## 3 Results and Discussion
### Target Responses of FBR and BIR
Rows (**a–c**) are the maximum base shear load (\(Q_{o}^{max}\)) normalized by the seismic weight (\(P_{s}\)); (**d–f**) are maximum drift and (**g–i**) are maximum displacement (\(u^{max}\)) of BIR. The parameters \(N_{sl}\) and \(H\) had the greatest influence on the maximum values of the drift and displacement of the top storage level of the rack (Figures 7e,f,h,i and 8e,f,h,i). This is also observed in the scatter plot corresponding to rows of Figures 7d,g and 8d,g, showing how the magnitude of the output variables increased as these parameters increased. The foregoing is explained due to the fact that by increasing either of these two parameters the structure became more slender and, therefore, more flexible and susceptible to greater displacement and deformation. The foregoing is valid for both FBR and BIR, which indicates that flexibility in these types of structures is important to take into consideration in the design. The parameters that are related to flexibility require special attention, being the ones that have the most influence on the response of the system. In the case of the FBR, the are the parameters were \(N_{sl}\) and \(H\). In the case of BIR, in addition to the previous parameters, \(H_{iso}\) was added, which is related to the flexibility of the isolation system. The fact that the parameter \(T_{iso}\) does not show relevant sensitivity in relation to the reduction in demand is highlighted, despite being a parameter directly related to the stiffness of the isolation system. This was due  
Figure 8: Scatterplot, Kolmogorov-Smirnov Statistics (KS) and conditional and unconditional CDFs of the target responses. Rows **(a–c)** are for the maximum base shear load (\(Q_{\phi}^{max}\)) normalized by the seismic weight (\(P_{s}\)); **(d–f)** are for the drift; and **(g–i)** are for the maximum displacement of the top of the FBR (\(u^{max}\) ). to the range of values considered for this parameter (Table 2). In this range, the structure was in the displacement zone of the design spectrum where the deformation demand was constant. This range was chosen to achieve the seismic isolation effect, due to the great flexibility of the racks considered in the analyzes. When observing the results shown in the bands of Figure 7d,g, a tendency to the reduce the floor drifts and the displacement of the isolation level was observed when increasing the \(H_{iso}\). This was because the isolation system became more flexible (as evidenced in Equation (1)). With the above, the fundamental period of the structure moved to the right of the spectrum (Figure 5a) causing the demand for spectral acceleration to decrease. In Figures 7d,g and 8d,g, marked increases are observed in the corresponding responses for high values of the parameter \(H\), with respect to low values of it. This is because as \(H\) increased, the superstructure became more flexible. This was also reflected in the sensitivity of this parameter in both FBRs and BIRs. This parameter is also related to the stability of the structure, since the higher \(H\) was, the less stable the structure was, accentuating the displacements due to second-order effects.