A Technical Theory of Dynamical Torsion for Beams of any Cross-Section Shapes

Abstract

In order to study the free torsional oscillations of beams, two parameters are introduced—a torsion parameter and a warping parameter—each of them by means of a statistical definition. Using the classical hypothesis of strength of materials, we reduce the dynamical comportment of the beam to a one-dimensional comportment. The four basic relations obtained present a similar form with those of bending motion of a Timoshenko beam. Hence equation of torsional motion is derived and usual cases of boundary conditions relevant to the problem are given. We conclude with a view of the possibilities of the theory, particularly in the numerical area of structural dynamics.