Keywords: lateral buckling, steel I-shaped beams, numerical modelling of steel beams, stability linear analysis, boundary conditions, mechanical behaviour of beams.

Lateral buckling in beams is a typical problem when the beams do not have enough lateral stiffness or lateral restrictions along of the length causing bending about the minor axis. Also, the lateral buckling is of particular importance during the erection or assembly, before the lateral bracing system is fully installed. In effect, it is during the act of installing the braces that many grave accidents have occurred.

Then, this paper is focused to study the buckling of the A-36 steel I-shaped beams with doubly symmetry subject to different boundary condition under uniform moment action for five spans (10, 15, 20, 25 and 30m). The development of the work is carried out using two types of analysis; the lateral torsional buckling elastic theory of beams, taking into consideration simply-supported and fixed end boundary conditions, as well as the effective length method and numerical techniques of bifurcation, employing the finite element method. The steel walls of the web and flanges the I-shaped beam are modelled with solid elements and shells elements to obtain by numerical stability analysis the critical moment.

The numerical results of the stability linear analysis, consisting of the maximum critical stresses corresponding to critical moment, were presented for two types of numerical models consisting of solid or shells elements with three different meshes.

Finally, the numerical results observed with the solid element model and the first meshing, are in good agreement with the analytical classical solution with simply-supported end conditions and the numerical solution completely describes the buckling pattern. The numerical results of the cases studied are compared with the two analytical solutions and the AISC recommendation.

For the others numerical models two scenarios were explored, with two further meshings (2, 3): (a) simply-supported ends (vertical plane) and fixed end (horizontal plane) and (b) fixed ends. With the scenario (a) different levels of approximation are found to be a function of the discretization (number of nodes and elements). The comparison between the two numerical approaches with respect to the analytic solution is shown to be less close to the theoretical solution but a major approximation with effective length approach, for k_y=0.5; k_z=1. And with scenario (b) two levels of approximation are found for the analytical solution (fixed ends) and it is observed that the numerical results are between 71 to 92% of the theoretical solution, while with the effective length approach (k_y=0.5; k_z=1) the results are almost 100%, with agreement to the curve.

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