## 3 Design Method for Seismically Isolated RC Frame-Core Tube Tall Building
### Proposed High-Efficiency Design Method  
According to the above requirements, solutions for the three critical problems are firstly proposed here. (1) For the appropriate \(T_{\text{f}}\), a statistical regression analysis is conducted based on the seismically isolated tall buildings designed by the authors, as shown in Figure 9. An equation, which describesthe relationship between the height and \(T_{\text{f}}\), is obtained as shown in Equation (1). Here, \(H\) represents the total height of the structure. \[T_{\text{f}}=0.193H^{0.5} \tag{1}\]  
(2) A certain extent of tensile stress may be observed for the isolators under the columns due to the overturning effect, a relatively large \(\sigma\)s is therefore usually adopted for these isolators. However, a \(\sigma\)s with excessive value is also not recommended because it may lead to a large \(\sigma_{\text{max}}^{\text{c}}\), which may exceed the specified limit value. Based on the design experience, the \(\sigma\)s is recommended to be approximately 10-12 MPa for the isolators under the columns. It is notable that the stress of the isolators under the corner of the core tube when subjected to MCE is lower than this of the isolators under the columns. Hence, a lower \(\sigma\)s can be adopted for such isolators and a \(\sigma\)s with the value ranged from 8 to 10 MPa is recommended for the isolators under the corner of the core tube, which is also based on the design experience. (3) The rational range of the yield ratio has been investigated in Section 2 and has been recommended in the range of 2-3%. To avoid the torsion effect, the LRB isolators are recommended for the columns and the corner of the core tube in the RC frame-core tube tall buildings. If these LRB isolators can lead to an acceptable yield ratio, the requirements of \(\beta\), \(\sigma_{\text{max}}^{\text{P}}\) and \(\sigma_{\text{max}}^{\text{t}}\) are considered easily satisfied. Based on the above discussion, a new high-efficiency design method, as shown in Figure 10, is proposed for the seismically isolated RC frame-core tube tall buildings. The entire design procedure is presented as follows:  
(1) Design of the superstructure. According to the height of the building, an appropriate value of \(T_{\text{f}}\) is calculated using Equation (1). Then, the superstructure is designed as a fixed-base structure with one-degree lower seismic intensity and with a \(T_{\text{f}}\) value approximate to the calculated value. (2) Selection of isolator numbers and sizes. Gravity analysis is conducted to calculate the axial forces under the columns and the shear walls. Then, according to the recommended compressive stress for different isolators, the demand for the area of the corresponding isolators can be calculated and appropriate numbers and sizes of the isolators can be selected. (3) Selection of the isolator types. LRB isolators are adopted for the isolators under the columns and the corner of the core tube. Then, the yield ratio is calculated. If the calculated yield ratio is lower than 2%, more LRB isolators are recommended to be adopted under the external wall. If the calculated yield ratio is higher than 3%, the LRB isolators under the corner of the core tube can be reduced first, followed by those under the columns. (4) Calculation of the design indexes. Figure 9: Relationship between the height and fundamental period of fixed-base structure. Modal analysis is conducted firstly to calculate the \(T_{\text{is}}\) and appropriate ground motions are selected. Based on these, THAs are performed to calculate the critical design indexes. (5) Validation and/or modification of isolation system. Because of the rational yield ratio adopted, \(\beta\), \(\sigma_{\text{max}}^{\text{P}}\) and \(\sigma_{\text{max}}^{\text{t}}\) can usually satisfy the requirements. If not, only limit modifications of the isolators are required. Subsequently, the MBD under the MCE is examined. If the MBD exceeds the limit value, the NFVDs are recommended to be introduced in the isolation system.