A Unified Theory for Distortion Analysis of Thin-Walled Hollow Sections

A novel unified theory for distortion analysis of thin-walled hollow section has been proposed based on the Hellinger–Reissner variational principle to account for distortional shear deformation effects. Based on the proposed theory, a finite segment model has been developed and the method for determining the distortion functions of the cross-section has been proposed. The rationality of approaches for determining distortional shear stress has been analysed and it is concluded that Bredt’s pure distortion does not exist in the single-cell hollow section. Comparisons and analyses have been performed between the proposed theoretical model and the existing four groups of theories in distortion analysis of thin-walled hollow section. Effects of distortional warping shear stress on the shear deformation has been investigated and the results indicate that the distortional shear deformation effect results in a decrease of the distortional warping stresses and shear stresses but an increase of the transverse bending stresses. The numerical study indicates that the distortional shear deformation effects can be ignored and the first derivative of the distortion angle can be employed as the distortional warping function for the conventional hollow sections of bridge structures.