# Improvement of Performance Level of Steel Moment-Resisting Frames Using Tuned Mass Damper System
## 7 Results and Discussion
### The Structural Seismic Performance  
The results for the structure controlled with the TMD system are shown in Table 4. As it is observed from the table, the reduction in the base shear is less than 3.49% under different earthquakes, even though the base shear has increased slightly during the earthquakes NE1 and AE. Hence, due to the insignificant reduction in the base shear under different earthquakes, it might be concluded that the optimization of the TMD parameters focused on reducing the drift will not have a significant effect on the base shear of structures. Table 4 shows that the average acceleration of the structure equipped with the TMD system has increased under the FE2 and AE earthquakes by about 5% but, for the rest of earthquakes, the parameters of TMD optimized based on drift can reduce the acceleration of the structure. Similar results have been obtained for the average displacement of the structure controlled with the TMD system. In fact, for the FE2, NE3 earthquakes, the average displacement of the controlled structure has increased while this parameter has decreased for other earthquakes. It should be noted that the negative and positive signs in Table 4 show the decrease and increase in the average reduction, respectively. In other words, the positive value shows that the parameter is reduced, and the negative value shows that it is increased.  
The maximum drift ratio of all stories and the roof displacement time history of the structure are depicted in Figures 6 and 7 with and without the TMD system subjected to the near- and far-field earthquakes. It is clear from the table that the maximum drift ratio of the stories has been reduced for all earthquakes. It is also observed that the roof displacement has increased for some earthquakes (e.g., FE2, and NE3). The controlled structure has been vibrated about a new plastic axis subjected to  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Earthquake** & \(K_{tmd}\) **(N/mm)** & \(C_{tmd}\) **(N-s/mm)** & \(M_{tmd}\) **(N-s\({}^{2}\)/mm)** \\ \hline FE1 & 404.94 & 770.18 & 180 \\ FE2 & 543.76 & 304.28 & 180 \\ FE3 & 490.1 & 942.89 & 180 \\ NE1 & 421.67 & 1753.1 & 180 \\ NE2 & 315.87 & 972.87 & 141 \\ NE3 & 405.02 & 500.0 & 180 \\ AE & 405.47 & 935.66 & 180 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Optimum parameters achieved for TMD subjected to the drift ratio constraint.  
these earthquakes, and the non-elastic deformation of the structure has increased. This indicates that the drift-optimized TMD system is unable to improve the seismic performance of the structure for some earthquakes.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Earthquake**} & \multicolumn{4}{c}{**Average Reduction (\%)**} \\ \cline{2-5}  & **Displacement** & **Drift** & **Acceleration** & **Base Shear** \\ \hline FE1 & 5.78 & 5.02 & 8.10 & 2.61 \\ FE2 & \(-\)20.56 & 25.08 & \(-\)5.25 & 0.81 \\ FE3 & 11.14 & 6.53 & 10.06 & 2.75 \\ NE1 & 14.81 & 10.96 & 3.15 & \(-\)2.49 \\ NE2 & 12.26 & 4.18 & 9.03 & 0.65 \\ NE3 & \(-\)31.34 & 42.92 & 19.69 & 3.49 \\ AE & 31.55 & 19.42 & \(-\)5.23 & \(-\)1.12 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The average reduction in the structural responses.  
Figure 6: Drift ratios of the stories and the time history of the displacement of the roof in the controlled and uncontrolled structure subjected to the far-field earthquakes.