## 2 Rational Range of the Yield Ratio of Isolation System
### Overview of the Prototype Buildings
The layouts of the LRB isolators, the NRB isolators and the NFVDs are schematically presented in Figure 2. The characteristic parameters of all isolators are presented in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **NRB** & **NRB** & **LRB** & **LRB** & **LRB** & **LRB** \\
**900** & **1100** & **900** & **1000** & **1100** & **1200** \\ \hline Notation & N9 & N11 & R9 & R10 & R11 & R12 \\ \hline Effective diameter (mm) & 900 & 1100 & 900 & 1000 & 1100 & 1200 \\ \hline Total rubber thickness (mm) & 176 & 216 & 176 & 197 & 216 & 235 \\ \hline Vertical stiffness (kN/m) & 3,630,000 & 4,519,000 & 4,168,000 & 4,639,000 & 5,550,000 & 5,940,000 \\ \hline Equivalent stiffness at 100\% & 1110 & 1358 & 2070 & 2300 & 2450 & 2600 \\ shear strain (kN/m) & / & / & 1070 & 1190 & 1310 & 1470 \\ \hline Horizontal yield force (kN) & / & / & 238 & 294 & 355 & 410 \\ \hline Rubber shear modulus & \multirow{2}{*}{0.32} & \multirow{2}{*}{0.32} & \multirow{2}{*}{0.32} & \multirow{2}{*}{0.32} & \multirow{2}{*}{0.32} & \multirow{2}{*}{0.32} \\ \cline{1-1} \cline{6-6} \cline{6-6} \cline{6-6} \cline{6-6} \cline{6-6} \cline  
The critical design parameters and indexes of the prototype buildings are listed in Table 2. The fundamental period of the corresponding fixed-base structure is denoted as \(T_{\text{f}}\). The isolation period, \(T_{\text{is}}\), is calculated using the equivalent stiffness of the isolators when the horizontal shear strain of isolator is 100% according to the GB50011-2010 [17]. The horizontal seismic absorbing coefficient, \(\beta\), which indicates the efficiency of the isolation system, is one of the most important indexes in the design of seismically isolated structures. It is defined as the maximum ratio of the shear force of the isolated structure to that of a fixed-base structure in each story subjected to the DBE [17]. For seismically isolated building with NFVDs, \(\beta\) is required to be no more than 0.38 according to the GB50011-2010 [17]. The horizontal seismic absorbing coefficient of C1 and C4 are both 0.36, which satisfy this specification. The MBD under the MCE is another important design index that determines the width of the isolation gap (i.e., \(D_{\text{g}}\)). Specifically, MBD = max{\(\eta_{i}\):\(u_{c}\)}, where \(\eta_{i}\) is the torsion influence coefficient (i.e., a scale factor to consider the effects of torsion) of \(i^{\text{th}}\) isolator with a value of 1.15 for the prototype buildings and \(u_{c}\) is the maximum displacement of the mass center of the isolation system under the MCE [17]. For each isolator, MBD is required to be no more than the smaller of the two values of 0.55 times the effective diameter of the isolator and 3.0 times the total rubber thickness. The MBD of C1 and C4 are both 488 mm as shown in Table 2, which strictly satisfy the specification of the GB50011-2010 [17]. In addition, \(D_{\text{g}}\) is required to be no less than 1.2 times the MBD. As for the prototype buildings, \(D_{\text{g}}\) is 600 mm, which is larger than 1.2 times the MBD (i.e., 585.6 mm). The maximum compressive and tensile stresses of the isolators are also important design indexes for the seismically isolated structures. According to the GB50011-2010 [17], the compressive stress of isolators under gravity load (i.e., \(\sigma_{\text{max}}^{\text{g}}\)) should be no more than 15 MPa. Furthermore, the compressive and tensile stresses of isolators under the MCE (i.e., \(\sigma_{\text{max}}^{\text{p}}\) and \(\sigma_{\text{max}}^{\text{t}}\)) should be no more than 30 MPa and 1 MPa, respectively. The typical results presented in Table 2 indicate that the design of the prototype buildings can meet the abovementioned requirements.