Exact element static stiffness matrices of shear deformable thin-walled beam-columns

Abstract

A simple but efficient method to obtain the exact static stiffness matrices is developed in order to perform the spatially coupled elastic and buckling analyses of shear deformable uniform beam-columns having non-symmetric thin-walled sections. First this numerical technique is accomplished via a generalized eigenvalue problem associated with 14 displacement parameters which produces both complex eigenvalues and multiple zero eigenvalues. Next polynomial expressions are assumed as trial solutions for displacement parameters and eigenmodes containing undetermined parameters equal to the number of zero eigenvalues are determined by invoking the identity condition to governing equations. And then the exact displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently exact static stiffness matrices are evaluated by applying member force–displacement relationships to these displacement functions. The lateral-torsional deflections and buckling loads of thin-walled beam-columns are evaluated and compared with analytic solutions and the results by straight beam element and ABAQUS’s shell element.