# Wind-Induced Dynamic Performance Evaluation of Tall Buildings Considering Future Wind Climate
## 2 Basic Settings for the Simulations
### Performance Evaluation of the Building Under Wind Loads
#### 2.2.2 Wind Loads Simulation  
Wind load time series can be obtained from the simulated wind velocity by quasi-steady approximation with aerodynamic coefficients. The along-wind load \(P_{u}(t)\) and across-wind load \(P_{v}(t)\) can be calculated by Equation (15) and Equation (16), respectively [34].  
\[P_{u,z}(t)=\frac{1}{2}\rho\bigl{(}\overline{U}_{z}+u_{z}(t)\bigr{)}^{2}C_{d,z }A_{u,z} \tag{15}\]  
\[P_{v,z}(t)=\frac{1}{2}\rho v_{z}^{2}(t)C_{l,z}A_{v,z} \tag{16}\]  
where \(\rho\) is the air density (\(\rho=1.25\) kg/m\({}^{3}\)); \(C_{d,z}\) and \(C_{l,z}\) are the drag coefficient and lift coefficient corresponding to height z; \(A_{u,z}\) and \(A_{v,z}\) are areas in along-wind and across-wind directions at the height of z. Lift coefficient \(C_{l,z}\) can be calculated by using Equation (17) [42], and drag coefficient \(C_{d,z}\) can be obtained by calculating the difference between the external pressure coefficient of the windward and leeward walls as given in Table 4 below by using Equation (18) [37]:  
\[C_{l,z}=0.045\biggl{(}\frac{D}{B}\biggr{)}^{3}-0.335\biggl{(}\frac{D}{B} \biggr{)}^{2}+0.868\biggl{(}\frac{D}{B}\biggr{)}-0.174 \tag{17}\]  
\[C_{d,z}=C_{pe1}-C_{pe2} \tag{18}\]Figure 5: Comparison of wind speed time histories at 44 th floor of the building in Y-direction for return period: (**a**) 10-year; (**b**) 50-year; (**c**) 100-year.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Conditions** & **Equations** \\ \hline Windward wall, \(C_{pe1}\) & — & \(C_{pe1}=0.8k_{z}+0.03(D/B)\) \\ \hline \multirow{2}{*}{Leeward wall, \(C_{pe2}\)} & \(D/B\leq 1\) & \(C_{pe2}=-0.5\) \\  & \(D/B>1\) & \(C_{pe2}=-0.5+0.25 ln(D/B)^{0.8}\) \\ \hline \multirow{2}{*}{Pressure distribution coefficients} & \(z\leq z_{b}\) & \(k_{z}=(z_{b}/H)^{2\alpha}\) \\  & \(z_{b}<z<0.8H\) & \(k_{z}=(z/H)^{2\alpha}\) \\ \multirow{2}{*}{for vertical profile, \(k_{z}\)} & \(z\geq 0.8H\) & \(k_{z}=(z/H)^{2\alpha}\) \\ \hline \end{tabular} where \(B\) represents the breadth of the building (perpendicular to the along-wind direction) (m); \(D\) represents the depth of the building (perpendicular to the across-wind direction) (m); \(z\) represents the height from the ground (m); and \(z_{b}\) represents height above the ground surface starting at the atmospheric boundary layer (m). In this study, the along-wind direction is the Y-direction of the building. The value of the lift coefficient is 0.058. Table 5 lists drag coefficients at representative heights of the building.  
\end{table}
Table 4: External pressure coefficients, \(C_{pe}\).  
Figure 6 compares the time histories of the along-wind load acting on the building at the 44 th floor for the same return periods (10-year, 50-year, and 100-year). Each sub-figure shows how wind loads fluctuate over time, illustrating the dynamic nature of wind forces.  
Figure 6: Comparison of wind load time histories at 44 th floor of the building in Y-direction for return period: (**a**) 10-year; (**b**) 50-year; (**c**) 100-year.