## 4 Finite Element Simulation Results
### Collapse Analysis of Transmission Tower-Line System at High Temperature  
Under the combined effects of fire and wind loads, the collapse process of the transmission tower-line system is influenced by temperature changes. The collapse process of the transmission tower-line system at different temperatures (400 \({}^{\circ}\)C and 600 \({}^{\circ}\)C) is analyzed and compared with the collapse process at ambient temperature. The collapse-resisting wind speeds of the transmission tower-line system under ambient temperature, 400 \({}^{\circ}\)C, and 600 \({}^{\circ}\)C conditions are 27 m/s, 26 m/s, and 12 m/s, respectively, as shown in Figure 9. It can be observed that with increasing temperature, the collapse-resisting wind speed of the observed members significantly decreases. This is because, at high temperatures, the yield strength of the steel gradually decreases with rising temperature, leading to a reduction in structural load-bearing capacity, which means the transmission tower-line system may fail at lower wind speeds.  
Figure 8: The collapse process of transmission towers under ambient temperature conditions (stress in Pa).  
Figure 7: The position of the observed members.  
The collapse process of the transmission tower-line system is shown in Table 3 and Figures 10 and 11. The results indicate that an increase in temperature accelerates the collapse process of the transmission tower-line system, causing it to lose stability in a shorter time. Compared to ambient temperature, under the 400 \({}^{\circ}\)C condition, the instability of observed member 1 occurs earlier at 2.95 s, followed by the failure of observed members 2, 3, and 4 within the next 0.05 s. Observed members 5, 6, 7, and 8 remain intact. The tower loses its load-bearing capacity and collapses. Under the 600 \({}^{\circ}\)C condition, the instability process is further accelerated, with observed member 1 failing at 2.7 s, followed by the failure of observed members 2, 3, and 4 within the next 0.15 s. This ultimately leads to the complete collapse of the transmission tower.  
During the collapse process of the transmission tower-line system, observed member 1 is always the first component to fail. The failure of observed members 2, 3, and 4 occurs shortly afterward. Under high-temperature conditions, the load-bearing capacity of various parts of the tower rapidly decreases, leading to almost simultaneous failure after instability. Observed members 5, 6, 7, and 8 remain intact. Observation member 1 is defined as the most critical member, and its stress-time history is shown in Figure 12.  
Figure 10: Collapse process of the transmission tower under 400 \({}^{\circ}\)C conditions. (stress in Pa).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Observed Members/Temperature** & **Ambient Temperature** & **400 \({}^{\circ}\)C** & **600 \({}^{\circ}\)C** \\ \hline Observed members 1 & 3.30 s & 2.95 s & 2.60 s \\ Observed members 2, 3, 4 & 3.55 s & 3.00 s & 2.75 s \\ Observed members 5, 6, 7, 8 & Intact & Intact & Intact \\ \hline \hline \end{tabular}
\end{table}
Table 3: Failure times of members under different temperature conditions.  
Figure 9: Collapse-resisting wind speed under different temperature conditions.