Plastic Buckling of Torispherical and Ellipsoidal Shells Subjected to Internal Pressure

Abstract

Thin metallic torispherical shells are used frequently in many industries as end closures on cylinders subjected to internal pressure and, for those torispheres which have diameter/thickness ratios greater than 400, elastic-plastic internal pressure buckling may occur. As yet, however, code rules to assist the designer with this buckling problem are not available in either the UK or the USA and one of the aims of this paper is to help to correct this situation. Elastic-plastic internal buckling pressures, for a range of perfect torispherical geometries and obtained with the aid of a sophisticated computer program, are given in the first part of the paper. These p_cr's are then utilized (a) to develop a relatively simple equation for predicting the internal buckling pressures of torispherical shells and (b) to assess the accuracy of another, even simpler, approximate buckling equation which was suggested recently (1). Next, the correlation between the theoretical predictions of p_cr and the experimental results is considered. The tests taken into account were (a) 5 in diameter machined model torispherical shells, (b) 20 in diameter spun ellipsoidal shells, and (c) 54 in diameter pressed and spun torispherical shells. The shells in (b) and (c) were not stress-relieved and a number of them were made from strain-hardening materials. The agreement between theory and experiment was good for the machined models and fairly satisfactory for the spun models. For the ellipsoidal shells there was also reasonably good agreement between the predictions of two simple design equations and the experimental results. The problems associated with the prediction of the internal buckling pressures of spun torispherical shells made from strain-hardening materials (e.g. stainless steel) are considered in the last section of the paper. Taking the results of the previous sections of the paper into account, and making some simplifying assumptions, a tentative design procedure for predicting the p_cr's of these ‘as-manufactured’ spun torispherical shells is proposed. This procedure is then checked by comparing its predictions with experimental buckling pressures found for eleven spun stainless steel heads and six crown and segment ones. The agreement between experiment and theory was quite satisfactory and it is hoped that the suggested procedure might become the first step towards the development of experimentally validated code rules for preventing the occurrence of buckling in these dished ends.