Lateral Influence Coefficients for a Thin Conical Shell Frustum

Thin conical shell components are often used in vertical process vessels, bins, and water storage tanks. When exposed to the elements, such structures may be subjected to lateral wind forces and seismic accelerations. For calculations of lateral response of such structures with simplified models, in the form of vertical beams, lateral influence coefficients for thin conical frustum shells are useful. To compute lateral influence coefficient for conical frusta, asymmetric solutions of shell equations for cones are needed. The literature on asymmetric solutions for conical shells is sparse. Hoff [1] derived equations suitable over a limited range of parameters for asymmetric response of conical shells and indicated possible solutions using Fourier and power series. In his discussion of Hoff’s work, Pohle [2] indicated that an asymptotic solution of the equations is useless because of its validity over an impractical range of parameters. Seide [3] derived equations that removed the limitations of Hoff’s equations. Wilson [4] proposed solutions by separation of variables and power series. The slowly converging power series were summed using a computer for a conical panel under distributed loading. Chandrashekhar and Karekar solved the equations for a conical frustum under wind loading by expanding the solution in Fourier series in the circumferential direction, and applying finite differences in the meridional direction. The difference equations were solved using a computer. Derived here are closed-form expressions for thin conical shell frusta based on the membrane theory of shells. These influence coefficients are compared with finite element results for a conical shell, with specific geometry and material properties, for which wall bending is included.