DEBONDING FAILURES OF RC BEAMS STRENGTHENED WITH EXTERNALLY BONDED FRP REINFORCEMENT: BEHAVIOUR AND MODELLING

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1 Asia-Pacific Conference on FRP in Structures (APFIS 2007) S.T. Smit (ed) 2007 International Institute for FRP in Construction DEBONDING FAILURES OF RC BEAMS STRENGTHENED WITH EXTERNALLY BONDED FRP REINFORCEMENT: BEHAVIOUR AND MODELLING J.G. Teng 1 and J.F. Cen 2 1 Department of Civil and Structural Engineering, Te Hong Kong Polytecnic University, Cina. cejgt@polyu.edu.k 2 Institute for Infrastructure and Environment, Scool of Engineering and Electronics Te University of Edinburg, UK. J.F.Cen@ed.ac.uk ABSTRACT Bot te flexural and sear strengts of reinforced concrete (RC) beams can be substantially enanced using externally bonded fibre reinforced polymer (FRP) composites. Failures of suc FRP-strengtened RC beams often occur by debonding of te FRP plate from te RC beam in a number of forms. Despite numerous teoretical and experimental studies on debonding failures of FRP-strengtened RC beams, considerable uncertainty still exists it te understanding of te failure mecanisms and it te accurate prediction of debonding failure loads. Tis paper provides a summary of te autor s understanding of te subject largely based on te researc of te autors and teir co-orkers. Te paper addresses te folloing tree issues: (a) classification of debonding failure modes; (c) mecanisms and processes of debonding failures; and (e) teoretical models for debonding failures. Te information presented in tis paper may serve as a useful basis for te future development of design provisions in design codes and guidelines. KEYWORDS FRP, RC beams, strengtening, debonding, beaviour, modelling, design INTRODUCTION Strengtening reinforced concrete (RC) structures it externally bonded fibre reinforced polymer (FRP) composites as become a popular tecnique in recent years (e.g. Teng et al. 2002). Te tecnique may be used to enance te load-carrying capacities of RC beams, slabs and columns as ell as te ductility of RC columns troug lateral confinement. Tis paper is concerned it RC beams tat are strengtened it externally bonded FRP reinforcement in te forms of seets/strips/plates (all referred to as plates unless specific differentiation becomes necessary) in eiter flexure or sear. FRP flexural strengtening of RC beams is commonly acieved by bonding an FRP plate to its tension face (Figure 1). Existing researc as son tat suc strengtened beams often fail by debonding of te FRP plate from te beam in one of several possible modes (e.g. Teng et al. 2000; 2002; Smit and Teng, 2002a; 2002b; Lu et al. 2007; Yao and Teng 2007). Despite te extensive existing researc, tere is still considerable uncertainty regarding many aspects of debonding failures, including te classification of debonding failure modes. Te sear capacity of an RC beam can also be effectively enanced using externally bonded FRP reinforcement in te form of complete raps, U jackets or side strips (Figure 2). of FRP from concrete occurs in almost all RC beams sear-strengtened it FRP (Cen and Teng 2003a, 2003b; Cao et al. 2005) altoug in te case of complete raps, debonding does not directly controls of te ultimate load (Cao et al. 2005). A RC beam Adesive layer A FRP Soffit plate Section A Figure 1 RC beam it an FRP plate bonded to its soffit Tis paper provides a summary of te autor s understanding of te subject largely based on te researc of te autors and teir co-orkers. Te paper starts it a systematic classification of debonding failure modes, 33

