## 2 Tower Mechanical Structure Modeling
The formula for calculating the line wind load is as follows:  
\[W_{x}=\alpha\cdot W_{o}\cdot\mu_{z}\cdot\mu_{sc}\cdot\beta_{c}\cdot d\cdot L_{ p}\cdot B_{1}\cdot\sin^{2}\theta,W_{o}=V^{2}/1600, \tag{1}\]  
where \(W_{x}\) is the standard value of horizontal wind load (kN) perpendicular to the wire and ground direction; \(\alpha\) is the wind pressure unevenness coefficient; \(\mu_{z}\) is the wind pressure height variation coefficient; \(\mu_{sc}\) is the body coefficient of the conductor or ground; \(\beta_{c}\) is the wind load adjustment coefficient of the conductor and ground of the 500 kV and 750 kV lines; \(d\) is the outer diameter of the conductor, ground, or the calculated outer diameter when icing (m); \(L_{p}\) is the pole tower horizontal distance (m); \(B_{1}\) is the guide, ground, and insulator string ice wind load increase factor; \(\theta\) is the angle between the wind direction and the direction of the wire or ground (\"); \(W_{o}\) is the standard value of the base wind pressure (kN); \(V\) is the wind speed at the base height of 10 m (m/s). The formula for calculating the wind load on the tower is as follows:  
\[W_{s}=W_{o}\cdot\mu_{z}\cdot\mu_{s}\cdot B_{2}\cdot A_{s}\cdot\beta_{z}, \tag{2}\]  
where \(W_{s}\) is the standard value of the tower wind load (kN); \(\mu_{s}\) is the body type coefficient of the member; \(B_{2}\) is the increase coefficient of the wind load of the tower member over ice; \begin{table}
\begin{tabular}{c c c c c c} \hline
**Component** & **Material** & **Density** & **Young’s** & **Poisson’s** & **Yield Strength** \\
**Name** & **Type** & **(g/cm\({}^{3}\))** & **Modulus (G\(\cdot\)Pa)** & **Ratio** & **(MPa)** \\ \hline Main Materials & Q345 steel & & & & \\ Slanting & Q235 steel & & & & \\ material & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Tower main material and slant material related parameters. A\({}_{8}\) is the calculated value of the projected area of the windward side member (m\({}^{2}\)); \(\beta_{\rm z}\) is the wind load adjustment coefficient of the tower. The formula for calculating insulator string wind load is as follows:  
\[\rm W_{1}=W_{o}\cdot\mu_{z}\cdot B_{1}\cdot A_{1}, \tag{3}\]  
where W\({}_{1}\) is the insulator string wind load standard value (kN); A\({}_{1}\) is the calculated value of insulator string bearing wind pressure area (m\({}^{2}\)). The wire and ground wire ice loads are related to the maximum tension of the conductor and ground wire. The values of the conductor and ground wire ice load under a 20 mmicing degree are shown in Table 2[19; 20; 21]. The calculation formula of the maximum tension of conductor and ground wire is as follows:  
\[\rm T_{max}=\frac{F_{max}\cdot C_{nl}}{k}, \tag{4}\]  
where T\({}_{max}\) is the maximum tension of the wire and ground wire; F\({}_{max}\) is the calculated pull-off force of the wire and ground wire; k is the safety factor of the wire and ground wire; C\({}_{nl}\) is the new line coefficient, which is usually 0.95 in conservative calculations. The MZ2-27 cat-head-type linear tower is an overhanging tower with bifurcated wire. The tower under a 20 mm icing degree carries 50% of the maximum tension of the conductor and 100% of the maximum tension of the ground wire. The ice-covered load of the tower is the gross value of the wire icing load and ground wire icing load. Thus, the formula for the ice-covered load of the tower can be derived as follows:  
\[\rm W_{f}=0.95\left(\frac{F_{max_{1}}}{2k_{1}}+\frac{F_{max_{2}}}{k_{2}} \right), \tag{5}\]  
where W\({}_{f}\) is the standard value of the ice load (kN); F\({}_{max_{1}}\) is the calculated pull-off force of the wire (kN); k\({}_{1}\) is the safety coefficient of the wire; F\({}_{max_{2}}\) is the calculated pull-off force of the ground wire (kN); k\({}_{2}\) is the safety coefficient of the ground wire.