## 5 Calculation of Reinforced Bearing Capacity
### Calculation Methods  
1. GB 50936-2014 [28]  
The calculation method of the bearing capacity of concrete-filled steel tubes in Chapter VI of GB 50936-2014 is shown as follows:  
\[N\leq N_{u} \tag{2}\]  
\[N_{u}=\varphi_{l}\varphi_{e}N_{0} \tag{3}\]  
\[N_{0}= \begin{cases}0.9A_{c}f_{c}(1+\alpha\varphi)&\left(\xi\leq 1/(\alpha-1)^{2} \right)\\ 0.9A_{c}f_{c}\big{(}1+\sqrt{\xi}+\xi\big{)}&\left(\xi>1/(\alpha-1)^{2}\right) \end{cases}  \tag{4}\]  
\[\xi=\frac{A_{s}f}{A_{c}f_{c}} \tag{5}\]  
\[\varphi_{l}= \begin{cases}1&(L_{e}/D\leq 4)\\ 1-0.0226(L_{e}/D-4)&(4<L_{e}/D\leq 30)\\ 1-0.115\sqrt{L_{e}/D-4}&(L_{e}/D>30)\end{cases}  \tag{6}\]  
\[\varphi_{e}= \begin{cases}\frac{1}{1+1.85\frac{\alpha}{L_{e}}}&(\varphi_{0}/r_ {c}\leq 1.55)\\ 1&(\varphi_{0}/r_{c}>1.55)\end{cases}  \tag{7}\]  
In the equations above, \(N\) is the design value of axial pressure on members, \(N_{u}\) is the design value of the axial compression bearing capacity, \(N_{0}\) is that of the axial compression bearing capacity of stub columns, \(\varphi_{l}\) is the reduction coefficient of slenderness ratio, \(L_{e}\) is the effective length, \(\varphi_{e}\) is the reduction coefficient of eccentricity, \(\alpha\) is a factor related to concrete grades, \(e_{0}\) is the larger eccentricity of the member, and \(r_{c}\) is the section radius of filled concrete. 2. GB 51367-2019 [12]  
The formulae in GB 51367-2019 relate to those in GB 50936-2014 but consider the effect of initial stress in the steel tube and include multiplying by the reinforcement strength correction coefficient \(\eta_{c}\), when \(N_{0}\) is calculated:  
\[N_{0}= \begin{cases}0.9\eta_{c}A_{c}f_{c}(1+\alpha\xi)&\left(\xi\leq 1/(\alpha-1)^ {2}\right)\\ 0.9\eta_{c}A_{c}f_{c}\big{(}1+\sqrt{\xi}+\xi\big{)}&\left(\xi>1/(\alpha-1)^{2} \right)\end{cases}  \tag{8}\]  
\[\eta_{c}= \begin{cases}0.85&(\varphi_{0 max}/f\leq 0.2)\\ 0.8&(0.2<\varphi_{0 max}/f\leq 0.4)\\ 0.75&(0.4<\varphi_{0 max}/f\leq 0.65)\\ 0.7&(\varphi_{0 max}/f>0.65)\end{cases}  \tag{9}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Code** & **GB 50936 [28]** & **GB 51367 [12]** & **EC 4 [38]** & **AISC [39]** & **AIJ [40]** & **AS 2327 [41]** \\ \hline \(f_{xk}\) & 20.1–50.2 & 20.1–50.2 & 16.9–38.5 & 17.8–51.3 & \(\leq\)41.8 & 17.8–73.3 \\ \(f_{xk}^{\prime}\) & 23.7–70.0 & 23.7–69.97 & 20–50 & 21–70 & \(\leq\)56.4 & 20–100 \\ \(f_{y}\) & 235–460 & 23.7–69.97 & 235–460 & \(\leq\)525 & 235.2–352.8 & \(<\)690 \\ \(D/t\) & \(\leq\)135\(\frac{205}{f_{y}}\) & \(D\geq 200\); & \(\leq\)90\(\frac{205}{f_{y}}\) & \(\frac{0.155}{f_{y}}\) & \(\leq\)\(\frac{15.20}{f_{y}/8}\) & \(\frac{0.155}{f_{y}}\) \\ \(\gamma_{c}\) & 1.4 & 1.4 & 1.5 & 1 & 3/1.5 & 1 \\ \(\gamma_{s}\) & 1.09–1.125 & 1.09–1.125 & 1.15 & 1 & 1.5/1.0 & 1 \\ \(k\) & 1 & 1 & 0.6 & C\({}_{1}\) & 0.2 & 0.72 \\ \(\xi\) & 0.5–2.0 & - & - & - & - & - \\ \(\alpha_{s}\) & - & - & 0.2–0.9 & \(\geq\)0.01 & - & 0.2–0.9 \\ \hline \hline \end{tabular} Note: \(C_{1}=0.1+2\Big{(}\frac{A_{c}}{A_{c}+A_{c}}\Big{)}\leq 0.3\).  
\end{table} 
Table 5: Detailing requirements of relevant standards. where \(\sigma_{0 max}\) is the maximum nominal stress. 3. EC 4 [37]  
Here the equations of a composite member under compression in EC 4 are given:  
\[N\leq\chi N_{0} \tag{10}\]  
\[N_{0}= \begin{cases}A_{sf}f+A_{c}f_{c}^{\prime}&(\overline{\lambda}>0.5)\\ \eta_{a}A_{sf}f+A_{c}f_{c}^{\prime}\Big{(}1+\eta_{c}\frac{t}{D}\frac{f_{g}}{f_ {c}^{\prime}}\Big{)}&(\overline{\lambda}\leq 0.5)\end{cases}  \tag{11}\]  
\[\eta_{a}=0.25(3+2\overline{\lambda});\eta_{c}=\eta_{c0}=4.9-18.5\overline{ \lambda}+17\overline{\lambda}^{2} \tag{12}\]  
\[\overline{\lambda}=\sqrt{\frac{N_{0}}{N_{cr}}};\ N_{cr}=\frac{\pi^{2}(EI)_{ eff}}{L^{2}} \tag{13}\]  
\(\chi\) is a reduction factor for the relevant buckling mode, \(\overline{\lambda}\) is the relative slenderness, \(f_{c}^{\prime}\) is the concrete cylinder strength design value, and \(N_{cr}\) is the elastic critical normal force. 4. AISC [39]  
\[N=\Phi_{c}N_{u}=0.75N_{u} \tag{14}\]  
\[N_{u}=