Buckling in Eccentrically Discharged Silos and the Assumed Pressure Distribution

Eccentric discharge in slender metal silos is known to be one of the most critical load conditions, responsible for many silo buckling disasters in the past. The high failure rate may be significantly attributed to difficulties in devising a suitable wall pressure representation for this condition. Where the flow of stored solids is eccentric and has partial contact with the wall in a slender silo, the solid exerts much lower pressures than the adjacent stationary solid. This pressure drop leads to very high local axial compression and causes buckling failure. Experimentally measured pressures indicate that a significant rise in pressure may occur just outside the flow channel, but its form and magnitude are not yet well understood because very detailed and expensive instrumentation is needed to obtain data that can define it. This paper explores the nonlinear structural behavior and buckling of a slender metal silo with and without specific inclusion of an adjacent rise in pressure, to determine whether it is a necessary part of any design pressure representation. To assist this investigation, the mechanics of the nonlinear behavior of a cylindrical silo under this load condition is explored using the analogy of a propped cantilever slice beam. Advantage is taken of a particular load condition that leads, by chance, to buckling at the same load factor for both linear and geometrically nonlinear analyses. This special case permits the detrimental effect of wall flattening and the beneficial effect of the changing prebuckling stress pattern to be explored to give a deeper insight into the behavior. The slice-beam analogy may also be generalized to describe the nonlinear behavior of any thin-walled cylindrical shell under meridional strip-like loads acting on part of the circumference.