The effect of uniformly spaced flexible ribs on the stresses due to self-equilibrating systems applied to long thin-walled cylinders

Abstract

In many problems relating to the stressing of thin-walled cylinders, and in particular those concerned with the stresses set up in a cylinder under torsion when one section is restrained against warping, it has been commonly assumed that sections have their shape retained by closely spaced stiff ribs. Justification for this assumption is that, for certain types of loading, the ribs of most practical structures do little work in maintaining the section shape (and the analysis is considerably simplified). In this report the effect of discrete, flexible ribs has been investigated and the results have been incorporated in a number of graphs which show the effect of rib-flexibility in a long thin-walled cylinder of arbitrary shape under end constraint. Some of the results of these investigations are, as would be expected, of a negative character, in that they show that for certain types of end conditions (roughly, those in which the predominating self-equilibrating loads act parallel to the cylinder axis) the effect of rib-flexibility is negligible. But rib-flexibility is of paramount importance when self-equilibrating shear-distorting forces are applied to a cylinder--such as occur at a wing cut-out or near an overhanging engine--and this report makes the stress distribution in such a case readily determinable. It is shown that the complete stress die-away pattern depends, apart from the boundary conditions, on two nondimensional parameters. These parameters are functions of the type of end constraint as well as of the structure dimensions and elastic constants. Expressions are given for determining these parameters when the cylinder shape and loading are arbitrary. The simplified case of a four-boom cylinder Of rectangular section under torque is treated separately in a second appendix. The solution is strictly true for a four-boom cylinder or when the self-equilibrating end-load system is orthogonal (eigenload); but as minimum-energy methods are used in the analysis, the results are believed to be substantially correct for a smoothly varying end-load system applied to a cylinder of arbitrary shape.