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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where a ( d LS1 ) and a ( d LS2 ) are the accelerations corresponding to the reference displacements on the capacity curve. The displacement demand for a specific limit state and for each façade is, thus, obtained from the intersection of the ADRS provided by the code and the line starting from the origin of the axes and having an inclination depending on the equivalent periods given by Eq. (3). Following the indications of CNTC19, the assumed values of the damping ratio of the over-damped ADRS are 8% and 10% for LS1 and LS2, respectively. Table 2 reports the seismic demand provided by the described procedure in terms of displacement for LS1 and LS2, and in terms of PGA for LS0. It is worth highlighting that the seismic demand does not depend on the restraining conditions of the façades for all the limit states. In fact, for LS0 it only depends on the PGA, assumed the same for all the locations (i.e., PGA = 0.056g), with slightly different S , while, Fig. 3a and Fig. 3b show that the displacement demand provided by the ADRS for LS1 and LS2, respectively, are coincident both for free (dashed line) and restrained (continuous line) rocking conditions, since the equivalent periods T LS1 and T LS2 intersect the ADRS along the vertical branches at constant displacement.

Table 2. Seismic demand related to LS0, LS1 and LS2, with reference to the design spectrum. LS0 PGA [g] LS1 d* LS1 [m] LS2 d* LS1 [m] Town Free rocking and Restrained condition Free rocking and Restrained condition Free rocking and Restrained condition Barano d’Ischia 0.056 0.091 0.124 Casamicciola Terme 0.056 0.091 0.124 Forio 0.053 0.091 0.124 Lacco Ameno 0.055 0.091 0.124 Serrara Fontana 0.054 0.091 0.124

2,5

2,5

ADRS LS2 CNTC19 Free condition Restrained condition

ADRS LS1 CNTC19 Free condition Restrained condition

2

2

1,5

1,5

Sa, a [m/s 2 ]

Sa, a [m/s 2 ]

1

1

0,5

0,5

0

0

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

Sa, d [m]

Sa, d [m]

a)

b)

Fig. 3. Superimposition of the equivalent periods for 14 façades under free (dashed lines) and restrained (continuous lines) rocking conditions with the design ADRS with reference to: a) LS1, and b) LS2.

3.2 Seismic assessment of the selected façades as capacity/demand ratio The reference values of the capacity parameters (acceleration for LS0, displacements for LS1 and LS2) for the 14 façades under study are reported in Table 3 both for free and restrained rocking conditions together with the indexes C/D representing the capacity/demand ratio for each limit state. As a first interesting remark, all the indexes for LS0 are higher than 1 both for free and restrained conditions, but with a significant increase (about 3-5 times) for the latter. Instead, for LS1 and LS2 the frictional resistances do not affect the capacity/demand ratio since the demands are the same (see Table 2) and the capacities too because d LS1 and d LS2 fall within the displacement ranges where the frictional resistances are ineffective (see Figure 2). It is worth noting that the safety indexes for LS1 and LS2 are always greater than 1 with a capacity/demand ratios similar to those for LS0 free rocking. These results are in very good agreement with the actual behaviour of the façades observed under the seismic event of 21 st August 2017. In