The goal of this paper is twofold. The first goal is to show that geometrically exact beam finite elements can be successfully employed to determine, accurately, the behaviour of steel I-section beams undergoing large displacements and finite rotations. For this purpose, a two-node geometrically exact beam element is presented and validated, which can handle arbitrary initial configurations (e.g. curved configurations), plasticity, geometric imperfections and residual stresses. The second goal is to employ the proposed element to assess the behaviour of I-section beams undergoing lateral-torsional buckling. In particular, the element is used to determine (i) elastic non-linear bifurcation loads (i.e., bifurcation loads accounting for pre-buckling deflections), (ii) large displacement elastic post-buckling paths including geometric imperfection effects and (iii) large displacement elastoplastic equilibrium paths accounting for geometric imperfections and residual stresses. Three support/loading cases are examined, namely: (i) simply supported beams under uniform moment, (ii) simply supported beams subjected to a mid-span vertical force and (iii) cantilevers subjected to a free end vertical force. Besides I-sections with standard height-to-width ratios, wider flange sections are also considered and it is demonstrated that, for the latter, the post-buckling behaviour is quite different from that of standard sections and an increase in the load carrying capacity is observed, which is not predicted by the current Eurocode 3  provisions. Based on the results obtained, a set of relevant conclusions are drawn.
- Eurocode 3
- Geometrically exact beam theory
- Large displacements
- Lateral-torsional buckling
- Post-buckling behaviour