Torsion of beams whose cross-section is a regular polygon of n sides

Abstract

E. Trefftz has discussed the problem of the torsion of a beam whose cross-section is bounded by a polygon with the help of the Schwarz-Christoffel transformation given by dw/dt=A(t-ξ₁)^a1/π (t-ξ₂)^a2/π...(t-ξ_n)^an/π, (1) where a1, a2, …, an are external angles of the polygon in the w-plane, and ξ1, ξ2, …, ξn are the points on the real ξ-axis in the t-plane that correspond to the angular points of the polygon in the w-plane. In the case of regular polygons a further transformation of the upper half of the t-plane into the interior of a circle in the z-plane with the help of the transformation Z=i-t/i+t (2) greatly simplifies the problem, and some definite results can be obtained.