A beam model for the flexural–torsional buckling of thin-walled members with some applications

A beam model aimed at describing the flexural–torsional buckling of thin-walled members with non-symmetric cross-sections is presented. Two beam axes are introduced, and strain is defined with respect to both. The shearing strain between the cross-section and one of the two axes is assumed to vanish; the warping is supposed to be linear in the twist. Non-linear hyperelastic constitutive relations are introduced; by means of standard localization and static perturbation techniques, the field equations describing the flexural–torsional buckling are obtained. One benchmark example is given and some numerical values of the critical load for various warping constraints at the beam ends are provided.