Transmission of concentrated forces into prismatic shells—I

Abstract

The work deals with the membrane and bending fields induced in prismatic shells by concentrated forces that are applied at the joints or ridges between two plates. Since many of the basic questions have little to do with supports or finite boundaries, an unbounded prismatic shell consisting of two semi-infinite plates is considered. This geometry lends itself to a straightforward analysis by Fourier transforms, and the results can be expressed in terms of exponential integrals of complex arguments for which tables are available. When the concentrated force lies in the plane of symmetry and is perpendicular to the ridge, an unexpected result is that the membrane forces remain bounded at the load point. In contrast, the moments and transverse shearing forces are singular at the point of loading. The asymptotic forms of the far fields show that the membrane forces decay more slowly than the moments and shearing forces. Thus the orders of the near and far fields reveal that the symmetri cally applied perpendicular force is transferred into the prismatic shell principally through bending, and diffused far away through membrane action.