# Improvement of Performance Level of Steel Moment-Resisting Frames Using Tuned Mass Damper System
## 7 Results and Discussion
### The Results for the Artificial Earthquake  
4.1 Seismic Performance of the Controlled and Uncontrolled Structures Exposed to the Artificial Earthquake  
Figure 12 presents the responses of the controlled and uncontrolled structures (i.e., drift ratio, maximum displacement, maximum base shear, and the maximum acceleration) exposed to the artificial earthquake. The figure indicates that the TMD system optimized based on the drift ratio can reduce all structural responses, except for the maximum acceleration of the structure. The optimized TMD system has also controlled the maximum acceleration of the fifth and sixth stories, but it has increased this value for the lower stories. 4.2 IDA for the Dynamic Performance of the Controlled and Uncontrolled Structures Exposed to the Artificial Earthquake  
The results of IDA for the structure subjected to artificial earthquakes are shown in Figure 13. The performance of the controlled structure shows an increase in the maximum acceleration values in the range of \(0.7\mathrm{g}\leq\mathrm{PGA}\leq 0.8\mathrm{g}\). The maximum acceleration of the structure has decreased for other PGA values. Moreover, the value of base shear has decreased for PGA smaller than \(0.5\mathrm{g}\) and remained constant for PGA larger than \(0.5\mathrm{g}\). Additionally, the results show that the performance of the structure has improved for the maximum displacement and drift ratio. Figure 12: Maximum drift ratio, displacement, base shear, and acceleration of the frame subjected to the artificial earthquake. 7.4.3 Investigation of the Performance Level of the Structure Subjected to the Artificial Earthquake  
The performance levels of the structure subjected to the artificial earthquake, based on the FEMA-356 [48], are presented in Figure 14. Based on FEMA-356, the maximum drift ratios of the controlled and uncontrolled structures have been categorized in the figure as:  
1. Immediate Occupancy \(\leq\) 0.7%;
2. 0.7% \(\leq\) Life Safety \(\leq\) 2.5%;
3. 2.5% \(\leq\) Collapse Prevention \(\leq\) 5%. As it can be observed from Figure 14, the six-story steel moment-resisting frame without TMD system has entered into the collapse prevention level for PGA larger than 0.8 g, but the performance level of the structure controlled with the TMD system has remained in the life safety range. Therefore, results indicate that the optimization of the TMD parameters to minimize the maximum drift ratio smaller than 2.5% substantially improve the seismic performance of the structure subjected to the artificial earthquake. It leads to a delay in the fracture of the bending connections (see FEMA-356 [48]), and it can help the beams and columns to sustain distortion. Figure 13: Results of Incremental Dynamic Analysis (IDA) analysis for the frame subjected to the artificial earthquake. Besides, to evaluate the capability of the method presented in this paper, the six-story steel moment-resisting frame structure is considered. For this purpose, two other objective functions (see Equation (25)) are considered, and the optimal values of the TMD system are computed under the artificial earthquake. Table 5 shows the optimal values of the TMD system for different objective functions. It should be noted that the constraints and upper and lower bounds are considered as in Equation (1) and Ref. [46]. \[