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The elastic load-carrying capacity and buckling trajectory of steel columns under compression with open and hollow cross-sections, whose axis is curved by spatial random fields, are studied in the article. As a result of the spatial curvature of the axis the cross-sections are subjected to compression, bending and torsion from the onset of loading. Numerical simulations are performed using the geometrically non-linear model created using the ANSYS software pack­age. Each simulation run has input random realizations of yield strength and the random field generated using the Latin Hypercube Sampling method. In the plane perpendicular to a perfectly straight column axis, the random observations of deformation trajectories of a node in the middle of the column height are studied. The increasing compression load moves the node along the curve path (open sections) or along the linear path (hollow sections). Large discrepancies in the deformation trajectories of open sections (curvilinear paths) and hollow sections (linear paths) were observed from the comparison of simulation runs. The average and design load-carrying capacities of compressed columns with open cross-sections are lower in comparison to columns with hollow cross-sections due to the lower efficiency of open cross-sections in torsion.

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The accuracy of the interaction methods for combined flexural and lateral torsional buckling are investigated using statistical data, which has become available after the introduction of Eurocode EN1993-1-1:2005. The freely available statistical data for geometric and material parameters for standard profiles are quite limited and as background documents are based on IPE 160 profile, our investigations are also based on this profile. A semi-probabilistic first order reliability approach is used and the resistance of the member is treated as a stochastic variable. Latin Hypercube Sampling is used for population sampling. This simulation approach for determination of the buckling interaction surface has not previously been reported. The Eurocode handles buckling interaction through two interaction equations. These equations include a number of interaction factors. The calculation of the interaction factors may be performed by one of two methods, referred to as Method 1 and Method 2. Both interaction methods make use of the buckling curves for determination of reduction factors for both flexural and lateral torsional buckling. The flexural buckling curve is well calibrated; however, this is not the case for lateral torsional buckling. It turns out that the methods may lead to unsafe designs when a lateral torsionally slender column is loaded predominantly in bending. The present paper investigates how the Eurocode emulate the complex behavior also for very slender beam-columns. The 0.1% quantile interaction curves are compared to those resulting from the use of Method 1 and Method 2.