3.12  78.00  0.000  0.347  Compression  454  Aly and Benmokrane (2005)  S  GFRP  Confined  Bottom  SC  19.1  6.32  2.09  36.65  0.018  0.443  Splitting  455  Aly and Benmokrane (2005)  S  GFRP  Confined  Bottom  SC  19.1  6.32  1.31  36.65  0.018  0.506  Splitting  456  Aly and Benmokrane (2005)  S  GFRP  Confined  Bottom  SC  19.1  6.32  2.09  36.65  0.018  0.522  Splitting  457  Aly and Benmokrane (2005)  S  GFRP  Confined  Bottom  SC  19.1  6.32  3.66  36.65  0.018  0.459  Splitting  458  Aly and Benmokrane (2005)  S  GFRP  Confined  Bottom  SC  19.1  6.32  2.09  36.65  0.018  0.569  Splitting  459  Aly and Benmokrane (2005)  S  GFRP  Confined  Bottom  SC  19.1  6.32  3.66  36.65  0.018  0.506  Splitting  460  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  7.00  3.37  68.42  0.035  0.993  Tensile  461  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.40  3.37  52.63  0.035  0.907  Splitting  462  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.40  3.37  52.63  0.035  0.828  Splitting  463  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  7.00  3.37  68.42  0.035  0.733  Splitting  464  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.56  3.37  84.21  0.035  0.570  Splitting  465  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.40  3.37  52.63  0.035  0.747  Splitting  117  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  466  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.56  3.37  68.42  0.035  0.868  Splitting  467  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.40  3.37  115.79  0.035  0.743  Splitting  468  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.32  3.37  52.63  0.035  1.094  Splitting  469  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  12.7  7.00  2.52  39.37  0.026  0.859  Splitting  470  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  12.7  6.56  2.52  62.99  0.026  0.718  Splitting  471  Aly et al. (2006)  S  GFRP  Confined  Bottom  SC  19.1  6.40  1.68  26.18  0.018  0.562  Splitting  472  Aly et al. (2006)  S  GFRP  Confined  Bottom  SC  19.1  6.56  1.68  36.65  0.018  0.500  Splitting  473  Aly et al. (2006)  S  GFRP  Confined  Bottom  SC  19.1  6.40  1.68  41.88  0.018  0.515  Splitting  474  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.32  3.37  84.21  0.035  0.816  Tensile  475  Aly et al. (2006)  S  CFRP  Confined  Bottom  SC  9.5  6.32  3.37  147.37  0.035  0.360  Shear  476  Aly et al. (2006)  S  GFRP  Confined  Bottom  SC  15.9  7.00  2.01  31.45  0.021  0.577  Tensile  477  Aly et al. (2006)  S  GFRP  Confined  Bottom  SC  15.9  6.56  2.01  44.03  0.021  0.450  Tensile  478  Aly et al. (2006)  S  GFRP  Confined  Bottom  SC  19.1  6.40  1.68  57.59  0.018  0.400  Tensile  479  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  52.63  0.035  1.094  Splitting  480  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  84.21  0.035  0.816  Tensile  481  Aly (2007)  S  CFRP  Confined  Bottom  SC  12.7  6.32  3.15  39.37  0.026  0.950  Splitting  482  Aly (2007)  S  CFRP  Confined  Bottom  SC  12.7  6.32  3.15  62.99  0.026  0.745  Splitting  483  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  52.63  0.035  0.838  Splitting  484  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  68.42  0.035  0.811  Splitting  485  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  84.21  0.035  0.591  Splitting  486  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  52.63  0.035  0.756  Splitting  487  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  68.42  0.035  0.900  Splitting  488  Aly (2007)  S  CFRP  Confined  Bottom  SC  9.5  6.32  4.21  115.79  0.035  0.753  Splitting  489  Aly (2007)  S  CFRP  Confined  Bottom  SC  15.9  6.32  2.52  31.45  0.021  0.640  Tensile  490  Aly (2007)  S  CFRP  Confined  Bottom  SC  15.9  6.32  2.52  44.03  0.021  0.466  Tensile  491  Aly (2007)  S  CFRP  Confined  Bottom  SC  19.1  6.32  2.09  26.18  0.018  0.569  Splitting  118  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  492  Aly (2007)  S  CFRP  Confined  Bottom  SC  19.1  6.32  2.09  36.65  0.018  0.519  Splitting  493  Aly (2007)  S  CFRP  Confined  Bottom  SC  19.1  6.32  2.09  41.88  0.018  0.522  Splitting  494  Aly (2007)  S  CFRP  Confined  Bottom  SC  19.1  6.32  2.09  57.59  0.018  0.405  Tensile  495  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  10  5.77  3.80  10.00  0.154  1.629  Pullout  496  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  16  5.77  2.38  10.00  0.096  0.399  Pullout  497  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  10  5.69  3.80  15.00  0.154  1.774  Pullout  498  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  10  5.59  3.80  20.00  0.154  2.163  Pullout  499  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  16  5.59  2.38  20.00  0.096  1.716  Pullout  500  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  10  6.07  3.80  10.00  0.154  2.206  Pullout  501  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  16  6.07  2.38  10.00  0.096  1.268  Pullout  502  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  10  6.43  3.80  15.00  0.154  2.471  Pullout  503  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  16  6.44  2.38  15.00  0.096  1.847  Splitting  504  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  10  6.27  3.80  20.00  0.154  1.882  Pullout  505  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  16  6.27  2.38  20.00  0.096  1.468  Pullout  506  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  10  5.77  3.80  10.00  0.154  0.139  Pullout  507  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  19  5.77  2.00  10.00  0.081  0.589  Pullout  508  Okelo (2007)  HB  CFRP  Confined  Bottom  SW  16  5.69  2.38  15.00  0.096  1.599  Compression  509  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  10  5.69  3.80  15.00  0.154  1.827  Tensile  510  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  19  5.69  2.00  15.00  0.081  1.195  Compression  511  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  10  5.59  3.80  20.00  0.154  2.038  Tensile  512  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  19  5.59  2.00  20.00  0.081  1.233  Compression  513  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  10  6.07  3.80  10.00  0.154  2.831  Tensile  514  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  19  6.07  2.00  10.00  0.081  1.119  Compression  515  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  10  6.44  3.80  15.00  0.154  1.847  Tensile  516  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  19  6.52  2.00  15.00  0.081  1.058  Compression  517  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  10  6.27  3.80  20.00  0.154  1.531  Tensile  119  SI  Ref  Test Type  FRP Type  Confinement  Bar Position  Bar  db  Surface  f c′  (mm)  c db  lembed db  Atr snd b  τm  Failure Mode  f c′  518  Okelo (2007)  HB  GFRP  Confined  Bottom  SW  19  6.27  2.00  20.00  0.081  1.133  Compression  519  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  6.19  1.89  76.42  0.041  0.646  Splitting  520  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  6.19  1.89  82.08  0.041  0.743  Splitting  521  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  6.19  1.89  82.08  0.041  0.873  Splitting  522  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  6.34  1.89  61.32  0.041  0.410  Splitting  523  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  6.34  1.89  61.32  0.041  0.473  Splitting  524  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  6.34  1.89  61.32  0.041  0.615  Splitting  525  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  6.34  1.89  61.32  0.041  0.584  Splitting  526  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  5.92  1.89  66.04  0.041  0.355  Splitting  527  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  5.92  1.89  66.04  0.041  0.744  Splitting  528  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  5.92  1.89  66.04  0.041  0.507  Splitting  529  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  5.92  1.89  70.75  0.041  0.558  Splitting  530  Thamrin and Kaku (2007)  nr  CFRP  Confined  Bottom  HL  10.6  5.92  1.89  75.47  0.041  0.372  Splitting  531  Rafi et al. (2007)  nr  CFRP  Confined  Bottom  SW  9.5  6.93  2.11  95.26  0.046  0.462  Shear  532  Rafi et al. (2007)  nr  CFRP  Confined  Bottom  SW  9.5  6.86  2.11  95.26  0.046  0.481  Compression  533  Mosley et al. (2008)  S  GFRP  Confined  Bottom  HL  16  6.21  2.38  28.56  0.021  0.369  Splitting  534  Mosley et al. (2008)  S  GFRP  Confined  Bottom  HL  16  6.15  2.38  28.56  0.032  0.316  Splitting  535  Mosley et al. (2008)  S  GFRP  Confined  Bottom  HL  16  5.39  2.38  19.06  0.032  0.321  Splitting  536  Mosley et al. (2008)  S  GFRP  Confined  Bottom  HL  16  5.20  2.38  19.06  0.032  0.341  Splitting  537  Mosley et al. (2008)  S  GFRP  Confined  Bottom  HL  16  6.42  2.38  19.06  0.032  0.460  Splitting  538  Mosley et al. (2008)  S  GFRP  Confined  Bottom  HL  16  6.40  2.38  19.06  0.032  0.436  Splitting  539  Mosley et al. (2008)  S  AFRP  Confined  Bottom  HL  16  6.26  2.38  28.56  0.032  0.387  Splitting  540  Mosley et al. (2008)  S  AFRP  Confined  Bottom  HL  16  5.36  2.38  19.06  0.032  0.347  Splitting  541  Mosley et al. (2008)  S  AFRP  Confined  Bottom  HL  16  6.29  2.38  19.06  0.032  0.493  Splitting  Note: Ref = Reference article; NB = Notched beam specimen; HB = Hinged beam specimen; S = Splice beam specimen; IHB = Inverted hinged beam specimen; nr = Not reported; HL = Helical lugged bars; SC = Sand coated bars; SW = Spiral wrapped bars; SW+SC = Spiral wrapped bars with sand coating  120  Appendix B Table B.1 Database of beam-type specimens failed by concrete splitting for deriving bond stress-slip relationship of FRP rebars in concrete Beam  1  2  3  Ref  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  FRP  Test  Type  Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c  c db  lembed  (mm)  (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  0.75  0  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  0  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  0.25  0.75  1.5  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  0.5  0.75  2.5  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  0.75  0.75  3.4  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  0  1.5  0  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  0.25  1.5  2  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  0.5  1.5  2.5  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  1  1.5  3.7  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  1.5  1.5  4  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  2  1.5  3.6  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  3  1.5  2.4  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  4  1.5  1.7  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  5  1.5  1.5  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  6  1.5  1.3  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0084  7  1.5  1.2  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  0  1.25  0  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  0.25  1.25  2  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  0.5  1.25  2.5  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  1  1.25  4.2  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  1.25  1.25  4.3  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  2  1.25  3.6  4.3  121  Beam  Ref  FRP  Test  Type  Type  Bar Surface  Confinement  db (mm)  4  5  6  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  f c′  (MPa)  c (mm)  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  3  1.25  2.7  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  4  1.25  2.5  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  5  1.25  2.3  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  6  1.25  2.2  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  7  1.25  2.1  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  0  1.5  0  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  0.25  1.5  1.7  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  0.5  1.5  2.3  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  1  1.5  3.9  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  1.5  1.5  4.5  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  2  1.5  4  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  3  1.5  2.7  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  4  1.5  2.5  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  5  1.5  2.3  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  6  1.5  2.2  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0249  7  1.5  2.1  4.