2 folloed by detailed descriptions of te mecanisms and processes of different debonding failure modes. Te paper ten presents teoretical strengt models for debonding failures. For simplicity, all discussions in tis paper are presented it explicit reference to a simply supported beam, but te design procedure can be easily applied to indeterminate beams. Fibre orientations and distributions Bonding sceme and notation = 90 SS90 US90 WS90 0 < 180 SS US WS φ 0 < 180, 0 φ < 180 SS/φ US/φ WS/φ =90 = 90 SP90 UP90 WP90 0 < 180 SP UP WP φ 0 < 180, 0 φ < 180 SP/φ UP/φ WP/φ Figure 2 Sear strengtening scemes for RC beams using externally bonded FRP reinforcement DEBONDING FAILURE MODES OF FLEXURALLY-STRENGTHENED RC BEAMS Classification of Failure Modes A number of distinct failure modes of RC beams bonded it an FRP soffit plate (i.e. FRP-plated RC beams) ave been observed in numerous experimental studies (Teng et al. 2002; Buyukozturk et al. 2004; Oelers and Seracino 2004; Yao and Teng 2007). A scematic representation of tese failure modes is son in Figures 3 and 4. Failure of an FRP-plated RC beam may be by te flexural failure of te critical section (Figure 3) or by debonding of te FRP plate from te RC beam (Figure 4). In te former type of failure, te composite action beteen te bonded plate and te RC beam is maintained up to failure, ile te latter type of failure involves a loss of tis composite action. failures generally occur in te concrete, ic is also assumed in te strengt models presented in tis paper. Tis is because, it te strong adesives currently available and it appropriate surface preparation for te concrete substrate, debonding failures along te pysical interfaces beteen te adesive and te concrete and beteen te adesive and te FRP plate are generally not critical. APFIS

3 may initiate at a flexural or flexural-sear crack in te ig moment region and ten propagates toards one of te plate ends (Figure 3a). Tis debonding failure mode is commonly referred to as intermediate crack (IC) induced interfacial debonding (or simply IC debonding) (Teng et al. 2002, 2003; Lu et al. 2007; Cen et al. 2006). may also occur at or near a plate end (i.e. plate end debonding failures) in four different modes: (a) critical diagonal crack (CDC) debonding (Figure 4b) (Oelers and Seracino 2004), (b) CDC debonding it concrete cover separation (Figure 4c) (Yao and Teng 2007), (c) concrete cover separation (Figures 4d and 4e) (Teng et al. 2002), and (d) plate end interfacial debonding (Figure 4f) (Teng et al. 2002). FRP Rupture Concrete Crusing (a) FRP rupture (b) Crusing of compressive concrete Figure 3 Conventional flexural failure modes of an FRP-plated RC beam Flexural crack Critical diagonal crack (a) IC debonding (b) CDC debonding (c) CDC debonding it concrete cover separation (d) Concrete cover separation (e) Concrete cover separation under pure bending (f) Plate end interfacial debonding Figure 4. failure modes of an FRP-plated RC beam IC Wen a major flexural or flexural-sear crack is formed in te concrete, te need to accommodate te large local strain concentration at te crack leads to immediate but very localized debonding of te FRP plate from te concrete in te close vicinity of te crack, but tis localized debonding is not yet able to propagate. Te tensile stresses released by te cracked concrete are transferred to te FRP plate and steel rebars, so ig local interfacial stresses beteen te FRP plate and te concrete are induced near te crack. As te applied loading increases furter, te tensile stresses in te plate and ence te interfacial stresses beteen te FRP plate and te concrete near te crack also increase. Wen tese stresses reac critical values, debonding starts to propagate toards one of te plate ends, generally te nearer end ere te stress gradient in te plate is iger. Figure 5. FRP-plated RC beam: IC debonding APFIS

4 A typical picture of flexural crack-induced debonding is son in Figure 5, ic sos tat a tin layer of concrete remained attaced to te plate suggesting tat failure occurred in te concrete adjacent to te adesiveto-concrete interface. IC debonding failures are more likely to occur in sallo beams and are, in general, more ductile tan plate end debonding failures. Concrete Cover Separation Concrete cover separation involves crack propagation along te level of te steel tension reinforcement. Failure of te concrete cover is initiated by te formation of a crack near te plate end. Te crack propagates to and ten along te level of te steel tension reinforcement, resulting in te separation of te concrete cover. As te failure occurs aay from te bondline, tis is not a debonding failure mode in strict terms, altoug it is closely associated it stress concentration near te ends of te bonded plate. A typical picture of a cover separation