# Behavior of Circular Hollow Steel-Reinforced Concrete Columns under Axial Compression
## 4 Analytical Behavior  
### Complete Mechanism of Circular HSRC Columns  
The finite element model of circular HSRC column 1-1 was taken as a representative example to analyze the load-deflection curves (\(N\)-\(u_{\text{m}}\)) so as to study the mechanism under axial compression. Figure 11 depicts schematics of the characteristic points of the typical example. Four characteristic points are selected on the \(N\)-\(u_{\text{m}}\) curve: Point \(A\) is the boundary point of the elastic stage of the column, at which the concrete begins to crush; point \(B\) indicates the yield of the longitude rebar; point \(C\) is where the specimen reaches the peak load; point \(D\) is when the left side of the mid-height column is cracked and crushed on the right side.  
The whole process of loading can be divided into four stages:  
(1) Stage 1 (_OA_), elastic stage I: the whole specimen is in the elastic stage. The load on the circular HSRC column increases linearly with its deflection.  
(2) Stage 2 (_AB_), elastic stage II: the longitudinal rebar and the steel tube are still in the elastic stage, and there is still a linear relationship between the load on the circular HSRC column and its deflection.  
(3) Stage 3 (_BC_), elastic-plastic stage: the load on the circular HSRC column increases nonlinearly with its deflection, and the bearing capacity of the column reaches a maximum.  
(4) Stage 4 (_CD_), bearing capacity decline stage: there is a nonlinear relationship between the load on the circular HSRC column and its deflection until the end of loading.  
Figure 12 illustrates the stress distribution at characteristic points of circular HSRC column 1-1. The principal stress of z direction S33 for concrete and Mises stress for the hollow steel tube and rebar were analyzed. Point A marks the boundary between the elastic stage I and elastic stage II. The longitudinal stress on the circular HSRC column is all compressive, with greater compression on the right side than on the left side of the cross-section. The stress values range between 23 MPa and 38 MPa. The maximum compressive stress is approximately 1.7 times the minimum compressive stress, showing a zonal distribution along the cross-section, as depicted in Figure 12a. Point \(B\) is the boundary between elastic stage II and the elastic-plastic stage. When the longitudinal rebar yields and enters the plastic deformation stage, the overall longitudinal stress on the circular HSRC column is still all compressive, and the stress is higher on the right side than the left side. The stress value is between 29 MPa and 55 MPa, and the maximum compressive stress is about 1.9 times the minimum compressive stress, implying a zonal distribution along the cross-section, as shown in Figure 12b. At point \(C\), the specimen reaches the peak load, the steel tube enters the plastic deformation stage, the overall longitudinal stress on the circular HSRC column is compressive, the stress value is higher on the right side than on the left side, the compressive stress value gradually decreases from the left to the right side, and the stress value is between 20 MPa and 67 MPa. The maximum compressive stress is approximately 3.5 times the minimum compressive stress, and the distribution along the cross-section is zonal, as shown in Figure 12c. At point \(D\), the left side of the concrete experiences tensile stress, causing concrete edge cracks, the left side of the entire circular HSRC column is under tension while the right side of the column experiences compressive stress, and the maximum value of the tensile stress occurs near the middle section, which has already reached the tensile strength of the concrete. Thus, the outer concrete begins to crack on the left side and crushes on the right side, as shown in Figure 12d. In the stress distribution diagram, the compression stress is negative, but the tensile stress is positive.  
Figure 11: Schematic diagram of the feature points.