Reduced Stiffness Buckling Analysis of Aboveground Storage Tanks with Thickness Changes

Abstract

The Reduced Stiffness Analysis (RSA) to compute lower bounds to buckling loads of shells has been employed by a number of researchers as a simple way to evaluate the buckling capacity of shells that display unstable behavior and imperfection-sensitivity. It allows the use of simple eigenvalue analysis, without having to perform incremental nonlinear analysis, and is based on the physical behavior of the shell which recognizes that a significant contribution to the stability of a shell under lateral pressure is provided by its membrane stiffness. Unstable post-critical behavior is associated with the loss of this stabilizing membrane contribution. Past use of the approach has been mainly restricted to cases of uniform shell thickness and uniform pressures in the circumferential direction, in which case analytical solutions are possible. Recent applications by the authors and other researchers have shown ways to compute the lower bounds using finite element analysis, for which a modified eigenvalue analysis is constructed by neglecting the membrane contributions to the matrix containing the initial stresses. This paper illustrates the application of the methodology to cases of pressure loaded shells with thickness changes in the meridional direction. A semi-analytical finite element code has been employed for the buckling analysis when uniform pressures act on aboveground steel tanks. The tanks are representative of those constructed for the oil industry, with diameter to thickness ratios of the order of 3000, and height to diameter ratios lower than one.