failure is son in Figure 6. Te cover separation failure mode is a rater brittle failure mode. Plate-End Interfacial Figure 6 FRP-plated RC beam: concrete cover separation A debonding failure of tis form is initiated by ig interfacial sear and normal stresses near te end of te plate tat exceed te strengt of te eakest element, generally te concrete. initiates at te plate end and propagates toards te middle of te beam (Figures 4f and 7). Tis failure mode is only likely to occur en te plate is significantly narroer tan te beam section, as oterise, failure tends to be by concrete cover separation (i.e. te steel bars-concrete interface controls te failure instead). CDC Figure 7. FRP-plated RC beam: plate end interfacial debonding Tis mode of debonding failure occurs in flexurally-strengtened beams ere te plate end is located in a zone of ig sear force but lo moment (e.g. a plate end near te support of a simply-supported beam) and te amount of steel sear reinforcement is limited. In suc beams, a major diagonal sear crack (critical diagonal crack, or CDC) forms and intersects te FRP plate, generally near te plate end. As te crack idens, ig APFIS

5 interfacial stresses beteen te plate and te concrete are induced, leading to te eventual failure of te beam by debonding of te plate from te concrete; te debonding crack propagates from te crack toards te plate end (Figure 8). In a beam it a larger amount of steel sear reinforcement, multiple sear cracks of smaller idts instead of a single major sear crack dominate te beaviour, so CDC debonding is muc less likely. Instead, cover separation takes over as te controlling debonding failure mode. In oter cases, particularly en te plate end is very close to te zero-moment location, CDC debonding leads only to te local detacment of te plate end, but te beam is able to resist iger loads until cover separation occurs (Figure 4c). Te local detacment due to CDC debonding effectively moves te plate end to a ne location it a larger moment, and cover separation ten starts from tis ne end. Te CDC failure mode is tus related to te cover separation failure mode. If a flexurally-strengtened beam is also sear-strengtened it U-jackets to ensure tat te sear strengt remains greater tan te flexural strengt, te CDC debonding failure mode may be effectively suppressed. Figure 8. FRP-plated RC beam: CDC debonding DEBONDING FAILURE MODES OF SHEAR-STRENGTHENED RC BEAMS Te sear failure process of FRP-strengtened RC beams involves te development of eiter a single major diagonal sear crack or a number of diagonal sear cracks, similar to normal RC beams itout FRP strengtening (Cen and Teng 2003a, 2003b). For ease of description, te existence of a single major diagonal sear crack (te critical sear crack) is assumed enever necessary. Tis treatment is conservative because recent researc as son tat te existence of multiple cracks is beneficial for te development of te maximum debonding stress in FRP (Teng et al. 2006; Cen et al. 2007). Eventual failure of almost all test beams occurred in one of te to main failure modes: tensile rupture of te FRP and debonding of te FRP from te concrete. Te FRP rupture failure mode as been observed in almost all tests on beams it complete FRP raps and in some tests on beams it FRP U-jackets, ile te debonding failure mode as been observed in almost all tests on beams it FRP side strips and most tests on beams it FRP U-jackets. Generally, bot failure modes start it a debonding propagation process from te critical sear crack. Tensile rupture starts in te most igly-stressed FRP strip, folloed rapidly by te rupture of oter FRP strips intersected by te critical sear crack. In beams it complete FRP raps, it is also common tat many of te FRP strips intersected by te critical sear crack ave debonded from te sides over te full eigt of te beam before tensile rupture failure occurs. In beams ose failure is by debonding of te FRP from te RC beam, failure involves a process of sequential debonding of FRP strips starting from te most vulnerable strip (Figure 9). Figure 9. FRP-strengtened RC beams: debonding of FRP U-jackets APFIS

