16 S..Pendbari et al I Composte Siructures 84(2008)114-124 bonded method and took around 1/8 of time compared to 2.1.2.Shear behavior of RC beams strengthened by FRPC the conventiona members strer Shear strengthening of RC elements can be provided by d i epoxy y g ible bers par f th ever.there is a gap in knowledge on the effect of impact Various experimental and analytical works related to and fatigue loadings on the beam.Repeated loading can shear strengthening of beams with different FRPC lami- lead to internal cracks in a member which can alter its nates for l.acked racked beam 701 Erki and Meier Shahav antafillou).Deniaud and Cheng Lees et al.9 Masoud et al.[73].Heffernan and Erki [74].Brena et al. Pellegrino and Modena [98].Adhikary and Mutsuyoshi nted experim [99].Zhang and Hsu [10 It was observed ed fro n the e Fib ical of ndicular to the shear cracks.Shear contribution enhanced through the use of externally bonded CFRP argely dependent on the stress range pends on se paramete ding sur e prepar The perimental studies dise sed above have hee substantiated by analytical approach at macro level.In of main and shearnt shear span to efctive depth ratio. strength of FRPC. the simpli ana strain dept of sheet across beam te lo method or working method ns with about 19%in 79wherein issues related to rational design of external strenthened RC beams for interpreting major modes o The ultimate resistance of beam ca not be taken into ng next interfac separation flexura by simple superp of shear capacity cont Parametric study was performed by Picard et al.[80 which steel and FRPC.This has been reported to be the major obstacle in development of an analytica wh s An e I on amount of the mai ultimate loa 1 strengthene d beam usually starts crete and FRPC Malek and Saadatmanesh 04.105 degrade,as cracks are developed in concrete.Stiffness deg developed equilibrium and compatibility equations using considered ir Further,compres lin ic m re,contrar assumed to be linea r in elastic models Therefore it is nec as well as after formation of crack.Khalifa et al.106 the crack generation tion in 1edearhomshearcnehe8oandPRP gn algorit comput con tribution tio strengthened RC heams 107-109 have presented analvtical models to calculate the ultimate shear capacity of strengthened beams by assuming steel and concre lan nate inear elastic b chavior of FRP materials.R hond-sli non- gn n S can et a to evaluate delamination failure mode.On the other hand ever,numerical modeling of shear strengthened RC beams Colotti et al.[88]proposed a the retical model base with FRPC has not yet been addressed adequately in open and force transfer between concrete and 2 13 Durability of rc heams strengthened by frpc gate serviceability (cracking and deformability)criteria Seasonal and daily temperature variations cause freezing Yang et al. ractu based finit erential the expansion betwee method was obs cover separation failure mode in FRPC strengthened Cross-directional (matrix dominated)properties such as RC and tensio transverse tensile/c but iound to be higbonded method and took around 1/8 of time compared to the conventional method. The quasi-static behavior of flexural members strength￾ened with FRPC is well documented in literature. How￾ever, there is a gap in knowledge on the effect of impact and fatigue loadings on the beam. Repeated loading can lead to internal cracks in a member which can alter its stiff- ness and load carrying characteristics. Barnes and Mays [70], Erki and Meier [71], Shahawy and Beitelman [72], Masoud et al. [73], Heffernan and Erki [74], Brena et al. [75] and Bonfiglioli et al. [76] presented experimental results for static and fatigue failure of beams strengthened with CFRPC sheets. It is observed from the results that fatigue life of reinforced concrete beams could be significantly enhanced through the use of externally bonded CFRPC laminate and it is largely dependent on the stress range applied to steel reinforcement. The experimental studies discussed above have been substantiated by analytical approach at macro level. In all the simplified analytical models, strain compatibility has been used to predict flexural behavior either by ulti￾mate load method or working stress method [9,29,46,77– 79], wherein issues related to rational design of externally strengthened RC beams for interpreting major modes of failure including flexural, interface separation, flexural￾shear crack and concrete cover rip off have been addressed. Parametric study was performed by Picard et al. [80], which highlights the importance of concrete compressive strength whereas An et