On the torsion of conical shells

In seeking to analyse the stress distribution in a complex structure, our object is really twofold. In the first place, if the stress in each part is accurately known, the strength of each part separately can be assessed on the basis of tests on simple units and the necessity for testing the complete structure may be avoided. In the second place, if the stress distribution can be expressed as a function of the geometry of the structure, the effect of varying that geometry, particularly with the object of realising Holmes’ one-hoss-shay, can be examined theoretically and arbitrary-features of the design can be eliminated. If our knowledge were complete, any structure designed to a maximal or minimal condition would not permit any variation from one ideal form, the design would be uniquely determined by the stated requirements.

Stress Analysis of Thin Metal Construction

Cox¹

1940

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

Hadji-Argyris¹,

Dunne²

1947

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.

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

Hadji-Argyris¹,

Dunne²

1949

As stated in the introduction to Section 6.5 the practically important case of an open section tube with no St. Venant torsional stiffness (see Fig. 38) will be treated as the limiting case of the open tube with J as J→0. It will be shown that the stress system g1h1over the open tube degenerates into a stress system gгhг which is statically equivalent to the torque TBS about the shear centre. This stress system is for a uniform cylindrical tube with no J identical to the Wagner-Kappus torsion-bending stress system in open tubes.