6 OTHER ASPECTS OF DEBONDING Te risk of debonding is increased by a number of factors associated it te quality of on-site application. Tese include poor orkmansip and te use of inferior adesives. Te effects of tese factors can be minimized if due care is exercised in te application process to ensure tat debonding failure is controlled by concrete. In addition, small unevenness of te concrete surface may cause localized debonding of te FRP plate but it is unlikely to cause te FRP plate to separate completely from te concrete member. Mecanical ancors and FRP U-jackets can be used in soffit plated beams to prevent plate end debonding. Te latter may be used for sear strengtening at te same time. For beams sear strengtened it FRP U-jackets and side strips, mecanical ancors can also be used to suppress FRP debonding failure, and tus cange te failure mode from debonding to rupture. Hoever, care needs to be excised to avoid local failure adjacent to te ancors. DEBONDING STRENGTH MODELS FOR FLEXURALLY-STRENGTHENED RC BEAMS Plate End Many factors control te likeliness of a particular plate end debonding failure mode for a given plated RC beam. For example, for an RC beam it a relatively lo level of internal steel sear reinforcement, eac of te plate end debonding modes (Figure 4) may become critical en te plate lengt or idt is varied. Wen te distance beteen a plate end and te adjacent beam support (plate end distance) is very small, a CDC may form, causing a CDC debonding failure of te beam (Figure 4b). If te plate end distance is increased, te CDC may fall outside te plated region, and only concrete cover separation is observed (Figure 4d). Beteen tese to modes, CDC debonding folloed by concrete cover separation (Figure 4c) may occur; tis mode is critical if te CDC debonding failure load is loer tan te sear resistance of te original RC beam as ell as te cover separation failure load so tat te load can still be increased folloing CDC debonding. As te plate end moves furter aay from te support, te cover separation mode remains te controlling mode, and te plate end crack tat appears prior to crack propagation along te level of steel tension reinforcement becomes increasingly vertical (Smit and Teng 2003). For te extreme case of a plate end in te pure bending region, te plate end crack is basically vertical (Figure 4e). For any given plate end position, if te plate idt is sufficiently small compared it tat of te RC beam, te interface beteen te soffit plate and te RC beam becomes a more critical plane tan te interface beteen te steel tension bars and te concrete, and plate end interfacial debonding (Figure 4f) becomes te critical mode. Hoever, tis mode rarely occurs en te RC beam and te bonded plate ave similar idts. Given te larger variety of parameters tat govern plate end debonding failures, te development of a reliable strengt model is not a simple task. Te recent model by Teng and Yao (2007) is te only model tat appears to cover all te variations. Te model caters for any combination of plate end moment and sear force via te folloing interaction curve: 2 V db, end M db, end + = 1.0 (1) Vdb, s M db, f ere V db,end and M db,end are te plate end sear force and te plate end moment at debonding respectively, M db,f is te flexural debonding moment, and V db,s is te sear debonding force. Te flexural debonding moment, ic is te bending moment tat causes debonding of a plate end located in te pure bending zone of a beam, is found from 0.488M u,0 M db, f = M (2) 1/ 9 u,0 ( α flexαaxialα ) ere α flex, α axial and α are tree dimensionless parameters defined by α flex = [( EI ) c, ( EI ) c,0]/( EI ) (3) c,0 α axial = E t /( Ecd ) (4) and α = bc / b, bc / b 3 (5) ere (EI) c, and (EI) c,0 are te flexural rigidities of te cracked section it and itout an FRP plate respectively; b, t and E are te idt, tickness and elastic modulus of te FRP plate respectively; E c is te elastic modulus of concrete, b c and d are te idt and effective dept of te RC beam respectively; and M u,0 is te teoretical ultimate moment of te unplated section ic is also te upper bound of te flexural debonding moment M db,f. 2 APFIS

