The diffusion of load into a semi-infinite sheet Parts 1 and 2

Abstract

In Part 1, the rigorous and the 'stringer-sheet' stress solutions are given for a point load applied in the plane of a semi-infinite sheet and at a finite distance from the boundary which is assumed to be free. From these are derived, by integration, some of the stresses produced by distributed loads applied along lines normal to the free boundary; attention is concentrated on the stresses along the line of action of the applied loads. The problem of finding the shear stresses adjacent to a load-carrying boom attached to the sheet and normal to the free edge is also investigated and integral equations for the shear stresses are derived. The integral equation obtained from the rigorous theory is not readily soluble, but it is shown that, as in the stringer-sheet solution, very large shear stresses are present adjacent to the boom and near the free edge of the sheet. The required variation of boom cross-sectional area along its length to cause any particular variation of shear stress adjacent to the boom is also given. In Part II, a theoretical investigation is made into the problem of stiffening a sheet to relieve the high stresses near the free edge and adjacent to a direct load-carrying boom attached to the sheet. For booms of constant cross-section the stress distribution depends, with certain assumptions, on two non-dimensional parameters, and curves are included for determining the peak stresses in the sheet and the loads in the stiffening structure over the practical range of these parameters. It is shown that if a given weight of stiffening material is to be distributed uniformly along the free edge of the sheet there is a particular shape of stiffener which gives lowest peak stresses in the sheet. The influence of rivet flexibility between boom and sheet is examined theoretically.