A direct one-dimensional beam model for the flexural-torsional buckling of thin-walled beams

Abstract

In this paper, the direct one-dimensional beam model introduced by one of the authors is refined to take into account nonsymmetrical beam cross-sections. Two different beam axes are considered, and the strain is described with respect to both. Two inner constraints are assumed: a vanishing shearing strain between the cross-section and one of the two axes, and a linear relationship between the warping and twisting of the cross-section. Considering a grade one mechanical theory and nonlinear hyperelastic constitutive relations, the balance of power, and standard localization and static perturbation procedures lead to field equations suitable to describe the flexural-torsional buckling. Some examples are given to determine the critical load for initially compressed beams and to evaluate their post-buckling behavior.

The effects of warping constraints on the buckling of thin-walled structures

“…In [Ruta et al 2006] some simple examples of flexural-torsional buckling and postbuckling phenomena have been investigated, showing the coincidence of the results with those in the literature, for instance in [Timoshenko and Gere 1961;Grimaldi and Pignataro 1979]. Further applications of the refined model are found in [Ruta et al 2008] where, for a simply supported compressed beam, the effect of warping constraints at the beam ends has been examined and the relevant critical loads have been presented.…”

“…A short description of the origins of the problem with references to related existing literature may be found in [Ruta et al 2006;.…”

“…In [Ruta et al 2006] the direct model introduced in [Tatone and Rizzi 1991;Rizzi and Tatone 1996] was refined in order to describe the flexural-torsional buckling of beams with nonsymmetric cross-sections. Strain measures are described with respect to both the centroidal and the shear center axes of the beam (as a first step, it is immaterial which of the shear centers presented in the literature is chosen).…”

“…A natural development of the studies performed in [Ruta et al 2006; appears to be the analysis of the buckling of more complex structures by means of the refined model. In this paper, the authors present two cases of interest in applications.…”

“…The second is a simple frame loaded by a dead force, known as a Roorda frame in the literature. We first summarize the key notes of the refined model (details are found in [Ruta et al 2006;); then, we present the field equations for the considered problems and some numerical results.…”