Keywords: thin-walled structures, flexural-torsional buckling, warping constraints.

Using a direct one dimensional beam model with an internal structure including a kinematical descriptor which accounts for gross warping, introduced in [1] and recast in a form suitable for a variational procedure in [2], the analysis of an L frame made up of thin walled beams is performed up to the initial postbuckling range.

The beam and column have uniform channel (U-shape) cross-sections with outer dimensions 100 mm (web) and 60 mm (flanges) and uniform thickness of 3 mm. The beam and column are arranged so that the axes of symmetries of the cross-sections are orthogonal to the plane of the frame. The frame is symmetric and symmetrically loaded.

In order to study the influence of warping on the postbuckling behaviour of the frame, three different configurations have been considered for the joint between beam and column: (a) box stiffened; (b) diagonal stiffened; and (c) diagonal-box (fully) stiffened. They result in three different boundary conditions on the warping transmission.

The three cases have been implemented and, for each case the buckling load, the corresponding buckling mode and the value of the initial postbuckling slope have been determined. Numerical results have been obtained by means of the finite element method using the COMSOL Multiphysics software.

For each joint configuration we have considered only the first two buckling loads. The results show that, for each one of the three cases, in the first buckling mode each bar exhibits torsion associated with plane flexure. The greatest difference is in the values of the critical load and postbuckling slope. In fact, while happens that the critical load increases passing from case (a) to case (c) (206005 < 225768 < 322593), only for the box stiffened joint, case (b), we find a non vanishing postbuckling slope.

By comparing the box and the diagonal stiffened joints, we can observe that while looking at the value of the critical load one could guess that the first type increases the strength of the frame, with respect to the second, their postbuckling behaviour counter balanced this conjecture.

Instead, the fully stiffened joint configuration shows a very good performance with respect to cases (a) and (b). In fact the buckling load obtained not only is higher than the first buckling loads of cases (a) and (b), but is associated to a symmetric postbuckling behaviour so that it is not worn down by imperfection sensitivity.

In conclusion the results show that, despite the geometric and dynamic symmetry of the frame, the occurrence of flexural torsional buckling can be associated to an asymmetric postbuckling as an effect of the warping transmission mechanism at the joint between the two beams, so that, depending on the transmission of warping between the beams, the frame can be imperfection sensitive.

1

G.C. Ruta, V. Varano, M. Pignataro, N.L. Rizzi, "A beam model for the flexural-torsional buckling of thin-walled members with some applications", Thin-Walled Structures, 46,816-822, 2008. doi:10.1016/j.tws.2008.01.020

2

N.L. Rizzi, V. Varano, "The effects of warping on the postbuckling behaviour of thin-walled structures", Thin-Walled Structures, (to appear). doi:10.1016/j.tws.2011.04.001

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