【正文】 ply improved the shear capacity by providing horizontal restraint. ● The shear design algorithms provided acceptable and conservative estimates for the strengthened beams. Remendations for future research are as follows: ● Experimental and analytical investigations are required to link the shear contribution of FRP with the load condition. These studies have to consider both the longitudinal steel reinforcement ratio and the concrete strength as parameters. Laboratory specimens should maintain practical dimensions. ● The strengthening effectiveness of FRP has to be addressed in the cases of short and very short shear spans in which arch action governs failure. ● The interaction between the contribution of external FRP and internal steel shear reinforcement has to be investigated. ● To optimize design algorithms, additional specimens need to be tested with different CFRP amount and configurations to create a large database of information. ● Shear design algorithms need to be expanded to include strengthening with aramid 16 FRP and glass FRP sheets in addition to CFRP. 6. Nomenclature A: Shear span fA :Area of CFRP shear reinforcements=2t f w f wb : Width of the beam crosssection D: Depth from the top of the section to the tension steel reinforcement centroid fd :Effective depth of the CFRP shear reinforcement (usually equal to d for rectangular sections and dyts for Tsections) fE :Elastic modulus of FRP (GPa) 39。 and CFRP debonding. Furthermore, two limits on the contribution of CFRP shear were proposed. The first limit was set to control the shear crack width and loss of aggregate interlock, and the second was to preclude web crushing. Also, the concrete strength and CFRP wrap ping schemes were incorporated as design parameters. In recent study [9,10], modifications were proposed to the 1998 design approach to include results of a new study on bond mechanism between CFRP sheets and concrete surface [14]. In addition, the model was extended to provide the shear design equations in Eurocode as well as ACI format. Comparing with all test results available in the literature to date, 76 tests, the design approach showed acceptable and conservative estimates [10,13]. In this section, the summary of the design approach is presented. The parison between experimental results and the calculated factored shear strength demonstrates the ability of the design approach to predict the shear capacity of the strengthened beams. demonstrates the ability of the design approach to predict the shear capacity of the strengthened beams. . Summary of the shear design approach — ACI format In traditional shear design (including the ACI Code), the nominal shear strength of an RC section is the sum of the nominal shear strengths of concrete and steel shear reinforcement. For beams strengthened with externally bonded FRP reinforcement, 10 the shear strength may be puted by the addition of a third term to account of the FRP contribution. This is expressed as follows: The design shear strength, nV? , is obtained by multiplying the nominal shear strength by a strength reduction factor for shear, ? . It was suggested that the reduction factor ? = given in ACI [12] be maintained for the concrete and steel terms. However, a more stringent strength reduction factor of for the CFRP contribution was suggested w10x. This is due to the relative novelty of this repair technique. Thus, the design shear strength is expressed as follows. . Contribution of CFRP reinforcement to the shear capacity The expression used to pute shear contribution of CFRP reinforcement is given in Eq. (3). This equation is similar to that for shear contribution of steel stirrups and consistent with the ACI format. The area of CFRP shear reinforcement, fA , is the total thickness of the sheet (usually ft2 or sheets on both sides of the beam) times the width of the CFRP strip f? . The dimensions used to define the area of CFRP in addition to the spacing fs and the effective depth of CFRP, fd ， are shown in Fig. 12. Note that for continuous vertical shear reinforcement, the spacing of the strip, fs , and the width of the strip, f? , are equal. In Eq. (3), an effective average CFRP stress fef , smaller than its ultimate strength, fuf , was used to replace the yield stress of steel. At the ultimate limit state for the member in shear, it is not possible to attain the full strength of the FRP [7,13]. Failure is governed by either fracture of the FRP sheet at average stress levels well 11 below FRP ultimate capacity due to stress concentrations, debonding of the FRP sheet from the concrete surface, or a significant decrease in the post cracking concrete shear strength from a loss of aggregate interlock. Thus, the effective average CFRP stress is puted by applying a reduction coefficient, R, to the CFRP ultimate strength as expressed in Eq. (4). The reduction coefficient depends on the possible failure modes (either CFRP fracture or CFRP debonding). In either case, an upper limit for the reduction coefficient is established in order to control shear crack width and loss of aggregate interlock. . Reduction coefficient based on CFRP sheet fracture failure The proposed reduction coefficient was calibrated on all available test results to date, 22 tests with failure controlled by CFRP fracture [10， 13]. The reduction coefficient was established as a function of ffE? (where f? is the area fraction of CFRP) and expressed in Eq.(5) for ?ff E? GPa. . Reduction coefficient based on CFRP debonding failure The shear capacity governed by CFRP debonding from the concrete surface was presented [9,10]as a function of CFRP axial rigidity, concrete strength, effective depth of CFRP reinforcement, and bonded surface configurations. In determining the reduction coeffici