PSI - Issue 78

Danilo D’Angela et al. / Procedia Structural Integrity 78 (2026) 1617–1624

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Fig. 1. Rigid block model (Housner, 1963). Equation (1) reports the motion equation in terms of rotational acceleration time history ( θ(t)̈ ), where p defines the block frequency parameter, ü g (t) is the input rotational acceleration at the base, and g is the gravity acceleration constant; p is defined as depicted in Equation (2). θ̈(t) =−p 2 {sin [α sgn(θ(t)) − θ(t)] + ü g g(t) cos[α sgn(θ(t)) − θ(t)]} (1) p=√ 4 3 R g ; (2) The motion equation was solved numerically through the Runge-Kutta ordinary differential equation (ODE) solver, assuming a unitary coefficient of restitution (Petrone et al., 2017). IDA analyses were carried out scaling the acceleration loading histories up to the overturning of the blocks, assuming the static overturning conditions as a reference (Equation (3)) (Dimitrakopoulos and Paraskeva, 2015). α θ ≥1 (3) 2.2. Loading histories Real ground motions (GMs) and floor motions (FMs) were considered as loading histories. Strong GMs were selected from the ATC 63 database (Applied Technology Council (ATC), 2008), and these included both near field (NF SGM; 28 records) and far field (FF SGM; 44 records) records, associated with magnitude greater than 6.5, PGA larger than 0.2 g, and PGV larger than 15 cm/s. FMs were derived from CESMD database (CESMD, 2017), and these were related to responses recorded within US reinforced concrete buildings, designed prior to 1975. In particular, near field (NF FM; 12 records) and far field (FF FM; 12 records) records were considered, and these equally referred to recording in low-, medium-, and high-rise buildings. A detailed description of these records can be found in (D’Angela et al., 2021) , and the related pseudo-acceleration spectral responses are depicted in Fig. 2, where median and 16/84 th percentile curves are reported.