Spatial Rotation Kinematics and Flexural–Torsional Buckling

Abstract

Abstract:This paper aims to clarify the intricacies of spatial rotation kinematics as applied to 3D stability analysis of metal framed structures with minimal mathematical abstraction. In particular, it discusses the ability of the kinematic relationships traditionally used for a spatial Euler-Bernoulli beam element, which are expressed in terms of transverse displacement derivatives, to detect the flexural-torsional instability of a cantilever and of an L-shaped frame. The distinction between transverse displacement derivatives and vectorial rotations is illustrated graphically. The paper also discusses the symmetry and asymmetry of tangent stiffness matrices derived for 3D beam elements, and the concepts of semi-tangential moments and semi-tangential rotations. Finally, the fact that the so-called vectorial rotations are independent mathematical variables are pointed out.

The effects of warping constraints on the buckling of thin-walled structures

“…In the literature there are numerical results obtained via refined finite element codes and experimental studies on the subject. Some of these, regarding a frame shaped spatial beam, are in [Kim and Kim 2000;Kim et al 2001;Gu and Chan 2005;Teh 2005]. Still, to the authors' knowledge, an analytical study derived from a geometrically exact model is not available and the results obtained here could be of importance in applications.…”

Beam element verification for 3D elastic steel frame analysis

“…The inclusion of the proper rotational behaviour of the nodal moments results in an asymmetric tangent stiffness matrix [18,24,40,[45][46][47][48]. However, the tangent stiffness matrix may be symmetrised as the asymmetric part vanishes at equilibrium (which also means that it is irrelevant to a linear buckling analysis), resulting in much less computational efforts and memory requirement [18,24,[48][49].…”