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©2012 CivilComp Ltd 



Y.L. Pi and M.A. Bradford
Centre for infrastructural Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia
Keywords: approximations, lateraltorsional buckling, postbuckling, rotation, second order.
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In the development of a finite beam element for the lateraltorsional buckling analysis of structures, a rotation matrix is usually used to derive the nonlinear straindisplacement relationship. 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 for the lateraltorsional buckling analysis of structures, while a second order rotation matrix is used in the formulation for the postbuckling analysis. Because approximations are made in these rotation matrices, these rotations do not satisfy the orthogonality and unimodular conditions. As a result, the approximations may lead to a loss of some significant terms in the straindisplacement relationship. Without these terms, the rigidspace body motion cannot be separated from the real deformations. The superimposed rigid body motions may lead to the development of selfstraining, which may in turn affect significantly the prediction of the lateraltorsional buckling loads and the postbuckling behaviour [1,2]. This paper investigates the effects of approximations on the elastic lateraltorsional buckling analysis and on the postbuckling analysis. It is found that the finite beam element based on the small rotation matrix cannot predict correctly lateraltorsional buckling loads of thinwalled beams in many cases, and that the finite beam element based on the second order rotation matrix will predict overstiff postbuckling responses.

 1
 Y.L. Pi, M.A. Bradford, B. Uy, "A spatially curvedbeam element with warping and Wagner effects", International Journal for Numerical Methods in Engineering, 63, 13421369, 2005.
 2
 Y.L. Pi, M.A. Bradford, "A rotation matrix for 3D nonlinear analysis", Australian Journal of Mechanical Engineering, 3(1), 3138, 2006.
