# Fragility Assessment and Reinforcement Strategies for Transmission Towers Under Extreme Wind Loads
## 3 Numerical Simulation Analysis  
### Model Establishment  
This study investigates the structural behavior of the ZM3-33 tower, a representative 220 kV transmission tower with a total height of 40.7 m. The design wind speed is specified as 33 m/s at a reference height of 10 m above ground level, with a minimum operating temperature of \(-\)5 \({}^{\circ}\)C and no ice accretion considered. The analysis incorporates LGJ-300/25 steel-core aluminum stranded conductors and JLB-40/80 aluminum-clad steel ground wires, consistent with the actual tower configuration. The tower structure is primarily composed of equal-leg angle steel members. Q355-grade steel is used for the main load-bearing components, including the tower body and legs, while Q235-grade steel is employed for bracing and auxiliary elements. The mechanical properties of these steel grades are summarized in Table 1. Both Q355 and Q235 steels share an elastic modulus (E) of 2.06 \(\times\) 10\({}^{5}\) N/mm\({}^{2}\) and a density (\(\rho\)) of 7850 kg/m\({}^{3}\). To characterize the material response, a bilinear hardening model is adopted. This model captures both the elastic and plastic stages of deformation. As depicted in Figure 2, in this idealized model, point \"a\" denotes the yield point where plastic deformation begins. \(\varepsilon_{k}\) represents the bending strain while \(\varepsilon_{y}\) represents the yield strain, \(\sigma_{y}\) is yield stress. The segment oa characterizes the linear elastic response of the material, governed by Hooke's Law, while segment ab represents the plastic deformation region, where the material exhibits a reduced stiffness due to strain hardening. The stress-strain relationship is defined as  
\[\sigma= \begin{cases}E_{0}\varepsilon&,\quad 0<\varepsilon<\varepsilon_{y}\\ \sigma_{y}+E_{1}(\varepsilon-\varepsilon_{t}),&\varepsilon>\varepsilon_{y} \end{cases}  \tag{1}\]  
where \(\varepsilon\) is strain, \(\sigma\) is stress, \(E_{0}\) is elastic modulus, and \(E_{1}\) is the tangent modulus in the plastic region, representing the strain hardening rate. For both Q235 and Q355 structural steel, material parameters were based on nominal values specified in Chinese steel standards. For both Q235 and Q355 structural steel, material parameters were based on nominal values specified in Chinese steel standards. Specifically, the yield stress was taken as 235 MPa for Q235 and 355 MPa for Q355, respectively. The ultimate tensile strength was assumed to be 370-500 MPa for Q235 and 470-630 MPa for Q355, based on standard ranges provided in the corresponding specifications. The transmission tower is divided into seven segments, is shown in Figure 3. A constant strain hardening modulus Et = 0.01E was adopted for both materials, in line with previous studies modeling tower member behavior under monotonic loading. It is to be noted that no additional coupon testing was conducted in this study, and the use of nominal material properties is a common engineering practice for large-scale tower simulations where component-level variability is not the primary focus. Overall, such bilinear model provides a computationally efficient yet sufficiently