A mathematical model to simulate the cyclic behavior of exposed base plates with extended anchor bolts in steel moment frames subjected to earthquakes

This paper presents a mathematical model to predict the cyclic behavior of Exposed Base Plates with Extended Anchor Bolts (the EBP-EAB model) typically used in industrial and residential steel buildings in countries located in high seismic zones. The research is motivated by the potential integration of these connections as part of the energy dissipative mechanisms of steel moment frames due to their high deformation capacities and excellent hysteretic characteristics. The EBP-EAB model simulates the connection behavior as an arrangement of two parallel springs. The first spring consists of a trilinear backbone curve and a set of rules for describing unloading, reloading, pinching, and modes of cyclic deterioration for strength and stiffness. The second spring allows the simulation of the intermediate plateau observed in the connection response by means of a multi-linear elastic material, where the behavior is nonlinear but elastic. A total of 10 parameters are required to define the coordinates of the EBP-EAB model, where six parameters (core) are obtained using mechanical principles while the remaining four (ancillary) are obtained using a constrained optimization process. Four bio-inspired optimization algorithms were explored to find the best solutions to minimize the error defined in this paper for the empirical calibration of the ancillary parameters. Validation results show that the EBP-EAB model is capable of integrating the features of the nonlinear behavior observed in these connections with reasonable accuracy. Recommendations for estimating the core parameters are detailed, while limitations of the EBP-EAB model are outlined. Finally, as an example application, the model is implemented in a nonlinear dynamic analysis of a steel moment frame representative of an office building subjected to earthquake loading. Results indicate that the model is numerically robust and that the frame equipped with EBP-EABs achieves similar interstory drift demands to those with conventional base plate connections, while preventing plastic hinge formation in the columns.