A closed form solution for the limit moment in the plastic torsion of an elliptical cylinder (Q1087363)

An expression for the applied moment in the torsion of an isotropic elliptical bar of constant cross section appears in virtually every text on the theory of linear elasticity. Its perfectly plastic counterpart, however, is surprisingly absent from similar texts on the classical theory of plasticity. The reason behind this absence lies in the complexity of a double integral that must be evaluated to obtain a closed form solution. In a previous work, the author [ibid. 61, 209-215 (1986; Zbl 0588.73058)] reduced the form of the solution of the applied moment for the plastic torsion of an ellipse to a single quadrature. In this note, the remaining integral of the previous analysis is evaluated to obtain a simple, closed form solution.