A Comprehensive Formula to Predict the Shear Contribution of FRP Sheets in Strengthened Reinforced Concrete Deep Beams

Retrofitting of reinforced concrete beams using fiber-reinforced polymer (FRP) sheets is one of the most commonly used methods to enhance shear and bending behavior. A comprehensive review shows that the presented formulas are insufficiently accurate to predict the shear contribution of FRP sheets. Researchers have also studied only 45° and 90° for the FRP sheets in previous research. This paper presents a comprehensive formula for evaluating the shear contribution of full- and U-wrap FRP sheets. For this purpose, experimental data are collected for angles of 45° and 90°. Then, two experimental tests are modeled using ABAQUS software. After verifying the models, the shear contribution of FRP sheets is determined for different values of the input parameters and at the angles of 30°, 60° and 75°. Therefore, to present a formula for evaluating the shear contribution of FRP sheets, multigene genetic programming is used. The results show that the presented formula has sufficient accuracy in computing the shear contribution of FRP sheets at angles of 30°, 45°, 60°, 75° and 90° in comparison with other existing formulas from codes and literature. The effect of width, thickness, the ultimate strain of FRP, effective depth of FRP, beam shear span length, the effective depth of the concrete beam, spacing between the FRP strips, compressive strengths, angle of FRP sheets, and elasticity modulus of FRP sheets is considered on computing the shear contribution of FRP sheets. The results show that the mean absolute percentage error (MAPE), root mean square error (RMSE), and R 2 for the proposed formulas are 12.48, 9.84 and 0.98, respectively, which performs better than the other existing methods.