7 Te sear debonding force V db,s, ic is te sear force causing debonding of a plate end located in a region of (nearly) zero moment, can be found from V db, s = Vc + ε v, ev it f y s ε v e ε y = (6), Es ere V c and ε V are te contributions of te concrete and te internal steel sear reinforcement to te sear v, e s capacity of te beam respectively, and V s is te sear force carried by te steel sear reinforcement per unit strain, i.e. V s = AsvEsvde / s (7) v ere A sv, E sv and s v are te total cross-sectional area of te to legs of eac stirrup, te elastic modulus and te longitudinal spacing of te stirrups respectively. In Eq. 6, ε v,e is te strain in te steel sear reinforcement, referred to ere as te effective strain, and tis effective strain may be ell belo te yield strain of te steel sear reinforcement ε y. It sould be noted tat te bonded tension-face plate also makes a small contribution to te sear debonding force V db,s but tis contribution is small and is ignored in tis debonding strengt model. Based on available test results, Teng and Yao (2007) proposed tat ε = 10 (8) v, e 1/ 2 ( α flexα Eαtα ) ere α flex and α are given by Eqs 3 and 5 respectively, ile te oter to dimensionless parameters are defined by α E = E / E (9) c and α ( t / d ) 1. 3 t = (10) For te predictions of V c in design, te design formula in any national code may be used. IC To simple and reliable IC debonding strengt models ave been developed by Teng et al. (2003) and Lu et al. (2007). Te first model (Teng et al. 2003) is a simple modification of te bond strengt model developed by Cen and Teng (2001). Lu et al. s (2007) model is based te results of an extensive finite element study. Cen et al. (2006) explored an alternative approac tat is based on rigorous analytical ork on te beaviour of te FRP-to-concrete interfaces beteen to adjacent cracks (Teng et al. 2006; Cen et al. 2007). Cen et al. s (2006) approac terefore as te most sound mecanics basis and is more versatile (e.g. it is applicable to all loading conditions). Primary researc presented in Cen at el. (2006) as son tis model to be promising, and furter ork is in progress. All te tree models mentioned above predict a stress or strain value in te FRP plate at ic IC debonding is expected to occur. According to Lu et al. s (2007) model, tis debonding stress is given by E σ dbic = 0.114(4.41 α) τ (11) max t τ max = 1. 5 f t (12) α = 3.41L ee / L d (13) 2.25 b / b c = (14) b / bc ere f t is te tensile strengt of concrete, L d (mm) is te distance from te loaded section to te end of te FRP plate ile L ee (mm) is given by L = E t (15) ee DEBONDING STRENGTH MODELS FOR SHEAR-STRENGTHENED RC BEAMS Several different approaces ave been used to predict te sear strengt of FRP-strengtened RC beams. Tese include te modified sear friction metod, te compression field teory, various truss models and te design code approac (Teng et al. 2004). Hoever, te vast majority of existing researc as adopted te design code approac ic is discussed belo. Te total sear resistance of FRP-strengtened RC beams in tis approac is APFIS

8 commonly assumed to be equal to te sum of te tree components from concrete, internal steel sear reinforcement and external FRP sear reinforcement respectively. Consequently, te sear strengt of an FRPstrengtened beam V n is given in te folloing form: V n = Vc + Vs + V (16) ere V c is te contribution of concrete, V s is te contribution of steel stirrups and bent-up bars and V is te contribution of FRP. V c and V s may be calculated according to provisions in existing design codes. Te contribution of FRP is found by truss analogy, similar to te determination of te contribution of steel sear reinforcement. To parameters are important in determining te FRP contribution: te sear crack angle ic is generally assumed to be 45 o for design use and te average stress (or effective stress) in te FRP strips intersected by te critical sear crack. Different models differ mainly in te definition of tis effective stress. It may be noted tat te design code approac neglects te interactions beteen te external FRP and internal steel stirrups and concrete. Te validity of tis assumption as been questioned by several researcers (e.g. Teng et al. 2002; Denton et al. 2004; Qu et al. 2005; Moamed Ali et al. 2006), but te approac is te