Bending of a pretwisted bar by terminal transverse load

The problem of bending of a pretwisted bar, cantilevered and loaded by transverse forces at the end, is dealt within the framework of the linear three-dimensional theory of elasticity. The stress components are assumed representable as a suitable series in the pretwist parameter k , whose coefficients can be determined by the solution of plane problems. This is possible if a suitable dependence on the axial coordinate is assigned. The boundary value problems which characterize the coefficients up to the second power are explicitly determined, and the solutions are calculated for an elliptical section. In this way we determine the approximate solution up to terms of order k 2 , to account for a moderate rate of pretwist. From the results of the mathematical analysis, some indications can be deduced regarding the effect of pretwist and a comparison can be made with the classical case of a straight bar.