## 4 CSA-BRB Ultimate Bearing Capacity Parasitic Bearing Restraint Ratio Threshold  
### Finite Element Model  
In this section, the FE software ANSYS 14.5 is used to establish the finite element model (FEM) of CSA-BRB for elastoplastic static bearing capacity analysis, and the contribution of the infill material is ignored in the numerical analysis. Both core and restrained external members are simulated using beam unit BEAM188 to save computational costs and improve computational efficiency. The core member uses a one-piece plate, and the restrained external system uses a combined section and forms a custom beam unit, as shown in Figure 3.  
The displacement couplings between the core and external restraining members are illustrated in Figure 4, where the lateral deformation of the core and external restraining members is coupled via point-to-point lateral deflection displacement; in the CSA-BRB mid-span, the axial displacement of the corresponding nodes of the core and external restraining members in the mid-span section is coupled to eliminate ribs at the end of the core are rigidly connected to the core. They are not coupled to the external restraining members.  
As shown in Figure 4, the two ends of the CSA-BRB are hinged to constrain the \(x\), \(y\), \(z\) displacements of the span nodes of the ribs on one side of the core and the \(x\), \(y\) displacements of the ribs on the other side; the overall lateral (\(x\)-direction) displacement of the CSA-BRB is also constrained to ensure that it bends around the \(x\)-axis; finally, the rotational displacement of the CSA-BRB around its axis (\(x\)-direction) is constrained to avoid rigid body rotation. Numerical analysis of elasticity and plasticity is carried out by applying an axial load \(P\) to the end of the CSA-BRB.  
For the calculations designed in this section, the kernel is selected from a hot-rolled steel plate, using Q235 steel with a yield strength of \(f_{y}=235\) MPa. The rectangular steel tubes of the outer restraining members are cold-formed thin-walled rectangular tubes of Q355 steel with a yield strength of \(f_{y}=355\) MPa. The end stiffeners are set to be elastic, and the module of elasticity of the steel \(E_{s}=206\) GPa, [PERSON]'s ratio \(\
u=0.3\). The material properties of the steel of the external restraining members are taken as ideal elastoplasticity; the \(\sigma\)-\(\varepsilon\) curve of the core is shown in Figure 5. The steel obeys the follower strengthening criterion during the elastoplastic analysis.  
Figure 4: Lateral displacement coupling between the core and the restrained system.  
Figure 3: Section of the CSA-BRB.  
It is well known that the load-carrying capacity of BRBs under pure compression is closely related to the material constitutive relation, the element type, and the boundary conditions of BRBs. The FEM adopted to analyze the load-carrying capacity of the CAS-BRB has been validated by a hysteretic test for CS-BRBs (as shown in Figure 6), which is carried out by [PERSON] et al. [22] and [PERSON] et al. [26]. Both the CS-BRB and CAS-BRB have similar material constitutive relations, element types, and boundary conditions. Therefore, the accuracy of the FEM in this article can be accepted.