## 5 Calculation Method for Bearing Capacity  
The calculation method of axial compressive bearing capacity is very important in the design of columns [20; 21]. When calculating the axial compressive capacity of RECFAT, it was necessary to consider the confinement ability of the aluminum tube. According to the stress distribution of the cross-section obtained from finite element analysis (Figure 11a), the arch effect still existed within the rectangular region, while the semicircular region exhibited better confinement capacity. In this section, a simplified model for circular-end aluminum tube concrete columns was presented, as shown in Figure 13. In the figure, \(A_{\rm cc}\) represented the area of strongly confined concrete in the circular-end section; \(A_{\rm sc}\) represented the area of strongly confined concrete in the rectangular section after deducting the weak fan-shaped confinement area. The fan-shaped area had a radius equal to the side length of the rectangle and an angle of 60\({}^{\circ}\).  
Figure 12: Parameter analysis. (**a**) The influence of concrete strength; (**b**) the influence of aluminum alloys.  
For the semicircular region of concrete, it could be simplified by splitting the aluminum tube concrete with a circular cross-section into two halves. Therefore, the calculation method for hoop confinement coefficient used for circular steel tube concrete could be applied [22]:  
\[\lambda_{\text{ac}}=\frac{f_{0.2}A_{\text{ac}}}{f_{\text{c}}A_{\text{cc}}} \tag{5}\]  
where \(A_{\text{ac}}\) is the cross-sectional area and conditional yield strength of the aluminum tube in the semicircular zone. \(A_{\text{cc}}\) and \(f_{\text{c}}\) are the concrete area and axial compressive strength in the semicircular area, respectively.  
For the rectangular region of concrete, as only two faces were confined by the aluminum tubes, in order to maintain conservatism and simplify the calculation, the strength enhancement of the rectangular region concrete was not considered [23]. Based on this, referring to the increase in concrete strength due to hoop confinement in steel tube concrete, the simplified calculation method for the axial compressive capacity of circular-end aluminum tube concrete columns was proposed as follows:  
\[N_{\text{u}}=A_{\text{a}}f_{0.2}+2A_{\text{cc}}(1+2A_{\text{ac}})f_{\text{c}}+ A_{\text{sc}}f_{\text{c}} \tag{6}\]  
In Equation (6), the first term represents the contribution of the aluminum tube to the load-bearing capacity, the second term represents the contribution of the semicircular region of concrete to the load-bearing capacity, and the third term represents the contribution of the rectangular region of concrete to the load-bearing capacity.  
Based on the experimental results, the aspect ratio had a significant influence on the compressive load-bearing capacity of the specimens. The variation in aspect ratio directly affected the slenderness ratio of the specimens. Therefore, in addition to Equation (6), a slenderness ratio stability factor was considered. The calculation method for the slenderness ratio stability factor is as follows:  
\[N_{\text{c}}=\phi N_{\text{u}} \tag{7}\]  
In Equation (7), \(\phi\) represents the stability factor for the slenderness ratio of the weak axis, which is equivalent to the load-carrying capacity improvement factor \(SI\). Referring to the relevant provisions in GB2002-2012, when the slenderness ratio \(\lambda\leq 28\), \(\varphi=1\). The calculation of \(\varphi\) is obtained by fitting \(SI(\varphi)\) with the weak axis slenderness ratio \(\lambda\), as shown in Equation (8):  
\[\phi=-0.013\lambda+1.32 \tag{8}\]  
Figure 13: Constrained model of circular-end aluminum tube.  
The calculations using Equation (7) were performed on the specimens in this study; the results are presented in Table 4. The error was 0.4%, with a coefficient of variation of 0.056, indicating that the proposed equation could reasonably estimate the axial compressive capacity of circular-end aluminum alloy tube-confined concrete.