## 5 Discussion
### Influence of Torque on the Limit Load Equation  
The influence of internal pressure, bending moment, and torque on the limit load of \(\mathrm{SP_{LWT}}\) was analyzed. Taking the non-dimensional axial force \(f_{1}\) in Equations (10)-(13) as zero, the limit load equation of \(\mathrm{SP_{LWT}}\) under the combination of internal pressure, bending moment, and torque was obtained. Figure 9a-d show the limit state surface of \(\mathrm{SP_{LWT}}\) under the combination of internal pressure, bending moment, and torque. It can be seen that the torque has a great influence on the limit load of \(\mathrm{SP_{LWT}}\). When the torque is low, it has little effect on the limit load curves of \(\mathrm{SP_{LWT}}\). With the gradual increase in torque, the influence of torque on the limit load curve becomes larger. When the torque is close to the limit torque of \(\mathrm{SP_{LWT}}\), the influence of internal pressure and bending moment on the limit load can be almost ignored, considering only the influence of torque on the limit load. The allowable torque of the equipment nozzles is shown in Table 2. The allowable torque is expressed in dimensionless form through the limit torque of \(\mathrm{SP_{LWT}}\) under single loads. The non-dimensional allowable torque on medium-low-pressure equipment and high-pressure equipment is represented by \(n_{\mathrm{I-g}}=N_{\mathrm{I-g}}/N_{\mathrm{LS}}\) and \(n_{\mathrm{I-h}}=N_{\mathrm{I-h}}/N_{\mathrm{LS}}\) respectively. For different diameters of pipe, the average of the non-dimensional allowable torque is \(n_{\mathrm{I-g}}=0.10\) for medium- and low-pressure equipment, and \(n_{\mathrm{I-h}}=0.33\) for high-pressure equipment. Figure 10 shows that the effect of the allowable torque on the limit load of \(\mathrm{SP_{LWT}}\) for \(n_{\mathrm{I}}\) is 0, 0.10, and 0.33. It can be seen that the range surrounded by the limit load curve of \(\mathrm{SP_{LWT}}\) is reduced with the increase in torque, which means that the load-bearing capacity of defective straight pipes is reduced, and the influence of torque on straight pipes with different local wall-thinning defects is different. Figure 8: Comparison of the limit load equations of straight pipes with local wall-thinning defects under the combination of internal pressure and bending moment with Ref. [28]. According to the allowable torque, the relative reduction in the average radius of the limit load curves of \(\mathrm{SP}_{\mathrm{LWT}}\) was calculated to quantitatively analyze the influence of the  
Figure 10: The effect of torque on the limit load curves of straight pipes with local wall-thinning defects under the combination of internal pressure and bending moment: (**a**) axial defect; (**b**) circumferential defect; (**c**) large-area defect; (**d**) small-area defect. Figure 9: The limit state surfaces of straight pipes with local wall-thinning defects under the combination of internal pressure, bending moment, and torque: (**a**) axial defect; (**b**) circumferential defect; (**c**) large-area defect; (**d**) small-area defect. torque on the load-bearing capacity of \(\mathrm{SP_{LWT}}\) under the combination of internal pressure and bending moment. Table 10 shows the relative reduction in the average radius of the limit load curves of \(\mathrm{SP_{LWT}}\) under the influence of torque. It can be seen that the load-bearing capacity of \(\mathrm{SP_{LWT}}\) in high-pressure equipment is more affected by torque than that in medium- and low-pressure equipment. For medium- and low-pressure equipment, the load-bearing capacity of \(\mathrm{SP_{LWT}}\) changed little under the influence of torque, reducing by 0.59-1.44%. The straight pipe with a circumferential defect was the most affected, while the straight pipe with a large-area defect was the least affected. For high-pressure equipment, the load-bearing capacity of \(\mathrm{SP_{LWT}}\) was greatly affected by torque, reducing by 6.67-9.03%. The straight pipe with an axial defect was the most affected, while the straight pipe with a large-area defect was the least affected.