## 5 Hysteretic Energy Dissipation Performance
### Hysteretic Energy Dissipation Performance  
Based on the numerical results of the static bearing capacity of the CSA-BRB, an example of the stability coefficient \(\varphi\geq 1.0\) is selected to analyze the elastic-plastic hysteretic performance, as shown in Table 3. The height of the web \(h_{w}\) (i.e., the spacing between the two limbs) in the external restraining members was varied to change the lateral stiffness of the external restraining members. In comparison, the cross-section and length of the two limbs of the CSA-BRB remain unchanged. Similarly, the CSA-BRB case is numbered according to the following formula CSA \(-l-\zeta\), where CSA stands for steel tube concrete restrained kernel split BRB, \(l\) is the length of the CSA-BRB, and \(\zeta\) is the restraint ratio of the CSA-BRB. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & \(b_{c}\times t_{c}/mm\) & \(P_{y_{c}}\)/\(kN\) & \(b_{f}\times h_{f}\times t_{w}/mm\) & \(h_{w}/mm\) & \(\zeta\) & \(\varphi\) \\ \hline CSA-20-\(\zeta\) & 240 \(\times\) 40 & 4512 & \(400\times 200\times 10\) & 200–340 & 1.91–3.37 & 1.03–1.60 \\ CSA-18-\(\zeta\) & 240 \(\times\) 30 & 3384 & \(360\times 150\times 10\) & 180–340 & 1.72–3.70 & 1.00–1.60 \\ CSA-15-\(\zeta\) & 240 \(\times\) 24 & 2707 & \(336\times 120\times 8\) & 180–310 & 1.87–3.82 & 1.02–1.60 \\ CSA-12-\(\zeta\) & 240 \(\times\) 24 & 2707 & \(336\times 120\times 8\) & 110–220 & 1.78–3.74 & 1.00–1.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Key geometric dimensions and results of the various components of CSA-BRB. Figure 11: Hysteretic load protocol of CSA-BRBs. Based on the results of the calculations, the CSA-BRB is divided into three types of modes based on its hysteretic energy consumption performance, as illustrated by the CSA-20-\(\zeta\) group calculation. Firstly, in axial load reciprocating load, the CSA-BRB core has not reached the total cross-section yield, i.e., the stability coefficient \(\varphi\) is less than 1.0, which cannot fully load an entire hysteretic loop during the hysteretic load process. The hysteresis curve of this type of CSA-BRB is severely pinched, and the energy dissipation capacity is low, so it cannot be used as an energy dissipation CSA-BRB for the seismic design of the structure. Secondly, when the stability coefficient of the CSA-BRB is within the range of \(1.0\leq\varphi<1.6\), in the axial load reciprocal load process, the core reaches complete cross-sectional yielding and enters the strengthening phase. This type of CSA-BRB completes the low-order hysteresis load, and only part of the hysteresis curve is full. Still, it cannot satisfy the established load requirements of energy dissipation capacity. Although this type of CSA-BRB has a particular energy dissipation performance, it cannot meet the plastic cumulative strain value requirements. There is no problem with the use of bearing members. It can be used to adjust the lateral stiffness of the structure, but it cannot be used for the energy dissipation design of the system. Thirdly, the type of CSA-BRB can be used as a dissipating energy member because it can fulfill the plastic cumulative strain value requirements, and the hysteresis curve is complete when the coefficient of stability of the CSA-BRB is 1.6. Take the calculation example CSA-20-2.90 (Figure 12) in the first group of calculation examples in Table 3 as an example; its restraint ratio is \(\zeta=2.90\). During the monotonic load process, when the axial compressive strain of the core in this example reaches 0.02, the CSA-BRB does not have an overall instability failure. Nevertheless, in the hysteretic analysis of the reciprocating axial load, when the axial strain of the core reaches 0.015, the overall instability and loss of the CSA-BRB occurred, which failed to meet the requirements of the energy-dissipating CSA-BRB for the cumulative plastic deformation index of the core, and did not form a complete hysteresis curve.