# Wind-Induced Dynamic Performance Evaluation of Tall Buildings Considering Future Wind Climate
## 3 Fragility Analysis for Human Occupant Comfort
### Fragility Analysis Results and Discussions  
In this study, the framework has considered the uncertainties of wind speed and damping in vibrations related to tall buildings occupant comfort problems. This study repeatedly carried out 1000 simulation cycles for each level of mean wind speed. The probability density distributions of the simulated peak acceleration responses of the building under historical, mid-future, and late-future wind loads for 10-year, 50-year, and 100-return periods are shown in Figure 11, Figure 12, and Figure 13, respectively. Three different types of distribution models were used to fit the simulated peak acceleration's PDF: the Normal, Gumbel, and Weibull distributions. The simulated peak acceleration data for all wind scenarios seems to be best-fit by the normal distribution. The simulated mean values of the peak acceleration data with the corresponding coefficient of variance (COV) from the normal distribution are listed in Table 9. For the 10-year return period, the mean value of maximum acceleration for historical conditions was 15.3973 milli-g, which increases to 15.9956 milli-g in mid-future conditions and further to 17.4820 milli-g in late-future conditions. For the 50-year return period, the mean value of maximum acceleration for historical conditions was 23.5594 milli-g, which increases to 25.2051 milli-g in mid-future conditions and further to 26.6818 milli-g in late-future conditions. For the 100-year return period, the mean value of maximum acceleration for historical conditions was 26.1526 milli-g, which increases to 28.0376 milli-g in mid-future conditions and further to 29.7324 milli-g in late-future conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Random Variables**} & \multirow{2}{*}{**Distribution Type**} & \multirow{2}{*}{**Wind Cases**} & \multirow{2}{*}{**Mean**} & \multicolumn{2}{c}{**Standard**} & \multirow{2}{*}{**COV**} \\  & & & & **Deviation** & & \\ \hline \multirow{6}{*}{Wind speed (m/s)} & \multirow{6}{*}{Gumbel distribution} & Historical 10-year & 24.9 & 1.245 & 0.05 \\  & & Mid-future 10-year & 25.3 & 1.265 & 0.05 \\  & & Late-future 10-year & 26.4 & 1.320 & 0.05 \\  & & Historical 50-year & 30.6 & 1.530 & 0.05 \\  & & Mid-future 50-year & 31.6 & 1.580 & 0.05 \\  & & Late-future 50-year & 32.5 & 1.625 & 0.05 \\  & & Historical 100-year & 32.2 & 1.610 & 0.05 \\  & & Mid-future 100-year & 33.3 & 1.665 & 0.05 \\  & & Late-future 100-year & 34.4 & 1.720 & 0.05 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Damping \\ ratio \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} Lognormal \\ distribution \\ \end{tabular} } & \multirow{2}{*}{All wind scenarios} & \multirow{2}{*}{0.02} & \multirow{2}{*}{0.003} & \multirow{2}{*}{0.15} \\  & & & & \\ \end{tabular}
\end{table} 
Table 8: Statistical parameters for windspeed and damping. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Return Period**} & \multirow{2}{*}{**Wind Cases**} & \multicolumn{2}{c}{**Normal Distribution**} & \multirow{2}{*}{**Failure**} \\  & & **Mean** & **Standard Deviation** & & **Probability** \\  & & **(mlli-g)** & **(mlli-g)** & **COV (\%)** & **(\%)** \\ \hline \multirow{2}{*}{10-year} & Historical & 15.3973 & 1.8958 & 12.3125 & 0 \\  & Mid-future & 15.9956 & 1.8201 & 11.3787 & 0 \\  & Late-future & 17.4820 & 2.0793 & 11.8939 & 0 \\ \hline \multirow{2}{*}{50-year} & Historical & 23.5594 & 2.7594 & 11.7125 & 25.50 \\  & Mid-future & 25.2051 & 3.2753 & 12.9945 & 46.00 \\  & Late-future & 26.6818 & 3.3870 & 12.6940 & 65.00 \\ \hline \multirow{2}{*}{100-year} & Historical & 26.1526 & 3.0134 & 11.5223 & 58.50 \\  & Mid-future & 28.0376 & 3.6689 & 13.0856 & 81.00 \\  & Late-future & 29.7324 & 3.3611 & 11.3045 & 95.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Mean value of peak acceleration responses and failure probability of the building. Figure 11: Probability density function of peak acceleration responses of the building for 10-year return period under: (**a**) historical; (**b**) mid-future; (**c**) late-future.