Finite-Element Formulations for the Distortional Analysis of Wide Flange Steel Beams

Abstract

Two finite-element formulations are developed for the general distortional analysis of beams with monosymmetric sections. In the first formulation, cubic and linear Hermitian polynomials are adopted to interpolate the nodal displacements; whereas in the second formulation, shape functions that exactly satisfy the governing field equations were used. Because the distortional lateral-torsional and the longitudinal-transverse responses are fully uncoupled, separate finite elements were developed for both types of behaviors. A comparison with other finite-element solutions and a recently developed distortional theory established the validity of the present formulations. A study was then performed on the stability and convergence characteristics of both elements. The new elements were then adopted to solve linearly static analysis of simple beams and beams with overhangs. The formulation is shown to reliably capture the difference in behavior between stiffened and unstiffened beams.