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  0  1.5  0  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  0.25  1.5  1.5  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  0.5  1.5  2  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  1  1.5  2.6  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0000  1.5  1.5  3.7  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  0  3.2  0  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  0.25  3.2  1.5  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  0.5  3.2  2  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  1  3.2  2.7  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  2  3.2  3.8  4.7  122  Beam  7  8  9  Ref  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  FRP  Test  Type  Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c  c db  lembed  (mm)  (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  3  3.2  4.2  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  3.2  3.2  4.7  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  4  3.2  3.5  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  5  3.2  3  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  6  3.2  2.5  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  7  3.2  2.3  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0168  8  3.2  2.1  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  0  2  0  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  0.25  2  1  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  0.5  2  1.5  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  1  2  2.2  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  2  2  3.5  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  6  2  3  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  7  2  2.9  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  8  2  2.7  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  9  2  2.5  3.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  27.50  2.292  300  0.0147  10  2  2.3  3.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0000  0  0.75  0  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0000  0.5  0.75  2  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0000  0.75  0.75  2.8  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0000  1  0.75  2.6  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  0  1  0  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  0.5  1  3  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  1  1  4.1  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  2  1  3  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  3  1  2.2  4.1  123  Beam  10  11  Ref  Kanakubo et al. (1993)  Kanakubo et al. (1993)  FRP  Test  Type  Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c  c db  lembed  (mm)  (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  4  1  2  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  5  1  1.8  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  6  1  1.7  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0084  7  1  1.6  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  0  1.2  0  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  0.5  1.2  3.2  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  1  1.2  4.2  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  1.2  1.2  4.5  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  2  1.2  4.2  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  3  1.2  4  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  4  1.2  3.8  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  5  1.2  3.5  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  6  1.2  3.3  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  7  1.2  3.1  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0168  8  1.2  2.8  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  0  1.2  0  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  0.5  1.2  3.3  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  1  1.2  4.4  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  1.2  1.2  4.6  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  2  1.2  4.2  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  3  1.2  4.1  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  4  1.2  3.8  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  5  1.2  3.7  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  6  1.2  3.5  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  7  1.2  3.3  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  27.50  2.292  300  0.0147  8  1.2  3  4.6  124  Beam  Ref  FRP  Test  Type  Type  Bar Surface  Confinement  db (mm)  12  13  14  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  f c′  (MPa)  c (mm)  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  25.00  1.923  300  0.0000  0  0.75  0  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  25.00  1.923  300  0.0000  0.25  0.75  2.3  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  25.00  1.923  300  0.0000  0.5  0.75  3.2  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  25.00  1.923  300  0.0000  0.75  0.75  3.5  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  0  1.25  0  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  0.25  1.25  2.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  0.5  1.25  3.2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  1  1.25  4.2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  1.25  1.25  4.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  2  1.25  3.6  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  3  1.25  2.6  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  4  1.25  2.1  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  5  1.25  1.9  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  6  1.25  1.7  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  7  1.25  1.5  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  0  1.25  0  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  0.25  1.25  2.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  0.5  1.25  3.2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  1  1.25  4.2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  1.25  1.25  4.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  2  1.25  3.5  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  3  1.25  3.1  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  4  1.25  3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  5  1.25  2.8  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  6  1.25  2.6  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  7  1.25  2.4  4.3  125  Beam  15  16  17  Ref  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  FRP  Test  Type  Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c  c db  lembed  (mm)  (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  8  1.25  2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  0  1.1  0  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  0.25  1.1  2.3  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  0.5  1.1  3.2  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  1  1.1  4.4  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  1.1  1.1  4.5  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  2  1.1  3.8  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  3  1.1  3.2  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  4  1.1  3  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  5  1.1  2.8  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  6  1.1  2.5  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  7  1.1  2.3  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0230  8  1.1  2.1  4.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0000  0  0.75  0  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0000  0.25  0.75  1.5  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0000  0.5  0.75  2  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0000  0.75  0.75  2.4  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0000  1  0.75  2.3  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0000  2  0.75  2.2  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  0  1.5  0  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  0.25  1.5  1.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  0.5  1.5  2  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  1  1.5  2.6  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  1.5  1.5  3.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  2  1.5  3.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  3  1.5  2.7  3.5  126  Beam  18  19  Ref  Kanakubo et al. (1993)  Kanakubo et al. (1993)  FRP  Test  Type  Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c  c db  lembed  (mm)  (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  4  1.5  2  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  5  1.5  1.4  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  6  1.5  1  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  7  1.5  0.8  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0078  8  1.5  0.7  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  0  2  0  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  0.25  2  1.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  0.5  2  2  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  1  2  2.6  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  2  2  3.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  3  2  2.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  4  2  2  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  5  2  1.7  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  6  2  1.6  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0155  7  2  1.