On membrane solutions for elevated shell-of-revolution tanks of certain meridional profiles

Abstract

This paper reports the findings of research into the possibility of certain shell forms for elevated reservoirs, initially conducted on the basis of the membrane hypothesis. In order to place the methods used and the findings obtained firmly into context, the paper begins by a review of the conditions of applicability of membrane solutions. Then, on the basis of a rectangular coordinate system, general expressions for membrane stress resultants are developed for elevated liquid-filled tanks in the form of shells of revolution of arbitrary meridian profiles. These expressions are next applied to selected profiles with zero slope at the pole (consistent with the smoothness requirements of the membrane hypothesis), and of reasonable shape for containment. A general discussion of the validity of the results, particularly for locations around the poles, is followed by a comparison of the membrane-stress variations for tanks of the same height and circular plan area, based on typical values of these dimensions. Finally, by defining a form efficiency parameter η, the tank of most desirable profile (from among the cases studied) is suggested.