Keywords: lateral-torsional buckling, critical moment, I and hat section, finite element method.

In current design codes the capacity prediction for lateral-torsional (LT) buckling is typically realized by using the critical moment (M_cr). Even though M_cr is important to properly determine, it is not easy to propose a method for the everyday practice: a method which is general, clear and simple-to-use. Formulae are available in some design standards, but they are not general enough. Another option is to use numerical methods, like the generalized beam theory (GBT) [1], the constrained finite strip method (cFSM) [2], or the finite element method (FEM). The cFSM and GBT software implementations are freely available [3,4]. They are fast and simple to use, but not appropriate for certain geometries and irregular loading and/or boundary conditions. The FEM is widely available, well-known and can handle nearly any practical engineering stability problems (with using shell finite elements), but it is demanding to separate the LT buckling mode from other potential buckling modes (local, distortional), and, in general, the proper application of a shell FEM model involves time-consuming pre- and post-processing.

In the research presented the calculation of M_cr is investigated. Various methods are considered, including the GBTUL and CUFSM software, analytical solution for the most basic cases, formulae of two design standards, and the finite element method. Critical moments are calculated and compared to each other for beams of various lengths, with mono-symmetrical and doubly-symmetrical cross-sections, under various loading and boundary conditions. The results show significant scatter which is especially true for the formulae considered which might strongly under or overestimate the critical moment even for some basic cases.

For practical calculations either GBT or a properly applied finite element model can be proposed, since both of these two methods lead to reasonably accurate results. GBT is simpler to use, but has some limitations. The applied FEM approach, is justified by the presented results, and at the moment this method can be considered as the most general approach to calculate critical moments.

1

N. Silvestre, D. Camotim, "Non-linear generalised beam theory for cold-formed steel members", International Journal of Structural Stability and Dynamics, 3(4), 461-490, 2003. doi:10.1142/S0219455403001002

2

S. Ádány, B.W. Schafer, "A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method", Journal of Constructional Steel Research, 64(1), 12-29, 2008. doi:10.1016/j.jcsr.2007.04.004

3

CUFSM Elastic Buckling Analysis of Thin-Walled Members by Finite Strip Analysis. CUFSM v3.12, 2006. http://www.ce.jhu.edu/bschafer

4

GBTUL, Buckling and Vibration Analysis of Thin-Walled Members, GBTUL 1.0beta, DECivil/IST, Technical University of Lisbon, 2008. http://www.civil.ist.utl.pt/gbt

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