PSI - Issue 78

Eleonora Bruschi et al. / Procedia Structural Integrity 78 (2026) 49–56

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Δ TR475years and Δ TR1950years / Δ TR475years respectively. Fig. 3 report, for the two case-study structures, the values of β 1 and β 2 for the dampers at each floor of the building, calculated for different ductilities µ DB of the damped bracing system.

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b)

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f)

g)

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Fig. 3 : β 1 and β 2 indexes for 3-story building and 6-story building, (a),(b) ,€ and (f) site of Benevento, (c), (d), (g) and (h) site of Tramutola.

For the 3-story structure, the diagrams show the tendency of both β 1 and β 2 to increase with increasing of µ DB . This trend is especially apparent in the results relevant to Benevento site (Fig. 3(a) and (b)) where β 1 and β 2 achieve their maxima at the first floor. In particular, β 1 increases from a minimum of 1.46 for µ DB =3 to a maximum of 2.35 for µ DB =13.5, while β 2 increases from 2.52 to 5.72 over the same range of µ DB . Lower amplifications are obtained for Tramutola (Fig. 3(c) and (d)), especially for the highest return period, where β 2 rises from 2.3 for µ DB = 3 to 2.67 for µ DB =13.5. In the 6-story building (Fig. 3(e) – (h)), the amplification index is less sensitive to µ DBs . In particular, by referring to the 4 th story of the building in Benevento that show the maxima of β 1 and β 2 , there is only a slight increase (from 1.78 to 1.96 for β 1 , and from 3.18 to 3.53 for β 2 ) passing from µ DB =5 to µ DB =13.5, while for the building in Tramutola the maximum values of β 1 and β 2 tend to remain constant or even to decrease. The values of β 1 and β 2 at each floor are used to build the lognormal distributions of the probability density function (pdf) in order to statistically estimate the amplification factor from the analyses and determine the values of β 1 and β 2 referred to the 95% fractile. Based on these results, the reliability at 95% of the hysteretic dampers installed in either building and in either site is guaranteed if they are designed for displacements equals to 1.6 ÷ 2.3 Δ TR475years when a return period of T R = 975 years (CLS1) is considered, and for displacements equal to 2.7 ÷ 5.6 Δ TR475years for T R = 1950 years (CLS2). It is worth noting that even for the less severe CLS1 the amplification of the design displacement largely exceeds the values recommended in current standards, i.e. 1.1 as per EN 15129, 1.2 as per D.M. 2018 and 1.3 as per ASCE (SEI 41-2017). Therefore, hysteretic dampers designed for the LLS according to current code would fail under a ground motion with T R = 975 years. In Fig. 4, the maxima values of the β indexes calculated for the two structures considering both sites are plotted with respect to the ratio between the PGAs of the non-collapse limit states CLS1 and CLS2 and the design PGA for LLS. For both buildings, disregarding a single data point, an almost linear dependency of the amplification index on the PGA ratio is apparent.

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a)

Fig. 4: Trend of β indexes with respect to PGA ratio