PSI - Issue 78

Laura Ragni et al. / Procedia Structural Integrity 78 (2026) 2094–2101

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where A is = 0.2827 m is = 0.6 m), h is = 0.184 m and the shear modulus G , assumed to be constant in the linear model, has been calculated for each tests as a function of the maximum shear strain ( γ max ) by means of the following expression: (2) The viscous constant of the Kelvin model of the single bearing ( c 0,is ) has been estimated from the equivalent damping ratio of the HCC test, that is ξ = 0.14 regardless the shear deformation, by using the following formula: 2 (corresponding to D G = 0.434∙ γ max (-0.45)

c 0,is =2 ξ k n,is / ω

(3)

where ω=2π f with f =0.5 Hz.

Fig. 4. Horizontal Cyclic Characterization (HCC) tests at different amplitudes (a) and comparison with the One Side Ramp (OSR) test

Differently, parameters of the Maxwell model for a single bearing were derived from LC tests. Specifically, the stiffness k 1,is was calculated as the ratio of the limit (elastic) force to the corresponding displacement, while the damping coefficient c 1,is was obtained by fitting the force-time curve. Although the linear model cannot capture force peaks and valleys, it still provides a good approximation of experimental results, making it a simple and effective tool for interpreting in-situ tests (Fig.5a). The difference between the nominal stiffness and the Maxwell model stiffness yields the Kelvin model stiffness k 0,is . Parameters for the bearing model are listed in Table 2, including maximum shear strain and shear modulus. Numerical simulations of HCC test cycles (Fig. 5b) show that while the model doesn't perfectly replicate the cycle shapes, the energy dissipation difference is only about 10%.

Fig. 5. Numerical simulation of the Lateral Capacity (LC) test (a) and 3 th cycle of the HCC test at the largest amplitude (b) Table 2: Model parameters of a single HDR bearing

k 1,is [kN/m]

c 1,is [kNs/m]

k 0,is [kN/m]

c 0 ,is [kNs/m]

G ( γ is ) [N/mm 2 ]

γ is [-]

2.18 0.307 150 840 323

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