Asymptotic Solutions for Warping and Distortion of Thin-Walled Box Beams

The equations of conventional thin plate theory are used to formulate an eigenvalue problem for effects of self-equilibrating end loads in thin-walled rectangular cross section tubes, or box beams. The problem is analyzed by a perturbation procedure, which is based on a small parameter proportional to the square root of the ratio of wall thickness to cross section width. Solution of the unperturbed problem yields a family of membrane and inextensional end-effect eigenfunctions which are found to have decay distances on the order of the beam width or shorter. The perturbation procedure is carried out to obtain closed form asymptotically valid solutions for warping and distortional effects which decay much more slowly. These asymptotic solutions compare favorably with previous analytical and experimental results.