Diffusion of antisymmetrical loads into, and bending under, transverse loads of parallel stiffened panels

Abstract

To present the general theory of diffusion of antisymmetrical concentrated end loads and edge loads into parallel stiffened panels, including the theory of bending of a parallel stiffened panel under arbitrary transverse loads. By combining the results of this paper with the results on diffusion of symmetrical loads given in R. & M. 1969 and R. & M. 2038 or in Appendix I to this paper it is possible to analyse the diffusion in a parallel panel under any arbitrary load or edge stress distribution. The methods developed in this paper permit a simplification and slight generalisation of the results obtained in R. & M. 1969 and 2038 for the symmetrical diffusion case in a parallel panel. The relevant formulae are given in Appendix I to this report. An alternative approach to the diffusion problem in parallel panels with given boom areas is presented in Appendix II. In general diffusion in parallel panels is determined by three parameters : the diffusion constant as defined by Cox (R. & M. 1860), the ratio of total area of edge members to total area of stringers plus effective sheet, and the ratio of total area of stringers plus effective sheet to the product of length of panel and sheet thickness. It is shown that the effect of transverse loads on the direct stresses in a parallel panel is equivalent to that of antisymmetrical edge loads producing the same bending moment at each section. The shear stress distributions differ by a constant value across each section. This difference is the shear stress produced by the shear force of the transverse load system assumed uniformly distributed over each cross-section. In all loading cases as mu increases the stress distribution in the panel approaches that indicated by the ordinary engineer's theory.