Out-of-plane buckling resistance of rolled steel H-section beam-columns under unequal end moments

A novel analytical model is proposed for establishing design criteria based on the decomposition of the in-plane deformation and out-of-plane stability states. First part of this study considered the in-plane buckling resistance of beam–columns. This study uses the results from Gizejowski et al. [42] to develop an analytical model for the inelastic out-of-plane buckling resistance of beam–columns subjected to a moment gradient. The elastic flexural–torsional buckling solution is combined with the in-plane solution via the generalised Ayrton–Perry model. In order to unify the recommendations for the resistance evaluation of beams, columns, and beam–columns, the model is customised to conform to the standard Eurocode technique of modelling buckling resistance of steel elements in compression or bending about the cross-sectional axis with the greater moment of inertia. As a result, the out-of-plane resistance interaction curves, expressed in dimensionless coordinates, which describe the beam–column flexural–torsional buckling resistance and consider lateral–torsional buckling effects, are obtained. The results of finite element simulations are used for the verification of the developed analytical formulation. Two numerical techniques of imperfection modelling are used: an equivalent geometric imperfection approach with the Maquoi–Rondal generalised initial imperfection and an approach that individually considers geometric and material imperfections. The results obtained from the proposed analytical model and those obtained using the Eurocode design criteria and other recent analytical proposals are compared. Finally, concluding remarks and directions of future studies are also presented.