Shear strength analysis and prediction for reinforced concrete beams without stirrups

The analysis of shear strength of longitudinally reinforced concrete beams, in which a constant shear force acts throughout the shear span, is performed. The shear mechanism is found to be governed by a second order differential equation linking the internal lever arm with the distance from the support. The solution of the shear governing equation is provided, and then the corresponding shear expression is parametrically defined by means of a mechanical analysis. The empirical parameters are determined from more than 900 test data and results found in the literature. The proposed shear strength formula predicts the experimental behavior in a more accurate and uniform way than most known expressions. It is also proposed a design formula, which is more consistent and reliable than the Eurocode one and even than the laborious procedures suggested by ACI Code and AASHTO Standards, since it exhibits a minor number of unsafe predictions.