Hoop stress approximation in offshore design codes

For a circular cylindrical vessel with an elastic material, Lame equations can accurately predict hoop stress variation within the vessel wall. However, because of the complexity involved in Lame formulations they are seldom used in design. In this paper, Lame equations are reproduced in terms of vessel outer and material cross-sectional areas and presented in a very simple format that enables hoop stress calculation without use of any approximation. Lame equations are also presented in terms of diameter-to-wall-thickness ratios in order to perform parametric studies. For a practical range of diameter-to-wall-thickness ratios the Lame hoop stress predictions are compared with approximate solutions of a selected design codes. For a range of loading conditions, comparison of results shows that a number of design codes overestimate the hoop stress. In contrast, a selection of offshore codes is shown to underestimate the hoop stress and, for a certain loading condition some codes ignore the hoop stress effect completely. The present paper also shows how the hoop stress approximation may lead to onerous results when the true wall axial stress is derived based on design code hoop stress formulations. It is concluded that what makes the present hoop stress formulations so important in design is their ability to interpret the mechanics of behavior that Lame equations strived to reveal.