Elastic-plastic failure loads of plane frames

Abstract

When deformations become finite, the load factor required to produce rigid-plastic deformation of a plane frame under proportional loading differs from the load factor at collapse as given by simple plastic theory. The effect of all work terms involving the squares of member rotations is investigated and a simple formula derived. The effect of finite deformations on the load capacities of elastic-plastic frames is then studied. It is shown theoretically that, if certain approximations are made, the Rankin© load, based on the rigid-plastic failure load and the lowest critical load, give a close estimate of the actual failure load of such a structure. The nature of the approximations made to arrive at this result shows under what circumstances the Rankine load cannot be expected to provide a close estimate of failure. Experimental and theoretical results illustrating the degree of correlation are presented and discussed.