# Fragility Assessment and Reinforcement Strategies for Transmission Towers Under Extreme Wind Loads
## 3 Numerical Simulation Analysis
### Wind Load Calculation  
In accordance with the reference [40], a comparative evaluation was conducted among the equivalent static wind load calculation methods specified in several international and national standards, including CEI/IEC 60826:2003, BS EN 50341-1:2012, ASCE Manual No. 74:2009, and China's national standard GB 50545-2010 [39]. The comparison revealed that the GB 50545-2010 method produced the most conservative wind load estimates, providing a higher margin of safety in structural design. Accordingly, this study adopts the GB 50545-2010 formulation for subsequent wind load analysis to ensure a conservative and safety-oriented evaluation of the transmission tower's structural performance.  
The wind speed \(V(z,t)\) at different sections of the transmission tower is expressed as the sum of the average wind speed \(\overline{V}(z,t)\) and the fluctuating wind speed \(v(z,t)\), as shown in Equation (4):  
\[V(z,t)=\overline{V}(z,t)+v(z,t) \tag{5}\]  
Given the inherent variability of atmospheric wind, the wind loads acting on different segments of the transmission tower must be modeled as a dynamic load. Furthermore, uncertainties associated with climate variability, terrain features, and wind direction necessitate a comprehensive evaluation of the structural response under different wind attack angles. In the present study, wind loads corresponding to the angles of 0\({}^{\circ}\) and 90\({}^{\circ}\) attack angle were calculated following the specifications outlined in DL/T 5551-2018 [41] and GB 50545-2010 [41], using the following standard Equation:  
\[W_{S}(t)=\mu_{Zc}\times\mu_{Sc}\times A_{Sc}\times V(z,t)^{2}/1.6 \tag{6}\]  
where \(W_{S}(t)\) is the standard wind load on the transmission tower structure (kN), \(\mu_{Zc}\) is the height variation coefficient of wind pressure, \(\mu_{Sc}\) is the shape coefficient, \(A_{Sc}\) is the projected area of the windward surface (m\({}^{2}\)). Specifically, the shape coefficient is a critical parameter that reflects the aerodynamic characteristics of the structural elements exposed to wind. This coefficient varies with structural geometry, wind approach angle, and member configuration.  
In addition, to evaluate wind direction effects beyond those prescribed by national codes, additional wind angles of 45\({}^{\circ}\) and 60\({}^{\circ}\) are considered in accordance with GB 50545-2010 [39]. The corresponding wind angle configurations are illustrated in Figure 8. The wind load acting on the ground conductor is determined using  
\[W_{x}=\alpha_{m}\cdot W_{0}\cdot\mu_{Zc}\cdot\mu_{Sc}\cdot\beta_{c}\cdot d \cdot L_{p}\cdot B\cdot\sin^{2}\theta \tag{7}\]  
where \(\alpha_{m}\) is the wind pressure non-uniformity coefficient, \(W_{0}\) is the standard value of the basic wind pressure (kN/m\({}^{2}\)), \(\beta_{c}\) is the wind load adjustment coefficient for the grounding wire, \(d\) is the calculated outer diameter of the conductor (m), \(L_{p}\) is the horizontal span of the transmission tower (m), \(B\) is the icing increase coefficient (in this study, B = 0), \(\theta\) is the angle between the wind direction and the conductor. To enhance computational efficiency, the distributed wind loads acting on the conductors were simplified and applied as equivalent concentrated forces at selected nodal locations. This approach is based on Equation (7). The transformation from a continuous to a discrete load representation is a common numerical strategy in large-scale structural simulations, particularly when modeling slender elements like cables or conductors in wind-sensitive systems. By replacing distributed line loads with equivalent point loads at finite element nodes, the system stiffness matrix becomes more tractable, reducing computational complexity and memory requirements. More importantly, this simplification facilitates faster and more stable convergence in the nonlinear finite element analysis.