# Reliability Analysis of Response-Controlled Buildings Using Fragility Curves
## 2 IDA Pre-Requirements (Target Building, Dampers, and Input Earthquakes)
### Ground Motion Record (GMR) Selection  
The selection of a proper and adequate suite of GMRs is highly important when conducting the IDA of the building. Japan is located along the subduction zone, with numerous active faults. The target buildings are designed in accordance with Japanese standards, so the collection of 20 distinct Japanese GMRs presented in Table 5 were selected, with a moment magnitude scale ranging from 6 to 9 Mw, and an epicenteral depth ranging from 6 to 66 km, consisting of both near-field and far-field earthquakes. GMRs were collected from different sites to have a wide range of spectral intensity. The acceleration response spectra for all of the GMRs are given in Figure 4. They were used as the input ground acceleration in the longitudinal direction of the building. To obtain the IDA curves of the buildings, analyses were performed by gradually increasing the intensities of GMRs until the required damage levels were obtained.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \multicolumn{4}{c}{**Hysteresis Damper**} & \multicolumn{4}{c}{**Oil Damper**} \\ \hline
**Story** & **Height (H)** & **Damper** & **Force** & **Stiffness** & **Damper** & **Damping** & **Releif** & \\
**Stiffness (K\({}_{\text{D}}\))** & **(K\({}_{\text{D}}\))** & **(Fy)** & **Stiffness** & **Stiffness** (K\({}_{\text{D}}\)) & **(Co)** & **Velocity (V\({}_{\text{r}}\))** & **Damping** \\ \hline  & **m** & **kN/mm** & **kN** & **kN/mm** & **kN-s/mm** & **cm/s** & **Ratio C\({}_{\text{1}}\)/Co** \\ \hline
10 & 4.0 & 16.82 & 112.17 & 0.02 & 27.30 & 5.67 & 38.6 & 0.02 \\
9 & 4.0 & 56.03 & 373.5 & 0.02 & 31.00 & 6.45 & 38.6 & 0.02 \\
8 & 4.0 & 74.52 & 496.83 & 0.02 & 37.92 & 7.88 & 38.6 & 0.02 \\
7 & 4.0 & 96.83 & 645.5 & 0.02 & 42.13 & 8.77 & 38.6 & 0.02 \\
6 & 4.0 & 98.52 & 656.67 & 0.02 & 50.23 & 10.45 & 38.6 & 0.02 \\
5 & 4.0 & 116.65 & 777.67 & 0.02 & 52.70 & 10.95 & 38.6 & 0.02 \\
4 & 4.0 & 124.6 & 830.67 & 0.02 & 56.50 & 11.75 & 38.6 & 0.02 \\
3 & 4.0 & 105.73 & 704.83 & 0.02 & 65.93 & 13.70 & 38.6 & 0.02 \\
2 & 4.0 & 118.15 & 787.67 & 0.02 & 66.02 & 13.72 & 38.6 & 0.02 \\
1 & 6.0 & 67.93 & 679.33 & 0.02 & 48.18 & 10.02 & 57.9 & 0.02 \\ \hline \end{tabular}
\end{table}
Table 4: Technical parameters of hysteresis and oil dampers.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Record Name** & **Depth (km)** & **Magnitude (Mw)** & **Duration (s)** & **PGA (g)** \\ \hline
1 & JP\_2000\_Tottori & 11 & 7.3 & 240 & 0.616 \\
2 & JP\_2011\_Tohoku & 24 & 9 & 300 & 0.572 \\
3 & JP\_2008\_Iwate & 8 & 7.2 & 300 & 0.701 \\
4 & JP\_2007\_Noto & 11 & 6.9 & 300 & 0.864 \\
5 & JP\_1997\_Kagoshima & 8 & 6.3 & 70 & 0.503 \\
6 & JP\_2016\_Kumamoto & 12 & 7.3 & 300 & 0.630 \\
7 & JP\_2003\_Hokkaido & 42 & 8 & 300 & 0.494 \\
8 & JP\_2003\_Miyagi & 42 & 8 & 300 & 0.737 \\
9 & JP\_2005\_Miyagi & 42 & 7.2 & 162 & 0.406 \\
10 & JP\_2018\_Osake & 13 & 6.1 & 124 & 0.812 \\
11 & JP\_2020\_Hachinohe & 35 & 6.3 & 156 & 0.326 \\
12 & JP\_2009\_Shizuoca & 23 & 6.5 & 219 & 0.451 \\
13 & JP\_1995\_Kobe & 17.9 & 6.9 & 50 & 0.630 \\
14 & JP\_2021\_Fukushima & 55 & 7.3 & 300 & 0.528 \\
15 & JP\_2004\_Chuetsu & 13 & 6.8 & 299 & 1.335 \\
16 & JP\_2001\_Gejvo & 51 & 6.4 & 193 & 0.566 \\
17 & JP\_2021\_Miyagi & 59 & 6.9 & 300 & 0.623 \\
18 & JP\_2003\_Hokkaido & 42 & 8 & 300 & 0.414 \\
19 & JP\_2011\_Miyagi & 142 & 7.1 & 193 & 0.428 \\
20 & JP\_2011\_Fukushima & 39 & 7 & 194 & 0.415 \\ \hline \end{tabular}
\end{table}
Table 5: Summary of input earthquake ground motions.