On the non-uniform torsion in thin-walled beams

It’s well known that thin-walled elastic theory represents an important simplified model to analyze various actual structures. Particularly, this model can be applied with good results to the analysis of ships with large deck openings, subjected to non-uniform torsion, whose distinctive feature is that they may undergo considerable warping deformations. In this paper the problem of the elastic equilibrium of a thin-walled beam is discussed from the beginning, assuming the fundamental hypothesis of Kollbrunner and Hajdin, 1972, based on the assumption that the longitudinal distribution of the warping deformations is an arbitrary function independent of the unit twist angle. Furthermore the effective longitudinal distribution of the applied torque is taken into due consideration to determine the longitudinal distribution of the warping function and the unit twist angle, in the hypothesis of restrained torsion. It is well known that a still unsolved problem is the role of transverse bulkheads, generally assumed as perfectly rigid in the evaluation of the bimoment longitudinal distribution. So a method, based on a global energy approach, is presented to take into account the deformability of transverse bulkheads, schematized as orthotropic plates. Finally, a numerical application to a ship with large deck openings is carried out, in order to evaluate the viability of the proposed method. A numerical comparison with the classical Vlasov theory is carried out, in order to highlight the role of the transverse bulkheads in the evaluation of warping stresses