Shear strength of reinforced concrete beams: Size effect and its fracture-mechanics basis

Accurate prediction of the shear strength of reinforced concrete beams is of paramount importance for shear-critical structures. Despite the complexity of failure mechanisms, shear failure can be comprehensively investigated by means of nonlinear cohesive (or quasibritle) fracture mechanics. This paper presents a review of recent works on shear failure of reinforced concrete beams at Northwestern University and shows that 1) the incorporation of fracture mechanics in concrete shear failure leads to correct prediction of the size effect on the shear strength; 2) the size effect in concrete shear can be analytically described by Bažant's size effect law for nominal strength of geometrically similar structures made of quasibrittle materials and failing after stable crack growth; 3) an approximate semi-empirical formula for shear strength can be derived by asymptotic matching after establishing the small- and large-size asymptotes, and its parameters can be identified by fitting the existing large database after minimizing the statistical bias; and 4) the size effect formula can be extended to beams with shear reinforcement. When compared with the compiled database and computational studies, the theoretical analysis based on cohesive fracture mechanics shows a satisfactory agreement with tests as well as finite element simulations. Furthermore, as shown by statistical analysis, if the size effect in shear strength is ignored or described by an unrealistic formula, a significant reduction of the structural safety margin, manifested by a change of failure probability from 10^-6 to as high as 10^-3, must be expected for beams of large sizes, regardless of whether the shear reinforcement is added or not.