al. [81] emphasized on amount of the main reinforcement. Stiffness of concrete structures usually starts to degrade, as cracks are developed in concrete. Stiffness deg￾radation due to cracking of concrete is not considered in the simplified linear elastic models. Furthermore, contrary to actual behavior, stress–strain curve of concrete is assumed to be linear in elastic models. Therefore, it is nec￾essary to account for the crack generation and stiffness degradation in refined non-linear analysis. Studies in this direction were performed using finite element method to capture flexural behavior of strengthened RC beams [82–86] by assuming perfect bonding between concrete￾steel and concrete-FRPC laminate. Thomsen et al. [87], for example, developed non-linear finite element models using bond-slip relationship between concrete and FRPC to evaluate delamination failure mode. On the other hand, Colotti et al. [88] proposed a theoretical model based on truss-analogy. A non-linear analysis was performed by Aiello and Ombres [89] considering tension stiffening and force transfer between concrete and FRPC to investi￾gate serviceability (cracking and deformability) criteria. Yang et al. [90] presented fracture mechanics based finite element analysis to capture debonding failure. The method was observed to successfully simulate concrete cover separation failure mode in FRPC strengthened RC beams. Sato and Vecchio [91] developed a simple equation to estimate crack spacing, its width and tension stiffening effect. 2.1.2. Shear behavior of RC beams strengthened by FRPC Shear strengthening of RC elements can be provided by epoxy bonding of FRPC materials with fibers parallel, as practically possible, to the direction of the shear stresses. Various experimental and analytical works related to shear strengthening of beams with different FRPC lami￾nates for uncracked/cracked RC beams are reported by Sharif et al. [92], Chajes et al. [93], Chaallal et al. [94], Tri￾antafillou [95], Deniaud and Cheng [96], Lees et al. [97], Pellegrino and Modena [98], Adhikary and Mutsuyoshi [99], Zhang and Hsu [100]. It was observed that the shear strength of virgin beam can be increased by 60–120% using FRPC sheets. Fiber orientation may be vertical or perpendicular to the shear cracks. Shear contribution to the total shear capacity of strengthened RC beams depends on several parameter including surface prepara￾tion, composite fabric shear reinforcement ratio, amount of main and shear reinforcement, shear span to effective depth ratio, strength of FRPC, number of FRPC layers, wrapping schemes, depth of sheet across beam section [99,101–103]. U-wrap of sheet provided the most effective strengthening for RC beams with about 119% increase in shear strength. The ultimate resistance of beam can not be taken into account by simple superposition of shear capacity contri￾butions because of complex interaction between concrete, steel and FRPC. This has been reported to be the major obstacle in development of an analytical formula that can correctly predict the ultimate load of strengthened beams in shear [101,102]. By assuming a perfect bond between concrete and FRPC, Malek and Saadatmanesh [104,105] developed equilibrium and compatibility equations using truss analogy method. Further, compression field theory was used to calculate shear force resisted by FRPC plate, crack inclination angle, stresses in stirrups before cracking as well as after formation of crack. Khalifa et al. [106] reviewed research on shear strengthening and proposed a design algorithm to compute contribution of FRPC to shear capacity of RC beams. Another group of researchers [107–109] have presented analytical models to calculate the ultimate shear capacity of strengthened beams by assuming linear elastic behavior of FRPC materials. Review on dif￾ferent shear design methods can be found in Micelli et al. [110] with commentary on adequacy of each method. How￾ever, numerical modeling of shear strengthened RC beams with FRPC has not yet been addressed adequately in open literature. 2.1.3. Durability of RC beams strengthened by FRPC Seasonal and daily temperature variations cause freezing and thawing cycles, differential thermal expansion between concrete and FRPC substrate, resulting in premature plate separation and ultimately failure of strengthened system. Cross-directional (matrix dominated) properties such as transverse tensile/compressive strength and in-plane shear were found to be highly affected by environmental effects but fiber was less sensitive to it. 116 S.S. Pendhari et al. / Composite Structures 84 (2008) 114–124