Slip-Dilatancy Model for Cracked Reinforced Concrete

A model is presented to calculate stresses, deformations, and crack width for a concrete slab or a shell wall that carries in-plane forces and is reinforced by a dense regular net of steel bars and containing one or two systems of straight, parallel, equisdistant, and densely distributed cracks. Friction on the cracks (aggregate interlock) and dilatancy due to their slip is approximately taken into account, and slipping cracks without contact are also allowed. The resulting stiffness matrix for concrete with frictional cracks is nonsymmetric and involves cross-terms relating the shear stress (or strain) and the normal strain (or stress), which implies that the principal strains and stresses in concrete are not co-axial. The proposed service stress design with crack slip never predicts smaller values of stresses in steel and concrete and of crack width than the classical frictionless design without crack slip. Significantly larger values are obtained when the angle between steel bars and principal stress is large. A single system of slipping cracks in contact is found to be always the critical case for maximum stresses and crack width.