## 5 Discussion
### Influence of Axial Force on the Limit Load Equation  
The influence of internal pressure, bending moment, and axial force on the limit load of \(\mathrm{SP_{LWT}}\) was analyzed. Taking the non-dimensional torque \(n_{\mathrm{l}}\) in Equations (10)-(13) as zero, the limit load equations of \(\mathrm{SP_{LWT}}\) under the combination of internal pressure, bending moment, and axial force were obtained. Figure 11a-d show the limit state surfaces of \(\mathrm{SP_{LWT}}\) under the combination of internal pressure, bending moment, and axial force. It can be seen that there were still some differences in the limit state surfaces of the straight pipes with four local wall-thinning defects, but the trend of overall change was the same. When the internal pressure, bending moment, and axial force were the same, the influence of the three loads on the limit load of \(\mathrm{SP_{LWT}}\) was roughly similar. When the axial force was large, the load-bearing capacity of the straight pipes for internal pressure and bending moment was reduced, meaning that the axial force has an impact on the load-bearing capacity of \(\mathrm{SP_{LWT}}\). The allowable axial force of the equipment nozzles is shown in Table 2. The allowable axial force is expressed in dimensionless form through the limit axial force of \(\mathrm{SP_{LWT}}\) under single loads. The non-dimensional allowable axial force on medium-low-pressure equipment and high-pressure equipment is represented by \(f_{\mathrm{1-g}}=F_{\mathrm{g}}/F_{\mathrm{LS}}\) and \(f_{\mathrm{1-h}}=F_{\mathrm{h}}/F_{\mathrm{LS}}\), respectively. For different diameters of pipe, the average of the non-dimensional allowable axial force is \(f_{\mathrm{1-g}}=0.05\) for medium- and low-pressure equipment, and \(f_{\mathrm{1-h}}=0.41\) for high-pressure equipment. Figure 12 shows that the effect of the allowable axial force on the limit load of \(\mathrm{SP_{LWT}}\) for \(n_{\mathrm{l}}\) is 0, 0.05, and 0.41. The range surrounded by the limit load curves of \(\mathrm{SP_{LWT}}\) is the relative value of the load-bearing capacity. When the range surrounded by the curve decreases, it means that the load-bearing capacity of the defective straight pipe is reduced. The load-bearing capacity of high-pressure equipment is lower than that of medium- and low-pressure equipment. According to the allowable axial force, the relative reduction in the average radius of the limit load curve of \(\mathrm{SP_{LWT}}\) was calculated to quantitatively analyze the influence of the axial force on the load-bearing capacity of \(\mathrm{SP_{LWT}}\) under the combination of internal pressure and bending moment. Table 11 shows the relative reduction in the average radius of the limit load curves of \(\mathrm{SP_{LWT}}\) under the influence of axial force. For medium- and low-pressure equipment, the load-bearing capacity of \(\mathrm{SP_{LWT}}\) changed little under the influence of axial force, reducing by 0.83-1.80%. The straight pipe with a circumferential defect was the most affected, while the straight pipe with an axial defect was the least affected. For \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Defect Type**} & **Medium- and Low-Pressure** & **High-Pressure** \\  & **Equipment** & **Equipment** \\ \hline Axial defect & 1.28\% & 9.03\% \\ Circumferential defect & 1.44\% & 9.01\% \\ Large-area defect & 0.59\% & 6.67\% \\ Small-area defect & 1.20\% & 8.41\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The relative reduction in the average radius of the limit load curves of straight pipes with local wall-thinning defects under the influence of torque. high-pressure equipment, the load-bearing capacity of SP\({}_{\text{LWT}}\) was greatly affected by axial force, reducing by 7.51-12.93%. The straight pipe with a circumferential defect was the most affected, while the straight pipe with a small-area defect was the least affected.