On the torsion of a prism with non-equilateral triangular cross-section

The exact solution of Saint–Venant’s problem of torsion of a prism with triangular cross-section is extended from the case when the latter is equilateral to a two-parameter family including isosceles and irregular triangles, but not covering all such shapes. The solution is based on a stress function which vanishes at sides of an arbitrary irregular triangle, whose shape is specified by three parameters. The condition that the stress functions satisfies the Poisson equation imposes one constraint on the three parameters, leading only two free. This covers all equilateral triangles, to which the well known Saint–Venant’s solution applies; it also covers a two-parameter family of isosceles and irregular triangles, corresponding to a generalization of Saint–Venant’s results. These include the stresses in the cross-section and torsional stiffness of the bar.