Note on the problem of twisting of a circular ring sector
The problem of twisting of a circular ring sector is of some interest in connection with the calculation of stresses and deformations in close-coiled helical springs. To be considered is a ring-sector under the action of two equal and opposite forces P along the axis through the center of the ring and perpendicular to the plane of the ring (Fig. 1). A formulation of the problem and an outline of results by 0. Gohner for sectors of solid circular and rectangular cross section may be found on pp. 355-361 in Theory of elasticity by S. Timoshenko. The purpose of the present note is to obtain explicit results for the twisting of ring sectors of hollow cross sections, with thin walls. Formulas will be obtained which have the same meaning for the present problem as R. Bredt's formulas have for the problem of St. Venant torsion of cylindrical rods. The problem may be considered as one of the membrane theory of thin shells of