Buckling instability of Vlasov thin-walled open-section beams: The Euler-Prandtl coupled problem

In the field of structural mechanics, the study of elastic stability is a very important stage in the design of slender, thin, and/or shallow elements. The loss of stability can lead to the global collapse of the structural element. This is achieved when the load applied to the structure reaches the critical value.There are two fundamental instabilities in rectilinear beams: the axial buckling, due to the axial force, and the lateral-torsional buckling, due to the bending moment. In general, these two instabilities may interact, when both axial force and bending moments are applied at the same time.The present paper will illustrate a three-dimensional coupled formulation, including Vlasov's Theory for thin-walled open-section beams. The compactness of the final expressions, made even more evident by the matrix formulation, allows us for a very convenient use in the case of automatic computations.