Closed-form model for ultimate capacity of bolted T-stubs within the Eurocode framework

Abstract

Abstract

Bolted T-stubs govern the flexural response of steel beam-to-column joints. Eurocode 3 Part 1–8 provides reliable formulations for stiffness and resistance, but does not address ultimate resistance and ductility, which are crucial for performance-based assessment. Advanced models capture the full response but are computationally demanding, while closed-form approaches have limited ability to represent failure mode interaction. This paper proposes a simplified closed-form analytical model to predict both ultimate resistance and deformation capacity of bolted T-stubs. The formulation is based on an improved classification of failure modes and introduces two main enhancements: a mechanically consistent evaluation of the resultant contact force position and the inclusion of transition mechanisms between flange-dominated and bolt-dominated behaviour. In addition to classical failure modes, two intermediate mechanisms (MEC-1.2 and MEC-2.3) are introduced to better represent the progressive evolution of collapse. Closed-form expressions are derived by accounting for flange plasticity, bolt elongation, and strain-hardening effects. The model is first verified against an advanced mechanical model through a parametric study on 138 cases, showing strong agreement, including in the identification of governing failure modes. It is then validated against 58 experimental tests, providing accurate predictions of both ultimate resistance and deformation capacity, with mean values of F u / F u , exp = 1.00 and δ u / δ u , exp = 0.94 , and coefficients of variation equal to 0.12 and 0.19, respectively. The proposed model ensures a superior balance between consistency, accuracy, and simplicity, providing a solid basis for design applications and future EN 1993-1-8 developments.