GNGTS 2013 - Atti del 32° Convegno Nazionale

obtained by applying the reduction factor q proposed by Fajfar in the N2 approach, and with the overdamped spectra, computed with a proper damping factor. The equivalent damping ratio to be used in the overdamped spectrum method is reported in Eq. (6). (6) According to Eq. 6, the damping ratios related to the plastic energy dissipated, are given by Eqs. 7a,b,c for the different cases investigated: (7a) (7b) (7c) Eqs. 7a, 7b and 7c are referred to fully dissipative, flag-shape and slip-type behaviour, respectively. Some alternative formulations to Eqs. 7b and 7c were developed, because they were found to be too conservative. Priestley et al. (2007) proposed the use of the equations provided in the following for the equivalent damping ratio of EP [Eq. (8)] and FS systems with [Eq. (9)]: (8) (9) The following spectra are compared: • The average elastic spectrum of the 15 recorded earthquakes, and the EC8 elastic spectrum; • The EC8 design spectrum obtained from the elastic EC8 spectrum using the behaviour factor q , in accordance with the N2 approach [Eqs. (3) and (4)]; • The EC8 overdamped spectra, obtained using the reduction factor , with in %, evaluated using both Eqs. 7a and 8 for the EP cases, Eqs. 7b or 9 for the FS case; • The average numerical spectrum obtained by integrating in time the 15 selected earthquake ground motions for a SDOF system characterized by a given ductility value µ . The results show a good agreement between the N2 design spectrum and the computed inelastic one, for every type of hysteretic cycle and ductility value. On the contrary, the over- damped spectrum method overestimates the inelastic spectrum in all cases. In general, better accuracy is obtained only for low ductility values and great amount of dissipated energy. More- over, this difference is greater for low periods. For the sake of completeness, also the total input energies have been calculated in the same analyses, including the separate contributions (elastic, hysteretic, damping, and kinetic). Reported results are referred to the case with µ = 2: Fig. 2a shows the spectra in ADRS format obtained with two hysteretic laws, EP (fully dissipative) and FS with C F = 0.01, which represent the limit conditions for analysed SDOF systems. 134 GNGTS 2013 S essione 2.1