Effects of approximations in analyses of beams of open thin‐walled cross‐section—part I: Flexural–torsional stability

Abstract

In formulating a finite element model for the flexural–torsional stability and 3-D non-linear analyses of thin-walled beams, a rotation matrix is usually used to obtain the non-linear strain–displacement relationships. Because of the coupling between displacements, twist rotations and their derivatives, the components of the rotation matrix are both lengthy and complicated. To facilitate the formulation, approximations have been used to simplify the rotation matrix. A simplified small rotation matrix is often used in the formulation of finite element models for the flexural–torsional stability analysis of thin-walled beams of open cross-section. However, the approximations in the small rotation matrix may lead to the loss of some significant terms in the stability stiffness matrix. Without these terms, a finite element line model may predict the incorrect flexural–torsional buckling load of a beam. This paper investigates the effects of approximations in the elastic flexural–torsional stability analysis of thin-walled beams, while a companion paper investigates the effects of approximations in the 3-D non-linear analysis. It is found that a finite element line model based on a small rotation matrix may predict incorrect elastic flexural–torsional buckling loads of beams. To perform a correct flexural–torsional stability analysis of thin-walled beams, modification of the model is needed, or a finite element model based on a second-order rotation matrix can be used. Copyright © 2001 John Wiley & Sons, Ltd.