Plastic Collapse, Shakedown and Hysteresis

Abstract

Recent analytical research on the topic of plastic collapse has led to the development of a new method which permits the direct computation of the generalized shakedown load of conventional rigid frame structures composed of flexural members made of elastic‐perfectly plastic materials. This new method is entirely based on energy principles and has led to the novel insight that alternating plasticity, shakedown and plastic collapse are simply three discrete points on a generalized “incremental collapse envelope,” which is analogous to the Goodman‐Gerber diagram for predicting fatigue strength of metals. Moreover, this new method for predicting the ultimate strength of rigid frame structures subject to varying‐intensity repeated loads can be generalized to yield information on useful life in a manner analogous to the Palmgren‐Miner Law for the cumulative fatigue damage of metals. Illustrative results from the application of the new method are given for one‐bay, two‐bay and three‐bay frame structures.