PSI - Issue 78

Stefano Bracchi et al. / Procedia Structural Integrity 78 (2026) 745–752

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(Bracchi et al. 2021, Bracchi and Penna 2021) and spandrels (Penna et al. 2014). Mechanical properties of masonry are obtained from calibration of experimental tests on piers of a similar typology, as done by Bracchi et al. (2019) for a similar building. Nonlinear static analyses are first carried out to define the capacity. Fig. 4 shows results of pushover analyses for the structure considered either as fixed-base or supported on the above LPMs, for IML 2-4-6. Results are expressed in terms of base-shear versus relative displacement. It can be noticed that SFSI effects are not relevant; only a small increment in ductility is observed for the x-direction, while in the y-direction, both capacity and ductility are not affected by the foundation compliance. Fig. 4 depicts also the failure mechanisms for two masonry walls, either neglecting or considering SFSI, for IML6. No significant differences in the failure mechanism are evident; in both the cases, shear failure is hence concentrated in a single level (ground level for the considered direction of analysis).

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(b)

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(d)

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Fig. 4. Pushover analysis results for three different IMLs, either neglecting or considering SFSI (a) and failure mechanisms for IML 6 with (c, e) or without (b, d) SFSI.

The seismic vulnerability is assessed in terms of frequency of exceedance of given thresholds of a selected Engineering Demand Parameter (EDP). As in previous works (Cattari et al. 2018, Bracchi et al. 2019, Penna et al. 2024, Lagomarsino et al. 2023), the maximum interstorey drift (among all stories), accounting for the average rotations of the nodes of the storey, is selected as EDP. The EDP thresholds are calculated by pushover analyses with two significant load patterns, one proportional to masses and one proportional to the product of masses and elevation, also indicated as inverse triangular. The maximum inter-storey drift is evaluated and the EDP is calculated as the minimum value between the positive and negative direction. Two performance states are considered, i.e. the global collapse (GC, corresponding to the attainment of a base shear decay of 50%) and the usability preventing damage condition (UPD) (Iervolino et al. 2023). The UPD condition is defined according to the multi-criteria adopted in previous works (Iervolino et al. 2023, Lagomarsino et al. 2023, Penna et al. 2024), i.e. as the occurrence of the first of three conditions: attainment of a base shear equal to 95% of the maximum base shear in the pushover curve, attainment of light/moderate damage in at least 50% of the piers and attainment of collapse in at least one pier (although not before the attainment of at least 85% of the maximum base shear). Thresholds corresponding to the attainment of GC and UPD performance states are then defined for the three building configurations corresponding to the IML considered. Nonlinear dynamic analyses are then carried out using couples of accelerograms selected by Iervolino et al. (2018). The intensity measure adopted for record selection is spectral acceleration at the fundamental period of the building S a (T 1 ) , with T 1 equal to 0.25s. According to the ground motions selection, twenty couples of accelerograms for each of the ten different return periods of the seismic action (associated with ten IMLs) are used in the analyses. The maximum EDP obtained from the dynamic analysis is then compared to the EDP threshold. It is worth highlighting