# Reliability Analysis of Response-Controlled Buildings Using Fragility Curves
## 1 Introduction
[17] used IDA to study the Tehran communications tower with various types of DMs and IMs, concluding that Sa(T\({}_{1}\)) is more efficient than PGA. In addition, during IDA-based seismic fragility analysis, the story drift ratio is also used as the quantitative index to separate the performance levels. The performance-based guidelines established by the Japan Structural Consultant Association (JSCA) [18] can be used to identify structural damage levels based on the story drift ratio. The second important step in performing IDA is the selection of appropriate GMRs possessing a minimum of scatter in their structural response. The selection of a proper suite of GMRs to reliably predict the limit-state capacity of buildings is still challenging due to the lack of a solid framework. Several methodologies for selecting suitable GMRs have been suggested. Most of these studies were looking for GMRs that were well-matched to the target spectrum, including in terms of design, uniform hazard, and conditional mean spectrums. Due to the uncertainty of earthquake excitation, a sufficient number of ground motions should be selected for IDA to accurately assess the seismic performance of the structure, and the selected earthquake records should cover the strongest earthquake action that the structure may suffer in the future. A set of ten to twenty records is usually enough to provide sufficient accuracy in the estimation of seismic demands, assuming a relatively efficient IM, like Sa(T\({}_{1}\)), for mid-rise buildings [19]. Each ground motion record needs to be appropriately scaled for higher intensities to cover the entire range of structural responses by a series of scale factors [13]. Since there is no efficient method to compare the structural performance of damper-equipped building, this paper employs a novel method and performs original work on the reliability analysis of response-controlled buildings using fragility curves. To evaluate and compare the seismic performance and reliability of damper-equipped buildings, this study analyzes the seismic performance of two major damper types (hysteresis and oil dampers) in a 10-story moment-resisting steel structure, and their fragility curves are then compared. Additionally, the efficiency of integrated systems was also investigated by combining the dampers in the building. The building models were analyzed using the frame analysis software STERA 3D [20], developed by one of the authors, and their dynamic responses were obtained. Sa(T\({}_{1}\)) was chosen as the IM since the building models used in this work are the first-mode-dominated structures. On the other hand, the story drift ratio was used as the DM. The story drift ratio is employed as a quantitative measure to distinguish structural performance levels during IDA-based seismic fragility assessments. To properly portray an earthquake scenario, a collection of 20 distinct Japanese GMRs that a building might face during its lifetime was selected. The IDA curves for each model were generated by analyzing the models for all 20 GMRs using the STERA 3D software. From the IDA curves, fragility curves for the story drift of the JSCA damage levels were obtained. Furthermore, energy responses were compared between the buildings with different types of dampers.