## 4 Test Results and Analysis
### Ductility  
Ductility is an important performance index in seismic research on structural engineering. In this paper, the energy equivalent method is used to calculate the displacement ductility coefficient \(\mu=\mathbf{\Delta}_{\text{u}}/\mathbf{\Delta}_{\text{y}}\), where \(\mathbf{\Delta}_{\text{y}}\) is the yield displacement and \(\mathbf{\Delta}_{\text{u}}\) is the limit displacement, which is taken as the corresponding displacement value when the load drops to \(0.85\mathbf{P}_{\text{u}}\). Figure 11 shows how the initial yield point of the specimen can be determined by the energy equivalence method. As shown in the figure, two lines \(\mathbf{OY}\)-\(\mathbf{YU}\) are drawn to make the areas of the two shadows in the figure equal (\(\mathbf{S}_{\text{OAB}}=\mathbf{S}_{\text{BYU}}\)), and the \(\mathbf{x}\) coordinate of the intersection of the two lines \(\mathbf{OY}\)-\(\mathbf{YU}\) and the skeleton curve is the initial yield displacement (\(\mathbf{\Delta}_{\text{y}}\)). The calculated values of \(\mu\) and each characteristic point are listed in Table 5, where \(\mathbf{P}_{\text{y}}\) and \(\mathbf{P}_{\text{f}}\) are respectively the load values corresponding to \(\mathbf{\Delta}_{\text{y}}\) and \(\mathbf{\Delta}_{\text{f}}\), and \(\mathbf{\Delta}_{\text{u}}\) is the displacement value corresponding to \(\mathbf{P}_{\text{u}}\). At the end of the loading, the positive load is reduced to \(0.85\mathbf{P}_{\text{u}}\), but the negative load is not, so only the positive ductility coefficient is given in the table, and the positive ductility coefficient of the frame is up to \(2.58\), which shows that the RACFST frame can meet the ductility requirements according to the design methods and construction measures.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Loading**} & \multicolumn{2}{c}{**Yield Point**} & \multicolumn{2}{c}{**Ultimate Point**} & \multicolumn{2}{c}{**Failure Point**} & \multirow{2}{*}{\multirow{2}{*}{\(\mu\)**=\(\mathbf{\Delta}_{\text{u}}/\mathbf{\Delta}_{\text{y}}\)}} & \multirow{2}{*}{\(\mu\)**average**} \\ \cline{3-3} \cline{5-10}  & & & \(P_{\text{y}}\) & & & & & & & \\ \hline RACFCST & + & 148.60 & 9.88 & 172.14 & 17.98 & 146.32 & 25.50 & 2.58 & \\ frame & - & 132.48 & 8.83 & 158.62 & 18.02 & 134.83 & — & — & \\ \hline \hline \end{tabular}
\end{table}
Table 5: The measured load and displacement at characteristic points.  
Figure 10: The skeleton curve of the RACFST frame.  
Table 6 shows the inter-story displacement angles (\(\theta_{y}\), \(\theta_{u}\) and \(\theta_{I}\)) of the characteristic points of the skeleton curve. According to the relevant provisions of Chinese standard GB50011-2010 [24], \"on the one hand, in the event of a moderate earthquake, the elastic inter story displacement angle of the structure shall be less than a specified limit value, 1/550 for reinforced concrete frame and 1/250 for multi-story and high-rise steel structure, so as to prevent the main structure of the building from being damaged and ensure the normal use function of the building\". In this experiment, the displacement angle is 1/91 when the frame yields, which is far greater than the limit value of the standard, indicating that the deformation ability of the frame in the elastic stage can comply with the requirements well. On the other hand, in the event of a large earthquake, the elastic inter story displacement angle of the structure should be less than a specified limit value (1/50), so as to prevent the collapse of the structure. In this experiment, when the frame is damaged, the inter-story displacement angle is 1/33, which is far greater than the limit value of 1/50 specified in the standard, so the RACFST frame has a potent anti-collapse ability.