# Seismic Response Effect on Base-Isolated Rigid Structures by Mass Eccentricity in Nuclear Plants
## 2 Analysis of Seismic Response in Base-Isolated Mass-Eccentric Structures
### Analysis of Design Requirements for Mass Eccentricity  
When referring to the Building Seismic Design Standards, KDS 41-17, provided by the Ministry of Land, Infrastructure, and Transport [9], if the maximum floor displacement, considering accidental eccentricity in one direction, is greater than 1.2 times the average floor displacement at both ends of a structure orthogonal to that direction, it is considered to be a torsionally irregular structure. Therefore, for torsionally irregular buildings, the torsional amplification factor \(A_{x}\) should be multiplied by the accidental torsional moment at each floor for calculation purposes.  
\[A_{x}=\left(\frac{\delta_{max}}{1.2\delta_{avg}}\right)^{2} \tag{1}\]  
(\(\delta_{max}\): Maximum displacement at \(x\)-th floor level, \(\delta_{avg}\): Average displacement at each corner of \(x\)-th floor level).  
In addition, according to the Safety Review Guide for Pressurized Water Reactors provided by the Korea Institute of Nuclear Safety (KINS) [10], structures, systems, and components classified as Seismic Category I should consider torsional effects during seismic analysis. In particular, the possibility of accidental torsion should also be considered. If the influence of eccentric mass on torsion during seismic analysis is deemed significant, the eccentric mass and its eccentricity should be included in the analysis model.  
Japan's JNES 2013 [11], concerning design policies for base-isolated structures, suggests that, for base-isolated structures, when the distance between the stiffness center and the mass center is significant, torsional behavior during an earthquake may occur, resulting in increased relative displacement. This consideration is due to the potential for eccentricity to cause structural damage through increased stress and potential collisions with nearby structures. Therefore, during seismic design, efforts should be made to place the stiffness center and mass center as close as possible. If there is a significant distance between the stiffness and mass centers, dynamic behavior characteristics and their impact should be assessed through analysis or testing, and appropriate measures should be taken.  
Furthermore, the American Society of Civil Engineers (ASCE) 4-16 [12], which provides seismic analysis guidelines for safety-related nuclear structures, requires the appropriate representation of the structure's mass center and stiffness center positions to explain the torsional effect caused by eccentricity. Therefore, in the case of structures where the mass center and stiffness center do not coincide, measures should be taken to ensure that the torsional stiffness and mass moment of inertia are considered in light of eccentricity. In summary, both domestic and international seismic design requirements emphasize the importance of conducting detailed analyses to understand dynamic characteristics and assess the impact of eccentricity on structural response when structures have significant levels of stiffness or mass eccentricity. Taking necessary actions in the design phase based on these assessments is crucial.