Outlooks in Saint Venant theory Part II. Torsional rigidity, shear-stress "and all that" in the torsion of cylinders with section of variable thickness

Abstract

We extend the perturbative procedure developed in [7] to the case of Saint Venant Cylinders with sections of variable thickness. In this way we are able to generalize the Kelvin and Bredt formulas for torsional rigidity of open and closed sections, respectively. We recover all the results available in technical literature. In particular we deduce an explicit analytical expression for warping function in the cases of open sections of triangular shape [17] and of the closed section studied using numerical methods by WANG [18].