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  0  2.75  0  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  0.25  2.75  1.5  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  0.5  2.75  2  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  1  2.75  2.6  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  2  2.75  3.4  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  2.75  2.75  3.8  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  3  2.75  3.7  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  4  2.75  3.1  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  5  2.75  2.4  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  6  2.75  1.8  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  7  2.75  1.3  3.8  127  Beam  Ref  FRP  Test  Type  Type  Bar Surface  Confinement  db (mm)  20  21  22  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  f c′  (MPa)  c  c db  lembed  (mm)  (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  27.50  2.115  300  0.0130  8  2.75  1.2  3.8  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0000  0  1.5  0  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0000  0.5  1.5  1.5  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0000  1  1.5  2  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0000  1.5  1.5  2.5  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  0  1.2  0  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  0.5  1.2  2.6  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  1  1.2  3.5  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  1.2  1.2  3.7  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  2  1.2  3  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  3  1.2  2.4  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  4  1.2  2  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  5  1.2  1.8  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  6  1.2  1.7  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  7  1.2  1.6  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0078  8  1.2  1.5  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  0  1.7  0  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  0.5  1.7  2.2  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  1  1.7  3.2  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  1.7  1.7  3.9  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  2  1.7  3.8  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  3  1.7  3.1  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  4  1.7  3.1  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  5  1.7  3  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  6  1.7  2.5  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  7  1.7  2.4  3.9  128  Beam  23  Ref  Kanakubo et al. (1993)  FRP  Test  Type  Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c  c db  lembed  (mm)  (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0155  8  1.7  2.2  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  0  1.7  0  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  0.5  1.7  1.8  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  1  1.7  3  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  1.7  1.7  4  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  2  1.7  3.6  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  3  1.7  3.4  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  4  1.7  3.2  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  5  1.7  3.1  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  6  1.7  2.9  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  7  1.7  2.8  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  27.50  2.115  300  0.0135  8  1.7  2.7  4  129  Table B.2 Database of beam-type specimens failed by rebar pullout for deriving bond stress-slip relationship of FRP rebars in concrete Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  Surface  1  2  Makitani et al. (1993)  Makitani et al. (1993)  (mm)  (MPa)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  0  0.05  0  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  0.05  0.05  13.8  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  0.1  0.05  13.6  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  0.2  0.05  13.4  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  0.5  0.05  13  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  1  0.05  12.8  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  2  0.05  13.2  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  3  0.05  13.6  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  4  0.05  13.8  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  5  0.05  13.6  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  6  0.05  13.5  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  7  0.05  13.4  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  8  0.05  13.2  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  9  0.05  13  13.8  CFRP  HB  SC  Confined  10  33.7  5.805  5.00  100  0.1570  10  0.05  12.8  13.8  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  0  0.15  0  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  0.1  0.15  18.2  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  0.15  0.15  19  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  0.5  0.15  18.6  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  1  0.15  18  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  2  0.15  17  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  3  0.15  15.6  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  4  0.15  15  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  5  0.15  14  19  130  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  3  4  Makitani et al. (1993)  Makitani et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  6  0.15  13.2  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  7  0.15  12.6  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  8  0.15  12  19  AFRP  HB  SC  Confined  10  30.1  5.486  5.00  100  0.1570  9  0.15  11.8  19  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  0  0.5  0  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  0.2  0.5  3.8  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  0.5  0.5  4.3  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  1  0.5  4.1  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  2  0.5  3.9  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  3  0.5  3.7  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  4  0.5  3.5  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  5  0.5  3  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  6  0.5  3.6  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  7  0.5  3.8  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  8  0.5  3.8  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  9  0.5  3.8  4.3  CFRP  HB  SW  Confined  10  29.4  5.422  5.00  100  0.1570  10  0.5  3.8  4.3  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  0  0.33  0  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  0.01  0.33  3.5  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  0.1  0.33  6.7  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  0.2  0.33  9.2  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  0.33  0.33  10.6  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  0.5  0.33  9.5  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  0.75  0.33  9.3  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  1  0.33  8.8  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  1.25  0.33  8.6  10.6  131  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  5  6  7  Makitani et al. (1993)  Makitani et al. (1993)  Makitani et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  95.4  0.0494  1.5  0.33  8.2  10.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  0  0.16  0  7.1  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  0.01  0.16  3.5  7.1  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  0.1  0.16  6.8  7.1  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  0.16  0.16  7.1  7.1  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  0.2  0.16  7  7.1  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  0.5  0.16  6.8  7.1  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  0.75  0.16  6.5  7.1  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  114.6  0.0411  1  0.16  6.1  7.1  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  0  0.075  0  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  0.01  0.075  1.6  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  0.075  0.075  7  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  0.1  0.075  6.9  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  0.2  0.075  6.8  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  0.5  0.075  6.5  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  0.75  0.075  5.8  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  1  0.075  5.1  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  1.25  0.075  4.7  7  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  152.4  0.0309  1.5  0.075  4.4  7  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  0  0.3  0  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  0.01  0.3  1.9  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  0.1  0.3  7.3  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  0.2  0.3  8.3  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  0.3  0.3  10.6  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  0.5  0.3  10  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  0.75  0.3  9.8  10.6  132  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  8  9  10  Makitani et al. (1993)  Makitani et al. (1993)  Makitani et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  1  0.3  9.3  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  1.25  0.3  8.9  10.6  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  127  0.0618  1.5  0.3  8.2  10.6  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  0  0.85  0  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  0.01  0.85  1.1  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  0.1  0.85  5.8  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  0.2  0.85  6.1  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  0.5  0.85  7.6  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  0.75  0.85  7.7  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  0.85  0.85  7.8  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  1  0.85  7.5  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  1.25  0.85  7.3  7.8  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  159  0.0494  1.5  0.85  7.2  7.8  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  0  0.25  0  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  0.01  0.25  1  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  0.1  0.25  3.8  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  0.2  0.25  5.6  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  0.25  0.25  6.6  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  0.5  0.25  6.5  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  0.75  0.25  6.4  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  1  0.25  6.2  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  1.25  0.25  6  6.6  GFRP  HB  SW  Confined  19.1  31  5.568  2.62  191  0.0411  1.5  0.25  6  6.6  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  0  0.2  0  6.4  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  0.01  0.2  0.8  6.4  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  0.1  0.2  3.4  6.4  133  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  11  12  13  Makitani et al. (1993)  Makitani et al. (1993)  Makitani et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  0.15  0.2  5.7  6.4  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  0.2  0.2  6.4  6.4  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  0.5  0.2  6.2  6.4  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  0.75  0.2  6  6.4  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  1  0.2  5.8  6.4  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  254  0.0309  1.25  0.2  5.3  6.4  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  0  0.25  0  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  0.01  0.25  2  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  0.1  0.25  6.6  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  0.2  0.25  7.5  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  0.25  0.25  10  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  0.5  0.25  10  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  0.75  0.25  9.9  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  1  0.25  9.8  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  1.25  0.25  9.6  10  GFRP  HB  SW  Confined  12.7  31  5.568  3.94  203.2  0.0618  1.5  0.25  9.5  10  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  0  0.75  0  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  0.01  0.75  2.7  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  0.1  0.75  4.8  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  0.2  0.75  5.3  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  0.5  0.75  6.1  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  