Buckling of very slender metal silos under eccentric discharge

Metal silos used to store granular solids often take the form of a cylindrical shell with an aspect ratio in the range 2 < H / D < 6 . It has long been recognised that the most serious load case for all silos is probably the condition of eccentric discharge of its stored solid, but in circular metal silos this is especially true. More failures have occurred under this condition than any other. This high failure rate is chiefly due to the complexity of the pressures exerted by an eccentrically discharging granular material, and the difficulty in understanding the pattern of stresses that develops in a shell wall under such unsymmetrical pressure regimes. The nonsymmetric behaviour of a shell structure under unsymmetrical pressures is not at all well described in the voluminous shell structures literature, and only a few studies have explored the mechanics leading to high local stresses which in turn lead to buckling failure under eccentric discharge. tudy follows an earlier initial exploration by Sadowski and Rotter (2010) [2], in which buckling in a moderately slender perfect silo was explored. Here, the work is taken further to explore a very slender structure, and to investigate the imperfection sensitivity of this failure mode. The pressures caused by eccentric discharge are characterised using the new rules of the European Standard EN 1991-4 (2006) [1] that define the actions in silos and tanks. Using this new improved description of unsymmetrical eccentric discharge pressures, it is now possible to perform relatively realistic calculations relating to this common but complicated shell buckling condition. The shell buckling calculations described here employ a pressure distribution formulated with the assumption of a parallel-sided flow channel and are undertaken using geometrically and materially nonlinear analyses in accordance with the European Standard EN 1993-1-6 (2007) [25] on the strength and stability of shells. The paper explores the structural behaviour of a slender silo under eccentric discharge, leading to buckling and including the critical effects of changes of geometry and imperfection sensitivity.