PSI - Issue 44

Luca Umberto Argiento et al. / Procedia Structural Integrity 44 (2023) 1388–1395 Luca Umberto Argiento et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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fact, the data of the survey collected in a predefined form (A-DC adopted by the Department of Italian Civil Protection, DPCM 2006) during the post-earthquake emergency phase show a damage level referred to the overturning of the façades null or negligible for all the inspected churches. Table 3. Capacity parameters and safety indexes for the two conditions of the façades under study, related to LS0. LS1 and LS2. ID church LS0 a LS0 = α g [m/s 2 ] LS1 [m] LS2 [m] Free rocking Restrained façade Free rocking and restrained façade Free rocking and restrained façade

C [m/s 2 ] 0.744 0.773 0.857 1.033 0.701 0.826 0.596 0.923 0.792 0.861 0.795 0.681 0.740 0.654

C/D CNTC19

C [m/s 2 ] 2.812 2.991 2.898 2.704 3.322 3.351 2.020 2.338 2.185 2.965 2.912 2.900 2.493 1.994

C/D CNTC19

C [m]

C/D CNTC19

C [m]

C/D CNTC19

SMC SMP SAP SPB SRO SOC SFA SMA SD SFS SRE CA SG

1.34 1.40 1.55 1.87 1.27 1.49 1.08 1.67 1.43 1.56 1.44 1.23 1.34 1.18

5.08 5.41 5.24 4.89 6.00 6.06 3.65 4.22 3.95 5.36 5.26 5.24 4.51 3.60

0.182 0.160 0.186 0.160 0.120 0.160 0.170 0.160 0.210 0.180 0.120 0.100 0.200 0.120

1.99 1.75 2.03 1.75 1.31 1.75 1.86 1.75 2.30 1.97 1.31 1.09 2.19 1.31

0.273 0.240 0.279 0.240 0.180 0.240 0.255 0.240 0.315 0.270 0.180 0.150 0.300 0.180

2.20 1.93 2.24 1.93 1.45 1.93 2.05 1.93 2.53 2.17 1.45 1.21 2.41 1.45

SL

C: Capacity, D: Demand

4. The role of friction and geometric parameters for homogeneous classes of vulnerability to implement future statistical analyses and fragility curves The following section is aimed to verify if there are any geometric parameters for the selected façades able to affect their seismic assessment in a similar way, so as to identify a sort of typological classes of vulnerability. This could be useful for performing future statistical analyses mostly based on structural details. As highlighted in section 3, the seismic assessment of the façades of the selected churches only depends on their capacity parameters since the acceleration and displacement demands do not change for them within each limit state. However, this is only a particular condition detected for these specific case studies, since, more in general, the rocking façades could be associated with different equivalent periods even for the same PGA or the ADRS could have intersections with the period lines in different branches. Therefore, focusing the attention on the capacity parameters only, the seismic assessment of the selected façades for LS1 and LS2 is mostly affected by their thickness, while frictional resistances have a great influence on LS0. The acceleration capacity related to the onset of the façade rocking is also influenced by geometric parameters, which, however, strongly depend on the presence or absence of the restraining actions of the sidewalls. Under free rocking conditions, the unique parameter affecting the onset of the façade is its vertical slenderness, λ f = H / s . Fig. 4a shows the capacity curves for the 14 façades divided according to three ranges of vertical slenderness : λ f > 13 (red curves), 11 < λ f < 13 (yellow curves) and λ f < 13 (green curves). These ranges can be respectively considered as representative of three typological classes of vulnerability: high, medium and low. On the other hand, when the stabilising contribution of frictional resistances exerted by the sidewalls is considered, the only s lenderness λ f is no longer representative to identify homogeneous classes of vulnerability for LS0 and a new criterion of classification is necessary. Therefore, the vertical slenderness of sidewalls λ s ( H / s t ) and the horizontal slenderness of the façade λ l ( L / s ) becomes the new reliable parameters that, considering the ranges reported in Table 4, allow to collect the acceleration capacities in three distinct groups. These are identified by different colours in Fig. 4b, where the high (red curves) and low (green curves) vulnerability classes are mostly distributed in the bottom and upper sides of the graph, respectively. It is important to highlight that the crucial role played by λ s and λ l is different. In fact, t he influence of λ l is due to the stabilising effect of the façade thickness s and the negative impact of the façade length L that reduces the contribution of frictional resistances with respect to the