Alternative approach to the buckling phenomenon by means of a second order incremental analysis

This article addresses the problem of determining the solicitation and deformation of beams with geometric imperfection, also called real beams under a compression action. This calculation is performed by applying the Finite Transfer Method numerical procedure under first-order effects with the entire compression action applied instantaneously and applying the action gradually under second-order effects. The results obtained by this procedure for real sinusoidal or parabolic beams are presented and compared. To verify the potential of the numerical procedure, the first and second-order effects of a beam with variable section are presented. New analytical formulations of the bending moment and the transverse deformation in the beam with sinusoidal imperfection subjected to compression are also obtained, under first and second-order analysis. The maximum failure load of the beams is determined based on their initial deformation. The results of solicitation and deformation of the real beam under compression are compared, applying the analytical expressions obtained and the numerical procedure cited. The beams under study are profiles with different geometric characteristics, which shows that it is possible to obtain maximum failure load results by varying the relationships between lengths, areas and slenderness. The increase in second-order bending moments causes the failure that originates in the beam, making it clear that this approach reproduces the buckling phenomenon. The article demonstrates that through the Finite Transfer Method the calculation of first and second-order effects can be addressed in beams of any type of directrix and of constant or variable section.