## 3 Project Overview
### Load Application  
Transmission lines are usually located outdoors and are subjected to wind loads year-round. When a fire occurs, transmission towers are exposed to the combined effects of fire and wind loads. This paper investigates the transmission tower-line system under fire conditions while simultaneously considering the effects of wind loads. The pulsating wind is a key factor in structural vibration, and relevant design parameters are taken based on specifications. The pulsating wind pressure under wind load is represented by Equation (9):  
\[P(h_{i},t)=I_{0}(h_{i})B(h_{i})u(t) \tag{9}\]  
where \(P(h_{i},\,t)\) is the fluctuating wind pressure value at height \(h_{i}\) above ground at time \(t\); \(I_{0}(h_{i})\) represents the spatial correlation of fluctuating wind pressure, which is a random variable with a variance of 1; \(u(t)\) is the wind speed spectrum; \(B(h_{i})\) is the wind pressure intensity coefficient, which is expressed as in Equation (10):  
\[B(h_{i})=A_{i}\mu_{s}(h_{i})\mu_{z}(h_{i})\omega_{0}\sqrt{\frac{24K_{r}}{\mu_{ z}(h_{i})}} \tag{10}\]  
In the formula, \(A_{i},\mu_{s}(h_{i}),\mu_{z}(h_{i}),\omega_{0}\) are the windward area of the structure at the height \(h_{i}\) above the ground, the wind load shape coefficient, the wind pressure height change coefficient, and the basic wind pressure; \(K_{r}\) is related to the roughness of the ground.  
The power spectral density function of the Davenport wind speed spectrum is represented by Equation (11):  
\[S_{u}(\omega)=\frac{4}{3}\pi\frac{a^{2}\omega}{(1+a^{2}\omega^{2})^{\frac{4}{3 }}} \tag{11}\]  
In the formula, \(\omega\geq 0\); \(a=\frac{600}{\pi\overline{V}_{10}}\).  
A MATLAB (2023) program was developed to calculate the Davenport gust wind speed spectrum. The program generates the required wind load dynamic time history, which is then input into ABAQUS to simulate the dynamic effect of wind load on the transmission tower. The wind load application points on the transmission tower structure are shown in Figure 3. Figure 5 presents the wind load time-history data at the top of the tower under a wind speed of 10 m/s. In addition to the wind load, gravity and an isothermal temperature field were also applied to the model.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Part** & **Material** & **Parameter** & **Numerical Value** \\ \hline \multirow{4}{*}{Inclined member} & \multirow{4}{*}{Q235} & Density/kg\(\cdot\)m\({}^{-3}\) & 7850 \\  & & Elastic modulus/GPa & 200 \\  & & Yield stress/MPa & 235 \\  & & Coefficient of linear expansion/\({}^{\circ}\)C & \(1.17\times 10^{-5}\) \\  & & Density/kg\(\cdot\)m\({}^{-3}\) & 7850 \\ Main member & \multirow{4}{*}{Q345} & Elastic modulus/GPa & 200 \\  & & Yield stress/MPa & 345 \\  & & Coefficient of linear expansion/\({}^{\circ}\)C & \(1.20\times 10^{-5}\) \\  & & Density/kg\(\cdot\)m\({}^{-3}\) & 3333 \\ Conductor & 2 \(\times\) LGJ-400/50 & Elastic modulus/GPa & 69 \\  & & Yield stress/MPa & 700 \\ Ground wire & \multirow{2}{*}{JLB-150} & Density/kg\(\cdot\)m\({}^{-3}\) & 6593 \\  & & Elastic modulus/GPa & 147 \\  & & Yield stress/MPa & 830 \\ \hline \end{tabular}
\end{table}
Table 1: Materials and parameters.