## 2 Materials and Methods  
Selective racks were analyzed in this research, as these are the most commonly used in the industry [1]. Two formulations or structural models were made with different support conditions for the racks: (i) fixed at the base, and (ii) with base-isolation. In these formulations, the Euler-Bernoulli stiffness matrix and consistent mass matrix of a 3D bar element with 12 degrees of freedom (DoF) were considered for beams and columns. The elements of the lattice system of the rack in the cross aisle direction were considered as 2 DoF axial-bar-type elements. These were located between the columns to provide lateral stiffness in the cross aisle direction (Figure 1; Table 1). On each storage level of the racks, two pallets (1 ton each) were installed on the beams. Racks of between 2 and 6 load level (4 up to 12 pallets) were analyzed. Each level was modeled as a rigid diaphragm with 3 DoF, plus one vertical DoF at each beam-column connection node. The masses of the pallets were added as a 2 ton translational inertia in both horizontal directions plus the corresponding rotational inertia of mass around the vertical axis. Regarding the vertical DoFs, the mass of the pallets was considered as load and not as inertia. The analysis contemplates the incorporation of geometric stiffness matrices in the column and diagonal elements of the lattice, in the cross-aisle direction. This allows for the characterization of the geometric non-linear behavior and the P-\(\Delta\) effect of the earthquake on the racks. In the last decade, investigations have been carried out whose focus is on the non-linear behavior of beam-column connections, [26; 27; 28; 29; 30]. The dynamic response of this type of fixed base structures is influenced by the non-linearity of the connections; however, the focus of this research is on the classification of the design parameters of the rack and the isolation system. This was done according to the influence of said parameters in reducing the seismic demand on the rack. The relevance of this research is in the sensitivity analysis that requires the study of multiple scenarios. These increase exponentially as the number of parameters considered in the analysis increases, as well as increasing the numerical complexity of the mathematical models. The enormous computational time involved in incorporating non-linear plastic connections would make sensitivity analysis impractical in this case, given the number of parameters already considered. Due to the above, non-linear plastic behavior models were not implemented in the beam-column connections of the racks. Experimental research has been carried out on scale models of the BIKD and functional prototypes of low strength and stiffness [13]. In recent months, the researchers co-authoring the present article have planned to conduct experimental trials of base isolated racks at 1:1 scale from 2 up to 6 storage levels. The BIKD to be used in the tested racks were designed and built with an adjustable height. We have decided not to mention that cost, as we know that such a small-scale production is not representative of the cost of the mass-produced device. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Profile** & **A [cm2]** & **I\({}_{\mathbf{x}}\) [cm4]** & **I\({}_{\mathbf{y}}\) [cm4]** & **r\({}_{\mathbf{x}}\) [cm]** & **r\({}_{\mathbf{y}}\) [cm]** & **C\({}_{\mathbf{w}}\) [cm6]** \\ \hline TX 100 \(\times\) 105 \(\times\) 3 & 9.95 & 138.88 & 135.00 & 3.68 & 3.74 & 3740 \\ TC 100 \(\times\) 50 \(\times\) 2 & 8.13 & 122.49 & 31.21 & 38.82 & 19.59 & 461.3 \\ CA 45 \(\times\) 22 \(\times\) 2 & 1.78 & 5.2 & 1.02 & 1.71 & 0.76 & 4.562 \\ C 58 \(\times\) 22 \(\times\) 2 & 1.99 & 9.72 & 1.11 & 2.21 & 0.75 & 5.882 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the cross-sections of the structural elements of the racks. Figure 1: Basic structuring of each level of the racks analyzed.