Finite beam element with exact shape functions for torsional analysis in thin-walled single- or multi-cell box girders

Abstract

In this paper, a new formulation of beam-type finite element for the non-uniform torsion of simple or continuous thin-walled single- or multi-cell box girder with open and closed cross-sections is developed, considering both torsional warping and shear deformation effects (primary shear deformation due to Saint-Venant torsion and secondary shear deformation due to restrained torsion). The warping displacement of the cross-section is defined as the product of warping function representing the warping moment along the girder axis and a series of segmental shape functions describing the warping shape of each wall of the cross-section. Two different warping functions haven been defined and incorporated in Model A and Model B. The girder is subjected to arbitrary distributed or concentrated twisting moment and restrained by the general torsional-bending boundary conditions. The governing differential equations pertaining to torsion and torsional warping are obtained through the principle of minimum potential energy and the proposed finite beam element is refined by selecting closed-form homogeneous solutions of the differential equations as interpolation functions. Numerical examples are presented regarding rectangular hollow section (RHS) girders and single- or multi-cell box girders with open and closed cross-sections and the results obtained are compared with those provided by pioneering work or examined by using commercial finite-element models to validate the proposed beam-type element and to demonstrate the wide range of applicability and the convenience of using it.