Elephant's foot buckling in pressurised cylindrical shells

Metal cylindrical bins, silos and tanks are thin shell structures subject to internal pressure from stored materials together with axial compression from the frictional drag of stored materials on the walls and horizontal loads. The governing failure mode is frequently buckling under axial compression. The internal pressure exerted by the stored fluids or solids can significantly enhance the buckling strength, but high internal pressures lead to severe local bending near the base. Local yielding then precipitates an early elastic-plastic buckling failure. This failure mode, commonly known as “elephant's foot buckling”, has received relatively little attention to date and until recently was often ignored in tank and silo design.
This problem is an unusual buckling condition, because it involves very high tensile stresses in one direction, coupled with rather small compressive stresses in the orthogonal direction. Thus, although it is a buckling failure involving considerable plasticity, it occurs at low buckling stresses and under conditions that appear to be classically “slender”. The normal concatenation of “slender” with “elastic” in buckling formulations does not apply at all here. This paper describes alternative approaches to the formulation of design rules for the elastic-plastic instability and collapse of axially-loaded internally-pressurised thin cylindrical shells adjacent to the base support. The differences between the different approaches arise from different conceptual models for the manner in which an elastic-plastic slender structure instability should be treated.