PSI - Issue 44

Marco Furinghetti et al. / Procedia Structural Integrity 44 (2023) 1490–1497 Marco Furinghetti et al. / Structural Integrity Procedia 00 (2022) 000 – 000

1493

4

equivalent radius of curvature is then 3080mm. The implemented circular sliding pads have a diameter equal to 160mm, and the maximum displacement capacity is equal to 325mm. The friction coefficient for the applied vertical load (850 kN) can be considered constantly equal to 8.5% . Thus, aiming at obtaining approximately same values through the fast design rule, the global performance point has been determined, by considering 2.2 sec and 40% as design period and equivalent viscous damping respectively. 4. Experimental hybrid simulations Aiming at evaluating the effectiveness of the adopted fast-design rule, the outcomes of an experimental hybrid testing campaign performed at the Laboratory of the EUCENTRE Foundation in Pavia (Italy) have been analyzed. According to the defined hybrid simulation framework, the Bearing Tester System has been used, for the stepwise evaluation of the response of the full-scale physical device, which has been considered representative of the whole isolation system of the case study structure. On the other hand, the building has been numerically modeled within the hybrid simulation algorithm, by considering a Multi Degree of Freedom (MDOF) oscillator. More specifically, a single horizontal translational degree of freedom has been defined at each story location of the building, referred to the ground location. Characteristics of the MDOF oscillator, in terms of mass, stiffness and damping matrices have been computed by adopting an ad hoc static condensation procedure (Furinghetti et al. 2020). In agreement with the aforementioned theoretical background, the dynamic system implemented in the hybrid simulation algorithm is defined as follows: ̿ ∙ ( ̈ 0 ̈ 1 ̈ 2 ̈ ⋮ 6 ) + ̿ ∙ ( ̇ 0 ̇ 1 ̇ 2 ̇ ⋮ 6 ) + ̿ ∙ ( 0 1 2 ⋮ 6 ) + 〈 〉 ∙ ∙ ( 1 0 0 0 ⋮ ) = − ̿ ∙ ( 1 1 1 1 ⋮ ) ∙ ̈ (1) Being:  ̿ , ̿ and ̿ the mass, damping and stiffness matrices respectively of the whole base-isolated system;  the relative translational degrees of freedom located at each level of the building with respect to ground;  ̈ the considered ground motion (Furinghetti et al. 2020, Iervolino et al 2009);  the number of implemented isolation bearings;  〈 〉 the experimental force of the physical sub-structuring, that is the DCSS device. The damping matrix has been computed by considering a multi-modal damping, with 5% for all vibration modes, and no damping for the first, second and third modes. Within the experimental hybrid simulations, the stepwise interaction between the physical and numerical substructures (namely the full-scale physical device and the numerical MDOF oscillator respectively) leads to the computation of the displacement response at all levels of the systems, as a consequence of the applied ground motions. In addition, experimental results have been compared to the related quantities returned by the same MDOF model, by numerically modeling the isolation force response, in agreement with the following hysteretic rule: 〈 〉 = ( 0 + ( ̇ 0 ) ∙ ℎ ( ̇ 0 )) (2) Being: