# Reliability Analysis of Response-Controlled Buildings Using Fragility Curves
## 2 IDA Pre-Requirements (Target Building, Dampers, and Input Earthquakes)  
### Target Buildings Description and Configurations  
A 10-story moment-resisting steel building was selected from the JSSI theme structures [21] to examine the performance of dampers. The building was designed with two different steel sections, namely the Trimmed Section (TS) and the Conventional Section (CS). The buildings have a rigid frame structure in both directions. A description of building models with different damper arrangements is given in Table 1. The columns of the buildings have a square box-shaped cross-section, while the beams are H-shaped. The dimensions of the structural columns listed in Table 2 represent the height, width, and thickness (H \(\times\) B \(\times\) t) of the column sections, while the dimensions listed in Table 3 represent the beam height, flange width, web thickness, and flange thickness (H \(\times\) B \(\times\) t\({}_{1}\)\(\times\) t\({}_{2}\)) of the structural beams, respectively. The TS building was deliberately designed to be weaker than the CS building to see the effect of the dampers. The steel was SN490B, which has yield and tensile strengths of 325 and 490 MPa, respectively [21]. The building models are first-mode-dominated structures, and the vibration effects of the other modes are minor, since more than 80% of mass participation is from the first mode of the buildings, as shown in Table 1. The STERA 3D software was used to model and analyze the target buildings. The beam element was modeled as a nonlinear bending spring, while the column element was modeled as a nonlinear vertical spring [22]. The analysis was performed in the longitudinal direction of the buildings only; hence, hysteresis and oil dampers were arranged in the longitudinal direction of the TS building, as shown in Figure 1. The top floor has dampers only in the center. The plan, elevation, and damper arrangement are shown in Figure 1a, while Figure 1b represents the 3D model of the building. The dimensions of structural columns and beams are summarized in Tables 2 and 3, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Concise Name** & **Model Description** & **Fundamental Period (T\({}_{1}\))** & **Mass Participation of First Mode** \\ \hline
10F\_TS\_FM & 10F TS Frame Model & 2.018 s & 82.8\% \\
10F\_TS\_HM & 10F TS Hysteresis Model & 1.356 s & 80\% \\
10F\_TS\_OM & 10F TS Oil Model & 2.018 s & 82.8\% \\
10F\_TS\_HOHM & 10F TS Hysteresis-Oil-Hysteresis Model & 1.501 s & 80.5\% \\
10F\_TS\_OHOHM & 10F TS Oil-Hysteresis-Oil Model & 1.685 s & 81.7\% \\
10F\_CS\_FM & 10F CS Frame Model & 1.323 s & 84.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of building models with different damper arrangements. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Story** & **Interior Column** & **Exterior Column** & **Corner Column** \\ \hline  & **TS** & **CS** & **TS** & **CS** & **TS** & **CS** \\  & **(H \(\times\) B \(\times\) t)** & **(H \(\times\) B \(\times\) t)** & **(H \(\times\) B \(\times\) t)** & **(H \(\times\) B \(\times\) t)** & **(H \(\times\) B \(\times\) t)** & **(H \(\times\) B \(\times\) t)** \\ \hline
9–10 & 350 \(\times\) 350 \(\times\)  
Figure 1: Target building (dimensions in mm): (a) plan, elevation, and damper configuration, (b) 3D model.