## 3 Seismic Performance of the Frame with CFST Dampers
### Hysteretic Loops Analysis of Three Components GJ-1,Gj-2 and GJ-3
When the displacement reaches 11.844 mm, the peak load is 2374.418 KN. When loading at the same level, the reduction in load-carrying capacity at the second loading is larger than that of GJ-1, and the difference is greater than 2%. At the later stage of displacement loading, when the load-carrying capacity is still greater than 85% of the peak bearing capacity, the hysteretic loop is generally in the shape of a shuttle. When the ultimate displacement is 39.509 mm, the corresponding load-carrying capacity is 1981.434 KN, less than 85% of the maximum load-carrying capacity. In general, the member at this stage still has seismic performance to a certain extent, but its energy dissipation capacity and ductility are ordinary. Compared with the hysteretic loops of GJ-1 and GJ-2, it can be seen from Figure 9c that the characteristic of the hysteretic loop of GJ-3 is that the load-carrying capacity decreases rapidly after reaching the peak value of 3030.285 KN. When the displacement reaches 23.30 mm, the load-carrying capacity is 2502.154 KN, which is less than 85% of the peak load-carrying capacity, and the component has been damaged. This indicates that GJ-3 has a higher horizontal load-carrying capacity than the previous two components, but its ductility is poor. From Figure 9a-c, it can be seen that the hysteretic loop of the frame structure with CFST dampers has the best solidity, with the smallest pinch and the best energy dissipation capacity. The load-carrying capacity of the GJ-3 skeleton curve decreases slightly and tends to be stable in the later period, and the comprehensive seismic performance is relatively stable. Its nonlinear displacement is large and its ductility is excellent. The cracking load, yield load, peak load, failure load, and yield strength ratio of the three members are shown in Table 1, where \(P_{c}\) is the horizontal load when the component cracks; \(P_{y}\) is the horizontal load when the component yields; \(P_{u}\) is the horizontal load when the component reaches the peak value; \(P_{\Delta}\) is the horizontal load when the component is damaged; \(\mu_{1}\) is the yield strength ratio, which is the ratio of yield load to peak load. By analyzing Table 1, it can be concluded that:  
1. There is little difference between the positive and negative loading data sizes of the models. 2. From GJ-1 to GJ-3, the yield load and peak load of the three components show a certain increasing trend. In terms of yield load, component GJ-3 is the largest, and \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{5}{c}{**Positive Loading**} & \multicolumn{5}{c}{**Negative Loading**} \\ \cline{2-10}  & \(P_{c}\) & \(P_{y}\) & \(P_{u}\) & \(P_{\Delta}\) & \(\mu_{1}\) & \(P_{c}\) & \(P_{y}\) & \(P_{u}\) & \(P_{\Delta}\) & \(\mu_{1}^{{}^{\prime}}\) \\ \hline GJ-1 & 492.4 & 1255.8 & 1669.5 & 1451.9 & 0.752 & 463.5 & 1201.5 & 1605.1 & 1419.3 & 0.748 \\ GJ-2 & 657.5 & 2167.2 & 2474.4 & 1981.4 & 0.876 & 624.8 & 2035.8 & 2343.9 & 1985.2 & 0.868 \\ GJ-3 & 816.8 & 2657.1 & 3030.2 & 2461.3 & 0.877 & 828.3 & 2701.4 & 2962.4 & 2408.4 & 0.912 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cracking load, yield load, peak load, failure load, and yield strength ratio of three components (unit: KN). component GJ-1 is the smallest, at about 47.3% of GJ-3. In terms of peak load, GJ-1 and GJ-2 are, respectively, 55.1% and 81.7% of GJ-3. It can be seen from the analysis that GJ-1 adds three CFST ductile columns to the pure frame, but it cannot increase its own lateral stiffness. GJ-2 cuts the middle of the wall to a certain height, reducing the lateral stiffness of the wall, and making the columns on both sides become relatively weak at the height of the cut. 3. Among the three members, GJ-1 has the smallest yield ratio and GJ-3 has the largest yield ratio. Although GJ-1 has a smaller peak load-carrying capacity, it has a higher plastic deformation capacity and can dissipate more energy during an earthquake.