Linear and non-linear stability analyses of thin-walled beams with monosymmetric I sections

The paper investigates beam lateral buckling stability according to linear and non-linear models. First, the classical linear stability solutions are derived from the stability equation in the case of monosymmetric cross-sections. Bending distribution, load height parameter and Wagner's coefficient effects are taken into account. In the second step, they are extended to non-linear stability by considering pre-buckling deformation and improved solutions are then obtained. Based on a finite element model developed for large torsion of thin-walled beams with open sections, the stability of beams under gradient moments (M0, ψM0, −1≤ψ≤1) is particularly investigated. It is then concluded that beam lateral buckling resistance depends not only on pre-buckling deformation but also on section shape and load distribution. For bisymmetric I beam, closed form solutions are possible and pre-buckling deformations have an incidence. In the case of beams with monosymmetric I and Tee sections, effects of pre-buckling deflections are important only when the largest flange is in compression under M0 and positive gradient moment. Analytical solutions are possible. For negative gradient moments all available solutions fail and numerical solutions are more powerful. Effect of gradient moments on stability of redundant beams is investigated at the end. Under such boundary conditions, important axial forces are present due to non-linear beam deformation. These forces, omitted in literature, have an incidence on stability. The element is then concerned with beam-column behaviour rather than beam stability.