The Torsion and Stretching of Spiral Rods (3rd Report)

Abstract

The equations of equilibrium, expressed in terms of stresses, with those of compatibility are reduced to two-dimensional forms for the present problem. For torsion, they are simplified in two extreme cases where (i) the angle between the helix and the axis of helix is small, and (ii) the angle between the helix and the plane perpendicular to the axis of helix is small. Integrating them, the expressions for stresses are derived in the forms, which contain two arbitrary functions. These arbitrary functions can be determined if the shape of the rod be specified. As an illustration of the procedure, a detailed solution for a coiled helical spring with a circular section is obtained by means of successive approximations, and the stresses on the section are discussed.