## 5 Calculation of Reinforced Bearing Capacity
### Data Fitting  
The test results in this paper show that the failure mode of RPC-filled steel tubular members, approximately 1.5 m in length and 60-159 mm in diameter, presents as an elastic-plastic instability state of the extreme point type. The constraint effect of the steel tubes on concrete is ignored when calculating the axial compression bearing capacity of members with a large length-to-diameter ratio in several codes; therefore, we recommend using the stable nominal bearing capacity (Equation (25)) as the axial compression bearing capacity of the composite member in the grid structure. The experimental result specimens without initial stress are compared with the calculation results of the national codes and shown in Figure 16a.  
\[N_{nom}=\varphi_{l}(A_{s}f+A_{c}f_{c}) \tag{25}\]  
For the specimens with initial stress, the strength correction factor \(\eta_{c}\) proposed in GB 51367 [12] was used to revise the calculated values of the national codes above. The calculated results are shown in Figure 16b, and the nominal bearing capacity of stability is corrected to  
\[N_{nom}=\varphi_{l}\eta_{c}(A_{s}f+A_{c}f_{c}) \tag{26}\]  
The experimental results and parameters from a total of 202 RPC-filled steel tubular stub columns [17; 18; 21; 42; 43; 44; 45; 46; 47; 48; 49; 50] and 40 long columns [21; 22; 46; 50] are displayed in Table 6. In these pre-existing results, the maximum length-to-diameter ratio of each specimen is 12, significantly less than that of the grid structure members researched above, and no initial stress acts on these specimens. The mean and standard deviation of the ratios of the calculated capacities (according to the codes) to the experimental capacities (from this paper) and the 242 results conducted in past studies are listed in Figure 17.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(\mathbf{D}\) & \(\mathbf{t}\) & \(\mathbf{f}\) & \(\mathbf{f_{c}}\) & \(\mathbf{L}\)/D & \(\mathbf{\xi}\) \\ \hline
83–219 & 1–16 & 244.9–453 & 53.19–154 & 2.65–12 & 0.057–3.133 \\ \end{tabular}
\end{table}
Table 6: Parameter range of tested specimen.  
Figure 16: Comparison of design values and test results. (**a**) composite members without prepress; (**b**) composite members with prepress.  
For RPC-filled steel tubular short columns, the mean values of \(N_{c}/N_{e}\) calculated by each of the six codes are 1.00, 0.85, 0.99, 0.59, 0.86, 0.60, and 0.83, and the standard deviations are 0.096, 0.082, 0.090, 0.054, 0.077, 0.057, and 0.084. Compared with GB 50936 [28], the estimated values of GB 51367 [12] are more conservative because the test results without initial stress are required to be reduced by \(\eta_{c}=0.85\) in GB 51367.  
For relatively long RPC-filled steel tubular columns, the mean values of \(N_{c}/N_{e}\) calculated by the six codes are 1.16, 1.03, 0.85, 0.64, 0.97, 0.73, and 0.96, and the standard deviations are 0.196, 0.179, 0.123, 0.100, 0.156, 0.123, and 0.144. GB 51367, AIJ and \(N_{nom}\) are the most accurate in predicting the bearing capacity of members, and of the two, the deviation of \(N_{nom}\) is the lowest. Thus, it is suggested that the \(N_{nom}\) defined in Equation (26) is taken as the ultimate bearing capacity when \(L_{e}/D>4\) and otherwise use GB 51367 [12].