## 4 Performance-Based Analysis
\[\lambda_{S_{a}}=k(S_{a})^{t} \tag{17}\]  
The parameters \(k\) and \(t\) adapted from the study for the fluctuation periods related to the buildings discussed in this study for the high-risk area are given in the Table 6. The uniform hazard curves obtained for all three frames are shown in the Figure 23:0  
Figure 23:1 Comparison of 50% curves of IDA curves obtained for all 3 structural frames. Figure 23:2 IDA curves obtained for a slightly damaged 20-story frame (by removing one beam and one column on the tenth floor in addition to removing one beam and one column on the fifth floor). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**t** & **k** & **T\({}_{\mathbf{1}}\)** & \\ \hline \multirow{3}{*}{\(-1.98\)} & \multirow{3}{*}{0.000137} & \multirow{3}{*}{0.965} & 20 story frame-slightly damaged (by removing one \\  & & & beam and one column on the tenth floor in addition to \\  & & & removing one beam and one column on the fifth floor) \\ \hline \multirow{3}{*}{\(-2.03\)} & \multirow{3}{*}{0.000351} & \multirow{3}{*}{0.701} & 20-story frame slightly damaged (by removing a beam \\  & & & and a column on the fifth floor) \\ \hline \multirow{3}{*}{\(-2.24\)} & \multirow{3}{*}{0.000159} & \multirow{3}{*}{0.568} & \multirow{3}{*}{Structural frame of 20 undamaged frames} \\  & & & \\ \end{tabular}
\end{table} 
Table 6: Calculated parameters k and t used in Equation (17). Figure 32: Comparison of fragility curves obtained from IDA curves for the level of failure corresponding to the level of failure of CP and IO for all three structural frames. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Spectral** & \multicolumn{2}{c}{**High Level Hazard**} & \multicolumn{2}{c}{**Medium Level Hazard**} & \multicolumn{2}{c}{**Low Level Hazard**} \\ \cline{2-6}
**Acceleration** & **k** & **t** & **k** & **t** & **k** & **t** \\ \hline S\({}_{\text{a}}\) (0.30) & \(1.890\times 10^{-3}\) & \(-2.653\) & \(8.422\times 10^{-4}\) & \(-2.683\) & \(1.861\times 10^{-4}\) & \(-2.888\) \\ S\({}_{\text{a}}\) (0.60) & \(5.653\times 10^{-4}\) & \(-2.131\) & \(2.661\times 10^{-4}\) & \(-2.191\) & \(1.861\times 10^{-5}\) & \(-2.510\) \\ S\({}_{\text{a}}\) (0.90) & \(1.787\times 10^{-4}\) & \(-2.005\) & \(8.947\times 10^{-5}\) & \(-2.105\) & \(1.861\times 10^{-5}\) & \(-2.367\) \\ S\({}_{\text{a}}\) (1.20) & \(7.460\times 10^{-5}\) & \(-2.021\) & \(3.444\times 10^{-5}\) & \(-2.140\) & \(1.861\times 10^{-6}\) & \(-2.451\) \\ S\({}_{\text{a}}\) (1.50) & \(5.356\times 10^{-5}\) & \(-2.021\) & \(2.473\times 10^{-5}\) & \(-2.140\) & \(1.861\times 10^{-6}\) & \(-2.451\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters in seismic hazard curves for three different zones. In order to calculate the Mean Annual Frequency of limit states (MAF) in this study, these values are very useful as quantities that reflect the probabilistic capacity of all structures based on earthquake uncertainties. These values can be used as a criterion for measuring the structural reliability of the buildings in comparison with other structures, or they can be used in the regulations related to the design of buildings [1]. In order to calculate the mean annual frequency, the following equation has been used. \[(\text{Collapse})=\int_{0}^{\infty}\text{P}[\text{Collapse}|\text{IM}=\text{ im}_{i}|\left|\frac{\text{d}\lambda(\text{IM}>\text{im}_{i})}{\text{dim}} \right|\text{d}(\text{im}) \tag{18}\]  
In this equation (Collapse), \(\lambda\) represents the functions of the mean annual incidence rate (MAF) of transmittance for IM, in which the quantity within the absolute value, the risk gradient of IM and the probability of failure or the same value is a function of fragility. Using high seismic hazard diagrams and fragility and numerical integration diagrams, Equation (18) is used. The values related to the mean annual incidence rate (MAF) of the IO and CP limit states for the structures are shown in the Table 7. These values are very useful as quantities that reflect the probabilistic capacity of the entire structure based on earthquake uncertainties.