# Study on Wind Resistance Performance of Transmission Tower Using Fixture-Type Reinforcement Device
## 3 Transmission Tower and Wind Load  
### Transmission Tower and Its Analytical Model  
To investigate the wind resistance performance of typical towers and the reinforcement effect of using FRD, the transmission tower shown in Figure 5a is selected as the research  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Original**} & \multicolumn{3}{c}{**Reinforced**} \\ \cline{3-5}  & & **2 Fixture Pairs** & **3 Fixture Pairs** & **4 Fixture Pairs** \\ \hline Peak Load (kN) & 69.2 & 87.3 & 95 & 95.4 \\ Changing Ratio & / & 26\% & 37\% & 38\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Peak loads of different models.  
Figure 4: Load–displacement curves of the models.  
prototype. For simplicity, this transmission tower is considered a structured body, and the welded connections between the components are not included. This type of transmission tower has been widely constructed in the rural areas of China. The overall height of this tower is 36.3 m, and the transmission cables are about 30 m above the ground. All the components of this transmission tower are L-shaped angled steel, but different components have different sectional dimensions and materials.  
Figure 5b demonstrates the two types of steel used in the construction of the transmission tower. The steel type of the green components is Q235, whose mechanical properties are the same as those in Table 1, while the blue components are made of Q345 with their mechanical properties given in Table 3. It can be seen from the comparison between the mechanical properties of the two types of steel that the only difference is the yield stress. In Figure 5c, the components with different sectional dimensions are labeled with different colors. The detailed information of the sectional dimensions of them are listed in Table 4. It can be seen that nine types of L-shaped angled steel components are used to construct the transmission tower, and the largest section of these components has a length of 80 mm and a thickness of 6 mm. In the transmission tower, the vertical component in the lower half of the height has sectional dimensions of 75 mm \(\times\) 5 mm and is exactly the main component investigated in Figure 2. Based on these geometrical dimensions of the components and the mechanical properties of the material, the finite element model of the transmission tower is built on the Abaqus platform. The components are simulated utilizing a two-node Euler beam element. The bottom of the tower is completely constrained, and for simplicity the soil-pile interaction is not considered in this study.  
The first 5 vibration modes and frequencies of this transmission tower are given in Figure 6 and Table 5 by conducting the dynamic property analysis. It can be seen that the first vibration mode is the tower bending with respect to the Y-axis in Figure 6a, and  
Figure 5: The transmission tower: (**a**) the prototype tower; (**b**) D = different steel type; (**c**) different section.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & \begin{tabular}{c} **Density** \\ **(kg/m3)** \\ \end{tabular} & \
\begin{tabular}{c} **Elastic Modulus** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Poisson Ratio** \\ **(MPa)** \\ \end{tabular} \\ \hline Q345 & 7850 & 2.06 \(\times\) 105 & 0.31 & 345 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mechanical properties of the Q345 steel.  
the vibration frequency is 1.575 Hz, which corresponds to a period of 0.635 s. The second vibration mode is the tower bending with respect to the X-axis, as shown in Figure 6b, and the vibration frequency is 1.577 Hz. The vibration periods of these two modes are very close because the vertical components of the tower are symmetrical in the two horizontal directions. The third and fourth vibration modes are also the bending deformation, and their frequencies are around 6.9 Hz. The first torsional vibration mode appears in the fifth order, as presented in Figure 6e, and the corresponding vibration frequency is 8.711 Hz.