# Seismic Performance Evaluation of Steel Buildings with Oil Dampers Using Capacity Spectrum Method
## 1 Introduction  
The capacity spectrum method (CSM) is a practical tool to evaluate the seismic performance of buildings using a response spectrum and an equivalent linear system. Since its original development by [PERSON] in 1975, it has been modified and adopted by different organizations [1]. For instance, in 1980, the Applied Technology Council (ATC) published guidelines to evaluate building performance using the CSM concept [2]. Similarly, in 1998, the Building Standard Law of Japan adopted the concept of CSM as one of the procedures for the seismic design of buildings [3]. Likewise, many researchers have assessed the accuracy of the method and applied it over a wide range of structural systems [4]. Consequently, a number of modifications have been proposed to improve the application of CSM depending on the structural type of buildings. Generally, the seismic assessment and design of structures equipped with damping devices require nonlinear time history analysis (THA), which is highly time-consuming. Some straightforward procedures have been proposed by researchers to evaluate the seismic performance of passively controlled buildings. [PERSON] and [PERSON] [5] developed a CSM-based procedure to estimate the amount of supplemental viscous damping, for a multi-story building, required to reduce roof displacement in the range of pre-defined target displacement. A similar concept is further illustrated by [PERSON] et al. [6], and [PERSON] and [PERSON] [7]. The study conducted by [PERSON] et al. [7, 8] introduced an improved version ofCSM to estimate the number of metallic dampers under earthquake loads. In the cases of the buildings with viscoelastic dampers, [PERSON] et al. [9] employed CSM to analyze the performance of the passively controlled buildings. [PERSON] and [PERSON] [10] compared shaking table test results of the scaled specimens equipped with hysteretic dampers and those obtained by the improved CSM procedures, and it was reported that the improved CSM had the potential to estimate maximum displacement with acceptable accuracy. [PERSON] et al. [11] discussed the optimal distribution of steel dampers along the height of the structures using the CSM procedure. [PERSON] et al. [12] proposed an alternative CSM method using the constant ductility inelastic spectra to estimate the seismic performance of structures with viscous dampers. [PERSON] [13] incorporated the CSM method to investigate the seismic risk of buildings in a seismically active region using capacity curves of individual buildings. Furthermore, the effectiveness of CSM to design and evaluate the retrofitting of RC buildings is extensively discussed and reported by researchers [14; 15]. [PERSON] et al. [16] proposed the following two simplified procedures, similar to CSM: the equivalent lateral force (ELF) and response spectrum procedures (RSP), which are adopted in the 2000 NEHRP and ASCE7 provisions for the design of passively controlled buildings. In the ELF method, the contributions of the first mode and residual mode are incorporated, whereas in the RSP method, the contributions of higher modes are also considered to estimate the response of buildings with damping devices. The oil damper device (OD) is widely used due to its excellent performance, including its durability of aging, durability under repeated loading cycles, low temperature dependence, high energy dissipation capacity, and stable mechanical properties [17; 18; 19; 20]. The bilinear-type oil damper, which has a relief valve and reduces the rate of increase in damping force when the relief velocity is exceeded, is commonly used in Japan, especially for high-rise buildings. [PERSON] et al. [21; 22] introduced a design procedure to minimize the story drift and acceleration of high-rise buildings by optimizing the OD relief force distribution along the height of the building. [PERSON] et al. [23] reported about the contribution of OD in a real size five-story steel building, tested on the E-defense shaking table in Japan. [PERSON] et al.