# Seismic Fragility Analysis of the Transmission Tower-Line System Considering Bol Slippage
## 3 Limit State Determination
### Results Analysis  
Figure 6 shows the base shear force-tower top displacement curves of the RM and the JM under the three load application methods. Under the same lateral load, the bolt slippage effect can significantly increase the displacement of the transmission tower, but the influence of the bolt slippage on the ultimate bearing capacity of the tower-line system is relatively small. The trends of the shear-displacement curves obtained through the three load application methods for each model are consistent, with a difference of less than 10%. Furthermore, the curve slope of the JM differs from that of the RM. The reason for this phenomenon is that as the external load reaches a certain level, the bolts at the angle steel joints start to slip. This indicates that ignoring the bolt slippage effect would fail to accurately reflect the stress state of the transmission tower during the whole loading process.  
To facilitate the statistical analysis of the force state on the transmission tower members, tower 1 is divided into five sections, as shown in Figure 5. Figure 7 shows the maximum stress ratio of the main members and diagonal members in each tower section under the height equivalent load distribution, where T denotes the tension members and C denotes the compression members. The stress ratio of the member is defined as the ratio of the design stress to the allowable stress of the member, and the allowable stress can be determined by the Chinese code [28]. Given the similar trends presented in the stress ratio curves of the RM and the JM, bolt slippage has a relatively small influence on the ultimate bearing capacity of the tower-line system. The loading ratio is defined as the ratio of the applied load to the ultimate load. When the loading ratio is 0-50%, the stress ratios of all the members increase linearly. When the loading ratio exceeds 50%, the slope of the stress ratio curve changes and the slope of the compressed curve changes more obviously. When the loading ratio reaches 68%, the stress ratio of the compressive diagonal member in section A2 reaches the peak value, and the buckling failure of the member occurs, resulting in more severe structural deformation. When the loading ratio is 100%, the tower fails. In  
Figure 5: Transmission tower section division.  
addition, the stress ratio of the tension side members is less than that of the compression side members, and the stress ratio of the compressive diagonal member in section A2 caused by the lateral load is the largest. Thus, the maximum stress ratio of the compression side members can reflect the degree of damage to the transmission tower.  
Figure 8 shows the damaged member locations of the RM and the JM under the height-equivalent load distribution. When the loading ratio reaches 100%, buckling failure occurs in more diagonal members, and these failed members are located mainly in sections A2 and A3 of the tower body. Currently, the transmission towers experience obvious deformation. In addition, the positions of the failure members of the RM and the JM are not exactly the same, which is due to the stress redistribution of the transmission tower members  
Figure 6: Base shear–tower top displacement curves.  
Figure 7: The maximum stress ratio of the transmission tower: (**a**) main members of RM; (**b**) main members of JM; (**c**) diagonal members of RM; (**d**) diagonal members of JM.  
when bolt slippage occurs at the angle steel joints. This situation shows that ignoring the bolt slippage effect leads to an incorrect estimation of the position of the failed members, which is not conducive to early design and later reinforcement and maintenance of the transmission tower.