Numerical behaviour of three-dimensional beam-to-column bolted steel joints under weak axis and strong axis loading

Bolted end-plate joints are characterized by a semi-rigid behaviour, ensuring a compromise between stiffness and rotational capacity, while effectively enabling the transfer of bending and shear forces. However, their design becomes significantly more intricate in three-dimensional configurations, where the coupled effects between the strong and weak axes (in- and out-of-plane bending) are only partially captured by conventional analytical approaches, particularly the component-based method proposed by Eurocode 3. This limitation may compromise the reliability of stiffness and strength predictions, thereby justifying the need for advanced numerical methodologies. Within this framework, the present study introduces a series of three-dimensional finite element models in ABAQUS, aiming to simulate the mechanical response of beam-to-column joints with bolted extended end-plates subjected to biaxial loading. These models integrate frictional contact, bolt pre-tensioning, and both material and geometric nonlinearities. The numerical framework was benchmarked against experimental data from the literature. Two typologies were considered: a partial configuration, employed for validation purposes, and a complete configuration, dedicated to an extensive parametric study. The assessment of the extracted moment–rotation curves enabled the identification of the governing mechanical parameters — namely initial rotational stiffness and plastic moment resistance — for each configuration, in order to perform a comparative analysis with the theoretical estimations derived from Eurocode 3.