Torsion of Equi-angular Polygonal Prism

Abstract

Trefftz's mathematical analysis in torsion problems is applied to the prismatic bars with polygonal section which has equal angles with symmetrical axes. The section sometimes takes a form of regular polygon, as the extreme case. In this paper, the maximum torsional stress at the middle point of the longer side is calculated by numerical integrals. The twisting moment is calculated independently of Treffetz's analysis, i.e., by determining a harmonic function which satisfles the boundary conditions. As to the experiment for verifying this calculation, the twisting angles have been measured with mirrors and telescopes, while the maximum torsional stresses by the use of the brittle coating and the electric resistance strain gages. The yielding regions of the bar have been discovered by the use of the brittle coating with a strain sensitivity of 0.2∼0.3%.