Distortional warping functions and shear distributions in thin-walled beams

Abstract

In the analysis of thin-walled beams it is often necessary to consider the effects of distortion of the cross-section. The distortion in the plane of the cross-section generates axial warping displacements. On the basis of a known in-plane distortional displacement mode it is possible to derive a unique warping function and the related shear stress distributions. Local axial equilibrium is used to derive the main differential equation for determination of the distortional warping function and shear distributions. In closed single- or multi-celled cross-sections it is necessary to introduce circulation shear force flows around the cells to achieve compatibility of the axial displacement. Methods for analysis of open and closed cross-sections are generalized to include distortional displacement modes. It is shown that axial extension, flexure and torsional warping are included as special cases of distortion. A generalization of the conventional orthogonalization procedure and a normalization technique for distortional modes are also presented. A triple cell cross-section is used to illustrate the generalized calculation procedure and computed results are presented.