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The eccentric bracing system equipped with vertical links is capable of providing high levels of stiffness, strength and ductility, and therefore, can be efficiently used for seismic retrofit of existing structures. This study aims to investigate the seismic reliability of steel moment-resisting frames retrofitted by this system using a novel combined series–parallel system approach. The seismic response of 4, 8 and 12-storey steel moment-resisting frames (MRFs) are evaluated under a set of design basis earthquakes (DBE) before and after retrofitting intervention. Adopting an engineering demand parameter approach (EDP-Based) for reliability assessment and development of analytical models for the frames using systems consisting of the series–parallel elements are the major distinctions between the present study and the other similar works. To estimate the global reliability of the frames, first, the reliability of each storey is individually derived based on various probable damage levels for the lateral-load resisting members. Then, the seismic reliability of the frame is globally obtained by combining the reliability of each storey for different damage levels in the lateral load-resisting subsystems. The results indicate significant impact of this type of bracing system on improvement of the performance level and load-carrying capacity of the frames along with reduction of the lateral displacements. It is shown that application of the vertical links can reduce the maximum inter-storey drifts by at least 60%, while it leads to at most 17% increase in the base shear. All retrofitted frames exhibited a performance level higher than the Life Safety (LS) when subjected to the DBE hazard level records (earthquakes with return period of 475 years). At the same level of earthquake intensity, in the cases when the drift corresponding to the LS performance level is used as the target, the reliability of the retrofitted frames was improved by more than 90% compared to the original frames for all damage states developed in the vertical links.

Seismic reliability analysis of steel moment-resisting frames retrofitted by vertical link elements using combined series–parallel system approach