28 F. Weber et al. d2 2 a u4=utot u3 u2 u1 üg üg u1 h3 h4 d1 d4 h1 h2 (ground) h2 h1 (ground) d1 d2 1 3 4 1 2 2 b R4, m4 R1, m1 R2, m2 R2, m2 R1, m1 R3, m3 d3 u2=utot Fig. 4.1 Sketches of triple FP (a) with articulated slider assembly and double FP (b) without articulated slider maximum credible earthquake (MCE), and to exhibit stiffening behavior for earthquakes beyond of MCE to limit the required maximum displacement capacity. This paper investigates if the above mentioned behavior improves the isolation of the structure. 4.2 Friction Pendulums Under Consideration 4.2.1 Triple Friction Pendulum The triple FP consists of the articulated slider assembly with sliding surfaces 2 and 3, the articulated slider in between and the main sliding surfaces 1 and 4 (Fig. 4.1a). The common design is that the effective radii 2 and 3 (Reff 2, Reff 3) are equal and approx. 8 times smaller than the equal effective radii 1 and 4 (Reff 1, Reff 4) that determine the isolation time period of the bearing Tiso D2 sReff 1 CReff 4 g (4.1) The friction coefficients 2 and 3 are usually selected to be small in the range of 1.5–2% while 1 is designed to produce medium friction around 3–5% and 4 high friction in the region of 8–11%. The restrainers on sliding surfaces 2 and 3 are required to initiate sliding on surfaces 1 and 4 and consequently always included in the triple FP. In contrast, the restrainers on surfaces 1 and 4 are not always included but are needed when the intended stiffening behavior due to sliding regime V for earthquakes beyond of MCE is desired and when the structural engineer specifies that the bearing must include end stoppers. For the first study of this paper the triple FP is designed according to the published design [1, 2] which represents a mock-up triple FP: Reff 1 DReff 4 D0.435m, Reff 2 DReff 3 D0.053m, 1 D3.1%, 2 D 3 D1.75%and 4 D11.4% where the friction values represent average values identified from testing [2]. The displacement capacities are d1 Dd4D0.064 m and d2 Dd3 D0.019 m that yield the total displacement capacity dtot D0.166 m. For the second study of this paper the parameters of the triple FP are optimized for minimum absolute structural acceleration which is described in the penultimate section. 4.2.2 Double Friction Pendulum The conventional, i.e. non-adaptive, double FP is composed of two bearing plates with equal effective radii Reff 1 DReff 2 and friction coefficients 1 and 2 that must be equal because the relative motions on surfaces 1 (u1) and 2 (u2) are coupled due to the non-articulated slider (Fig. 4.1b). For the first study the isolation time period given by the sum (Reff 1 CReff 2) is equal to that of the triple FP (1), the equal friction coefficients 1 D 2 are tuned by trial and error and dtot is the same as for the mock-up triple FP. For the second study of this paper a double FP with articulated slider is assumed which allows optimizing the double FP by different 1 and 2.
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