## 2 Rational Range of the Yield Ratio of Isolation System
### Rational Value of the Yield Ratio  
To identify the rational yield ratio for the RC frame-core tube tall buildings located in high seismic regions, the following two principles are followed: (1) the horizontal seismic absorbing coefficient, \(\beta\), is required to be no more than 0.38 as specified in the GB50011-2010 [17]; (2) the MBD under the MCE should not exceed 540 mm. In consideration of the difficulties in design of such seismically isolated tall buildings, the committee recommended that the limit width of the isolation gap could increase to 650 mm, which meant that the MBD could raise to approximate 540 mm (i.e., 650/1.2 \(\approx\) 540 mm).  
The values of \(\beta\) and MBD for the 28 study cases with different yield ratios and different seismically isolated schemes are calculated and presented in Figures 4-7. The following conclusions can be drawn:  
(1) The recommended upper limit of the yield ratio is 3% and the upper limit is determined by the \(\beta\). When the yield ratio is no more than 3%, the value of \(\beta\) of all 28 study cases do not exceed 0.38, which means that the expected efficiency of the isolation system is successfully achieved and 3% can be regarded as the upper limit. In addition, \(\beta\) decreases with the decrease in yield ratio, indicating that a lower yield ratio can achieve a better isolation efficiency. However, the value of \(\beta\) becomes steady when the yield ratio decreases to 2%, which means the continuous decrease of the yield ratio below 2% cannot lead to better isolation efficiency.  
(2) The upper limit of the yield ratio can increase to a certain level when the building height is smaller than 80 m or the CBI scheme is adopted. The upper limit of the yield ratios of C1 with the height of 79.2 m (3% for the PBI scheme) is lower than that of C4 with the height of 65.8 m (3.5% for the PBI scheme), indicating a higher upper limit of the yield ratio can be adopted for a building with a height lower than approximately 80 m. In addition, when the yield ratios of the PBI scheme and the CBI scheme both reached 3% for C1, the value of \(\beta\) for the CBI scheme is lower than that for the PBI scheme, indicating that a larger value of the yield ratio can be adopted for the CBI scheme.  
(3) The recommended lower limit of the yield ratio is 2%. When the yield ratio is no less than 2%, the MBD under the MCE are all lower than 540 mm, which satisfy the requirements specified by the limit value of the isolation gap. The MBD generally decreases with the increase of the yield ratio, indicating that a higher yield ratio can better control the MBD, thereby satisfying the demand of the isolation gap. In addition, with the increase of the height of the building, the lower limit of the yield ratio can adopt a smaller value (e.g., 1.8% for C1 with the PBI scheme). However, the isolation efficiency becomes steady when the yield ratio decreases to 2% as mentioned above, while  
Figure 3: Response spectra of design ground motions.  
Based on the above discussion, it can be concluded that the upper and lower limits of the yield ratio are determined according to the requirements of the horizontal seismic absorbing coefficient and the width of the isolation gap, respectively. A yield ratio in the range of 2-3% is considered rational for the seismically isolated RC frame-core tube tall buildings.