# Fragility Assessment and Reinforcement Strategies for Transmission Towers Under Extreme Wind Loads
## 1 Introduction
Findings consistently show that initial geometric imperfections [19], internal bending moments in primary load-bearing members [20], and eccentric axial loading [21] are critical factors influencing overall structural stability and collapse modes. In a detailed study, [PERSON] et al. [22] identified six distinct failure modes in angle steel components with low slenderness ratios, emphasizing the significant role of joint configuration, slenderness ratio, and width-to-thickness ratio in determining failure behavior. Reinforcement strategies for transmission towers have primarily focused on strengthening vulnerable structural components to enhance overall stability and resistance to failure. [PERSON] et al. [23] investigated the effects of bolt pre-tightening force, slip load, and dynamic stiffness on the performance of reinforced joints. [PERSON] et al. [24] explored the impact of bolt quantity, connection configurations, and the number of connecting plates through a combination of experimental tests and finite element simulations, providing a more comprehensive understanding of joint reinforcement behavior. [PERSON] et al. [25] reported that reducing weld spacing had a negligible effect on the compressive strength of reinforced angle steel. [PERSON] et al. [26] explored strengthening existing bolted joints in transmission towers using GFRP and steel reinforcement plates. Their experiments compared the load-sharing behavior of GFRP and steel retrofits, concluding that both materials significantly enhanced the tensile capacity of aged bolted joints. [PERSON] et al. [27] developed a three-dimensional continuum element model to simulate reinforcement strategies using panel and bolt connections. [PERSON] et al. [28] proposed a diagonal rod stiffening technique that effectively shifted the dominant failure mode from diagonal bracing buckling to main leg buckling. This transition in failure mechanism resulted in a substantial increase in the ultimate load-bearing capacity of the tower. [PERSON] et al. [29] introduced an innovative clamping reinforcement method, which achieved a 21.96% improvement in ultimate bearing capacity. Despite notable advancements in component-level testing, evaluating individual angle steel members under axial or eccentric loading conditions fails to capture the global structural behavior of transmission towers or accurately assess the effectiveness of reinforcement strategies at the system level. Traditional numerical simulation methods, which typically adopt uniform modeling scales (e.g., beam or shell elements for the entire structure), often encounter difficulties in simultaneously resolving both global deformation patterns and localized stress concentrations, especially during progressive failure and collapse scenarios. To address these limitations, multi-scale simulation methods have emerged as a promising alternative [30]. Multi-scale simulation refers to a computational strategy that couples different modeling resolutions or element types--typically coarse-scale global models (e.g., beam or shell elements) with fine-scale local models (e.g., solid or continuum elements)--within a unified framework through interface constraint techniques, allowing for simultaneous and consistent analysis of both macroscopic structural performance and microscopic damage evolution [31; 32]. This methodology enables localized phenomena such as yielding, buckling, or fracture to be modeled with high fidelity, without compromising the computational efficiency required for simulating the entire tower structure. Compared to traditional component-level modeling, which isolates structural members and neglects interaction effects, multi-scale modeling captures the global load redistribution, progressive failure propagation, and structure-reinforcement interactions with significantly greater accuracy [33]. [PERSON] et al. [34] validated the effectiveness of multi-scale modeling by comparing simulation outcomes with rigid frame models, truss models, and experimental data.