P–I diagram method for combined failure modes of rigid-plastic beams

Closed-form solutions of pressure-impulse (P–I) diagrams for simply supported and fully clamped rigid-plastic beams subjected to impact load are developed. Two failure categories, i.e., bending failure and shear failure, are considered and the responses of the beams are analyzed based on five transverse velocity profiles. With proper failure criteria, the critical P–I equations for bending and shear failure are derived. After the simplification of the critical P–I equations, the influences of the shear-to-bending strength ratio and the boundary conditions on the P–I diagrams are discussed. The results are compared with those based on a single-degree-of-freedom (SDOF) model. It is shown that the proposed P–I diagram method can be conveniently applied to assess beam damage extents and damage patterns. Especially, the P–I diagrams have good agreement with those based on an elastic, perfectly plastic model when severe damage occurs.