Elastic stability of U-shaped members in bending considering pre-buckling displacements. (August 2017) - Beyer, André; Boissonnade, Nicolas; Khelil, Abdelhouahab; Bureau, Alain
Abstract: The present paper describes a theoretical study on the effect of pre-buckling displacements on the elastic instability of U-shaped members. Expressions for the elastic critical bending moments under mono-axial bending and the elastic critical load amplification factor for the case of bi-axial bending are derived and validated through elastic geometrically non-linear analysis including a geometric imperfection. It will be shown that pre-buckling displacements have a non-negligible influence on the behaviour of U-shaped members, especially when subjected to minor-axis and bi-axial bending. It will be shown that, contrariwise to the natural feeling, U-shaped members under minor-axis bending may, in some cases, be sensitive to elastic instability (lateral-torsional buckling). Moreover, the validated analytical expressions show that shorter members are more sensitive to elastic instability under minor-axis bending than their longer counterparts! Highlights: The elastic stability of U-shaped members is studied theoretically. The influence of pre-buckling displacements on elastic stability of U-shaped members in bending is highlighted. The analytical solutions are confirmed based on numerical Finite Element simulations.