The General Theory of Cylindrical and Conical Tubes Under Torsion and Bending Loads

Abstract

This paper presents a rational method of stressing single or many cell tubes particularly of the type encountered in wing structures. The theory has been developed for conical or cylindrical tubes of arbitrary cross-section the shape of which is maintained by a closely spaced system of diaphragms rigid in their own planes and parallel to the root section. Within the limits of the assumptions the theory is exact for right cylindrical tubes, and is applicable with adequate accuracy to cylindrical or conical tubes in which the inclination of any generator to the normal to the root plane does not exceed 10°.The analysis given unifies the theories of bending and torsion and shows that the commonly used method of separating the bending and torsion loads by means of a shear centre is in general incorrect.The formulae have been developed in such forms that attention is concentrated on the necessary corrections to the stresses as indicated by the ordinary engineers' theory. These correction terms include all effects of shear lag, diffusion, and end effects hitherto taken into account only in some very special cases.Particularly important for practical applications is the structure consisting of a number of direct stress carrying members (booms) connected by walls effective only in shear. The simplest structure of the latter type is the four-boom tube with or without nose and trailing cells, and in this case explicit formulae are given which are immediately applicable to practical calculations. Formulae are also given for the more complex case of a six-boom tube in which the two extra booms are introduced to represent more accurately the direct stress carrying capacity of the top and bottom panels between the two spars.