Concentrated Loads Applied to Shallow Shells

Solutions are developed for concentrated forces and moments applied to the apex of nonaxisymmetric shallow shells. The influence of a shell's geometry and its edge support condition, on stresses and displacements, is shown through numerical examples involving each of the concentrated loadings. For a given concentrated loading, the behavior of shallow shells is similar to that of a flat plate, in the immediate neighborhood of the applied loading. However, the influence of both the shell's geometry and its edge support condition is felt significantly in a region sufficiently far removed from the point of load application. Shells having negative Gaussian curvature are shown to be particularly sensitive to tangential displacement restraints, and to lose most of their membrane load carrying capacity if tangential restraint is lacking.