A thin-walled beam element based on semi-analytical solution modes

Abstract

Using energy principles, a thin-walled beam element is introduced for the analysis of beams with deformable crosssections that are prone to distortion. The beam element is based on previously attained semi-analytical displacement solution modes of an advanced thin-walled beam model. The first-order beam element for linear analysis handles shear deformations related to both Timoshenko and Mindlin-Reissner type deformations, warping effects of torsion, crosssection distortion including associated warping effects, as well as the transverse displacement effect from normal stress. The formulation can handle both open and closed cross-sections without special attention. The formulation of the displacement solution modes and the stiffness integration of the products of the advanced displacement modes using the Hadamard product are described. The paper also presents the transformations between modal degrees of freedom and element displacement degrees of freedom. Four examples show the beam element capabilities and good agreement with results obtained using the shell and solid elements of a commercial finite element program. The kinematic assumptions that the thin-walled beam model accommodates leads to local shear stress transfer at corners. This transfer of shear stresses is not normally seen in thin-walled beam formulations or shell models. However, the shear transfer is verified through examination of a finite element model using solid elements.

Mode‐based Beam and Connection Analysis of Frames

“…An example is the approach given by Basaglia et al (11) introducing a joint element within the framework of GBT that includes higher order effects such as distortional displacements. Beams and columns are modelled using the advanced beam element formulation previously presented by the authors (14,15). Here, non-aligned finite beam elements are assembled with rigid links and springs.…”

“…Thus, the idea presented here gives an approach that stands out in the way that no prior special assessment of the joint is required other than building a standard finite element model of it. Beams and columns are modelled using the advanced beam element formulation previously presented by the authors (14,15). In addition, a joint is modelled with a discretization of finite shell elements assembled in a joint element.…”

“…Beams and columns within a frame shall be modelled as beam elements adopting the advanced beam theory presented by the authors, (14,15). Hence, a beam element is based on a linear elastic analysis and support members having a thin-walled cross section.…”

Steel frames analyzed by use of advanced displacement mode‐based beam and joint elements

“…The beam theory by Hansen & Jönsson [10] can handle straight, thinwalled members with open and closed multi-cell cross-section, which may even have branched parts, as for example, those shown in Figure 3.…”

“…The advanced beam theory that is used in this paper is the one developed by Hansen & Jönsson [9,10], though it is believed that any advanced beam theory that is based on cross-sectional displacement modes could be used, such as GBT or the higher-order beam theory by Vieira et al [11,12] with some modification.…”