## 3 Seismic Performance of the Frame with CFST Dampers
### Displacement Ductility Factor of Three Components GJ-1, GJ-2 and GJ-3  
The displacement and ductility factor of three components are shown in Table 2, where \(\Delta_{c}\) is the crack displacement; \(\Delta_{y}\) is the yield displacement; \(\Delta_{u}\) is the peak load-carrying capacity displacement; \(\Delta_{\Delta}\) is the ultimate displacement (the displacement corresponding to the frame failure); \(\mu_{2}=\Delta_{\Delta}/\Delta_{y}\) is the ductility factor of the specimen.  
By analyzing Table 2, it can be concluded that:  
1. From the perspective of the model itself, the difference between the positive and negative loading data of each indicator is small, but the difference between the same indicator of different models is large.
2. The crack displacement of GJ-1 is about 2-3 times that of GJ-2 and GJ-3, indicating that the stiffness of GJ-1 is significantly less than that of GJ-2 and GJ-3 in the early stage of loading.
3. In terms of yield displacement, the positive and negative data of GJ-2 and GJ-3 are roughly the same, which are about 73.6% of GJ-1. The stiffness values before yield of GJ-2 and GJ-3 are almost the same and much larger than GJ-1.
4. From the peak load-carrying capacity displacement to the ultimate displacement, it can be seen that the nonlinear displacement of GJ-1 is significantly increased compared with GJ-2 and GJ-3: GJ-1 is 116.8% higher than GJ-2, GJ-1 is 194.1% higher than GJ-3, and GJ-2 is 35.9% higher than GJ-3 under positive loading. Under negative loading, GJ-1 is 113.9% higher than GJ-2, GJ-1 is 185.3% higher than GJ-3, and GJ-2 is 33.3% higher than GJ-3.
5. In terms of displacement ductility factor, the factor of GJ-1 is obviously larger than that of GJ-2 and GJ-3, and more than 10. It can be seen from the comparison of the three components that the displacement ductility factor of GJ-1 is higher than that of GJ-2 by 56.7% and higher than that of GJ-3 by 113.9%. The displacement ductility factor of GJ-2 is higher than that of GJ-3 by 36.5%.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{6}{c}{**Positive Loading**} & \multicolumn{6}{c}{**Negative Loading**} \\ \cline{2-11}  & \(\Delta_{c}\) & \(\Delta_{y}\) & \(\Delta_{u}\) & \(\Delta_{\Delta}\) & \(\mu_{2}\) & \(\Delta_{c}\) & \(\Delta_{y}\) & \(\Delta_{u}\) & \(\Delta_{\Delta}\) & \(\mu_{2}^{\prime}\) \\ \hline GJ-1 & 2.933 & 8.147 & 17.014 & 85.659 & 10.514 & 2.510 & 7.925 & 17.383 & 85.088 & 10.736 \\ GJ-2 & 1.448 & 5.888 & 11.844 & 39.509 & 6.710 & 1.259 & 5.770 & 11.019 & 39.773 & 6.893 \\ GJ-3 & 1.051 & 5.924 & 11.976 & 29.122 & 4.915 & 1.354 & 5.985 & 11.988 & 29.829 & 4.984 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Displacements and ductile factor of three components.  
From the perspective of \(\Delta_{\Delta}/\Delta_{u}\), the ratio of the three components is GJ-1:GJ-2:GJ-3 = 2.07:1.24:1, which shows that GJ-1 still has excellent load-carrying capacity after reaching the maximum peak load-carrying capacity. When reaching the maximum load-carrying capacity, the frame shows obvious plasticity, and the load-carrying capacity decreases gently, while GJ-2 and GJ-3 show obvious brittleness, which has a negative impact on earthquake resistance.  
To sum up, the displacement ductility factor of the frame with CFST dampers is significantly greater than that of the energy-dissipated low-rise concrete shear wall with CFST short columns and the ordinary low-rise concrete shear wall. The frame with CFST dampers has good ductility and late load-carrying capacity. After the frame has reached the maximum load-carrying capacity, it can still maintain good stiffness and load-carrying capacity. In addition, it can maintain the overall working performance of the frame in the round-trip action and has good energy dissipation capacity.