Plastic-Rigid Analysis of Long Beams Under Transverse Impact Loading

Abstract

Abstract The object of this paper is to set forth the results of an investigation of the behavior of long beams under transverse, constant-velocity impact loading, when a plastic-rigid type of analysis is adopted. It was expected that such an analysis would be satisfactory for problems involving large strains, and easier to evaluate than the corresponding elastic-plastic solution. Consideration is first given to the case of ideal plasticity. Elastic strains are neglected and the material of the beam is assumed to flow plastically at a constant yield limit. In this case expressions for the bending moment, shear force, curvature and deflection distributions along the beam are obtained analytically for any given impact velocity. The manner in which the solution for a beam having an elastic-ideally plastic bending moment-curvature relationship converges to the plastic-rigid solution, as EI increases, is discussed. Consideration is next given to the case of work-hardening where the material is assumed to obey a plastic-rigid bending moment-curvature relationship consisting of a straight line with nonzero slope. Unfortunately, difficulty arises in finding a solution analytically in this case. However, by considering the solution for a beam having the corresponding elastic-plastic bending moment-curvature relationship and a large EI-value, some speculation as to the probable form of the solution may be made.