# Fragility Analysis of Transmission Towers Subjected to Downburst Winds
## 3 Typical Engineering Case Study
### Fragility Analysis  
#### 3.5.1 Downburst Wind Load Case  
In this paper, the wind-induced response of the transmission tower is carried out by simulating the downburst wind field with different direction angles and different radial distances (\(R=0.1D-3D,\Delta R=0.1D,D=600\) m). The tower top displacement under the downburst at each direction angle first increases and then decreases with the increase in radial distance. Compared with the nonlinear buckling analysis results for each direction angle, the radial distance between the maximum tower top displacement at different direction angles exceeding the threshold displacement values of different damage states for the first time and the last time can be obtained. The radial distance when different damage states occur at different angles is shown in Tables 7-9, and the curve of radial distance vs. failure probability for different damage states of the 220 KV transmission tower at different wind angles can be obtained, as shown in Figure 16. It can be found that the location where the maximum response occurs is \(R=1.6D\), and the range of radial distance for slight  
Figure 14: Initial buckling member position and corresponding probability at each direction angle of the deterministic model. Figure 13: Stress nephogram of initial buckling state at \(0^{\circ}\) direction angle. damage status is wider than that for severe damage at all direction angles--the range far greater than the radial distance of collapse. The reason is that the wind-induced response of the transmission tower under the downburst is the same as the mean wind speed of the downburst, which increases first and then decreases with the increase in the radial distance. After severe damage occurs to the transmission tower, only a small amount of load needs to be added to generate significant displacement, thus reaching a collapsed state. Therefore, the radial distance between the occurrence of severe damage and the collapse is relatively close, and the distance from slight damage is relatively far. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Damage States**} & \multicolumn{4}{c}{**Wind Attack Angle**} \\ \cline{2-5}  & **0\({}^{\circ}\)** & **45\({}^{\circ}\)** & **60\({}^{\circ}\)** & **90\({}^{\circ}\)** \\ \hline \multirow{2}{*}{Slight damage} & 0.7–2.4 & 1.0–2.4 & 0.9–2.6 & 1.0–2.1 \\ \hline \multirow{2}{*}{Severe damage} & 0.9–2.2 & 1.3–2.2 & 1.2–2.4 & 1.3–1.8 \\ \hline \multirow{2}{*}{Collapse} & 1.0–2.1 & 1.4–2.1 & 1.3–2.3 & 1.4–1.7 \\ \hline \multirow{2}{*}{Critical radial distance} & 1.6 & 1.6 & 1.6 & 1.6 \\ \hline \end{tabular}
\end{table} 
Table 7: Dimensionless radial distance (R/D) with different angles in different damage states (220 KV). Figure 15: Initial buckling member position and corresponding probability at different direction angles of uncertain model. In this paper, a total of 120 load cases are analyzed, considering 4 wind attack angles and 30 radial distances. For each case, 20 structural samples are applied in the nonlinear  
Figure 16: The curve of radial distance vs. failure probability for different damage states of the transmission tower at different wind angles. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Damage States**} & \multicolumn{4}{c}{**Wind Attack Angle**} \\ \cline{2-5}  & **0\({}^{\circ}\)** & **45\({}^{\circ}\)** & **60\({}^{\circ}\)** & **90\({}^{\circ}\)** \\ \hline \multicolumn{1}{c}{Slight damage} & 1.0–2.2 & 1.2–2.2 & 1.2–2.3 & 1.2–2.0 \\ \hline \multicolumn{1}{c}{Severe damage} & 1.2–1.9 & 1.4–2.0 & 1.4–2.1 & 1.4–1.8 \\ \hline \multicolumn{1}{c}{Collapse} & 1.3–1.8 & 1.5–1.9 & 1.5–2.0 & 1.5–1.7 \\ \hline \multicolumn{1}{c}{Critical radial distance} & 1.6 & 1.6 & 1.6 & 1.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Dimensionless radial distance (R/D) with different angles in different damage states (110 KV).