Fracture mechanics model applied to shear failure of reinforced concrete beams without stirrups

A fracture mechanics model for the flexural-shear failure of reinforced concrete beams without stirrups is presented. A phenomenological study shows that flexural-shear failure is triggered by the propagation of a splitting crack at the level of the longitudinal reinforcement. Assuming that the ultimate shear load is reached when the splitting crack starts to propagate, a predictive model is developed. The critical load is obtained considering the energy balance of the system during splitting crack propagation. The position of the critical diagonal crack is obtained using Kim and White's semi-empirical formula. By making a number of simplifying assumptions and using the empirical formula for the assessment of the fracture energy proposed by the CEB-FIP Model Code, an analytical formula is obtained. The model is benchmarked against an empirical formula proposed by the CEB-FIP Model Code. The two formulas are shown to have the same form and the predictions are shown to be in agreement.