PSI - Issue 78

Roberta Di Chicco et al. / Procedia Structural Integrity 78 (2026) 497–504

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chosen in the second-floor level. The re sults of the worst analyses are reported in Table 2, where α SLV is the seismic safety index, which is defined as the ratio between the capacity peak ground acceleration and the demand peak ground acceleration; therefore, values close to one indicate that the structure is verified for the considered limit state.

Table 2. Results of the non-linear static analyses.

Nr.

Direction

Seismic load Eccentricity [cm]

α SLV [-]

10 17

+X +Y

Uniform -220 Uniform 87.12

0.911 0.536

The aggregate exhibits significantly higher vulnerability in the Y-direction, as clearly indicated by the observed damage pattern, reported in Figure 5. Severe failures and cracking occurring in the elastic phase are observed in the Y-direction at the third level, highlighting the limitations of applying non-linear static analyses to buildings with irregular elevation profiles capturing its global behaviour.

a)

b)

Fig. 5. In- plane damage mechanisms corresponding to the worst analyses in: (a) X-direction and (b) Y-direction.

3.2. Fragility curves The seismic response of the aggregate - assumed to be governed solely by in-plane behaviour- was determined through non-linear static analyses. These analyses were conducted on the 3D equivalent frame (EF) model of the entire aggregate. Using the capacity curves obtained from the worst-case analyses in both principal directions (i.e. corresponding to a lower seismic safety index), fragility curves expressed in terms of spectral displacement were generated. The damage thresholds in this mechanical method were defined based on the displacement limits of the single-degree-of freedom (SDoF) bi-linear system representing the structural model. These displacements are functions of the elastic and ultimate displacements of the SDoF system, as outlined by Lagomarsino et al.,2021 and presented in Table 3. The fragility functions were then computed as:

(1) where the standard deviation (β) is adopted for all the damage levels, Φ [•] is the cumulative normal distribution function and Sd and β are the median and the standard deviation of the corresponding normal distribution, respectively.