A novel beam element with nine DOFs per node for resolving the warping-distortion compatibility in analysis of frames and curved beams made of I-sections

Abstract

Warping-distortion coupling is common in frames and curved beams made of I-sections, which tends to decrease significantly the lateral and torsional resistance of structures. Traditionally, it has been difficult to consider such effects in structural analysis, because the warping and distortional degrees of freedom (DOFs) of two connected elements at a common joint cannot be easily transformed to a common coordinate system for global stiffness assembly. The purpose of this paper is to conquer such a problem. By introducing the symmetric and anti-symmetric distortion modes, in addition to the warping and conventional six DOFs, this paper develops a new theory that consists of nine DOFs per node for the two-node I-beam element. The three deformational DOFs of the cross-section, i.e., the symmetric distortion, anti-symmetric distortion and warping, can be regarded as three mechanical couples relating to the twisting, shearing and bending, respectively, of the two flanges in the opposite sense. This allows all the DOFs of the connected elements at a common joint to be easily transformed to the global coordinates for stiffness assembly. As a result, the warping-distortion compatibility problem that occurs in frames and curved beams is resolved. In the exemplar studies, the present beam element has been demonstrated to be capable of producing results that are in excellent agreement with those of the shell element for the lateral deformation of angled frames with unstiffened and stiffened joints and of curved beams with various boundary conditions. It is also observed that the cross-sectional distortion effect becomes more manifest in curved I-beams of high curvature or of high flange-to-web rigidity ratio.