least involved for design, most mature and appears to be conservative for design in general. Te most advanced model for FRP debonding failure folloing te design code approac is probably tat developed by Cen and Teng (2003b) ic employed an accurate bond strengt model (Cen and Teng 2001), leading to accurate predictions. According to Cen and Teng (2003b), te contribution of te FRP to te sear strengt of te RC beam for a general strengtening sceme it FRP strips of te same idt bonded on bot sides of te beam (Figure 10) and it an assumed critical sear crack of θ =45, is given by ( sin + cos ) V, e = 2 f et (17), s ere f,e is te average stress of te FRP intersected by te sear crack at te ultimate limit state, t is te tickness of te FRP, is te idt of eac individual FRP strip (perpendicular to te fibre orientation), s is te orizontal spacing of FRP strips (i.e. te centre-to-centre distance of FRP strips along te longitudinal axis of te beam), is te angle of te inclination of fibres in te FRP to te longitudinal axis of te beam (measured clockise for te left side of te beam as son in Figure 2), and,e is te effective eigt of te FRP bonded on te eb: e = zb z (18), t ere z t and z b are te coordinates of te top and te bottom ends of te effective FRP (Figure 10): = (19) z t d, t zb = 0.9d ( d ) (20) in ic d,t is te distance from te compression face to te top end of te FRP (tus d,t = 0 for complete rapping), is te eigt of te beam, and d is te distance from te compression face to te loer end of te FRP. Wen FRP is bonded to te full eigt of te beam sides, Eq. 18 reduces to, e = 0. 9d as z t =0 and z b =0.9d. 0.1d Sear crack tip b f d,t z t T f 0.9d d,e θ z b z d b Figure 10. A general sear strengtening sceme Te FRP stress distribution at debonding failure is non-uniform ciefly because te bond lengts of te FRP strips vary it te vertical position of te critical sear crack at a given section. Cen and Teng (2003b) expressed te average (or effective) stress in te FRP along te critical crack f,e at te ultimate limit state as f, e = D σ (21),max in ic σ,max is te maximum stress tat can be reaced in te FRP intersected by te critical sear crack and D is te stress distribution factor: APFIS

9 f (22) σ,max = min E ' α L f c t πλ 1 cos 2 2 if λ 1 πλ πλ sin (23) D = 2 π 2 1 if λ > 1 πλ ere te coefficient α as te best fit value of and te 95 percentile caracteristic value of for design based on Cen and Teng s (2001) bond strengt model, L reflects te effect of bond lengt and te effect of te FRP-to-concrete idt ratio. Te expressions for L and are 1 if λ 1 (24) L = πλ sin if λ < s sin 2 (25) = 2 1+ s sin Note tat ( sin ) s is less tan 1 for FRP strips it gaps. It becomes 1 en no gap exists beteen FRP strips and for continuous seets or plates, yielding te loer limit value of 2 2 for. Te normalised maximum bond lengt λ, te maximum bond lengt L max and te effective bond lengt L e of te FRP strips are given by L λ = max (26) L e, e for U jackets sin (27) Lmax =, e for side plates 2sin E t L e = (28) ' fc Te number 2 appears in te denominator for side plates in Eq. 27 because te FRP strip it te maximum bond lengt appears at te loer end of te critical sear crack for U-jacketing but at te middle for side plates. Equation 23 is applicable to bot U-jackets and side strips. Te actual calculated values are different for tese to cases even if te configuration of te bonded FRP is te same on te beam sides because te maximum bond lengt L max for U-jackets is tice tat for side strips (see Eq. 27). CONCLUDING REMARKS Tis paper as been concerned it debonding failures of RC beams strengtened in eiter flexure or sear it externally bonded FRP reinforcement. A systematic classification of possible debonding failure modes as been presented. Te mecanisms and processes of te different debonding failure modes ave been examined in detail. Furtermore, advanced strengt models for te key debonding failure modes ave been summarised. Te materials presented in tis paper may be directly applied in te practical design of FRP strengtening systems for RC beams and serve as a useful basis for te future development of design provisions in design codes and guidelines. APFIS

