A substantial number of studies have been done on the shear strengthening of reinforced concrete (RC) beams with externally bonded carbon fibre reinforced polymers (CFRP). However, in reference to shear, there are still many questions concerning the complexity and nature of the failure mechanism of RC structures strengthened in shear using CFRP. This is particularly true for concrete deep beams because of the nonlinearity of the stress distribution. This study had the goal of developing a simple procedure or model for estimating the shear capacity of RC deep beams strengthened with CFRP sheets. The proposed model was designed based on an extension of the strut-and-tie model (STM) used for un-strengthened RC deep beams to the case of those shear strengthened with CFRP sheets. The technique avoided the traditional trial-and-error procedure for obtaining the unknown coefficients of the proposed model. It utilized a particle swarm optimization algorithm (PSO), in which the optimal STM of an CFRP-strengthened RC beam was determined by searching for the optimum unknown coefficients (stress distribution and concrete tensile stress reduction factors). This model considered the effects of two CFRP failure modes, namely the CFRP debonding and CFRP tensile rupture failure modes. The proposed model was validated using experimental data collected from the current study and existing literature. The hybrid PSO-STM predicted a mean value = 1.1, SD = 0.098, and coefficient of variation (CoV) = 8.9%. These results showed that the proposed model has high accuracy and consistency and it can accurately estimate the ultimate shear strength of CFRP-strengthened RC deep beams.
This study proposes an energy absorption model for predicting the effect of loading rates, concrete compressive strength, shear span-to-depth ratio, and longitudinal and transverse reinforcement ratio of reinforced concrete (RC) beams using the particle swarm optimization (PSO) technique. This technique avoids the exhaustive traditional trial-and-error procedure for obtaining the coefficient of the proposed model. Fifty-six RC slender and deep beams are collected from the literature and used to build the proposed model. Three performance measures, namely, mean absolute error, mean absolute percentage error and root mean square error, are investigated in the proposed model to increase its accuracy. The design procedure and accuracy of the proposed model are illustrated and analysed via simulation tests in a MATLAB/Simulink environment. The results indicate the minimal effect of swarm size on the convergence of the PSO algorithm, as well as the ability of PSO to search for an optimum set of coefficients from within the solution space.
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