Keywords: thin-walled members, linear buckling analysis, generalised beam theory, constrained finite strip method.

The generalised beam theory (GBT) presents two main advantages over the finite element method (FEM) when it is applied to perform linear buckling analysis of thin-walled members. On the one hand, it allows designers to consider the distortion of the cross-section by means of beam-type finite elements. As a consequence, the use of GBT involves a substantial reduction of the computational cost [1]. On the other hand, it allows the calculation of elastic buckling loads of pure (uncoupled) modes, or of chosen combinations of pure modes. This is useful under different circumstances: when the degree of interaction between modes is investigated; when it is necessary to know the contribution of a specific mode to a combined buckling mode; or to determine the dominant mode of buckling to know which degree of post-critical reserve is to be expected.

Some of the concepts of GBT where translated into the finite strip method (FSM) by Ádány and Schafer [2]. They developed the constrained finite strip method (cFSM) for the calculation of pure buckling loads. The idea of the method is to obtain pure buckling loads by forcing the FSM model of the member to buckle in pure GBT modes. This is achieved by properly constraining the nodal displacements of the finite strip model.

The aim of the investigation presented in the paper is to extend the cFSM constraining approach to the finite element method. Since the use of the FEM with shell elements is rather common in the field cold-formed design, the authors of the present study believe that it makes sense to try to combine this method with GBT. The investigation is performed from the principles already stated by Ádány and Schafer [2]. What is actually done is to modify the cFSM formulation of the cross-section constraints to take into account the deformation of the member in the longitudinal direction.

The first part of the paper is devoted to the presentation of the theoretical fundamentals of GBT and to show how to constrain finite element analyses. Afterwards, a practical explanation on the implementation of the constraining procedure in a commercial finite element software is included. An illustrative example of a pure mode calculation is also presented and, finally, three additional examples are shown to fully verify the method. Elastic buckling loads obtained in the constrained finite element analyses are compared to buckling loads obtained via GBT and cFSM, which are calculated with the programs GBTUL and CUFSM, respectively.

Generally speaking, the results obtained with the new proposed method are accurate, when compared to the existing methods. It should be pointed out, however, that in some cases some deviations from the reference values exist. These derivations are expected to be eliminated in the near future.

1

R. Schardt, "Lateral Torsional and Distortional Buckling of Channel- and Hat- Sections", J. Construct. Steel Research, 31, 243-265, 1994. doi:10.1016/0143-974X(94)90012-4

2

S. Ádány, B.W. Schafer, "Buckling mode decomposition of single-branched open cross-section members via finite strip method: Derivation", Thin-Walled Structures, 44, 563-584, 2006. doi:10.1016/j.tws.2006.03.013

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