# Fragility Analysis of Transmission Towers Subjected to Downburst Winds
## 3 Typical Engineering Case Study
### Fragility Analysis
#### 3.5.2 Comparison between ABL Wind and Downburst Wind  
According to the above basic steps of fragility analysis of the transmission tower under the downburst, fragility curves in different directions can be obtained. At the same time, fragility curves under the ABL wind are carried out to compare and analyze the similarities and differences between them.  
The basic steps of fragility analysis under the ABL wind are given as follows:  
1. Considering the uncertainty of the transmission tower, the Latin hypercube sampling method is used to simulate 20 random structure samples, denoted by \(S_{i}\), \(i=1,2,\cdot\cdot\cdot,20\);  
2. The nonlinear buckling analysis is conducted for each structure sample \(S_{i}\) to determine the threshold displacement values of the collapse of the structure \(\Delta_{c_{i}}\);  
3. Incremental dynamic analysis (IDA) is carried out for a structure sample \(S_{i}\) under different basic wind speeds (\(v\) = 30-75 m/s, the increment is 0.1 m/s) to obtain the curve of maximum tower top displacement vs. basic wind speed, and the wind speed corresponding to the threshold displacement value of collapse can be found. They are denoted as \(v_{c_{i}}\).  
4. Considering the uncertainty of the transmission tower and the randomness of fluctuating components under the same basic wind speed, a total of 20 curves of maximum displacement vs. basic wind speed can be obtained. A total of 20 sets of \(\Delta_{c_{i}}\) and \(v_{c_{i}}\) (\(i=1,2,\cdot\cdot\cdot,20\)) can be determined.  
5. From these values for \(v_{c_{i}}\), the wind-induced fragility curves of the transmission tower can be drawn for a wind attack angle.  
The above method is used for fragility analysis under the ABL wind. Wind fluctuations can be treated as the stationary Gaussian process and could be simulated using the spectral representation method [45; 46]. Kaimal spectrum is used for the longitudinal wind fluctuation component. The terrain is set as category B and the profile exponent is 0.16. According to quasi-steady assumptions and the Chinese code (DL/T 5154-2012), the wind speed can be converted into wind load.  
The transmission tower is a typical wind-sensitive structure. Because almost half of the wind load on the tower comes from large-span transmission lines, the wind load effect on the tower varies significantly in different wind directions. On the other hand, the ultimate wind resistance capacity of the tower is also different from the wind attack angle [47; 48; 49]. Both of these reasons lead to the significant variation in the fragility curves at different angles. Therefore, it is essential to study the influence of the wind attack angle on the fragility curves.  
The fragility curves of the 220 KV transmission tower under the ABL wind and downburst are shown in Figures 17-20. Through comparison, it is found that with the increase in a wind direction angle, the critical collapse wind speed of the tower increases; the most unfavorable direction angle is 0\({}^{\circ}\), and the most favorable direction angle is 90\({}^{\circ}\). The critical collapse wind speed at each direction angle of the transmission tower under the downburst is significantly less than that under the ABL wind, and the larger the direction angle is, the greater the difference in critical collapse wind speed is. Similarly, the fragility curve of 110 KV and 35 KV transmission towers under the ABL wind is compared with the fragility curve of the collapse state under the downburst, as shown in Figures 21-24. The fragility curves of the tower under the downburst are more dangerous than the curves under the ABL wind with the attack angle increasing from 0\({}^{\circ}\) to 90\({}^{\circ}\).  
Figure 19: Fragility curve of severely damaged state under downburst.  
Figure 17: Fragility curve of collapse state of 220 KV transmission tower under ABL wind.  
Figure 21: Fragility curve of collapse state of 110 KV transmission tower under ABL wind.  
Figure 22: Fragility curve of collapse state under downburst.