# Seismic Response Effect on Base-Isolated Rigid Structures by Mass Eccentricity in Nuclear Plants
## 3 Sensitivity Analysis of Base Isolation Response Due to Mass Eccentricity
### Results of the Sensitivity Analysis of Seismic Response by Mass Eccentricity
However, beyond 10% eccentricity, the average acceleration in the X direction starts to decrease significantly, reaching a minimum acceleration that is about 20% lower than the initial value at around 50% eccentricity. Beyond 50% eccentricity, the X-direction acceleration gradually increases again. In contrast, the Y-direction average acceleration shows a linear response increase of up to about 15% as eccentricity increases. The eccentricity sensitivity of horizontal acceleration response at the center of gravity is shown in Figure 6.  
In order to examine the changes in more detail, we checked the acceleration responses at the four corner points from A1 to A4, which correspond to the corner positions of the upper structure, as shown in Figure 3. Since A2 and A1 are symmetrical with respect to the Y axis, we omitted some of them and present them in Figure 7.  
The acceleration response in the Y direction, which serves as the reference for mass eccentricity, exhibits the same response characteristics as the average acceleration in Figure 8. However, as seen in Figure 7a, as eccentricity increases, the X-direction acceleration at point A2, where the center of mass gets closer, initially increases due to the eccentricity of the mass, but then linearly decreases after about 20% eccentricity. This is because, as indicated by the earlier modal analysis results, as eccentricity increases, the contribution of the torsional mode rises, leading to an initial increase in acceleration due to the combined behavior of translation and torsion modes. Figure 5: Seismic inputs for analysis. (**a**) Acceleration response spectra; (**b**) Acceleration time histories for 0.3 g DRS. Figure 6: Eccentricity sensitivity of horizontal acceleration at the mass center. However, as shown in Figure 7b, as eccentricity increases, the change in the center of mass's position due to the change in the rotational center position results in variations in acceleration values at specific points. Due to this phenomenon, the X-direction acceleration responses at A2 and A4 exhibit opposite characteristics. Therefore, during the seismic design of structures with mass eccentricity, it is important to pay attention to such peak response characteristics at around 20% eccentricity depending on the upper structure's position. Next, the displacement sensitivity to mass eccentricity during seismic responses is examined. As shown in Figure 8, the Y-directional displacement response exhibits a linear increase of up to 25% as eccentricity increases. In contrast, the X-directional displacement initially shows little change in response, but starting from around 50% eccentricity, it exhibits an approximately 30% increase. This indicates that special attention is required when dealing with significant eccentricities, particularly in the case of large eccentricities, in the context of X-direction displacement. The sensitivity of displacement response for points A2 and A4, as shown in Figure 9, indicates that, as eccentricity increases, there is an increase in the influence of torsional behavior, leading to an increase in displacement response. In other words, as eccentricity increases, the response at point A2, where the mass center is closer, increases due to the influence of torsion behavior. Conversely, the response at point A4, which is farther from the mass center, decreases in overall response due to the out-of-phase effect of increased X-direction displacement. For instance, at eccentricity of around 20%, the maximum displacement response can be observed to increase by approximately 20% or decrease by nearly 30%, depending on the location of the upper structure. Figure 8: Eccentricity sensitivity of horizontal displacement at the mass center. Figure 7: Eccentricity sensitivity of horizontal acceleration at A2 and A4 points. (**a**) A2 Point; (**b**) A4 Point.