Fracture Analysis of Cracking in Concrete Beams

An energy balance criterion, based on fracture mechanics concepts, is proposed for predicting the loads at which concrete members develop rapidly propagating cracks. After an initial period during which microcracks increase slowly in length and extent over a critical region of the member, an unstable running crack develops when the rate of energy released by continuing microcrack growth exceeds the energy inputed to the system. The shape of the growing microcrack zone is determined by the stress intensity factors for the extremities of the principal axes of that zone. A critical strain energy release rate, G_c, is determined from direct tensile data and its appropriateness verified by showing that strength and size effects are correctly predicted for modulus of rupture specimens. Diagonal tension cracking load expressions for reinforced concrete beams are developed using that G_c value and energy criterion. Those expressions correctly predict the effects established from tests of the moment of shear ratio, reinforcement ratio, type of loading, and size of member.