# Dynamic Response of Slender Vertical Structures Subjected to Thunderstorm Outflows
## 3 Numerical Application
### Thunderstorm Wind Velocity and Loading Modeling  
The data employed in the study were recorded by 14 bi- or tri-axial ultrasonic anemometers installed in the ports of Genoa, La Spezia, Livorno, and Savona by the Department of Civil, Chemical, and Environmental Engineering (DICCA), and include 129 thunderstorm outflow records at a duration of 10 min [43]. Anemometers were mounted at a height, \(h_{a}\), reaching at least 10 m above the ground, mainly on high-rise towers or antenna masts at the top of buildings, in order to avoid local effects and to register undisturbed wind velocities. Figure 3 shows, as an example, one anemometer per each location considered. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Structure** & \(\begin{array}{c}\mathbf{H}\\ \mathbf{[m]}\end{array}\) & \(\begin{array}{c}\mathbf{n_{1}}\\ \mathbf{[Hz]}\end{array}\) & \(\begin{array}{c}\mathbf{n_{2}}\\ \mathbf{[Hz]}\end{array}\) & \(\begin{array}{c}\mathbf{n_{3}}\\ \mathbf{[Hz]}\end{array}\) & \(\begin{array}{c}\mathbf{m_{1}}\\ \mathbf{[kg]}\end{array}\) & \(\begin{array}{c}\mathbf{m_{2}}\\ \mathbf{[kg]}\end{array}\) & \(\begin{array}{c}\mathbf{m_{3}}\\ \mathbf{[kg]}\end{array}\) & \(\mathbf{\zeta}\) \\ \hline Lighting & 15.76 & 0.53 & 3.16 & 8.76 & 164.37 & 83.65 & 46.17 & 0.002 \\ Telecommunications tower & 98 & 0.49 & 3.23 & 7.25 & 482,989.76 & 166,620.00 & 53,764.00 & 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main properties of the two structure test cases. Figure 1: Structure test cases: (**a**) steel lighting pole; (**b**) reinforced concrete telecommunications tower. Figure 3: _Cont._  
Figure 2: Vibration modes: (**a**) lighting pole, (**c**) telecommunications tower; width of the structure (star dots): (**b**) lighting pole, (**d**) telecommunications tower. All the anemometers have a sampling rate of 10 Hz, a precision of 0.01 m/s for the velocity, and \(1^{\circ}\) for the direction. A detailed study of the data collected has been carried out by [PERSON] et al. [29]. As an example, Figure 4 shows four samples of thunderstorm wind speeds recorded in the ports of Genoa, Livorno, Savona, and La Spezia. Figure 4: Examples of recorded thunderstorm wind speeds in different ports (slowly varying mean wind speed in dashed lines): (**a**) Genoa (\(h_{a}=61.4\) m); (**b**) Livorno (\(h_{a}=75\) m); (**c**) Savona (\(h_{a}=28\) m); (**d**) La Spezia (\(h_{a}=10\) m). Figure 3: Anemometers in the port areas of (**a**) Genoa \(h_{a}=61.4\) m); (**b**) Livorno (\(h_{a}=75\) m); (**c**) Savona (\(h_{a}=28\) m); and (**d**) La Spezia (\(h_{a}=10\) m). The ensemble values of the maximum mean wind speed, turbulence intensity, and integral length scale read \(\overline{v}_{\text{max}}=16.01\) m/s, \(\overline{l}_{v}=0.12\), and \(L_{v}=27.32\) m, respectively [20, 29], while the modulating function \(\gamma(t)\) of the slowly varying mean wind speed average trend is defined according to the model of [PERSON] and [PERSON] [38]:  
\[\gamma(t)= \begin{cases}\frac{1-\gamma^{*}}{2}\big{[}\cos\big{(}\frac{2\pi t}{T }\big{)}+1\big{]}+\gamma^{*}&,\ |t|<\frac{T}{2}\\ \gamma^{*}&,\ |t|\geq\frac{T}{2}\end{cases}  \tag{43}\]  
where the parameters \(\gamma^{*}=0.54\) and \(T=169.81\) s. Concerning the vertical profile of the mean wind velocity associated with the thunderstorm outflow, the model from [PERSON] and [PERSON] [44] is adopted as outlined in Appendix A (Equation (A1)). The analyses are carried out by fixing \(h=20\) m and using the different values of the nose height, i.e., \(z_{m}=25\), \(50\), \(75\), \(100\) m. As an example, the vertical mean speed profile of the thunderstorm outflow and synoptic wind are plotted in Figure 5a,b for the lighting pole and telecommunications tower, respectively. Note that for the lighting pole (Figure 5a), the typical nose shape is not visible since the nose tip is located above the structure, whilst it is clearly detectable for the telecommunications tower, especially at lower values of \(z_{m}\).