## 5 Calculation of Load Carrying Capacity
### Comparison Calculations of Load Carrying Capacity
To further investigate the difference between the two calculation methods, when the corrosion ratio (\(D_{\rm w}=20\%\)) of specimens is large, the load carrying capacities of specimens with different slenderness ratios and diameter-to-thickness ratios are compared, as shown in Figures 12 and 13, where \(\delta\) is the relative error, \(\delta=(N_{\rm cs}-N_{\rm cm})/N_{\rm cs}\times 100\%\); \(\lambda\) is the slenderness ratio, \(\lambda=\) /\(\hat{\mu}\); \(\hat{\mu}\) is the length of circular steel tube; \(\hat{\mu}\) is the radius of gyration of circular steel tube; and \(D\)/\(\hat{\mu}\) is the diameter-to-thickness ratio. As shown in Figure 12, with the increase of slenderness ratio, the difference between the two methods becomes smaller and smaller. With the slenderness ratio 66 as the limit, the difference between \(N_{\rm cs}\) and \(N_{\rm cm}\) decreases first and then increases with the ascent of eccentricity (\(e=0\)-\(100\) mm). Figure 13 shows that, when the diameter-to-thickness ratio is relatively small, the load carrying capacity calculated by three specification formulas considering the material degradation method is higher than that calculated by the section reduction method, but such a small diameter-to-thickness ratio is not usually used in practical engineering. In the common range of engineering, the calculation results of the three specifications are not the same, among which the difference of calculation results of GB 50017-2017 increases slightly with the increase of the diameter-to-thickness ratio, and the overall difference is not more than 3%. However, the calculation results of EN 1993-1-1 and ANSI/AISC 360-16 all show mutation points. This is mainly resulted from the finer classification of steel tubes in these two specification calculation formulas, and the calculation formulas or parameters of different categories of steel tubes are slightly different. When considering material degradation or section reduction to simulate uniform corrosion, two methods can be used to calculate different categories of steel tubes, and then different parameters or calculation formulas will be taken. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen ID**} & \multirow{2}{*}{\(N_{\rm t}\)/kN} & \multicolumn{2}{c}{**GB 50017-2017**} & \multicolumn{2}{c}{**EN 1993-1-1**} & \multicolumn{2}{c}{**ANSI/AISC 360-16**} \\ \cline{3-8}  & & \(N_{\rm cs}\)/kN & \(N_{\rm cm}\)/kN & \(N_{\rm cs}\)/kN & \(N_{\rm cm}\)/kN & \(N_{\rm cs}\)/kN & \(N_{\rm cm}\)/kN \\ \hline C0-0 & 391.5 & 341.5 & 341.5 & 342.8 & 342.8 & 302.4 & 302.4 \\ C0-30 & 377.9 & 339.8 & 338.8 & 341.1 & 340.0 & 300.8 & 299.9 \\ C0-90 & 363.8 & 344.0 & 342.7 & 345.2 & 343.9 & 304.3 & 303.2 \\ C0-180 & 313.3 & 299.8 & 296.6 & 300.8 & 297.6 & 265.2 & 262.4 \\ C0-270 & 295.6 & 275.0 & 271.0 & 275.9 & 272.0 & 243.3 & 239.8 \\ C0-360 & 316.8 & 272.7 & 267.7 & 273.6 & 268.7 & 241.2 & 236.9 \\ C15-0 & 239.8 & 203.1 & 203.1 & 222.3 & 222.3 & 193.5 & 193.5 \\ C15-30 & 238.1 & 192.4 & 191.9 & 210.5 & 210.0 & 183.3 & 182.9 \\ C15-90 & 217.8 & 190.0 & 189.2 & 207.8 & 207.0 & 181.1 & 180.3 \\ C15-180 & 191.6 & 179.8 & 178.0 & 196.6 & 194.7 & 171.3 & 169.7 \\ C15-270 & 191.7 & 167.4 & 164.8 & 183.0 & 180.2 & 159.5 & 157.0 \\ C15-360 & 181.3 & 163.6 & 160.8 & 178.8 & 175.9 & 155.8 & 153.2 \\ C35-0 & 152.4 & 130.3 & 130.3 & 146.2 & 146.2 & 129.9 & 129.9 \\ C35-30 & 166.7 & 130.8 & 130.6 & 146.8 & 146.5 & 130.4 & 130.1 \\ C35-90 & 170.5 & 139.5 & 139.0 & 156.4 & 156.0 & 139.0 & 138.6 \\ C35-180 & 143.1 & 119.0 & 117.5 & 133.3 & 131.6 & 118.6 & 117.1 \\ C35-270 & 140.5 & 108.7 & 107.2 & 121.9 & 120.2 & 108.3 & 106.8 \\ C35-360 & 133.8 & 105.6 & 103.6 & 118.2 & 116.1 & 105.2 & 103.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis results of specimens by using section reduction method and material degradation method. Figure 12: Relationship between \(\delta\) and \(\lambda\): (**a**) GB50017-2017; (**b**) EN 1993-1-1; and (**c**) ANSI/AASC 360-16.