32 F. Weber et al. philosophy of the triple FP the effective radii Reff 2 DReff 3 are designed to be smaller thanReff 1 DReff 4 so that sliding regime II is activated without force step due to triggered restrainers on concave plates 1 and 3. In order to comply with this design methodology, Reff 2 DReff 3 are selected to be eight times smaller than Reff 1 DReff 4 as Reff 1/Reff 2 D8 is in accordance to the design given in [1, 2]. The displacement capacities d2 Dd3 are scaled by approx. the same factor as the effective radii which yields d2 Dd3 D0.07m. 4.6.4 Restrainers 1 and 4 The previous study demonstrated that the activation of sliding regime V due to restrainers 1 and 4 worsens the isolation of the structure dramatically. The previous study further demonstrated that the isolation deteriorates completely when the full displacement capacity of the bearing is used, i.e. all restrainers are triggered. Therefore, restrainers 1 and 4 are omitted for the optimization of the triple FP. 4.6.5 Optimization Parameters Due to the definition of the isolation time period of 3.5 s whereby Reff 1 and Reff 4 of the triple FP are given, due to the design of the articulated slider assembly of the triple FP which is in agreement with the common design philosophy of the triple FP and due to the neglect of restrainers 1 and 4 of the triple FP in order to avoid bad isolation of the structure due to sliding regime V and when all restrainers are triggered the triple FP can be optimized for minimum acceleration response of the structure (2) by variation of the friction coefficients 1 and 4. Similarly, the double FP with same isolation time period as the triple FP and without end stoppers on sliding surfaces 1 and 2 is optimized for minimum acceleration response of the structure (2) by variation of the friction coefficients 1 and 2. As 1 and 2 can be different a double FP with articulated slider is assumed. 4.6.6 Optimization Results Exemplarily for all optimization cases, i.e. four earthquakes scaled to three PGAopt, two optimization results are plotted in Figs. 4.4 and 4.5. The following can be observed: • The optimal friction coefficients of the triple and double FPs and the resulting absolute structural acceleration are very similar. • The optimal friction coefficients can be different (El Centro NS, Fig. 4.4) or equal (Loma Prieta, Fig. 4.5); if they are different it is not relevant which one is higher (valid for triple and double FPs). 4.6.7 Isolation Performance of Optimized Triple FP The isolation performances of the optimized triple and double FPs are computed for the El Centro NS, the Kobe, the Loma Prieta and the Northridge accelerograms that are scaled to PGAs ranging from 0.25 m/s2 up to 150% of PGAopt assuming that the FPs are optimized at the PGA corresponding to DBE and that the PGA of MCE is around 150% of the PGA of DBE. The isolation performances accompanied by the total bearing displacement as an important economical parameter are depicted in Figs. 4.6, 4.7, 4.8, and 4.9 for PGAopt D5 m/s 2; showing also the results due to the optimizations at 2.5 and 7.5m/s2 is not possible due to the limited number of pages of the manuscript but the results are qualitatively similar. It is seen that the optimized triple and double FPs approximately yield the same absolute structural accelerations and total bearing displacements. This outcome is explained by the fact that the triple FP mutates to a double FP by the optimization which
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