A method to evaluate the axial buckling load of periodic Vierendeel beams

Abstract

This paper presents some closed form solutions for the buckling problem of periodic Vierendeel girders subjected to compressive axial loads. These are obtained by studying a geometrically non-linear ideal discrete beam, composed of cells or panels that deform only according to the inner forces transferring modes of the girder unit cell. In particular, the recursive equations governing the equilibrium of this discrete system are derived by the virtual works principle. Then, they are exactly solved and formulae for the critical loads are achieved. Although the ideal girder deforms with geometrically not compatible longitudinal shear strains, it gives very accurate predictions in a wide range of conditions of technical interest. These theoretical results are used as starting point for the analysis of the stiffening effect yielding a Euler critical load significantly higher than the buckling load evaluated on the basis of the classical Engesser’s assumptions. Specifically, by an ideal girder auxiliary solution, the discrete systems of self-equilibrated inner bending moments (self-moments) restoring the longitudinal shear strains compatibility are studied and it is shown that the axial loads under which these moments exist are accurate critical loads estimates of the real girder. Closed form solutions are obtained also for this problem and a simplified formula is derived for evaluating real girders buckling loads. The applicability of the reported solutions is verified by a validation study based on a series of finite element girder models.