This paper aims to apply a performance-based earthquake engineering approach to assess the assurance of flexural frames whose members are jointed together by using new modified RBS connections, namely, semi-rigid welded steel connections, which obey a progressive failure mechanism. First, the structural members and connections are modeled and predesigned in ETABS software, and then, using OpenSees software, a series of nonlinear progressive failure analyses are performed on the built models extracted from ETABS. To this end, three types of multi-story structures with 3, 10, and 15 are modeled. The models are subjected to 15 earthquakes, such as Northridge (1994), Kobe (1995), Chichi (1999), Bam (2003), Tabas (1978), and so on. The connections are modeled by a series of rotational springs whose nonlinear behavior is estimated by a three-line curve that is established based on the modified Ibarra–Krawinkler deterioration model. Finally, obtaining the maximum ground acceleration versus the maximum relative drift of the floors, the fragility curves of the structures for a collapse level (CP) are determined, through which the seismic performances of the models are evaluated. The results show that by reducing the number of structural floors, the ductility of structures was reduced, and by increasing the ductility of structures, higher drifts in structures were achieved at the same seismic level. The average amount of ductility reduction coefficient in structures with RBS was 1.06 times those without RBS, which indicates that the energy dissipation capacity in structures without RBS connection is higher than in those with RBS. Local analysis of connections shows a 9% increase in the plastic rotation capacity if RBS connections are used. The ductility of all frames with RBS connection increased slightly compared to frames without RBS.