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Buckling should be carefully considered in steel assemblies with members subjected to compressive stresses, such as bracing systems and truss structures, in which angles and built-up steel sections are widely employed. These type of steel members are affected by torsional and flexural-torsional buckling, but the European (EN 1993-1-2) and the American (AISC 360-16) design norms do not explicitly treat these phenomena in fire situation. In this work, improved buckling curves based on the EN 1993-1-2 were extended by exploiting a previous work of the authors. Moreover, new buckling curves of AISC 360-16 were proposed.

The buckling curves provided in the norms and the proposed ones were compared with the results of numerical investigation. Compressed angles, tee and cruciform steel members at elevated temperature were studied. More than 41,000 GMNIA analyses were performed on profiles with different lengths with sections of class 1 to 3, and they were subjected to five uniform temperature distributions (400–800 C) and with three steel grades (S235, S275, S355).

It was observed that the actual buckling curves provide unconservative or overconservative predictions for various range of slenderness of practical interest. The proposed curves allow for safer and more accurate predictions, as confirmed by statistical investigation.

This paper provides new design buckling curves for torsional and flexural-torsional buckling at elevated temperature since there is a lack of studies in the field and the design standards do not appropriately consider these phenomena.

The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams. These formulations capture the warping torsional effects of open cross‐sections and are suitable for the analysis of the nonlinear buckling and post‐buckling of thin‐walled frames with generic cross‐sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU‐running time.

The definition of the corotational framework for a two‐noded three‐dimensional beam element is presented, based upon the works of Battini .The definitions of the local element kinematics and displacements shape functions are developed based on both Timoshenko and Bernoulli assumptions, and considering low‐order as well as higher‐order terms in the second‐order approximation of the Green‐Lagrange strains. Element forces interpolations and generalized stress resultant vectors are then presented for both mixed‐based Timoshenko and Bernoulli formulations. Subsequently, the local internal force vector and tangent stiffness matrix are derived using the principle of virtual work for displacement‐based elements and the two‐field Hellinger‐Reissner assumed stress variational principle for mixed‐based formulations, respectively. A full comparison and assessment of the different local element models are performed by means of several numerical examples.

In this study, it is shown that the higher order elements are more accurate than the low‐order ones, and that the use of the higher order mixed‐based Bernoulli element seems to require the least number of FEs to accurately model the structural behavior, and therefore allows some reduction of the CPU time compared to the other converged solutions; where a larger number of elements are needed to efficiently discretize the structure.

The paper reports computation times for each model in order to assess their relative efficiency. The effect of the numbers of Gauss points along the element length and within the cross‐section are also investigated.