Design equations for RC beams strengthened in shear with externally bonded FRPs

In this study, a new methodology to develop design equations for the FRP debonding strain is presented for reinforced concrete beams strengthened in shear with externally bonded FRPs. The proposed equations are based on a r egression analysis of a large number of numerical models. Two separate design equations are proposed: one for side-bonded FRPs, and the other for U-wrapped beams. To create the design equations, the numerical results obtained from an extensive finite element model are integrated into statistical analyses in three steps. Firstly, the response surface methodology (RSM) is used as a substitute for the finite element model. For this step, five parameters are considered: the ratio of the steel stirrups, the elastic modulus of the FRP, the thickness of the FRP, the concrete compressive strength, and the width ratio of the FRP to the concrete beam. Secondly, a Monte Carlo simulation is performed to create an extensive number of modelling results. Thirdly, a n onlinear regression analysis is employed to generate design equations describing the FRP debonding strain. The design equations of the FRP debonding strain proposed in this study are then compared with test measurements and with the strains predicted by the design guidelines of ACI, fib and BS. The new design equations are found to compare very well with a wide r ange o f independent experimental d ata. T he p roposed eq uations can b e considered as an excellent tool for practical design calculations.