Mechanical behaviour and non-linear analysis of deep beams using softened truss model

The aim of this study is to expand the application of the non-linear softened truss model for membrane elements on deep beams. The softened truss model employs three equations for equilibrium, three for compatibility and four equations for the constitutive laws of materials. The constitutive equations for both the concrete and steel are based on the actually observed stress-strain relationships. The model has two important attributes. The first is the non-linear association of stress and strain. The second, and perhaps more remarkable, is the softening of concrete in compression due to tensile strains in the perpendicular direction. The softened truss model is capable of predicting the entire load-deformation history because it takes into account all the equations governing the equilibrium condition, the compatibility condition, and the constitutive laws of materials. For deep beams, one of the most important factors influencing behaviour is the effective transverse compression, which is dependent on the shear-span-to-depth ratio. For a constant shear force, the more slender a beam is, the less effective the transverse compression will be. In this study, the softened truss model is expanded to take into account the influence of this important factor. In the revised version of the model, it is shown that the effective transverse compression is not only dependent on the shear-span-to-depth ratio but also on the horizontal shear reinforcement ratio and the yield strength of the reinforcement in the longitudinal direction and the size of the specimen. The improved softened truss model is applied on 80 deep beam tests. It is apparent from the results that the revised model gives very accurate predictions of the shear strength of deep beams and is an improvement on the existing version of the model.