## 5 Conclusions  
The main findings of the present study are concluded as follows:  
1. The average amount of the ductility reduction coefficient in structures without RBS obtained 1.06 times that of structures with RBS connection. Therefore, energy dissipation capacity in structures with RBS connection is higher than in structures without RBS connection.
2. Local analysis of connections showed a 9% increase in plastic rotation capacity if RBS connections are used. However, the increase in the coefficient of behavior of steel frames modeled with such a connection was not significant. It seems that connecting the beam with the reduced cross-section of the bending connection beams, by concentrating the stresses in a place away from the connection, is a suitable solution to solve this problem.
3. The ductility of all frames with RBS connection was increased compared to frames without RBS. The increasing amount was about 0.03% and 0.11 in terms of the behavior coefficient and the ductility coefficient, respectively.
4. Regardless of the seismic hazard values in calculating the failure probability, with decreasing the rotation time, the probability of collapse (or not estimating the CP functional level) in the structure decreases at a constant level of seismic intensity.
5. The ductility of structures decreased with decreasing the number of structural layers. The curves obtained by incremental nonlinear dynamic analysis (IDA) became horizontal at a lower seismic intensity level, which indicates that with increasing ductility of structures the higher drifts can be achieved in structures at the same seismic level, which witnessed better behavior of the structures.
6. As the stiffness of the connections decreases, the effective period of the structure increases and the spectral acceleration decreases accordingly.
7. The results of folding curves showed that the use of RBS semi-rigid connections has a significant effect on the linear part of IDA curves and with increasing drifts, the reduction in structural resistance against seismic forces is significant.
8. The RBS semi-rigid connection increases the demand for ductility in beams. In other words, the results of the nonlinear analysis showed that the increase in the behavior coefficient in the connection with the beam with reduced life is more than the normal connection.
9. With decreasing connection stiffness, the percentage of participation of higher modes has increased, so in structures with semi-rigid connections, the number of effective modes in the structure is higher than the rigid state ratio.
10. By reducing the stiffness of the connections, the ductility of the structures increases and also the displacement of the structures increases.
11. As the stiffness of the connections increases, the amount of knot rotation decreases and the final strength also decreases.
12. The studied structures with high ductility are probably less damaged annually than the other cases, and the structure with the shape Low acceptability can be considered as a next option.
13. By using the results and the methods introduced in this study, the damage curves can be easily obtained for the country of IRAN, which is part of the ATC58 project to determine the possible damage to structures and its application in the country's insurance industry.  
**Author Contributions:** Conceptualization, M.S.; Data curation, M.M.; Investigation, M.M.; Methodology, M.M. and M.S.; Project administration, M.S.; Resources, M.M.; Software, M.M.; Supervision, M.S.; Validation, M.S.; Writing--original draft, M.M.; Writing--review & editing, M.S. and M.M.; All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author, upon reasonable request.  
The authors would like to thank Editor-in-Chief, Editor and anonymous reviewers for their valuable reviews.  
The authors declare no conflict of interest.