## 3 Test Results and Analysis
### Calculation Methods Already Available  
There are three main methods for calculating the prevailing international positive section load capacity of steel and concrete columns. First, the Code for Design of Combined Structures (JG) 138-2016) issued by the Ministry of Housing and Urban-Rural Development of China [22] stipulates the calculation method. Its proposed section steel load-carrying capacity of concrete columns is calculated in accordance with the assumption of a flat section, ignoring the tensile strength of the concrete; taking into account the stiffening effect of the concrete, it is assumed that the sections with the required width to thickness ratio will not buckle locally during loading. The axial compressive load capacity of the combined column in the code is calculated according to Formula (1):  
\[N=0.9\varphi\big{(}f_{c}A_{c}+f_{y}A_{s}+f_{a}A_{a}\big{)} \tag{1}\]  
where  
\(f_{c}\) is the axial compressive strength of concrete (MPa);  
\(A_{c}\)--cross-sectional area of the concrete (mm\({}^{2}\));  
\(f_{y}\),\(f_{a}\)--yield strength of longitudinal bars and sections;  
\(A_{a}\)--cross-sectional area of longitudinal bars and sections;  
\(\varphi\)--the axial compression stability factor of the combined steel and concrete column, determined _from_ the length to the slenderness table;  
\[\lambda=\frac{l_{0}}{i} \tag{2}\]  
\(l_{0}\)--calculated length of the member (mm)  
\(i\)--minimum radius of gyration of the section (mm)  
\[i=\sqrt{\frac{E_{c}I_{c}+E_{a}I_{a}}{E_{c}A_{c}+E_{a}A_{a}}} \tag{3}\]  
\(E_{c}\), \(E_{a}\)--modulus of elasticity of concrete, steel sections (MPa)  
\(I_{c}\), \(I_{a}\)--moment of inertia of the concrete and steel sections (mm\({}^{4}\))  
The second calculation method for steel structures, mostly adopted in Europe and the USA, considers the reinforcement of the strength and stiffness of the section columns by adding an expansion factor to the external concrete or replacing the concrete with an equivalent steel structure and calculating the load bearing capacity in accordance with the steel design method, such as the American Institute of Steel Construction AISC-LRFD (2005) Code [23], which uses the following calculation formula:  
\[\lambda_{c}\leq 1.5P=A_{s}\Big{(}0.685^{\lambda_{c}^{2}}\Big{)}\big{[}F_{y}+0.7F_{ yr}(A_{r}/A_{s})+0.6f_{c}^{\prime}(A_{c}/A_{s})\big{]} \tag{4}\]  
\[\lambda_{c}>1.5P=A_{s}\Big{(}\frac{0.877}{\lambda_{c}^{2}}\Big{)}\big{[}F_{y}+ 0.7F_{yr}(A_{r}/A_{s})+0.6f_{c}^{\prime}(A_{c}/A_{s})\big{]} \tag{5}\]  
in the formula,  
\(\lambda_{c}\)--slederness ratio parameter, \(\lambda_{c}=\frac{Kl}{r\pi}\sqrt{\frac{F_{y}}{E_{m}}}\);  
\(K\)--effective length factor;  
\(R\)--rotational radius of the buckling section;  
\(L\)--free length of steel-reinforced concrete columns;  
\(E_{m}\)--the converted elastic modulus of the steel-reinforced concrete column;  
\(E\), \(E_{c}\)--elastic modulus of steel and concrete;  
\(A_{s}\), \(A_{r}\), \(A_{c}\)--section area of steel, longitudinal reinforcement and concrete;\(F_{y}\), \(F_{y}\), \(F_{yr}\), \(f_{c}^{\prime}\)--yield strength of steel, longitudinal reinforcement and compressive strength of concrete.  
The third, the Soviet theory of equating steel sections to reinforcing bars and then calculating them in accordance with reinforced concrete structures, is that the sections can be deformed and fully bonded to the concrete in a coordinated manner.  
In accordance with the specifications JGJ 138-2016 [22] and AISC-LRFD [23], the positive section compressive load bearing capacity of the PSRPC axial compression column was calculated, and the comparison between the calculated results and the test results is shown in Figure 11. The calculation results of our code JGJ 138-2016 [22] are closer to the test values, and the calculation results of both codes are on the conservative side.