Approximate Analysis of Twisted Parallelepiped

In order to establish relatively simple, accurate formulas for the calculation of torsional rigidities and stresses, the Rayleigh direct (approximate) energy method is combined with the Euler indirect variational method in the analysis of an elastic parallelpiped (i.e., a shaft of rectangular cross section) subjected to end torques. The formula obtained for the calculation of the maximal sharing stress is then improved by an iteration. The single set of formulas derived is valid for both the narrow and bulky cross sections, in contrast to the two different sets of formulas obtained by Timoshenko and Goodier. The numerical values of the torque and shearing stress are calculated and compared with other known results. The accuracy achieved herein is such as to obviate the need for an evaluation of the infinite series in the exact analysis (significant errors do not exceed one percent even in the case of a square cross section).