A theoretical model for including the effect of monotonic shear loading in the analysis of reinforced concrete beams

• The proposed model effectively incorporates the effect of shear loading.
• The transverse reinforcement is an effective mechanism of shear transfer.
• The effect of diagonal cracking is quite adequately captured.
• The proposed model quite accurately predicts the response of beams failing in shear.
• Traditional beam theories should be avoided when analyzing shear-critical beams.

This paper presents a model for the analysis of reinforced concrete beams under monotonic loading conditions, including axial, bending, and shear forces, in order to effectively capture the mechanisms of shear transfer. The proposed model, or “PR model,” is based upon the Timoshenko Beam Theory, with the additional inclusion of two significant elements: a parabolic-shaped variable shear strain profile where the concrete is in compression and a straight line segment bounded by the neutral axis on the one hand and by the longitudinal reinforcement in tension on the other. The profile is defined by only three parameters, which are obtained by satisfying inter-layer longitudinal equilibrium at three strategic locations. The constitutive material model for reinforced concrete follows the basic assumptions of the Modified Compression Field Theory (hereinafter “MCFT”). The validity of the model is established by analyzing its results under Bresler–Scordelis and Vecchio–Shim experimental tests. The model is further tested through comparison with additional traditional kinematic assumptions. Despite the assumption of a simple shear strain profile, the PR model gives reasonable predictions of the load–deflection response and the ultimate load capacity for the experimental tests validated. Therefore, it is suitable for analysis of shear-critical reinforced concrete beams subjected to monotonic loading conditions. However, additional validation tests are required for proving the accuracy of the proposed model. Additional developments of the formulation are still required extending it to cross sections different from the rectangular one and to general loading conditions.