## 4 Discussion
### Energy Dissipation  
The three key parameters expressing the energy dissipation capacity for CFST column connections are the total dissipation energy (\(W_{\text{total}}\)), the equivalent viscous damping coefficient (\(\xi_{\text{e}}\)), and the dissipated energy capability (\(E_{\text{e}}\)). The total dissipation energy (\(W_{\text{total}}\)) is the cumulative dissipation energy (\(W\)) described as a function of the drift ratio, where \(W\) is the area of the \(P\)-\(\Delta\) hysteresis curve at a certain cycle time. The dissipated energy capability (\(E_{\text{e}}\)) and the equivalent viscous damping coefficient (\(\xi_{\text{e}}\)) are calculated from Equations (5) and (6). Figure 14 describes the idealized load versus deflection relationship, where \(S_{\text{ABC}}\) and \(S_{\text{CDA}}\) refer to the upper half area and lower half area of the hysteresis loop, respectively, and \(S_{\text{OBE}}\) and \(S_{\text{ODF}}\) refer to the corresponding triangular areas.  
\[E_{\text{e}}=\frac{S_{ABC}+S_{CDA}}{S_{OBE}+S_{ODF}} \tag{5}\]  
\[\xi_{\text{e}}=\frac{E_{\text{e}}}{2\pi} \tag{6}\]  
Table 5 compares the dissipated energy capability (\(E_{\text{e}}\)), the equivalent viscous damping coefficient (\(\xi_{\text{e}}\)), and the total dissipation energy (\(W_{\text{total}}\)) in the limit state. Figures 15 and 16 exhibit the equivalent viscous damping coefficients (\(\xi_{\text{e}}\)) of each hysteresis loop versus the drift ratio and the total dissipation energy (\(W_{\text{total}}\)) related to the drift ratio, respectively. These experimental results show:  
1. The specimens that failed in mode I (ST-1, ST-2, and ST-5) have a better energy dissipation performance than the specimens that failed in mode II (ST-3, ST-4, and ST-6).
2. Among the specimens that failed in mode II, the energy dissipation capacity of specimen ST-3, with a thinner end-plate, is the best; a reduction of the steel beam section helps to increase the energy dissipation capacity of joints.  
Figure 14: An idealized hysteretic loop.  
An increasing end-plate thickness results in a reduction in the equivalent viscous damping coefficient (\(\xi_{\rm e}\)) for those specimens with failure mode II. The end-plate thickness has little influence on the energy dissipation capacity for the connections with failure mode I. Those connections mainly dissipate energy through CFST columns.
4. The influence of the steel tube thickness on the equivalent viscous damping coefficient (\(\xi_{\rm e}\)) is related to the end-plate thickness. For the joints with thinner end-plates, the thickness of the steel tube had little effect on the equivalent viscous damping coefficient (\(\xi_{\rm e}\)), which can be attributed to the fact that the thinner end-plate played a major role in energy dissipation. For the joints with thicker end-plates, the effective viscous damping coefficient (\(\xi_{\rm e}\)) increased with a decreasing steel tube thickness. This result suggests that the CFST columns dominated the energy dissipation.  
Figure 16: Wtotal related to drift ratio.  
Figure 15: \(\xi_{\rm e}\) versus drift ratio.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & \(E_{e}\) & \(\xi_{e}\) & \(W_{\rm total}\) (kN\(\cdot\)m) \\ \hline ST-1 & 1.263 & 0.201 & 23.74 \\ ST-2 & 1.318 & 0.210 & 39.80 \\ ST-3 & 1.042 & 0.166 & 15.57 \\ ST-4 & 0.540 & 0.086 & 5.51 \\ ST-5 & 0.830 & 0.132 & 38.27 \\ ST-6 & 0.770 & 0.123 & 11.86 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Key parameters of energy dissipation in the limit state.