Failure criterion for reinforced concrete beams and plates subjected to membrane force, bending and shear

Abstract

Abstract In this paper, a failure criterion for reinforced concrete plates is derived through the kinematic method in the framework of the limit analysis theory. This criterion is expressed in terms of the stress resultant variables: membrane force, shear force and bending moment at once. The aim of the authors is to be able to predict the failure of reinforced concrete plate structures in statics or in slow dynamics using directly the internal forces (membrane and shear forces and moment) resulting from a finite-element computation. In a first step, a beam criterion is derived. The closed form expression of the criterion shows that it is made up of two parts, one independent of the moment (i.e. depending only on the normal force and the shear force) and one depending on the normal force, the shear force and the bending moment. This structure of the criterion allows to determine two failure modes: shear failure and bending failure. Then in a second step, the beam criterion is extended to the case of reinforced concrete plates. The obtained criterion is partly numerical and partly a close form expression. It gives an upper bound of the load, and when this limit load is reached, the criterion is able to supply, on one hand, the failure mode (as seen in the beam case) and, on the other hand, the angles of the failure plane in the reinforced concrete plate section. Thirdly, the criterion is implemented in the finite element software Europlexus and validated with respect to punching experimental tests. We show that the criterion must be used with an effectiveness factor applied on the concrete compressive strength.