## 3 Layout and Design of the Test Structures  
The seismic response of r.c. framed buildings can be notably influenced by the nonlinear behavior of the bearings used in the base-isolation system. These devices must \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **Horizontal, Vertical and Rotational Stiffness** \\ \hline VEL & \(K_{H0}\) & \(K_{V0}\) & \(K_{\Theta 0}\) \\ CM1 & \(K_{H0}\cdot\mu_{H1}\) & \(K_{V0}\cdot\mu_{V1}\) & \(K_{\Theta 0}\) \\ CM1C & \(K_{H0}\cdot\mu_{H1}\) & \(K_{V0}\cdot\mu_{V2}\) & \(K_{\Theta 0}\) \\ CM2 CR & \(K_{H0}\cdot\mu_{H1}\cdot\mu_{H2}\) & \(K_{V0}\cdot\mu_{V2}\) & \(K_{\Theta 0}\cdot\mu_{\Theta 1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Stiffnesses parameters of the elastomeric bearing in the different models. retain their ability to function also when subjected to nonlinear effects including those due to the tensile axial loads resulting from the combined action of vertical and seismic loads (i.e., cavitation, post-cavitation and buckling). To identify and study the consequences of such phenomena and estimate their importance in comparison with other nonlinear effects, three office buildings with three-(B3), seven-(B7) and ten-storeys (B10) are considered below. Their r.c. framed structures include masonry infill walls located along the perimeter, regularly distributed in elevation. In particular, the frames along X direction have two lateral bays of 4 m and two central bays of 5 m, those along Y direction contain two bays of 5 m (Figure 2a) while the first floor and upper floors are of 4 m and 3 m in height, respectively (Figure 2b). The superstructures of the above buildings are designed in line with the Italian seismic code NTC18 [6]. To this end, a live load equal to 2 kN/m\({}^{2}\) for all the floors and a gravity load equal to 4.98 kN/m\({}^{2}\), 6.28 kN/m\({}^{2}\) and 6.68 kN/m\({}^{2}\) for the top, intermediate and base-isolated floors, respectively, are considered; an average weight of about 2.7 kN/m\({}^{2}\) for the masonry infill walls located along the exterior perimeter is also assumed. Seismic loads are evaluated on the basis of the masses summarized in Table 2 and assuming: elastic response of the superstructure (behaviour q\({}_{H}\) = 1.0); medium-dense subsoil (type class C); high-risk seismic zone, with peak ground acceleration in the horizontal direction \(PGA_{H}\) = 0.201 g, at the life-safety (LS) limit state, and \(PGA_{H}\) = 0.264 g, at the collapse prevention (CP) limit state. Moreover, a yield strength of 375 MPa for the steel and a cylindrical compressive strength of 25 MPa for the concrete are assumed to design both the beams and columns of the test structures, whose geometric dimensions are summarized in Tables 3-5. The base-isolation system of the test structures is made up of fifteen (i.e., \(n_{b}\) = 15) identical high-damping-rubber-bearings (HDRBs). The first step in their design consists of evaluating the horizontal and vertical stiffnesses (\(K_{H0}\), \(K_{V0}\)) of the single elastomeric device considering the same fundamental vibration period in the horizontal direction (i.e., \(T_{1H}\) = 2.5 s) and selecting a nominal stiffness ratio \(\alpha_{K\ 0}\)= \(K_{H0}/K_{V0}\) (i.e., 400, 1200, 2400). To this end the following formulas can be used  
\[K_{H0}=\frac{m_{tot}}{n_{b}}\bigg{(}\frac{2\pi}{T_{1H}}\bigg{)}^{2},\qquad K_{ V0}=\alpha_{K0}K_{H0} \tag{28}\]  
Figure 2: Three-, seven- and ten-storey structures—(a) plan; (b) elevation (dimensions in cm).