Shear strength of concrete members without transverse reinforcement: A mechanical approach to consistently account for size and strain effects

Many theories and empirical formulae have been proposed to estimate the shear strength of reinforced concrete members without transverse reinforcement. It can be noted that these approaches differ not only in the resulting design expressions, but also on the governing parameters and on the interpretation of the failure mechanisms and governing shear-transfer actions. Also, no general consensus is yet available on the role that size and strain effects exhibit on the shear strength and how should they be accounted. This paper reviews the various potential shear-transfer actions in reinforced concrete beams with rectangular cross-section and discusses on their role, governing parameters and the influences that the size and level of deformation may exhibit on them. This is performed by means of an analytical integration of the stresses developed at the critical shear crack and accounting for the member kinematics. The results according to this analysis are discussed, leading to a number of conclusions. Finally, the resulting shear strength criteria are compared and related to the Critical Shear Crack Theory. This comparison shows the latter to be physically consistent, accounting for the governing mechanical parameters and leading to a smooth transition between limit analysis and Linear Elastic Fracture Mechanics in agreement to the size-effect law provided by Bazant et al.