0.75  0.75  6.2  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  1  0.75  6  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  1.25  0.75  6  6.2  GFRP  HB  SW  Confined  15.9  31  5.568  3.14  305.6  0.0494  1.5  0.75  6  6.2  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  0  0.5  0  5.8  134  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  14  15  Makitani et al. (1993)  Makitani et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  0.01  0.5  1  5.8  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  0.1  0.5  3.3  5.8  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  0.2  0.5  3.6  5.8  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  0.5  0.5  5.8  5.8  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  0.75  0.5  5.5  5.8  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  1  0.5  5.2  5.8  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  1.25  0.5  5  5.8  GFRP  HB  SW  Confined  25.4  31  5.568  1.97  406.4  0.0309  1.5  0.5  4.9  5.8  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  0  5.8  0  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  0.5  5.8  7.8  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  1  5.8  9  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  2  5.8  10.6  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  3  5.8  12  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  4  5.8  13  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  5  5.8  13.6  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  5.8  5.8  14  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  6  5.8  13.6  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  7  5.8  12.6  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  8  5.8  10.3  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  9  5.8  7.6  14  CFRP  HB  HL  Confined  10  26  5.099  5.00  100  0.1570  10  5.8  6  14  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  0  10  0  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  0.5  10  10.2  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  1  10  10.8  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  2  10  11.4  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  3  10  12  15.6  135  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  16  17  18  Makitani et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  4  10  12.8  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  5  10  13.4  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  6  10  14  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  7  10  14.8  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  8  10  15  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  9  10  15.2  15.6  GFRP  HB  HL  Confined  10  30.9  5.559  5.00  100  0.1570  10  10  15.6  15.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  0  4.5  0  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  0.5  4.5  8  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  1  4.5  9.6  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  2  4.5  11  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  3  4.5  14.2  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  4  4.5  15.6  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  4.5  4.5  16.6  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  5  4.5  16  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  6  4.5  15.6  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  7  4.5  15.2  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  8  4.5  15  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  9  4.5  14.8  16.6  AFRP  HB  HL  Confined  10  28.9  5.376  5.00  100  0.1570  10  4.5  14.6  16.6  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  0  0.75  0  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  0.25  0.75  1.5  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  0.5  0.75  2.5  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  0.75  0.75  3.4  3.4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  0  1.5  0  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  0.25  1.5  2  4  136  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  19  20  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  0.5  1.5  2.5  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  1  1.5  3.7  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  1.5  1.5  4  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  2  1.5  3.6  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  3  1.5  2.4  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  4  1.5  1.7  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  5  1.5  1.5  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  6  1.5  1.3  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0084  7  1.5  1.2  4  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  0  1.25  0  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  0.25  1.25  2  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  0.5  1.25  2.5  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  1  1.25  4.2  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  1.25  1.25  4.3  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  2  1.25  3.6  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  3  1.25  2.7  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  4  1.25  2.5  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  5  1.25  2.3  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  6  1.25  2.2  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  7  1.25  2.1  4.3  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  0  1.5  0  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  0.25  1.5  1.7  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  0.5  1.5  2.3  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  1  1.5  3.9  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  1.5  1.5  4.5  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  2  1.5  4  4.5  137  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  21  22  23  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  3  1.5  2.7  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  4  1.5  2.5  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  5  1.5  2.3  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  6  1.5  2.2  4.5  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0249  7  1.5  2.1  4.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  0  1.5  0  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  0.25  1.5  1.5  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  0.5  1.5  2  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  1  1.5  2.6  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0000  1.5  1.5  3.7  3.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  0  3.2  0  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  0.25  3.2  1.5  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  0.5  3.2  2  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  1  3.2  2.7  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  2  3.2  3.8  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  3  3.2  4.2  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  3.2  3.2  4.7  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  4  3.2  3.5  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  5  3.2  3  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  6  3.2  2.5  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  7  3.2  2.3  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0168  8  3.2  2.1  4.7  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  0  4  0  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  0.25  4  1  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  0.5  4  1.5  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  1  4  2.2  5.5  138  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  24  25  26  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  2  4  3.5  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  3  4  4.6  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  4  4  5.5  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  5  4  4.3  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  6  4  3  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  7  4  2.9  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  8  4  2.7  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  9  4  2.5  5.5  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.29  300  0.0147  10  4  2.3  5.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0000  0  0.75  0  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0000  0.5  0.75  2  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0000  0.75  0.75  2.8  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0000  1  0.75  2.6  2.8  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  0  1  0  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  0.5  1  3  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  1  1  4.1  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  2  1  3  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  3  1  2.2  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  4  1  2  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  5  1  1.8  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  6  1  1.7  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0084  7  1  1.6  4.1  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  0  1.2  0  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  0.5  1.2  3.2  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  1  1.2  4.2  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  1.2  1.2  4.5  4.5  139  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  27  28  29  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  2  1.2  4.2  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  3  1.2  4  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  4  1.2  3.8  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  5  1.2  3.5  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  6  1.2  3.3  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  7  1.2  3.1  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0168  8  1.2  2.8  4.5  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  0  1.2  0  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  0.5  1.2  3.3  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  1  1.2  4.4  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  1.2  1.2  4.6  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  2  1.2  4.2  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  3  1.2  4.1  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  4  1.2  3.8  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  5  1.2  3.7  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  6  1.2  3.5  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  7  1.2  3.3  4.6  AFRP  IHB  HL  Unconfined  12  34.5  5.874  2.29  300  0.0147  8  1.2  3  4.6  CFRP  IHB  SW  Unconfined  13  33.1  5.753  1.92  300  0.0000  0  0.75  0  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  1.92  300  0.0000  0.25  0.75  2.3  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  1.92  300  0.0000  0.5  0.75  3.2  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  1.92  300  0.0000  0.75  0.75  3.5  3.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  0  1.25  0  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  0.25  1.25  2.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  0.5  1.25  3.2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  1  1.25  4.2  4.3  140  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  30  31  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  1.25  1.25  4.