GNGTS 2022 - Atti del 40° Convegno Nazionale

282 GNGTS 2022 Sessione 2.2 C DS2 =0.4 · d 0 (2) where d 0 is the spectral displacement corresponding to a spectral acceleration equal to zero. In order to apply the Capacity Spectrum Method, the seismic input has been evaluated by considering the spectra obtained from spectrum-compatible accelerograms referring to 8 different return periods T R . To this purpose, the software REXEL (Iervolino et al., 2010) has been employed. For each damage limit state, DS i , the fragility curve can be obtained as a function of a specific Intensity Measure IM, indicative of the intensity of the seismic input, through a conditional probability cumulative distribution function: (3) By considering the Peak Ground Acceleration, PGA, as IM, and assuming a log-normal distribution, fragility curves can be derived through the following equation (CNR-DT, 2014): (4) where: - Φ[•] is the lognormal standard distribution function; - μ lnDIiIPGA is the mean value of the logarithm of the variable DI DSi conditioned on the given value of PGA; - σ lnDIiIPGA is the dispersion of the natural logarithm of the variable DI DSi conditioned on the given value of PGA. The conditional mean values of the variable DI DSi have been defined for each value of the PGA through the following expression: (5) where A DSi and B DSi are coefficients obtained by a linear regression of the logarithm of the DI DSi versus the logarithm of the PGA (Nielson and DesRoches, 2007). On the other hand, the dispersion values have been evaluated through  the following equation: (6) where: - σ m represents the uncertainty of the model, estimated applying the equation: (7) being n the number of the generated virtual buildings; - σ rtr represents the uncertainty due to the record-to-record variability, estimated as (Lagomarsino and Cattari, 2014): (8)