Shear Capacity Model with Variable Orientation of Concrete Stress Field for RC Beams Strengthened by FRP with Different Inclinations

A design-oriented analytical model able to evaluate the shear capacity of reinforced concrete (RC) beams strengthened with fiber-reinforced polymer (FRP) sheets or strips oriented in any direction is proposed. The formulation of the model is based on the variable-inclination stress-field approach, aiming to extend the provisions of current European standards to beams strengthened in shear using FRP. The main novelty of the model lies in taking into account the possible different inclination of steel stirrup and FRP reinforcement in determining the orientation of a compressed concrete stress field, and in shear strength evaluation, overcoming the approximation of the known models with variable inclination of the concrete strut in the assessment of concrete strut capacity, in which the value that has to be assigned to the shear reinforcement direction is not defined, that is, either that of the steel stirrup or the external FRP reinforcement. The proposed model is able to take into account different steel stirrup and external FRP shear reinforcement orientation in assessing the reduction of the steel transverse reinforcement efficiency due to the brittle failure of the composite and also as a function of the effective composite to yielding steel strain ratio. Moreover, regarding the former aspect, a simplified approximate procedure is proposed for solving the drawbacks related to verifying compressed concrete strength in the suggested method of application of code models for RC beams strengthened by means of FRP reinforcement inclined with a different slope from the pre-existing steel stirrup. Complete and U-shaped schemes are considered. The effectiveness of the proposed model adopting different relations for assessment of the FRP effective strains proposed in the literature is investigated, differentiating them by shape of the cross section and by the possible presence of fiber-anchoring devices. The shear capacity predicted by the model and those obtained using international codes and literature models are compared against the experimental results, proving that the proposed model is the most effective in predicting the shear strength when considering specimens having steel stirrups and FRP shear reinforcement arranged with different inclinations.