## 4 Conclusions  
Numerical analyses were conducted to investigate whether the nonlinear effect, or A-\(\Delta\) effect, and the correlation of the wind forces and the torsional moment had an impact on the wind-induced response. For the analysis, a newly developed wind-loading model, which includes the effect of correlation between the wind forces (forces and moments) was used to simulate wind forces that were applied to generalized structural models with and without the A-\(\Delta\) effect. The numerical results indicate that the impact of the A-\(\Delta\) effect on the wind-induced response is negligible and that the most important effect on the wind-induced response is due to the correlation between the wind forces and the torsional moment. More specifically, it is concluded that:  
* In all the structural models analyzed, the median and the extreme data, as well as the outliers of the response ratio (\(R_{X}\), \(R_{\tilde{X}}\), \(R_{Y}\), and \(R_{\tilde{Y}}\)) values are very close to one for all the values considered of \(\Omega_{\theta}\). The latter indicates that the A-\(\Delta\) effect does not have an important impact on wind-induced displacement and acceleration.
* The correlation coefficient between the wind forces (i.e., \(\rho_{FxM}\) and \(\rho_{FyM}\)) has the most important impact on the response, indicating that different levels of correlation of the wind forces and the torsional moment have to be considered in the evaluation of the wind-induced response.  
Figure 7: Comparison of rotational velocity without and with the A\(-\Delta\) effect for all the structural models considered for \(\Omega_{\theta}=1\), and \(\rho_{FxM}=0.75\) and \(\rho_{FyM}=0.5\). Blue dots: without the A\(-\Delta\) effect; cross: with the A\(-\Delta\) effect.  
The wind-induced rotational velocity with and without the A-\(\Delta\) effect is practically the same, indicating that the A-\(\Delta\) effect has a marginal impact on it.
* The results presented in this study show that the A-\(\Delta\) effect has a marginal impact on the wind-induced response; however, the evaluation of the wind-induced response considering the nonlinear behavior of the structure (i.e., material or element nonlinearity) is very scarce in the relevant literature. Different to the nonlinear response of structures under seismic action, where the nonlinear response is likely to reduce compared to the linear response, wind-induced response will not necessarily behave in the same way, as nonlinearity may cause the structure to become more flexible with a consequent increase in the dynamic response of the structure. Further analyses are required to evaluate the impact of the material and element nonlinearity on tall buildings subjected to partially correlated wind loads.  
Conceptualization, A.L.-I. and A.P.-E.; Methodology, A.L.-I. and A.P.-E.; Investigation, A.L.-I., A.P.-E., and R.N.-G.; Writing--original draft, A.L.-I., A.P.-E., and R.N.-G.; Writing--review and editing, A.P.-E. and R.N.-G.; Resources, A.L.-I. and A.P.-E.; Supervision, A.L.-I. and A.P.-E. All authors have read and agreed to the published version of the manuscript.  
This work was supported by UNAM-PAPIIT IN103422.  
No data are available for this study.  
The financial support of the National Council for Science and Technology (CONACYT) of Mexico and the Institute of Engineering are gratefully acknowledged.  
The authors declare no conflict of interest.