Generalized spring model for steel bolts in tension considering uncertainty and loading speed

Quantifying the rotational ductility of connections is key to studying the robustness of steel structures under extreme hazards and loading scenarios. In partial-strength bolted steel connections, the ultimate failure state is typically governed by bolt rupture. Simulating bolts using solid finite element models can be inconvenient for practical applications due to high computational demands and lengthy calibration procedures of the material damage parameters. Additionally, current bolt models do not capture the uncertainty associated with the bolt's elongation capacity. To address these challenges, a trilinear empirical spring model is proposed to accurately capture the bolt response up to failure while incorporating uncertainty; thereby supporting studies related to reliability and performance-based engineering. Two multi-variate empirical expressions are developed to predict the bolt's elastic stiffness and plastic elongation, as a function of its size, grade, grip, and thread lengths, providing improved accuracy across a wide range of bolt geometries. These expressions are derived from an extensive dataset of bolt assemblies under uniaxial tension, compiled from literature and supplemented by 200 newly tested specimens. The proposed model is applicable in finite element simulations employing axial connectors, numerical mechanics-based analyses, or design applications. The model is validated against experimental data at both the component and joint scales for various bolt grades and connection topologies, highlighting the impact of the bolt's response uncertainty on the joint-level ductility. The implications of high loading speed, representative of real dynamic hazard, on the bolt's response parameters are also quantified.