## 4 Numerical Results
Graphs similar to the previous ones are plotted in Figure 6, referring to the B7 structure (\(\alpha_{K0}=1200\)). subjected to the Imperial Valley EQ. Specifically, ductility demands at the first level confirm that CM2 CR model is the least conservative among those examined (Figure 6a-c), with percentage reduction of about \(-95.7\%\) and \(-165.5\%\), similar to those observed for the B3 structure. Effects of the vertical component of the Imperial Valley EQ, characterized by high values of spectral acceleration in the range of vibration periods of interest for the selected structure (see Figure 3b and \(T_{1V}\) values in Table 6) are more evident at the mid-span sections at the seventh floor (Figure 6e), where bending moments due to the vertical seismic loads are more important than those due to the horizontal ones. More evident differences among the four HDRB models can be observed by examining the ductility demands of beams and columns provided by the IDAs of the B7 structure with nominal stiffness \(\alpha_{K0}=1200\). As shown in Figure 7 for the Northridge EQ, after an initial overlapping of results the ductility demands take different values depending on the HDRB model used in the IDA. In particular, at the lower storeys the highest and lowest values of ductility demands are obtained by the VEL and CM2 CR models, respectively, with a percentage reduction of about \(-223.2\%\) and \(-528.3\%\) at the end and mid-span section of the beams respectively, while at the top storey the different models provide very close values. To complete the comparison, the results provided the IDA of the B10 structure. Figure 8 shows the ductility demands of beams and columns obtained carrying out the IDA of the test structure with nominal stiffness ratio \(\alpha_{K0}=1200\), subjected to Chi-Chi EQ. These results prove that all the HDRB models lead to comparable values of the ductility demand for all the columns and for all the mid-span sections of the beams while differences between the CM2 CR model and the other models concern the end sections of the beams. Specifically, ductility demands for beams under the Chi-Chi ground motion, characterized by high values of the corresponding pseudo-acceleration (see Figure 3a), are more evident, especially at the lower storeys (Figure 8a,d), while the addition of the vertical component of Chi-Chi ground motion is negligible at the upper storeys (Figure 8g,j). After having analyzed how the CM2 CR model can influence the evaluation of the ductility demands of beams and columns, the influence of this numerical model on the predictions of the seismic response of the HDRBs is investigated in Figure 9.  
Figure 4: Ductility demands of the B3 structure subjected to the Imperial Valley EQ: end sections (**a**,**d**,**g**) and mid-span sections (**b**,**e**,**h**) of beams; end sections (**c**,**f**,**i**) of columns. Figure 5: Response parameters of the base-isolation system for the B3 test structure subjected to the Imperial Valley EQ. (**a–c**) main parameters of the base-isolation systems. Figure 6: Ductility demands of the B7 structure subjected to the Imperial Valley EQ: end sections (**a,d**) and mid-span sections (**b,e**) of beams; end sections (**c,f**) of columns. Figure 7: Ductility demands of the B7 structure subjected to the Northridge EQ: end sections (**a**,**d**,**g**,**l**) and mid-span sections (**b**,**e**,**h**,**m**) of beams; end sections (**c**,**f**,**i**,**n**) of columns. Figure 8: Ductility demands of the B10 structure subjected to the Chi-Chi EQ: end sections (**a**,**d**,**g**,**l**) and mid-span sections (**b**,**e**,**h**,**m**) of beams; end sections (**c**,**f**,**i**,**n**) of columns.