## 4 CSA-BRB Ultimate Bearing Capacity Parasitic Bearing Restraint Ratio Threshold
### Axial Elastic-Plastic Bearing Capacity  
Based on the finite element model (FEM) of the steel tube restrained core split BRB, four sets of examples were designed based on the width-thickness ratio and the CSA-BRB length of the core, as shown in Table 1. The lateral stiffness of the restrained external system  
Figure 5: The \(\sigma\)-\(\varepsilon\) curves of the cores. Figure 6: Verification of the FEM adopted in this study using the experimental results of [PERSON] et al. [22] and [PERSON] et al. [26]. (**a**) Observed performance of CS-BRB specimens. (**b**) Hysteretic responses were obtained from tests and FE analyses. is modified in each of these scenarios by changing the height \(h_{w}\) of the web in the restrained external system (the spacing between the two limbs) while the cross-section of the two limbs of the CSA-BRB remains constant. The CSA-BRB cases are numbered according to CSA \(-l-\zeta\), where CSA stands for steel tube concrete restrained kernel split BRB, \(l\) is the CSA-BRB length, and \(\zeta\) is the CSA-BRB's restraint ratio and is calculated according to Equation (1). An elastic buckling analysis was carried out for the arithmetic example in Table 1, and the restraint ratio was calculated by Equation (1). On this basis, the elastoplastic bearing capacity of the monotonic axial compressive load is analyzed for the designed example, and the ultimate compressive bearing capacity of CSA-BRB under axial monotonic load is obtained. The stability factor \(\varphi\) of the CSA-BRB is calculated from this. In the calculation, an initial geometric defect of the first-order buckling mode is applied to the CSA-BRB, the initial flaw amplitude of which is taken to be \(1/500\) of the length of the member, where the residual stresses in the CSA-BRB are equivalently taken into account. The additional effect of residual stresses in the asset is equivalent. Figures 7 and 8 illustrate the load-displacement curves, the deformation, and stress distributions of a member in various stages for some instances. Following the Code for Seismic Design of Building Structures (GB50011-2016) [26], the kernel axial displacement must be added to meet the strain requirement of 0.02. Based on the load-displacement curves given in Figure 7 and the stress and deformation diagrams shown in Figure 8, the influence of the restraint ratio on the failure mode of the CSA-BRB can be analyzed. With the help of the concept of the column stability factor, the ratio of the ultimate load of the CSA-BRB to the core yield load can be defined as the stability factor \(\varphi\). For CSA-20-0.80, the low restraint capacity of its external restraining members on the core makes its restraint ratio \(\zeta<1.0\); that is, the CSA-BRB is bound to experience overall instability before the core yields when the stability factor \(\varphi\) is less than 1. Despite their restraint ratios, the CSA-20-1.15, CSA-20-1.43, and CSA-20-1.74 experience overall instability before the entire portion of the core yields, even when undesirable effects, such as initial mount faults, are taken into consideration. The stability factor \(\varphi<1.0\) declines as the restraint ratio \(\zeta\) decrease when the CSA-BRB reaches its peak axial compression load at an axial compressive strain \(\varepsilon=0.001\) in the core. After the overall instability occurs, the axial load-carrying capacity of the specimen rapidly decreases, and the CSA-BRB is subsequently damaged. The maximum stress in the external restraining members has already yielded when the CSA-BRB reaches its peak load, after which the plastic zone expands rapidly, and the CSA-BRB undergoes overall instability. For CSA-20-1.91, CSA-20-2.09, CSA-20-2.27, and CSA-20-2.47, the restraint ratio \(\zeta\) of the CSA-BRB is more significant, and when the axial compressive strain in the core is \(\varepsilon=0.001\), the core yields in the entire section and its stability coefficient \(\varphi\geq 1.0\).