## 4 Study on Ultimate Bearing Capacity
### Comparison between Test Values and Calculated Values in Specifications of Bearing Capacity  
Circular CFST columns are widely used. The specifications of various countries have given clear calculation formulas of bearing capacity. The bearing capacity formulas of EC4, AISC360-10, and GB50936-2014 are briefly introduced here. (1) Bearing capacity formula in European code EC4 [25]. \[N_{u}=\varphi N_{pl} \tag{2}\]  
\[N_{pl}=\eta_{2}A_{s}f_{y}/\gamma_{s}+(1+\eta_{1})t/d(f_{y}/f_{ck})A_{c}f_{ck}/ \gamma_{c} \tag{3}\]  
\[\varphi=1/(\phi+\sqrt{\phi^{2}-\overline{\lambda}^{2}}) \tag{4}\]  
\[\phi=0.5[1+0.21(\overline{\lambda}-0.2)+\overline{\lambda}^{2}) \tag{5}\]  
where \(\varphi\) is the stability coefficient; \(\eta_{1}\) and \(\eta_{2}\) both represent the coefficient considering the confinement effect, \(\eta_{1}\geq 0\), \(\eta_{2}\leq 1\); \(t\) and \(d\) are the thickness and diameter of the steel tube, respectively; \(\gamma_{s}\) and \(\gamma_{c}\) are the partial factors for materials of steel tube and concrete, respectively; \(\overline{\lambda}\) represents the equivalent slenderness ratio. (2) Bearing capacity formula in American code AISC360-10 [26]. This code converts the strength of concrete into steel to obtain the nominal compressive strength of steel \(F_{cr}\), and then calculates the bearing capacity of CFST axial compression members from \(F_{cr}\):  
\[N_{u}=0.85A_{s}F_{cr} \tag{6}\]  
\[\left\{ \begin{array}{ll}F_{cr}=(0.658\overline{\lambda}^{2})F&my&\overline{ \lambda}\leq 1.5\\ F_{cr}=(0.877/\overline{\lambda}^{2})F_{my}&\overline{\lambda}>1.5\end{array} \right. \tag{7}\]  
\[F_{my}=f_{y}+0.85f_{c}^{\prime}(A_{c}/A_{s}) \tag{8}\]  
where \(f_{c}^{\prime}\) represents the cylinder strength of concrete. (3) Bearing capacity formula in Chinese code GB50936-2014 [29]. \[N_{u}=\varphi_{e}\varphi_{l}N_{0} \tag{9}\]  
\[\left\{ \begin{array}{ll}N_{0}=0.9A_{c}f_{c}(1+\alpha\xi)&\xi\leq 1/(\alpha-1)^{ 2}\\ N_{0}=0.9A_{c}f_{c}(1+\sqrt{\xi}+\xi)&\xi>1/(\alpha-1)^{2}\end{array} \right. \tag{10}\]  
where \(\varphi_{e}\) represents the reduction coefficient of bearing capacity considering the effect of eccentricity; \(\varphi_{l}\) is the reduction coefficient of bearing capacity considering the effect of slenderness ratio; \(\alpha\) is thecoefficient related to the strength grade of concrete; \(\xi\) represents the casing hoop coefficient of CFST members, as shown in Table 1.  
According to above introduction, it can be summarized as the following points: (1) The three codes all adopt the superposition method, that is, the CFST bearing capacity is equal to the bearing capacity of steel tube plus that of concrete; (2) These three codes all consider the effect of slenderness ratio on bearing capacity; (3) Bearing capacity formulas in Chinese GB50936-2014 and European EC4 consider the confinement effect, while American AASC360-10 does not. Therefore, AASC 360-10 is safer; (4) GB50936-2014 considers the effect of eccentricity, while EC4 and AASC360-10 do not. In order to compare the test values of bearing capacity of 32 specimens with the calculated values of EC4, AASC 360-10, GB50936-2014, and other specifications, the bearing capacities of 32 specimens are calculated by using Formulas (2), (6), and (9), as shown in Table 4 and Figure 9. Percentage error analysis between the calculated values in three specifications in Table 4 and the test values in this paper is carried out, as shown in Table 5.  
As can be seen from Tables 4 and 5, and Figure 9, the calculated values in specifications of various countries are generally in good agreement with the test values in this paper. GB50936-2014 (\(\mu\) = 98.59%, \(\sigma\) = 1.56%) fits best and the second is EC4 (\(\mu\) = 97.16%, \(\sigma\) = 1.93%). The calculated value of AASC360-10 (\(\mu\) = 90.47%, \(\sigma\) = 1.43%) is the most conservative, that is, with the highest security.