# Fragility Assessment and Reinforcement Strategies for Transmission Towers Under Extreme Wind Loads
## 3 Numerical Simulation Analysis
### Model Establishment
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Tower Section** & **Q355-Grade Steel** & **Q235-Grade Steel** \\
**Number** & & L80 \(\times\) 6, L70 \(\times\) 5, L63 \(\times\) 5, L56 \(\times\) 5, L56 \(\times\) 4, \\  & & L50 \(\times\) 4, L45 \(\times\) 4, L40 \(\times\) 3 \\
2 & L125 \(\times\) 10 & L63 \(\times\) 5, L56 \(\times\) 5, L45 \(\times\) 4, L40 \(\times\) 3 \\
3 & L125 \(\times\) 8 & L63 \(\times\) 5, L56 \(\times\) 5, L65 \(\times\) 4, L45 \(\times\) 4, L40 \(\times\) 3 \\
4 & L100 \(\times\) 10 & L80 \(\times\) 6, L63 \(\times\) 5, L56 \(\times\) 4, L45 \(\times\) 4 \\
5 & L90 \(\times\) 7, L75 \(\times\) 6 & L56 \(\times\) 4, L50 \(\times\) 4, L45 \(\times\) 4, L40 \(\times\) 3 \\
6 & L100 \(\times\) 8, L80 \(\times\) 6, L63 \(\times\) 5 & L75 \(\times\) 5, L63 \(\times\) 5, L56 \(\times\) 4, L50 \(\times\) 4, L45 \(\times\) 4 \\
7 & L125 \(\times\) 8, L100 \(\times\) 8, L75 \(\times\) 6, L63 \(\times\) 5 & L75 \(\times\) 6, L70 \(\times\) 5, L63 \(\times\) 5, L56 \(\times\) 5, L56 \(\times\) 4, \\  & & L50 \(\times\) 4, L45 \(\times\) 4, L40 \(\times\) 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of the transmission tower angle steel components. accurate approximation of the material behavior under wind-induced stresses, and it has been widely validated in similar transmission tower collapse and buckling analyses. For the finite element analysis, the transmission tower structure was discretized using a nonlinear finite element approach. Beam elements (B31) were employed to model primary members, following the methodology proposed by [PERSON] and [PERSON] [38], who demonstrated the effectiveness of this strategy in capturing both elastic and plastic responses under incremental wind loading. To replicate the real-world boundary constraints, fixed supports are applied at the tower base, ensuring that translational and rotational degrees of freedom are fully restrained. The complete finite element model, including all geometric and boundary conditions, is shown in Figure 4. This model forms the basis for subsequent simulations aimed at evaluating structural performance, identifying failure modes, and assessing the effectiveness of reinforcement strategies under various wind loading scenarios. To assess the adequacy of the transmission tower's structural design, a modal analysis was performed. This analysis is crucial for evaluating the dynamic characteristics of the tower, particularly in light of its high flexibility. This study focuses on the first three natural vibration modes, as these are most influential in determining the tower's dynamic response. The corresponding mode shapes are illustrated in Figure 5. The first mode, with a natural frequency of 1.6992 Hz, is characterized by longitudinal bending deformation along the height of the tower. The second mode, with a frequency of 2.2081 Hz, involves lateral bending deformation, indicating displacement perpendicular to the tower's longitudinal axis. The third mode represents the overall torsional deformation of the structure, occurring at a frequency of 3.5536 Hz. Figure 3: Division of transmission tower sections. Figure 2: Stress–strain curves of steel.