## 3 Parametric Analysis and Results
### Structural Characteristics and Peak Responses
As indicated in [10], the aspect ratios (\(H/L\) and \(H/W\)) are of paramount importance in the evaluation of the wind-induced response with particular attention to the torsional moment. 1.1 Impact of \(\Omega_{\theta}\) and \((\rho_{FxM},\rho_{FyM})\) on the Mean Peak Responses  
To further evaluate the influence of \(\Omega_{\theta}\) and the correlation pair \((\rho_{FxM},\rho_{FyM})\) on the structural response, the analysis procedure described in Section 3.1 was repeated with the \(\Omega_{\theta}\) values varying from 0.8 to 2. Figure 5 presents the variation of the mean peak displacement, rotation, and acceleration with respect to \(\Omega_{\theta}\) and \((\rho_{FxM},\rho_{FyM})\). The plots of the mean peak displacement shown in Figure 5 indicate that \(\Omega_{\theta}\) and \((\rho_{FxM},\rho_{FyM})\) have an important impact, and that in some cases the combination of certain values of \(\Omega_{\theta}\) and \((\rho_{FxM},\rho_{FyM})\) produces a greater mean peak displacement for all the structural models analyzed. It can also be observed in Figure 5 that, as expected, the most important parameter in the calculation of the mean peak rotation is \(\Omega_{\theta}\), and that only in the cases where \(\Omega_{\theta}<1\), the importance of considering \((\rho_{FxM},\rho_{FyM})\) gain relevance. The plots of mean peak acceleration shown in Figure 5 are relatively uniform along \(\Omega_{\theta}\) and \((\rho_{FxM},\rho_{FyM})\), as this was predefined in the scaling of the  
Figure 4: Comparison of mean peak responses of the structural models considering different correlation pairs without the A\(-\Delta\) effect: (**a**) displacement; (**b**) rotation; (**c**) acceleration. Figure 3: Mean peak responses of the structural models without the A\(-\Delta\) effect: (**a**) displacement; (**b**) rotation; (**c**) acceleration. wind forces. The results presented in Figure 5 are concordant with previous experimental studies carried out by [15; 16; 17], where the correlation of wind forces were shown to have a very important impact on the wind-induced response. Figure 5: Comparison of mean peak responses of the structural models considering different correlation pairs without the A\(-\Delta\) effect: (**a,d,g,j,m**) and (**p**) displacement; (**b,e,h,k,n**) and (**q**) rotation; (**c,f,i,l,o**) and (**r**) acceleration. 3.1.2. Impact of the A-\(\Delta\) effect, \(\Omega_{\theta}\), and (\(\rho_{FxM}\), \(\rho_{FyM}\)) on the Peak Responses  
To evaluate the influence of the nonlinear A-\(\Delta\) effect, the nonlinear response was calculated with Equation (5) in order to calculate the response ratios from Equation (10). Figure 6 presents the variation of \(R_{X}\) and \(R_{\tilde{X}}\). In Figure 6, the boxplots present statistics of the 30 samples of \(R_{X}\) and \(R_{\tilde{X}}\) for different values of \(\Omega_{\theta}\) and (\(\rho_{FxM}\), \(\rho_{FyM}\)) for all the structural models considered. For each boxplot, the median of the samples is indicated with a central mark, the lower and upper bounds of the box indicate the 25 th and 75 th percentiles, the most extreme data points not considered outliers are represented by whiskers, and the outliers are plotted individually using the cross symbol [21]. In Figure 6a, a rectangle is included to group the first five boxplots, which represent the variation of \(R_{X}\) for different values of (\(\rho_{FxM}\), \(\rho_{FyM}\)) for \(\Omega_{\theta}\) equal to 0.8. The subsequent boxplots were used to show the impact of \(\Omega_{\theta}\) on \(R_{X}\) for different levels of correlation of the wind forces. It can be observed in Figure 6 that, for all the structural models analyzed, the median of the \(R_{X}\) values is very close to one for all the values considered of \(\Omega_{\theta}\). It is also observed  
Figure 6: Influence of the A\(-\Delta\) effect on the displacement and acceleration in the X-direction: **(a,b)** Model 1; **(c,d)** Model 2; **(e,f)** Model 3; **(g,h)** Model 4; **(i,j)** Model 5; **(k,I)** Model 6.