10 ACKNOWLEDGMENTS Tanks are due to Drs L. Lam, X.Z. Lu and S.T. Smit as ell as Professors J. Yao, L.P. Ye and H. Yuan, among oters, for teir contributions to te researc ic forms te basis of te information presented in tis paper. Tey ould also like to acknoledge te financial support provided by te Researc Grants Council of te Hong Kong Special Administrative Region and te Natural Science Foundation of Cina, Te Hong Kong Polytecnic University and te Royal Society (Grant No. IS 16657). REFERENCES Buyukozturk, O., Gunes, O. and Karaca, E. (2004). Progress on understanding debonding problems in reinforced concrete and steel members strengtened using FRP composites, Construction and Building Materials, 18(11), Cao, S.Y., Cen, J.F., Teng, J.G., Hao, Z. and Cen, J. (2005), in RC beams sear strengtened it complete FRP raps, Journal of Composites for Construction, ASCE, 9(5), Cen, J.F. and Teng, J.G. (2001) Ancorage strengt models for FRP and steel plates bonded to concrete, Journal of Structural Engineering, ASCE, 127(7), Cen, J.F. and Teng, J.G. (2003a) Sear capacity of FRP strengtened RC beams: FRP rupture, Journal of Structural Engineering, ASCE, 129(5), Cen, J.F. and Teng, J.G. (2003b) Sear capacity of FRP strengtened RC beams: FRP debonding, Construction and Building Materials, 17(1), Cen, J.F., Teng, J.G. and Yao, J. (2006), "Strengt model for intermediate crack debonding in FRPstrengtened concrete members considering adjacent crack interaction", Proceedings, 3rd International Conference on FRP Composites in Civil Engineering (CICE 2006), December, Miami, Florida, USA, Cen, J.F., Yuan, H. and Teng, J.G. (2007), " failure along a softening FRP-to-concrete interface beteen to adjacent cracks in concrete members, Engineering Structures, 29, Denton, S.R., Save, J.D. and Porter, A.D. (2004) Sear strengtening of reinforced concrete structures using FRP composites, Proceedings, International Conference on Advanced Polymer Composites for Structural Applications in Construction, Woodead Publising Limited, Abington Cambridge U.K., Lu, X.Z., Teng, J.G., Ye, L.P and Jiang, J.J. (2007). Intermediate crack debonding in FRP-strengtened RC beams: FE analysis and strengt model, Journal of Composites for Construction, ASCE, 11(2), Moamed Ali M.S., Oelers, D.J. and Seracino R. (2006). Vertical sear interaction model beteen external FRP transverse plates and internal steel stirrups, Engineering Structures, 28(3), Oelers, D.J. and Seracino, R. (2004). Design of FRP and Steel Plated RC Structures, Elsevier, UK. Qu, Z., Lu, X.Z. and Ye, L.P. (2005) "Size effect of sear contribution of externally bonded FRP U-Jackets for RC beams", Proceedings, International Symposium on Bond Beaviour of FRP in Structures, 7-9 December, Hong Kong, Cina, Smit, S.T. and Teng, J.G. (2002a). FRP-strengtened RC beams-i: Revie of debonding strengt models, Engineering Structures, 24(4), Smit, S.T. and Teng, J.G. (2002b). FRP-strengtened RC structures. II: Assessment of debonding strengt models, Engineering Structures, 24(4), Smit, S.T. and Teng, J.G. (2003). Sear-bending interaction in debonding failures of FRP-plated RC beams, Advances in Structural Engineering, 6(3), Teng, J.G. and Yao, J. (2007). Plate end debonding in FRP-plated RC beams-ii: Strengt model, Engineering Structures, 29(10), Teng, J.G., Lam, L., Can, W. and Wang, J.S. (2000). Retrofitting of deficient RC cantilever slabs using GFRP strips, Journal of Composites for Construction, ASCE, 4(2), Teng, J.G., Cen, J.F., Smit, S.T. and Lam, L. (2002). FRP-Strengtened RC Structures, Jon Wiley and Sons, UK. Teng, J.G., Smit, S.T., Yao, J. and Cen, J.F. (2003). Intermediate crack induced debonding in RC beams and slabs, Construction and Building Materials, 17(6&7), Teng, J.G., Lam, L. and Cen, J.F. (2004). Sear strengtening of RC beams using FRP composites, Progress in Structural Engineering and Materials, 6, Teng, J.G., Yuan, H. and Cen, J.F. (2006). FRP-to-concrete interfaces beteen to adjacent cracks: teoretical model for debonding failure, International Journal of Solids and Structures, 43(18-19), Yao, J. and Teng, J.G. (2007). Plate end debonding in FRP-plated RC beams-i: Experiments, Engineering Structures, 29(10), APFIS