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  2  1.25  3.6  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  3  1.25  2.6  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  4  1.25  2.1  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  5  1.25  1.9  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  6  1.25  1.7  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  7  1.25  1.5  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  0  1.25  0  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  0.25  1.25  2.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  0.5  1.25  3.2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  1  1.25  4.2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  1.25  1.25  4.3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  2  1.25  3.5  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  3  1.25  3.1  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  4  1.25  3  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  5  1.25  2.8  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  6  1.25  2.6  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  7  1.25  2.4  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  8  1.25  2  4.3  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  0  1.1  0  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  0.25  1.1  2.3  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  0.5  1.1  3.2  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  1  1.1  4.4  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  1.1  1.1  4.5  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  2  1.1  3.8  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  3  1.1  3.2  4.5  141  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  32  33  34  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  4  1.1  3  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  5  1.1  2.8  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  6  1.1  2.5  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  7  1.1  2.3  4.5  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0230  8  1.1  2.1  4.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0000  0  0.75  0  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0000  0.25  0.75  1.5  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0000  0.5  0.75  2  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0000  0.75  0.75  2.4  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0000  1  0.75  2.3  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0000  2  0.75  2.2  2.4  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  0  1.5  0  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  0.25  1.5  1.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  0.5  1.5  2  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  1  1.5  2.6  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  1.5  1.5  3.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  2  1.5  3.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  3  1.5  2.7  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  4  1.5  2  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  5  1.5  1.4  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  6  1.5  1  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  7  1.5  0.8  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0078  8  1.5  0.7  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  0  2  0  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  0.25  2  1.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  0.5  2  2  3.5  142  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  35  36  37  Kanakubo et al. (1993)  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  1  2  2.6  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  2  2  3.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  3  2  2.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  4  2  2  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  5  2  1.7  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  6  2  1.6  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0155  7  2  1.5  3.5  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  0  2.75  0  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  0.25  2.75  1.5  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  0.5  2.75  2  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  1  2.75  2.6  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  2  2.75  3.4  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  2.75  2.75  3.8  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  3  2.75  3.7  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  4  2.75  3.1  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  5  2.75  2.4  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  6  2.75  1.8  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  7  2.75  1.3  3.8  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.12  300  0.0130  8  2.75  1.2  3.8  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0000  0  1.5  0  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0000  0.5  1.5  1.5  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0000  1  1.5  2  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0000  1.5  1.5  2.5  2.5  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  0  1.2  0  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  0.5  1.2  2.6  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  1  1.2  3.5  3.7  143  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  38  39  Kanakubo et al. (1993)  Kanakubo et al. (1993)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  1.2  1.2  3.7  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  2  1.2  3  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  3  1.2  2.4  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  4  1.2  2  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  5  1.2  1.8  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  6  1.2  1.7  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  7  1.2  1.6  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0078  8  1.2  1.5  3.7  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  0  1.7  0  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  0.5  1.7  2.2  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  1  1.7  3.2  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  1.7  1.7  3.9  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  2  1.7  3.8  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  3  1.7  3.1  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  4  1.7  3.1  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  5  1.7  3  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  6  1.7  2.5  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  7  1.7  2.4  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0155  8  1.7  2.2  3.9  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  0  1.7  0  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  0.5  1.7  1.8  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  1  1.7  3  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  1.7  1.7  4  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  2  1.7  3.6  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  3  1.7  3.4  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  4  1.7  3.2  4  144  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  40  41  42  Larralde et al. (1994)  Larralde et al. (1994)  Larralde et al. (1994)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  5  1.7  3.1  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  6  1.7  2.9  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  7  1.7  2.8  4  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.12  300  0.0135  8  1.7  2.7  4  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0  0.012  0  3.77  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0.002  0.012  1.49  3.77  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0.004  0.012  1.71  3.77  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0.006  0.012  2.28  3.77  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0.008  0.012  2.63  3.77  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0.01  0.012  3.29  3.77  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0.012  0.012  3.77  3.77  GFRP  IHB  SW  Unconfined  12.7  29  5.385  2.99  127  0.0000  0.014  0.012  3.51  3.77  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0  0.02  0  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.002  0.02  1  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.004  0.02  1.25  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.006  0.02  1.62  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.008  0.02  1.87  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.01  0.02  2.36  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.012  0.02  2.75  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.014  0.02  3.06  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.016  0.02  3.44  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.018  0.02  3.88  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.02  0.02  4.35  4.35  GFRP  IHB  SW  Unconfined  12.7  34  5.831  2.99  178  0.0000  0.022  0.02  4  4.35  GFRP  IHB  SW  Unconfined  12.7  37  6.083  2.99  279  0.0000  0  0.007  0  2.48  GFRP  IHB  SW  Unconfined  12.7  37  6.083  2.99  279  0.0000  0.002  0.007  1.4  2.48  145  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  43  44  Benmokrane et al. (1996)  Benmokrane et al. (1996)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  SW  Unconfined  12.7  37  6.083  2.99  279  0.0000  0.004  0.007  1.92  2.48  GFRP  IHB  SW  Unconfined  12.7  37  6.083  2.99  279  0.0000  0.006  0.007  2  2.48  GFRP  IHB  SW  Unconfined  12.7  37  6.083  2.99  279  0.0000  0.007  0.007  2.48  2.48  GFRP  IHB  SW  Unconfined  12.7  37  6.083  2.99  279  0.0000  0.008  0.007  1.88  2.48  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  0  4  0  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  0.01  4  1.7  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  0.1  4  5.6  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  0.2  4  5.7  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  1  4  6.3  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  2  4  7.1  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  3  4  7.5  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  4  4  7.7  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  5  4  7.7  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  6  4  7.7  7.7  GFRP  HB  HL  Unconfined  12.7  31  5.568  3.94  127  0.0606  7  4  7  7.7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  0  1.5  0  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  0.01  1.5  0.5  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  0.1  1.5  3.6  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  0.2  1.5  6.2  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  1  1.5  6.9  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  1.5  1.5  7  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  2  1.5  7  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  3  1.5  6.9  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  4  1.5  6.7  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  5  1.5  6.4  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  6  1.5  6  7  146  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  45  46  47  48  Ehsani et al. (1996)  Ehsani et al. (1996)  Ehsani et al. (1996)  Ehsani et al. (1996)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  7  1.5  5.9  7  GFRP  HB  HL  Unconfined  25.4  31  5.568  1.97  254  0.0303  8  1.5  5.7  7  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  203  0.0000  0  1.27  0  9.6  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  203  0.0000  0.025  1.27  6.8  9.6  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  203  0.0000  0.06  1.27  8.4  9.6  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  203  0.0000  0.38  1.27  8.8  