The Ayrton–Perry approach is the basis of Eurocode 3 rules for buckling resistance, with distinct curves and imperfection factors depending on section type, steel grade, and other parameters. For generic members – built-up or not, uniform or not, with complex supports or not – the code allows either the general method (clause 8.3.4 of Eurocode 3) or advanced numerical simulations. Yet, the general method shows wide scatter and often underestimates resistance, while numerical analyses are time-consuming and strongly user-dependent. To overcome these limitations, the general formulation was introduced by Tankova et al. (2018) for members with variable geometry, loads, and supports and recently extended to mono-symmetric I-beams. However, it has only been validated for Class 1 and 2 sections, not for Class 4. This paper extends the general formulation to uniform and non-uniform slender I-section beams subjected to arbitrary loads, boundary conditions, and partial lateral restraints. An advanced numerical model, calibrated against experimental data, was employed to conduct a comprehensive parametric study considering different cross-sections, a range of normalized slenderness values, S460 and S690 steel grades, and different load applications. The proposal was compared with the numerical results, demonstrating a safe-sided and well-calibrated solution for the buckling resistance of high-strength steel slender I-section beams.

The General Formulation has proven to be a practical, design-focused solution for the stability design of different member configurations - built-up or not, uniform or non-uniform, with complex or simple support conditions. It was recently extended for mono-symmetric I-section beams, but its applicability to slender section members remains unexplored. This work aims to expand the scope of the General Formulation to include Class 4 I-section beams. A numerical model was calibrated to assess the lateral-torsional buckling resistance of beams. A parametric study was conducted on S690 HSS slender I-section beams under uniform bending moment, considering different cross-sections, normalized slenderness, prismatic and non-prismatic beams, simply-supported and arbitrary boundary conditions. Finally, the numerical results were compared to the analytical ones of the General Formulation and Eurocode 3, supporting the applicability of the General Formulation due to its good correlation with the numerical model.

This paper aims to assess the influence of geometrical imperfections and residual stresses on the reliability of the stability design rules for steel columns in Eurocode 3 considering a full probabilistic approach and further validate the new buckling curves in the scope of the ongoing revision of the Structural Eurocodes. A reliability assessment of major- and minor-axis flexural buckling of high-strength steel (HSS) welded I-section columns was performed, considering all basic variables as random, including the geometrical and material imperfections, in addition to the material properties of steel and the geometry of the cross-section. An advanced finite element model calibrated with experimental test results is used to perform a very large (290,126 simulations) parametric study covering the majority of practical geometries. Subsequently, Monte Carlo simulation is used to estimate the design values of the buckling resistance that correspond to the target probability of failure of the Eurocodes. Finally, these values are compared to the proposed buckling curves for HSS columns, showing good agreement and supporting their adoption in the revised EN 1993–1-1. It is also concluded that it is on the safe side to carry out a reliability assessment with deterministic reference values for structural imperfections.

The use of high strength steel (HSS) has been consolidated around the world because of its numerous advantages mostly for high-rise buildings and large span bridges. As it provides the possibility of a design with slender sections, substantial reduction in the structure weight is expected, but special attention should be given to the stability of the HSS compression members. However, the existing design codes for HSS columns are limited and based on experimental data related to normal strength steel (NSS) materials, which is responsible for an inaccurate resistance prediction. In this sense, the present paper aimed to investigate the buckling behavior of S690 HSS welded I-section columns failing by flexural buckling around the both principal axes and beam-columns failing by lateral torsional buckling. The experimental campaign contemplated 4 pin-ended columns, in which 2 were tested about their major-axis and the other 2 about the minor-axis, and also 2 beam-columns, including supplementary experimental to measure the geometric imperfections, residual stresses and material properties of the S690 welded I-section columns and beam-columns. In the following, a numerical model was built and validated against the experimental results and afterwards employed to perform a sensitivity study considering different membrane residual stress patterns. Finally, the European [1,2], American [3], and Australian [4] codes were assessed by comparing the design resistances with the results from the experimental tests and the collected test data of relevant studies, showing in general a considerable level of conservatism.