Membrane theory treatment of eccentric flows in concentric hoppers

This paper presents an initial study of the effects of an accidental eccentric flow channel that sometimes develops in the conical hopper of a metal storage silo. A simple assumed pressure regime is adopted, based on studies of eccentric discharge in cylindrical silos, and the structural actions are analysed using shell membrane theory. The results are verified against a finite element analysis. A set of equations is derived which give the complete membrane stress state in the hopper under such an unsymmetrical pressure regime.Under symmetrical loading, silo hoppers are subject to biaxial tension, with failure normally governed by material rupture due to tensile meridional membrane stresses. It is found that the eccentric flow channel leads to dramatically increased meridional membrane stresses at the transition. Compressive membrane stresses are also found near the hopper outlet and at the sides of the flow channel near the transition. A reasonably close correlation is found between the derived membrane theory equations in a right circular conical hopper and linear elastic finite element predictions.