Hyperboloids of Revolution Supported on Columns

The governing homogeneous equations of the bending theory of thin shells of revolution are solved for a hyperboloid of revolution in a form suitable for representing a column-supported boundary. For the case of dead loading, a superposition representation is used to derive a set of explicit expressions for the stress resultants. The arbitrary constants are evaluated using boundary conditions which are representative of those occurring in hyperbolic cooling towers. The data presented indicates that the consideration of the discrete support system in the analysis, rather than the idealized continuous boundary, results in an increase in stresses in the vicinity of the base of the shell. Parametric studies are also shown to illustrate the influence of the total number of columns and the shell thickness on the magnitude of the stress resultants near the base of the shell.