# Fragility Analysis of Transmission Towers Subjected to Downburst Winds
## 3 Typical Engineering Case Study
### Uncertain Finite Element Model  
The 110 KV, 220 KV, and 35 KV linear transmission towers were selected as the research objects, with tower heights of 25 m, 28.2 m, and 33.9 m, respectively. The conductor of the 110 KV transmission tower was LGJ-400/35, and the ground wire was GJ-50. The conductor of the 220 KV transmission tower was LGJX-400/50, and the ground wire was GJ-50. The 35 KV transmission tower conductor was JL/LB20A-240/40, and the ground wire was GJ-55. The spans were 178 m, 339 m, and 320 m, respectively. The main material of the transmission tower was Q345-type angle steel, while the others were Q235-type angle steel. The three-dimensional finite element model of the transmission tower established using ANSYS software is shown in Figures 5-7. During the analysis, the ideal elastoplastic assumption was employed to consider the material nonlinearity. In addition, the yield strength criterion of the material followed the [PERSON] criterion, and the bilinear kinematic hardening rule was used to model the constitutive model of the steel material. Figure 4: Flow chart of the proposed fragility analysis framework. Figure 5: Finite element model of the 110 kV transmission tower. Figure 6: Finite element model of the 220 kV transmission tower. Figure 7: Finite element model of the 35 kV transmission tower. [PERSON] et al. (2015) and [PERSON] et al. (2018) compared the decoupling and coupling approaches through the numerical simulation analysis of dynamic response and found that tower line decoupling analysis can obtain good calculation accuracy and greatly reduce the time domain calculation time of wind vibration response of tower-line coupling system structures [42; 43]. In this paper, the tower-line decoupling analysis is considered. Figure 8 shows the finite element model of conductor/ground wire. Table 2 shows the mechanical parameters of the cable of the 220 KV transmission tower. The insulator is the component that connects these cables to the transmission tower. The conductor insulator and the ground wire insulator are used, and their length is 4.5 m. The mechanical parameters of the insulator are given in Table 3. The link10 element is used for the conductor and insulator. The time history analysis is conducted according to the model in Figure 8, and the reaction force at the end of the insulator is extracted and will be exerted on the tower as a concentrated load. As mentioned previously, the material properties are an important factor that requires comprehensive consideration. The main material property parameters of steel include density, Poisson's ratio, elastic modulus, yield strength, and so on. Table 4 lists the parameter values considered in the uncertainty analysis and their corresponding probability distribution. After that, the Latin hypercube sampling method is used to simulate the random variables, and the generated random samples are used to establish the structural uncertainty finite element model. This paper considers the influence of the uncertainty of density, Poisson's ratio, elastic modulus, and yield strength on vulnerability. Note that in tables, COV denotes the coefficient of variation. Figures 9 and 10 plot the generated random samples and indicate that the generated results are consistent with the target distribution type. \begin{table}
\begin{tabular}{c c c} \hline
**Material Properties** & **Conductors (LGJX-400/50)** & **Ground Wires (GJ-50)** \\ \hline Cross-sectional area & 3.68 \(\times\) 10\({}^{-4}\) m\({}^{2}\) & 0.495 \(\times\) 10\({}^{-4}\) m\({}^{2}\) \\ Initial tension & 123,400 N & 32,993 N \\ Elastic modulus & 6.9 \(\times\) 10\({}^{10}\) Pa & 1.85 \(\times\) 10\({}^{11}\) Pa \\ Line expansion coefficient & 1.930 \(\times\) 10\({}^{-5}\)\({}^{\circ}\)C & 1.15 \(\times\) 10\({}^{-5}\)\({}^{\circ}\)C \\ Density & 3.35 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\) & 7.96 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\) \\ \hline \end{tabular}
\end{table} 
Table 2: The mechanical parameters of conductors and ground wires. Figure 8: Finite element model of conductor/ground wire.