PSI - Issue 44

312 Fabrizio Paolacci et al. / Procedia Structural Integrity 44 (2023) 307–314 Fabrizio Paolacci et al. / Structural Integrity Procedia 00 (2022) 000–000 value of 1.3, the maximum number of combinations has been set to the value = 5 × 106, whereas the other options have been set on default. 6

(a) (b) Figure. 2: a) target UHS for different return periods , , b ) seismic hazard curves of Amatrice (Italy) The agreement, already good in the case of non-scaled accelerograms, can be further improved by scaling the records along with the two principal directions by adopting the same scale factor in the range 0.82-1.27. To check the robustness of the method, a second group of 5 × 30 accelerograms was extracted, called Set B, obtained with the same methodology applied to the same database but without the accelerograms that appear in the Set A. For brevity, the following graphs refer to Set A only. Subsequently, the fragility curves and risk values obtained using the two sets will be compared. 4.1. Analysis of the seismic response The modal analysis of the frame is first performed to primarily evaluate the dynamic characteristics of the model. In particular, the first period is in y-direction and equal to 0.748 sec, whereas the second one is in the x-direction and equal to 0.701 sec, both with more than 86% of participant mass. In order to investigate the nonlinear response of the building model, preliminary nonlinear pushover analyses have been performed in both longitudinal and transverse directions using a load pattern proportional to the first mode shape. As a control node, the center of gravity of the top floor has been selected. The results of the analyses are shown in Fig 3. It can be noticed as the capacity curves (Fig. 3a) in both directions, represented by the total base shear and the roof drift ratio, are similar. This is mainly due to the symmetry of the system. The same figure shows the point corresponding to the limit state as defined by Eurocode8 part 3 that provides the corresponding values of the chord rotation. They refer to the condition of Damage Limitation (DL), Significant Damage (SD) and Near Collapse (NC). It can be noticed that the yielding condition of the frame, corresponding to a drift of 0.5%, is consistent with the limit state DL. The subsequent limit states forces the frame till a maximum drift of 1.6%, which corresponds to the NC limit state. The damage is mainly concentrated at the first floor, as showed in Fig. 3b, where the maximum drift is plotted along the height. 4.2. Fragility analysis and risk assessment For the application of the proposed framework for risk assessment, fragility analysis has been conducted by using a Multiple- Stripe analysis (Mackie and Stojadinovic 2005). In particular, for each return period the maximum demand/capacity ratio ( Ú ) has been derived from the nonlinear analysis. Given that a three-dimensional analysis must be performed, this ratio has been evaluated as combination of the response in and direction, as follows: ( θ θ L ⁄ ) tot = o(( θ θ L ⁄ ) x 2 ) + L( θ θ L ⁄ ) y 2 M (8)