Energy Equivalence Approach for Analysis of Reinforced Concrete Beams under Mixed Mode Loading

Abstract

Concrete being a composite, heterogeneous material, an accurate prediction of its behaviour under combined bending and shear is an open problem. In this work, a method is proposed to address this problem by bringing an equivalence between the normal stress (σ) and shear stress (τ ). Finite element modelling is used as a tool for predicting the response of plain concrete beams under mode I and mixed mode I-II loading. Beams of three different sizes are modelled using finite element analysis and the results are validated through available experimental data. The proposed method considers a scaling factor, which is in proportion to the relative contribution of shear and normal stress. It is observed that the same amount of energy is associated with behaviour under a pure normal stress and a combined normal and shear stress field and consequently, a ratio is proposed to convert shear stress to an equivalent normal stress.