Rough Cracks in Reinforced Concrete

Equations derived are which relate the normal and shear stresses transmitted across a crack due to aggregate interlock to the opening and slip displacements. Average strains due to a system of parallel continuous cracks are superimposed on the strains due to the solid concrete between the cracks. The response of cracked concrete reinforced by a regular net of bars is then calculated using an incremental loading procedure. The stress-displacement relations exhibit a singularity at the initial state of zero displacements and the initial crack opening must begin at zero slip. Responses to various types of loading are calculated and the variation of the secant friction coefficient, crack dilatancy due to slip and the effect of crack opening are studied. The theory allows designing for a maximum crack width if the crack spacing is known. The previously proposed slip-free concept yields limit loads which are found to correspond to the states just before the start of a rapid increase in crack opening, while the classical frictional approach yields limit loads that are achieved only after very wide cracks develop.