# Improvement of Performance Level of Steel Moment-Resisting Frames Using Tuned Mass Damper System
## 8 Conclusions  
The performance-based design of the steel structure controlled with the TMD system has been investigated in this paper. All studied earthquakes have been scaled in such a way that all have had the PGA value equal to 1 g. Then, the optimum parameters of the TMD system have been calculated using a meta-heuristic algorithm (i.e., WCA) focused on minimizing the maximum drift ratio of the stories based on the FEMA-356 subjected to the scaled earthquakes. For this purpose, two different frame buildings (i.e., a six-story and a 10-story moment-resisting frame) have been considered and modeled with the OpenSees software. The optimum parameters of the TMD system have been computed subjected to the scaled earthquakes. Then, PGA has been changed in the range of 0.1 g to 1 g in IDA, and the responses of the controlled structure have been examined. The results of the study show that the base shear decreases for the PGA value smaller than 0.5 g under all earthquakes studied. At the same time, for all records with PGA larger than 0.5 g, the TMD system does not make any considerable reduction in the base shear value of the controlled structure. This sentence is correct for the maximum drift ratio. Finally, the responses of controlled structure (i.e., the maximum acceleration and displacement) have almost decreased for all regions of PGA.  
Moreover, the results of the investigation show that optimizing the TMD parameters, based on minimizing the drift ratio, decreases the structural displacement, and improves the seismic behavior of the structure based on FEMA-356. The results also indicate that the response of the controlled and uncontrolled structure (e.g., drift ratio, maximum displacement, maximum base shear) is reduced during the artificial earthquake. Additionally, the optimization of the TMD parameters, to keep the maximum drift ratio smaller than 2.5%, improves the seismic performance of the structure subjected to  
Figure 18: Results of IDA analysis for the frame subjected to the artificial earthquake.  
the artificial earthquake. It leads to a delay in the fracture of the bending connections, and it can help the beams and columns to sustain distortion.  
Finally, a comparison between the traditional objective functions and the proposed objective function (i.e., the maximum drift ratio of less than 2.5%) has been presented. The results show that the optimum parameters of the TMD system based on the proposed objective function have a better performance in reducing the structural responses in comparison with the other previously used objective functions.  
Conceptualization, M.D., R.K., and H.H.; methodology, M.D., R.K., H.H., A.J.-G., and R.J.; software, M.D., R.K., and H.H.; validation, M.D., R.K., H.H., A.J.-G., and R.J.; formal analysis, M.D., R.K., and H.H.; investigation, M.D. and R.K.; writing--original draft preparation, M.D., R.K., and H.H.; writing--review and editing, A.J.-G. and R.J. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflicts of interest.