PSI - Issue 44

Giorgia Cianchino et al. / Procedia Structural Integrity 44 (2023) 219–226 Giorgia Cianchino et al. / Structural Integrity Procedia 00 (2022) 000–000

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3.1. Damage levels on the capacity curve In order to assess the damage levels associated with the obtained capacity curves, four thresholds of Damage T(D k) were defined according to (Lagomarsino, 2015): • T(D1) - Light damage level. This point corresponds to 70% of LD2; • T(D2) - Moderate damage level. Usually, this level corresponds to the peak of the capacity curve where the spectral acceleration value is reached. It represents the actual point of activation of the mechanism and the beginning of the plastic plateau; • T(D3) - Extended damage level. It represents the last point before the decreasing branch of the curve; • T(D4) – Collapse. It corresponds to the complete collapse of the structure (zero acceleration). These thresholds define the ranges for the 5 Damage Levels (DL), according to the EMS-98 Macro-seismic scale. 3.2. Seismic demands Identifying the possible sources of uncertainty is very important to define reliable fragility curves. In particular, when evaluating the fragility curves of a specific building, the seismic demand is considered among the main aleatory sources (Masi et al. 2021). Therefore, in the present work, the uncertainty due to the seismic demand is taken into account by selecting an appropriate number of ground motions. A total of 130 natural records, corresponding to different return periods, selected from the ReLUIS group leading the Work Package "WP4 - Seismic Risk Maps – MARS1", were chosen for the purpose (Manfredi et al. 2022). They were divided into 9 families, each one corresponding to a pre-selected range of Peak Ground Acelerations (PGA). Then each family has been associated to the mean PGA of the range (Table 3).

Table 3. Range and average PGA of the 9 families of seismic inputs Family Range of Pga [m/s 2 ] Mean Pga [g] Family 1 0.4 < Pga ≤ 1.0 0,07 Family 2 1.0 < Pga ≤ 1.5 0,13 Family 3 1.5 < Pga ≤ 2.0 0,18 Family 4 2.0 < Pga ≤ 3.0 0,26 Family 5 3.0 < Pga ≤ 4.0 0,34 Family 6 4.0 < Pga ≤ 5.0 0,46 Family 7 5.0 < Pga ≤ 6.0 0,56 Family 8 6.0 < Pga ≤ 7.0 0,66 Family 9 7.0 < Pga ≤ 8.0 0,80

The selected accelerograms were transformed into Acceleration-Displacement to allow to compare the seismic capacity versus the seismic demand. 3.3. Demand vs. Capacity The methodological approach used in this paper graphically assesses the possible earthquake-induced damage that a structure may suffer by identifying the so-called performance point (PP) (Fajfar 1999). This is defined by projecting onto the capacity curve the point where the demand elastic spectrum intercepts the extension of the elastic line of the curve. The coordinates of that point define the maximum expected acceleration and displacement, hence PP represents the condition in which the structure is found under the considered specific seismic input. Therefore, the comparison between capacity and demand makes possible to define the level of expected seismic damage (Chopra and Goel 1999) depending on the position of PP. This procedure is exemplified in Fig.3 with reference to archetype building#1.