Simplified Formulas for External Pressure Design

Design of vessels for external pressure currently requires a chart-based solution or analytical approaches which are not necessarily intuitive. In this paper, we propose simple formulas for the external pressure evaluation of pipes and other cylindrical pressure vessels. We present a conceptual comparison between the elastic and elastic-plastic stability of structural columns and that of cylindrical vessels of long, intermediate, and short length. Their common features allow an accurate and straightforward approach for external pressure design. The approach is also extended to spherical caps, conical vessels, and formed heads. We compare the method presented to the current acceptance criteria from various design codes, including the ASME Boiler and Pressure Vessel Code Section VIII, Code Case 2286, and EN 13445-3, as well as codes for steel and aluminum structures. In further discussion, the simplified method is compared against the results of more than 500 experiments on the buckling of cylindrical and spherical vessels published over the past two centuries. This simple but accurate approximation is conceptually intuitive, analytically straightforward, and shows potential utility in pressure vessel design codes, as well as piping design codes such as B31 that currently reference ASME VIII for external pressure design.1