Weight function calculation method for analyzing mixed-mode shear cracks in reinforced concrete beams

Based on a virtual crack extension (VCE) technique in finite element method (FEM), this paper proposes a rational method of calculating weight functions for inclined shear cracked RC beams with any geometry. As an inclined shear crack in an RC beam is geometrically determined by the absolute dimensions, shear span to beam depth ratio, crack inclined angle and crack initiation location, the relations between the weight functions and these parameters are investigated by either following theoretical equations or varying the parameters in a certain range. The range is determined to enclose the geometries of inclined critical shear cracks of a large set of RC beams which were tested under a bending load but failed due to the propagation of a critical inclined shear crack. Moreover, a method of calculating the weight functions of a shear cracked RC beam with any geometrical properties is developed numerically using the weight functions calculated and provided in this study. As a result, it is possible that the shear behaviors of RC beams can be even studied conveniently but also comprehensively following the theoretical fracture mechanic approach.