On the Plastic Buckling of Plates According to the Flow Theory

Abstract

IN THIS JOURNAL OF July, 1950, Dr. Pearson calculates the plastic buckling stress of a compressed plate that is simplysupported at both unloaded sides, assuming plastic flow. He also assumes that during buckling the entire plate deforms plastically in analogy with the tangent modulus theory (Engesser load) for columns. In contrast, in a previous paper, Handelman and Prager had assumed that unloading occurs in part of the plate in analogy with the reduced modulus theory (von Karman load) for columns. Handelman and Prager's assumption led to disagreement with tests, as is shown in Fig. 1, where the plastic buckling stress <rcr is plotted against <TE/E (<TE is the elastic buckling stress and E is the elastic modulus). The circles refer to the experiments by Pride and Heimerl. In his paper, however, Dr. Pearson tries to show that , if the entire plate is assumed to remain plastic, a fair agreement with the tests is obtained, as is shown in his Fig. 10 and also in Fig. 1 of this item. In Fig. 1 the curve according to the present writer's theory ' 5 is also given, as calculated by Pride and Heimerl.