9.6  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  203  0.0000  0.76  1.27  9.3  9.6  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  203  0.0000  1.02  1.27  9.5  9.6  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  203  0.0000  1.27  1.27  9.6  9.6  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  559  0.0000  0  1.02  0  3.87  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  559  0.0000  0.025  1.02  2.67  3.87  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  559  0.0000  0.06  1.02  3.38  3.87  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  559  0.0000  0.38  1.02  3.7  3.87  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  559  0.0000  0.76  1.02  3.83  3.87  GFRP  HB  HL  Unconfined  28.575  28  5.292  2.00  559  0.0000  1.02  1.02  3.87  3.87  GFRP  HB  HL  Unconfined  28.575  28  5.292  4.00  661  0.0000  0  1.27  0  3.58  GFRP  HB  HL  Unconfined  28.575  28  5.292  4.00  661  0.0000  0.025  1.27  2.25  3.58  GFRP  HB  HL  Unconfined  28.575  28  5.292  4.00  661  0.0000  0.06  1.27  3  3.58  GFRP  HB  HL  Unconfined  28.575  28  5.292  4.00  661  0.0000  0.38  1.27  3.23  3.58  GFRP  HB  HL  Unconfined  28.575  28  5.292  4.00  661  0.0000  0.76  1.27  3.53  3.58  GFRP  HB  HL  Unconfined  28.575  28  5.292  4.00  661  0.0000  1.02  1.27  3.56  3.58  GFRP  HB  HL  Unconfined  28.575  28  5.292  4.00  661  0.0000  1.27  1.27  3.58  3.58  GFRP  HB  HL  Unconfined  28.575  28  5.292  6.00  762  0.0000  0  1.02  0  3.28  GFRP  HB  HL  Unconfined  28.575  28  5.292  6.00  762  0.0000  0.025  1.02  1.95  3.28  GFRP  HB  HL  Unconfined  28.575  28  5.292  6.00  762  0.0000  0.06  1.02  2.6  3.28  GFRP  HB  HL  Unconfined  28.575  28  5.292  6.00  762  0.0000  0.38  1.02  3.02  3.28  147  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  49  50  51  Cosenza et al. (1999)  Cosenza et al. (1999)  Cosenza et al. (1999)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  HL  Unconfined  28.575  28  5.292  6.00  762  0.0000  0.76  1.02  3.25  3.28  GFRP  HB  HL  Unconfined  28.575  28  5.292  6.00  762  0.0000  1.02  1.02  3.28  3.28  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  0  0.5  0  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  0.05  0.5  1.7  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  0.1  0.5  3  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  0.25  0.5  8.2  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  0.5  0.5  11.3  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  0.75  0.5  10.9  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  1  0.5  9.4  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  1.5  0.5  8.5  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  2  0.5  8  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  2.5  0.5  7.6  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  3  0.5  7.3  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  3.5  0.5  7  11.3  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.91  63.5  0.0000  4  0.5  6.8  11.3  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  0  0.25  0  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  0.05  0.25  9  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  0.1  0.25  13.6  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  0.25  0.25  16.5  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  0.5  0.25  15.5  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  0.75  0.25  14.2  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  1  0.25  13.2  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  1.5  0.25  10.8  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  2  0.25  8.5  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  63.5  0.0000  2.5  0.25  6  16.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  0  0.22  0  14.5  148  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  52  53  Defreese & Wollmann (2002)  Defreese & Wollmann (2002)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  0.05  0.22  9  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  0.1  0.22  13.2  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  0.22  0.22  14.5  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  0.25  0.22  14.2  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  0.5  0.22  14.2  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  0.75  0.22  14.1  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  1  0.22  14  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  1.5  0.22  13.8  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  2  0.22  13.7  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  2.5  0.22  13.7  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  3  0.22  13.7  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  3.5  0.22  13.7  14.5  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.91  127  0.0000  4  0.22  13.7  14.5  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0  0.32  0  15.7  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.025  0.32  7  15.7  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.05  0.32  8.75  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.15  0.32  10.5  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.32  0.32  15.75  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.64  0.32  10.5  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  1.27  0.32  9.8  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  2.54  0.32  9.45  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  5.06  0.32  9.63  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  7.62  0.32  10.85  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  10.16  0.32  11.55  15.75  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0  0.32  0  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.16  0.32  8.78  10.71  149  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  54  55  Defreese & Wollmann (2002)  Defreese & Wollmann (2002)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.32  0.32  10.71  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  0.64  0.32  10.7  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  1.27  0.32  10  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  1.91  0.32  9.66  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  2.54  0.32  9.48  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  5.06  0.32  10  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  7.62  0.32  10.88  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  63.5  0.0000  10.16  0.32  11.24  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  12.7  0.32  8.78  10.71  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  0  0.64  0  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  0.32  0.64  17.2  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  0.64  0.64  17.6  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  1.27  0.64  17.2  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  2.54  0.64  16.38  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  5.08  0.64  15.8  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  7.62  0.64  16.15  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  10.16  0.64  16.38  17.6  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.50  95.3  0.0000  12.7  0.64  9.36  17.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  0  0.64  0  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  0.32  0.64  17.36  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  0.64  0.64  18.26  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  1.27  0.64  17.3  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  2.54  0.64  15.7  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  5.08  0.64  11.65  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  10.16  0.64  10.98  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  15.24  0.64  10.08  18.26  150  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  56  57  58  Defreese & Wollmann (2002)  Defreese & Wollmann (2002)  Defreese & Wollmann (2002)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  20.32  0.64  9.52  18.26  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  0  0.51  0  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  0.25  0.51  15.7  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  0.5  0.51  16.6  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  0.51  0.51  16.6  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  1.27  0.51  14.1  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  2.54  0.51  13.2  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  5.08  0.51  10.1  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  7.62  0.51  10.1  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  10.16  0.51  8.85  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  79.5  0.0000  12.7  0.51  7.84  16.6  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  0  0.32  0  16.8  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  0.13  0.32  14.9  16.8  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  0.32  0.32  16.8  16.8  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  0.64  0.32  16.39  16.8  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  1.27  0.32  14.53  16.8  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  2.54  0.32  12.14  16.8  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  5.08  0.32  10.36  16.8  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.39  119.3  0.0000  7.62  0.32  8.2  16.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0  0.32  0  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0.13  0.32  13.9  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0.32  0.32  15.04  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0.64  0.32  15  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  1.27  0.32  14.42  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  2.54  0.32  13.18  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  5.08  0.32  10.7  15.04  151  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  59  60  61  Defreese & Wollmann (2002)  Defreese & Wollmann (2002)  Defreese & Wollmann (2002)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  7.62  0.32  9.69  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  10.16  0.32  9.6  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  12.7  0.32  9.58  15.04  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0  0.32  0  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0.13  0.32  13.04  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0.32  0.32  13.8  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  0.64  0.32  12.8  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  1.27  0.32  11.2  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  2.54  0.32  9.31  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  5.08  0.32  8.2  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  10.16  0.32  7.38  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  95.5  0.0000  15.24  0.32  7.08  13.8  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  0  0.51  0  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  0.32  0.51  15.74  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  0.51  0.51  16  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  0.64  0.51  16  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  1.27  0.51  14.96  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  2.54  0.51  13.52  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  5.08  0.51  10.58  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  7.62  0.51  7.48  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  10.16  0.51  4.64  16  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  0  0.64  0  14.2  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  0.32  0.64  13.93  14.2  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  0.64  0.64  14.2  14.2  