On the Validity of the Plastic Theory of Structures for Collapse Under Highly Localized Loading

Abstract

This paper investigates the significance of structural theory solutions for structures composed of perfectly plastic materials when the loading is of a highly localized nature. Limit analysis is applied to illustrative problems in order to compare the actual collapse loads with those provided by the structural theory. For strip loading problems it is found that, as the width of the loaded region decreases, the transition from failure predicted by structural theory to failure due to local plastic flow is very abrupt, and the structural theory is accurate even for strip widths which are small compared to the thickness of the structural element. For a circular plate under a central disk of pressure, however, the results obtained indicate that plate theory does not apply when the diameter of the disk is less than the plate thickness.