Torsion of Solid and Hollow Rectangular Beams

The derivation of an expression for the St. Venant torsional stiffness of a beam of variable torsional rigidity is given, and this is applied to the evaluation of this stiffness for tapering solid and thin hollow rectangular beams, the results being compared against convergent solutions. The effect of angle of taper on the accuracy of the method is assessed by comparing the exact solution of a tapering beam of solid circular section against a solution using a method similar to that proposed for rectangular sections. The inclusion of warping restraint is then affected. A general derivation of the stiffness of a prismatic beam is given, and applied to beams with rectangular solid and thin hollow sections. A method is then given for the evaluation of the stiffness of a tapering beam of solid rectangular section restrained from warping, and finally the expressions for the stresses induced due to torsion are presented.