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  1.27  0.64  13.98  14.2  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  2.54  0.64  12.9  14.2  152  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  62  63  Okelo (2007)  Okelo (2007)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  5.08  0.64  11.35  14.2  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  7.62  0.64  10.73  14.2  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  10.16  0.64  9.2  14.2  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.66  143.3  0.0000  12.7  0.64  9  14.2  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  0  0.74  0  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  0.5  0.74  11.5  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  0.74  0.74  13.4  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  1  0.74  13.3  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  1.4  0.74  13.2  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  1.5  0.74  12.8  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  2  0.74  12.2  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  3  0.74  12  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  4  0.74  12.5  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  5  0.74  12.8  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  6.25  0.74  12.4  13.4  CFRP  HB  HL  Confined  10  36.9  6.075  3.80  160  0.0785  7.5  0.74  11.8  13.4  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  0  1.45  0  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  1  1.45  7.1  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  1.45  1.45  7.7  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  1.5  1.45  7.7  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  2  1.45  4.5  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  3  1.45  3.5  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  4  1.45  3  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  5  1.45  2.8  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  6.25  1.45  2.4  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  7.5  1.45  2.2  7.7  153  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  64  65  Okelo (2007)  Okelo (2007)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  8.75  1.45  2  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  10  1.45  1.8  7.7  CFRP  HB  HL  Confined  16  36.9  6.075  2.38  160  0.0491  11.25  1.45  1.6  7.7  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  0  0.86  0  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  0.5  0.86  10.6  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  0.86  0.86  11.8  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  1  0.86  11.8  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  2  0.86  10.7  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  3  0.86  10  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  3.5  0.86  7.5  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  4  0.86  7.4  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  5  0.86  7.3  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  7.5  0.86  6.8  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  10  0.86  6.2  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  12.5  0.86  5.7  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  15  0.86  5  11.8  CFRP  HB  HL  Confined  10  39.3  6.269  3.80  200  0.0785  17.5  0.86  4.8  11.8  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  0  0.79  0  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  0.5  0.79  8.2  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  0.79  0.79  9.2  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  1  0.79  9.2  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  1.5  0.79  7.3  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  2  0.79  5.5  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  3  0.79  5.5  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  4  0.79  5.3  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  5  0.79  5.2  9.2  154  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  66  67  Okelo (2007)  Okelo (2007)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  7.5  0.79  5.1  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  10  0.79  5  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  12.5  0.79  4.8  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  15  0.79  4.7  9.2  CFRP  HB  HL  Confined  16  39.3  6.269  2.38  320  0.0491  17.5  0.79  4.5  9.2  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  320  0.0491  20  0.79  4.2  9.2  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  0  3.35  0  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  2.5  3.35  6.9  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  3.35  3.35  6.9  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  4  3.35  6.9  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  5  3.35  6  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  6.25  3.35  5.5  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  7.5  3.35  4.5  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  10  3.35  2.7  6.9  GFRP  HB  HL  Confined  19  41.5  6.442  2.00  150  0.0413  12.5  3.35  1.7  6.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  0  1.39  0  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  0.5  1.39  15.3  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  1  1.39  15.5  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  1.3  1.39  15.9  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  1.39  1.39  15.9  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  1.5  1.39  11  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  2  1.39  12  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  3  1.39  12.4  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  4  1.39  10.5  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  5  1.39  8  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  7.5  1.39  7  15.9  155  Beam  Ref  FRP Type  Test Type  Bar  Confinement  db  f c′  (mm)  (MPa)  Surface  68  Okelo (2007)  f c′  c db  lembed (mm)  Atr snd b  si  sm  τi  τm  (mm)  (mm)  (MPa)  (MPa)  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  10  1.39  6.5  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  12.5  1.39  6  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  15  1.39  5.4  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  17.5  1.39  5.2  15.9  CFRP  HB  HL  Confined  10  41.5  6.442  3.80  150  0.0785  20  1.39  5.4  15.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  0  2.26  0  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  0.5  2.26  10.8  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  1  2.26  11.6  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2  2.26  11.7  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2.1  2.26  11.8  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2.2  2.26  11.9  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2.26  2.26  11.9  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2.3  2.26  11.9  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2.4  2.26  10  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2.5  2.26  10  11.9  CFRP  HB  HL  Confined  16  41.5  6.442  2.38  240  0.0491  2.6  2.26  10  11.9  156  Appendix C Table C.1 Database of beam-type specimens for deriving slip corresponding to peak bond stress of FRP rebars in concrete SI  Ref  FRP Type  Test Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c db  lembed  sm  sm  (mm)  Atr snd b  (mm)  lembed 0.0033  Failure Type  1  Daniali (1990)  GFRP  HB  HL  Confined  11.2  31  5.568  3.402  305  0.04  1.016  Pullout  2  Daniali (1990)  GFRP  HB  HL  Confined  11.2  31  5.568  3.402  305  0.025  1.016  0.0033  Pullout  3  Daniali (1990)  GFRP  HB  HL  Confined  11.2  31  5.568  3.402  305  0.029  0.94  0.0031  Pullout  4  Daniali (1990)  GFRP  HB  HL  Confined  19.94  31  5.568  2.229  508  0.014  3.302  0.0065  Pullout  5  Daniali (1990)  CFRP  HB  HL  Confined  10  32.4  5.692  3.8  150  0.051  0.86  0.0057  Pullout  6  Daniali (1990)  CFRP  HB  HL  Confined  10  31.3  5.595  3.8  200  0.051  0.99  0.005  Pullout  7  Daniali (1990)  CFRP  HB  HL  Confined  10  36.9  6.075  3.8  100  0.051  0.74  0.0074  Pullout  8  Daniali (1990)  CFRP  HB  HL  Confined  16  36.9  6.075  2.375  160  0.032  1.45  0.0091  Pullout  9  Daniali (1990)  CFRP  HB  HL  Confined  10  41.4  6.434  3.8  150  0.051  1.39  0.0093  Pullout  10  Daniali (1990)  CFRP  HB  HL  Confined  10  39.3  6.269  3.8  200  0.051  0.86  0.0043  Pullout  11  Daniali (1990)  GFRP  HB  HL  Confined  19  33.3  5.771  2  190  0.027  2.13  0.0112  Pullout  12  Daniali (1990)  CFRP  HB  HL  Confined  16  41.5  6.442  2.375  240  0.032  2.26  0.0094  Splitting  13  Makitani et al. (1993)  CFRP  HB  SC  Confined  10  33.7  5.805  5  100  0.079  0.05  13.8  Pullout  14  Makitani et al. (1993)  AFRP  HB  SC  Confined  10  30.1  5.486  5  100  0.079  0.15  19  Pullout  15  Makitani et al. (1993)  GFRP  HB  SW  Confined  15.9  31  5.568  3.145  95.4  0.049  0.33  0.0035  Pullout  16  Makitani et al. (1993)  GFRP  HB  SW  Confined  12.7  31  5.568  3.937  127  0.062  0.3  0.0024  Pullout  17  Makitani et al. (1993)  GFRP  HB  SW  Confined  15.9  31  5.568  3.145  159  0.049  0.85  0.0053  Pullout  18  Makitani et al. (1993)  GFRP  HB  SW  Confined  12.7  31  5.568  3.937  203  0.062  0.25  0.0012  Pullout  19  Makitani et al. (1993)  GFRP  HB  SW  Confined  15.9  31  5.568  3.145  306  0.049  0.75  0.0025  Pullout  20  Makitani et al. (1993)  GFRP  HB  HL  Confined  25.4  31  5.568  1.969  254  0.03  1.5  0.0059  Pullout  21  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  10  28  5.292  1  38  0  0.47  0.0124  Splitting  22  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  10  28  5.292  2  38  0  0.63  0.0166  Pullout  157  SI  Ref  FRP Type  Test Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c db  lembed  sm  sm  (mm)  Atr snd b  (mm)  lembed  Failure Type  23  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  10  28  5.292  2  76.2  0  0.68  0.0089  Pullout  24  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  28  5.292  1  76.2  0  1.33  0.0175  Splitting  25  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  28  5.292  1  76.2  0  1.62  0.0213  Splitting  26  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  28  5.292  2  76.2  0  1.15  0.0151  Pullout  27  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  28  5.292  2  76.2  0  1.25  0.0164  Pullout  28  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  28  5.292  2  152  0  1.21  0.0079  Pullout  29  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  39.2  6.258  2  305  0  1.53  0.005  Pullout  30  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  39.2  6.258  4  406  0  1.52  0.0037  Pullout  31  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  39.2  6.258  4  406  0  1.77  0.0044  Pullout  32  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  47.7  6.907  2  305  0  1.72  0.0056  Pullout  33  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  47.7  6.907  2  305  0  2.23  0.0073  Pullout  34  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  47.7  6.907  4  406  0  1.43  0.0035  Pullout  35  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  19  47.7  6.907  4  406  0  1.59  0.0039  Pullout  36  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  29  27.7  5.258  1  102  0  1.16  0.0114  Splitting  37  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  29  27.7  5.258  2  102  0  1.44  0.0142  Pullout  38  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  29  27.7  5.258  2  203  0  1.44  0.0071  Pullout  39  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  29  39.7  6.302  4  660  0  1.43  0.0022  Pullout  40  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  29  39.7  6.302  4  660  0  2.23  0.0034  