## 3 Test Results and Analysis
### Calculation of Load-Carrying Capacity Based on Hoop Restraint Action  
The calculation methods in the existing codes do not take into account the effect of restraint on the force performance of concrete. [PERSON] [24] considered that hoop bars have a lateral restraint on concrete, which can put concrete in a three-way compressive stress state and can improve the axial compressive strength of concrete. His proposed model of hoop-constrained concrete columns considers that the restraint boundary curve in the plane of hoop-constrained concrete and between the hoop bars on both sides is parabolic, assuming an initial angle of 45 degrees. According to the lateral restraint action, the concrete can be divided into two different zones--the invalid constraint zone and the valid constraint zone [25]--as shown in Figure 12.  
Figure 11: Comparison of test results and standard calculation results.  
Figure 12: Division of different constrained areas of the RPC section of the PSRPC column.  
The RPC has no transverse restraint and is in a state of unidirectional compressive stress; therefore, the axial compressive strength of the RPC can be used. As section H is an open section, the restraint of the section is not considered. The restraining effect of the hoop on the RPC in the effective restraint zone is calculated as follows.  
Effective restraint RPC area at hoop section \(A_{e0}\):  
\[A_{e0}=b_{s}h_{s}-2\times\frac{w_{0}^{2}}{6} \tag{6}\]  
Effective restraint area of RPC at the midpoint of the two hoop layers:  
\[A_{e}=\left(b_{s}h_{s}-2\times\frac{w_{0}^{2}}{6}\right)\left(1-\frac{s^{ \prime}}{2b_{s}}\right)\left(1-\frac{s^{\prime}}{2h_{s}}\right) \tag{7}\]  
Effective restraint factor of hoop reinforcement on RPC in the effective restraint zone \(K_{e}\):  
\[K_{e}=\frac{A_{e}}{b_{s}h_{s}} \tag{8}\]  
The effective restraint zone is subjected to the lateral compressive stress in the y-direction of hoop \(f_{l}\):  
\[f_{l}=K_{e}\rho f_{yh} \tag{9}\]  
\[\rho=\frac{V_{s}}{s^{\prime}bh} \tag{10}\]  
in the formula:  
\(f_{yh}\)--standard value of the tensile strength of the hoop reinforcement;  
\(\rho\)--the volume hoop ratio between the centerline of two adjacent hoop layers;  
\(V_{s}\)--hoop volume;  
\(s^{\prime}\)--distance between the centerline of two adjacent layers of hoop reinforcement.  
Concrete strength improvement factors:  
\[k=-1.254+2.254\sqrt{1+\frac{7.94f_{l}}{f_{co}}} \tag{11}\]  
in the formula:  
\(f_{co}\)--axial compressive strength of unconstrained RPC.  
Axial compressive strength of hoop restrained RPC \(f_{co}\):  
\[f_{ce}=kf_{co} \tag{12}\]  
According to specification JGJ138-2016 [22], the ultimate load on the PSRPC column is shared by the steel section, the unrestrained zone RPC and the restrained zone RPC, and the modified calculation formula is proposed as follows:  
\[N_{max}=0.9\varphi(N_{a}+N_{co}+N_{ce})=0.9\varphi(f_{a}A_{a}+f_{co}A_{co}+f_{ ce}A_{co}) \tag{13}\]  
in which:  
\(N_{a}\)--the axial force carried by the profile;  
\(N_{ct}\)--the axial force assumed by the RPC in the invalid constraint zone;  
\(N_{ce}\)--the axial force assumed by the RPC in the effective constraint zone.  
As shown in Figure 13, the test results of the axial compression specimens were compared with the calculated results according to Equations (3)-(13). The results show that the deviation between the test results and the calculation results of the modified formula is within 10%, and the modified formula considering the hoop restraint effect can predict the ultimate load capacity of such specimens more accurately.