J.M. Rotter

Linear bifurcation of perfect column-supported cylinders: Support modelling and boundary conditions

Abstract Large elevated silos and tanks are generally supported on a number of columns. The discrete supports of the columns give rise to high stresses adjacent to the column terminations. In particular, very high meridional compressive stresses arise above each column termination and these can lead to buckling of the shell at a load much lower than that for a uniformly supported shell. This paper presents a study of the linear bifurcation buckling behaviour of column-supported thin elastic perfect cylinders using the finite element method. Cylinders on both rigid and flexible column supports are studied, and the effects of varying several shell parameters are examined. The effects of the top and bottom edge boundary conditions are also investigated. It is well recognised that the linear bifurcation load is only an upper bound on the actual elastic buckling load, because the effects of large deflections and initial imperfections are ignored. Nevertheless, our understanding of the buckling behaviour of these structures is so limited that the results obtained here provide a significant starting point from which more elaborate studies may follow.

The effects of patch loads on thin-walled steel silos

This paper reports on the results of a detailed parametric study into the effects of patch loads on the stresses in thin-walled circular steel silos. Firstly, an analysis of the effects of a typical patch load on the stresses in a silo wall is presented. The results show that the stresses set up are complex and that they could potentially lead to failure of the silo by either elastic buckling or plastic collapse. A parametric study is then conducted which examines the effects of varying the circumferential width of the patch load, the vertical extent of the load, the point of application of the load and the pressure distribution within the load. The results show that the circumferential width of the applied load and the pressure distribution both strongly affect the form and magnitude of the stresses produced in the silo wall. The magnitudes of stresses in the silo wall were found to vary almost linearly with the vertical extent of the patch load.

Strengthening silos and tanks against elephant's foot buckling

Publisher Summary The chapter demonstrates the boundary condition incompatibility that leads to elephants foot buckling in metal silos and addresses tanks using a light ring attached at a critical position on a shell wall. Metal silos and tanks are susceptible to an elastic-plastic instability failure at the base boundary condition known as elephants foot buckling, due to its characteristic shape. This form of buckle occurs under high internal pressure accompanied by axial forces in the shell structure. Current international standards for both static design and earthquake design include a provision to ensure that this failure mode is prevented. However, this is done by increasing the wall thickness of the bottom course or strake. The strengthening effect should be sensitive to the size of a ring stiffener, with rings that are too small and rings that are too large, both causing lower strengths than the optimal ring size. The chapter presents an interesting example of a structural behavior in which the provision of a larger amount of material than the optimum leads to reduced strength. The results are suitable for generalization and adoption into international standards for the structural design of cylindrical shells.