On the Exact Solution of Non-Uniform Torsion for Beams with Asymmetric Cross-Section

This paper deals with the problem of non-uniform torsion in thin-walled elastic beams with asymmetric cross-section, removing the basic concept of a fixed center of twist, necessary in the Vlasov’s and Benscoter’s theories to obtain a warping stress field equivalent to zero. In this new torsion/flexure theory, despite of the classical ones, the warping function will punctually satisfy the first indefinite equilibrium equation along the beam axis and it wont’ be necessary to introduce the classical congruence condition, to take into account the effect of the beam restraints. The solution, based on the Fourier development of the displacement field, is obtained assuming that the applied external torque is constant along the beam axis and on both beam ends the unit twist angle and the warping axial displacement functions are totally restrained. Finally, in order to verify the feasibility of the proposed method and to compare it with the classical theories, two applications are carried out. The first one, relative to an open profile, is necessary to test the numerical method adopted to find the solution; the second one, instead, is relative to a simplified containership section, considered as full restrained in correspondence of two adjacent transverse bulkheads. Keywords—Non-uniform torsion, Asymmetric cross-section, Fourier series, Helmholtz equation, FE method.