Pullout  41  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  29  44.8  6.69  4  660  0  1.71  0.0026  Pullout  42  Ehsani et al. (1993)  GFRP  IHB  HL  Unconfined  29  44.8  6.69  4  660  0  1.37  0.0021  Pullout  43  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  1.923  300  0  0.75  0.0025  Splitting  44  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.016  1.25  0.0042  Splitting  45  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.031  1.25  0.0042  Splitting  46  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.046  1.1  0.0037  Splitting  47  Kanakubo et al. (1993)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0  0.75  0.0025  Splitting  48  Kanakubo et al. (1993)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.016  1.5  0.005  Splitting  49  Kanakubo et al. (1993)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.031  2  0.0067  Splitting  158  SI  Ref  FRP Type  Test Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c db  lembed  sm  sm  (mm)  Atr snd b  (mm)  lembed  Failure Type  50  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0  1.5  0.005  Splitting  51  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0.016  1.2  0.004  Splitting  52  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0.031  1.7  0.0057  Splitting  53  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0.027  1.7  0.0057  Splitting  54  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  1.923  300  0  0.75  0.0025  Splitting  55  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.016  1.25  0.0042  Splitting  56  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.031  1.25  0.0042  Splitting  57  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.046  1.1  0.0037  Splitting  58  Kanakubo et al. (1993)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0  0.75  0.0025  Splitting  59  Kanakubo et al. (1993)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.016  1.5  0.005  Splitting  60  Kanakubo et al. (1993)  GFRP  IHB  SW  Unconfined  13  33.1  5.753  2.115  300  0.031  2  0.0067  Splitting  61  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0  1.5  0.005  Splitting  62  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0.016  1.2  0.004  Splitting  63  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0.031  1.7  0.0057  Splitting  64  Kanakubo et al. (1993)  CFRP  IHB  SW  Unconfined  13  34.5  5.874  2.115  300  0.027  1.7  0.0057  Splitting  65  Ehsani et al. (1996)  GFRP  HB  HL  Unconfined  28.58  28  5.292  2  203  0  1.27  0.0063  Pullout  66  Ehsani et al. (1996)  GFRP  HB  HL  Unconfined  28.58  28  5.292  4  661  0  1.27  0.0019  Pullout  67  Ehsani et al. (1996)  GFRP  HB  HL  Unconfined  28.58  28  5.292  6.002  762  0  1.02  0.0013  Pullout  68  Ehsani et al. (1996)  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0  1.5  0.005  Splitting  69  Ehsani et al. (1996)  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0  1.5  0.005  Splitting  70  Ehsani et al. (1996)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0  1.5  0.005  Splitting  71  Ehsani et al. (1996)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0  3.2  0.0107  Splitting  72  Ehsani et al. (1996)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0  4  0.0133  Splitting  73  Tighiouart et al. (1998)  GFRP  HB  SW  Confined  12.7  31  5.568  3.937  76.2  0.062  0.13  0.0017  Pullout  74  Tighiouart et al. (1998)  GFRP  HB  SW  Confined  15.9  31  5.568  3.145  95.4  0.049  0.33  0.0035  Pullout  75  Tighiouart et al. (1998)  GFRP  HB  SW  Confined  12.7  31  5.568  3.937  127  0.062  0.3  0.0024  Pullout  76  Tighiouart et al. (1998)  GFRP  HB  SW  Confined  12.7  31  5.568  3.937  203  0.062  0.25  0.0012  Pullout  159  SI  Ref  FRP Type  Test Type  Bar Surface  Confinement  db  f c′  (mm)  (MPa)  f c′  c db  lembed  sm  sm  (mm)  Atr snd b  (mm)  lembed  Failure Type  77  Cosenza et al. (1999)  GFRP  HB  HL  Unconfined  12.7  37  6.083  5.906  63.5  0  0.5  0.0079  Pullout  78  Cosenza et al. (1999)  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.906  63.5  0  0.25  0.0039  Pullout  79  Cosenza et al. (1999)  GFRP  HB  HL  Unconfined  12.7  40  6.325  5.906  127  0  0.22  0.0017  Pullout  80  Cosenza et al. (1999)  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0.017  1.5  0.005  Splitting  81  Cosenza et al. (1999)  CFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0.05  1.5  0.005  Splitting  82  Cosenza et al. (1999)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0  1.5  0.005  Splitting  83  Cosenza et al. (1999)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0.034  3.2  0.0107  Splitting  84  Cosenza et al. (1999)  AFRP  IHB  HL  Unconfined  12  33.1  5.753  2.292  300  0.029  4  0.0133  Splitting  85  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.5  63.5  0  0.15  0.0024  Pullout  86  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.5  63.5  0  0.32  0.005  Pullout  87  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  12.7  23.4  4.837  5.5  95.3  0  0.64  0.0067  Pullout  88  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.393  79.5  0  0.64  0.0081  Pullout  89  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.393  79.5  0  0.51  0.0064  Pullout  90  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  15.9  23.4  4.837  4.393  119  0  0.32  0.0027  Pullout  91  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.657  95.5  0  0.32  0.0034  Pullout  92  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.657  95.5  0  0.32  0.0034  Pullout  93  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.657  143  0  0.51  0.0036  Pullout  94  Defreese & Wollmann (2002)  GFRP  IHB  HL  Confined  19.1  23.4  4.837  3.657  143  0  0.64  0.0045  Pullout  95  Aly (2007)  CFRP  S  SC  Confined  9.5  40  6.325  4.211  800  0.012  3.44  3.28  Splitting  96  Aly (2007)  CFRP  S  SC  Confined  19.1  40  6.325  2.094  700  0.006  2.709  3.3  Splitting  97  Aly (2007)  CFRP  S  SC  Confined  19.1  40  6.325  2.094  800  0.009  2.36  3.74  Splitting  160  Appendix D 4.5  4.5 Experimental Beam 1  Experimental Beam 2  4  Predicted  Predicted  3.5  3.5  3  3  Bo n d Stress (M Pa)  B o n d Stre s s (M Pa )  4  2.5 2 1.5  2.5 2 1.5  1  1  0.5  0.5  0  0  0  1  2  3  4  5  6  7  8  0  1  2  3  4  Slip (mm)  5  7  8  5  5 Experimental Beam 3  4.5  Experimental Beam 4  4.5  Predicted  Predicted  4  3.5  3.5 B o n d Stress (M Pa)  4  3 2.5 2 1.5  3 2.5 2 1.5  1  1  0.5  0.5  0  0  0  1  2  3  4  5  6  7  8  0  1  2  3  Slip (mm)  4  5  6  7  8  Slip (mm)  5  4  Experimental Beam 6  4.5  Experimental Beam 5  3.5  Predicted  Predicted  4  3 B o n d Stre s s (M Pa )  3.5  Bo n d Stre s s (M Pa )  Bo n d Stress (M Pa)  6  Slip (mm)  2.5 2 1.5  3 2.5 2 1.5  1 1  0.5  0.5  0  0  0  0.2  0.4  0.6  0.8 Slip (mm)  1  1.2  1.4  1.6  0  1  2  3  4  5  6  7  8  9  Slip (mm)  161  3  4 Experimental Beam 7  3.5  Predicted  2.5  Bo n d Stre s s (M Pa )  B o n d Stre s s (M Pa )  3 2.5 2 1.5  Experimental Beam 8  2  Predicted  1.5  1  1 0.5  0.5 0  0  0  2  4  6  8  10  12  0  0.2  0.4  0.6  Slip (mm)  0.8  1  1.2  Slip (mm)  4  5 Experimental Beam 9  3.5  Experimental Beam 10  4.5  Predicted  Predicted  4 3  Bo n d Stre ss (M Pa )  Bond S tress (M P a)  3.5 2.5  2  1.5  3 2.5 2 1.5  1  1 0.5  0.5 0  0 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0  1  2  3  Slip (mm)  4  5  6  7  8  9  Slip (mm)  5 Experimental Beam 11  4.5  Predicted  4  Bo n d Stre ss (M Pa )  3.5 3 2.5 2 1.5 1 0.5 0 0  1  2  3  4  5  6  7  8  9  Slip (mm)  Figure D.1 Predicted vs. experimental bond stress-slip curves for specimens with helical lugged FRP bars having splitting mode of failure. 162  4  5 4.5  Experimental Beam 2  3.5  Experimental Beam 1 4  Predicted  Predicted  3 Bo nd S tress (M P a)  Bon d S tress (M P a)  3.5 3 2.5 2  2.5  2  1.5  1.5 1  1 0.5  0.5 0  0  0  1  2  3  4  5  6  7  8  0  1  2  3  4  Slip (mm)  5  6  7  8  9  Slip (mm)  4  5 Experimental Beam 11  4.5  Experimental Beam 4  3.5  Predicted  Predicted  4 3 Bond S tress (M P a)  Bo n d Stre ss (M Pa )  3.5 3 2.5 2  2.5  2  1.5  1.5 1  1 0.5  0.5 0  0  0  1  2  3  4  5  6  7  8  0  9  1  2  3  4  5  6  7  8  9  Slip (mm)  Slip (mm)  5  4  4.5  Experimental Beam 5  3.5  Predicted  Experimental Beam 6  4  Predicted  3 Bon d S tress (M P a)  Bo n d Stress (M Pa)  3.5  2.5 2 1.5  3 2.5 2 1.5  1 1  0.5  0.5  0  0  0  1  2  3  4  5  Slip (mm)  6  7  8  9  0  1  2  3  4  5  6  7  8  9  Slip (mm)  163  3  5 4.5  Experimental Beam 8 2.5  Experimental Beam 7  4  Predicted  Predicted Bo nd S tress (M P a)  Bo nd S tress (M P a)  3.5 3 2.5 2  2  1.5  1  1.5 1  0.5  0.5 0  0  0  1  2  3  4  5  6  7  8  9  0  0.5  1  Slip (mm)  2  2.5  4  3  Experimental Beam 10  3.5  Predicted  Experimental Beam 9  2.5  Predicted  3  2  Bon d S tress (M P a)  Bo n d Stress (M Pa)  1.5 Slip (mm)  1.5  1  2.5  2  1.5  1  0.5 0.5  0  0  0  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  0  0.1  0.2  0.3  0.4  0.5  0.6  0.8  4.5  4.5 4  4  Experimental Beam 11  Experimental Beam 12 Predicted  Predicted  3.5  3.5  3  3  Bo n d Stre s s (M Pa )  B o n d Stress (M Pa)  0.7  Slip (mm)  Slip (mm)  2.5 2 1.5  2.5 2 1.5  1  1  0.5  0.5  0  0 0  1  2  3  4  5  Slip (mm)  6  7  8  9  0  1  2  3  4  5  6  7  8  9  Slip (mm)  Figure D.2 Predicted vs. experimental bond stress-slip curves for specimens with spiral wrapped FRP bars having splitting mode of failure. 164  Appendix E Table E.1 Values of Ct from the finite element analysis of the 105 confined beam specimens failed by splitting of concrete  SI  Reference  Specimen  Ct  1  Daniali (1990)  Sp-1  0  2  Sp-2  0  3  Sp-3  0  4  Sp-4  0  5  Sp-5  0  Sp-1  0  7  Sp-2  0  8  Sp-3  0  9  Sp-4  0  Sp-1  3.7  11  Sp-2  3.7  12  Sp-3  2.9  13  Sp-4  2.9  14  Sp-5  0  15  Sp-6  0  Sp-1  0  17  Sp-2  0  18  Sp-3  0  19  Sp-4  0  20  Sp-5  0  21  Sp-6  0  22  Sp-7  0  23  Sp-8  0  24  Sp-9  0.8  25  Sp-10  0.8  26  Sp-11  2.2  27  Sp-12  2.5  6  10  16  Daniali (1991)  Faza (1991)  Tighiouart et al. (1998)  165  SI  Specimen  Ct  28  Sp-13  1.7  29  Sp-14  1.8  Sp-1  2.5  31  Sp-2  2.6  32  Sp-3  0.4  33  Sp-4  2.0  34  Sp-5  0  35  Sp-6  0  36  Sp-7  0  37  Sp-8  0  38  Sp-9  2.0  39  Sp-10  2.1  40  Sp-11  0.3  41  Sp-12  0.8  42  Sp-13  0.7  43  Sp-14  0.7  Sp-1  0  45  Sp-2  0  46  Sp-3  0  47  Sp-4  0  48  Sp-5  0  49  Sp-6  0  50  Sp-7  0  51  Sp-8  0  52  Sp-9  0  Sp-1  2.0  54  Sp-2  5.2  55  Sp-3  2.4  56  Sp-4  1.2  30  44  53  Reference  Tighiouart et al. (1999)  Mosley (2000)  Aly and Benmokrane (2005)  166  SI  Specimen  Ct  57  Sp-5  5.2  58  Sp-6  2.9  Sp-1  3.9  60  Sp-2  3.7  61  Sp-3  3.5  62  Sp-4  4.0  63  Sp-5  3.1  64  Sp-6  4.4  65  Sp-7  4.7  66  Sp-8  4.8  67  Sp-9  4.6  68  Sp-10  4.7  69  Sp-11  4.5  70  Sp-12  4.7  71  Sp-13  2.9  Sp-1  4.5  73  Sp-2  4.6  74  Sp-3  3.8  75  Sp-4  3.4  76  Sp-5  2.7  77  Sp-6  0  78  Sp-7  2  79  Sp-8  3.8  80  Sp-9  2.9  81  Sp-10  2  82  Sp-11  1.8  83  Sp-12  2.6  59  72  Reference  Aly et al. (2006)  Aly (2007)  84  Okelo (2007)  Sp-1  5.8  85  Tharmin and Kaku (2007)  Sp-1  4.3 167  SI  Specimen  Ct  86  Sp-2  5.2  87  Sp-3  6.0  88  Sp-4  0.3  89  Sp-5  2.3  90  Sp-6  3.1  91  Sp-7  3.1  92  Sp-8  0  93  Sp-9  5.1  94  Sp-10  2.4  95  Sp-11  2.9  96  Sp-12  0  Sp-1  0  98  Sp-2  0  99  Sp-3  0  100  Sp-4  0  101  Sp-5  0  102  Sp-6  0  103  Sp-7  0  104  Sp-8  0  105  Sp-9  0  97  Reference  Mosley et al. (2008)  168  Biblography  Achillides, Z., and Pilakoutas, K. (2004). “Bond behaviour of fibre reinforced polymer bars under direct pullout conditions.” Journal of Composites for Construction, V. 8, No. 2, pp. 173-181. ACI Committee 440 (1996). “State of the art report on fibre reinforced plastic (FRP) reinforcement for concrete structures (ACI 440-96, Reapproved 2002)”. American Concrete Institute, Farmington Hills, MI, 68 pp. ACI Committee 408 (2003). “Bond and development of straight reinforcing bars in tension (ACI 408-03)”. 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