# Fragility Assessment and Reinforcement Strategies for Transmission Towers Under Extreme Wind Loads
## 6 Conclusions  
This study investigated the instability and collapse behavior of a 220 kV ZM3-33 transmission tower subjected to strong wind conditions, with a focus on identifying structural vulnerabilities and evaluating the effectiveness of reinforcement strategies. A concurrent multi-scale finite element model was developed to analyze the weak region of the structure, and a traditional perforated plate reinforcement method was applied. The key findings are summarized as follows:  
* By accounting for wind load uncertainties and variations in wind direction, the 45\({}^{\circ}\) wind angle was identified as the most critical loading condition for the ZM3-33 transmission tower. Collapse is primarily initiated by plastic instability in the main structural members of the third section. As wind speed increases, the lower part of this section simultaneously enters the plastic yield phase, resulting in a rapid decline in load-bearing capacity. The critical wind speed at which collapse occurs is approximately 37 m/s. * Comparative analysis of natural frequencies, displacement responses, and stress distributions between the rigid frame model and the concurrent multi-scale model evidenced the enhanced accuracy of the latter. The multi-scale model effectively captures localized stress concentrations while maintaining consistency in global structural behavior, thereby validating its suitability for high-fidelity structural assessments. * The applied reinforcement strategy significantly improved the transmission tower's structural performance. The tower top displacement was reduced by approximately 10%, and the stress levels in the main tower leg members decreased by 13% to 21% under wind loading. However, non-uniform stress distribution in the auxiliary members indicates suboptimal force transmission. The current study focuses on a single tower configuration, with a specific geometry, material grade (Q235 and Q355 steel), and conductor configuration. While this provides a realistic and practical case for model development and validation, it inherently limits the direct transferability of the results to towers of different voltage classes, geometries, or structural layouts. Generalizing the reinforcement strategies or failure modes observed here to dissimilar tower types may require additional parametric studies or recalibration of key model parameters. On the other hand, the wind loads were simulated using a deterministic approach based on codified equations (DL/T 5551-2018, GB 50545-2010) and further simplified by applying concentrated forces on conductor nodes. Although this study considers multiple wind attack angles, the wind field is assumed to be horizontally uniform \begin{table}
\begin{tabular}{c c c c c} \hline
**Wind Angle** & **0\({}^{\circ}\)** & **45\({}^{\circ}\)** & **60\({}^{\circ}\)** & **90\({}^{\circ}\)** \\ \hline No.4 & 26.54 & 37.52 & 31.90 & 28.72 \\ No.3 & 23.60 & 30.01 & 30.36 & 28.15 \\ No.2 & 25.36 & 37.37 & 31.44 & 27.51 \\ No.1 & 27.00 & 38.91 & 32.20 & 29.36 \\ \hline \end{tabular}
\end{table} 
Table 6: Stress of auxiliary material. and does not include spatial turbulence, localized phenomena, e.g., downbursts [42; 43], typhoons [44], and tornadoes [45; 46]. Therefore, the results provided are most applicable to synoptic-scale wind conditions and may not fully capture dynamic response behaviors induced by transient or spatially complex wind events. Furthermore, this study evaluates the performance of one conventional reinforcement method (perforated plate bolted strengthening). Although the method is validated and shows improved stress reduction, other reinforcement techniques--such as FRP jacketing, welded stiffeners, or adaptive dampers--were not considered. Additionally, further refinement of the multi-scale modeling approach is recommended, with a focus on improving interface coupling techniques to enhance simulation accuracy and computational efficiency. Formal analysis, J.Y. ; Investigation, J.Y. ; Resources, L.W. ; Writing--original draft, J.Y. ; Writing--review & editing, Z.S.