PSI - Issue 44

Francesco Nigro et al. / Procedia Structural Integrity 44 (2023) 1704–1711 F. Nigro, R. Falcone, E. Martinelli/ Structural Integrity Procedia 00 (2022) 000–000

1709

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LS (SLD) a limit value of 0,5% is adopted (as in the case of a structure with fragile infill walls), while the drift capacity at the Ultimate LS (SLV) is computed according to “Equation A.1” of EN 1998-3:2005, accounting for the variation of the axial force caused by the seismic action. Moreover, it should be highlighted that the parameter PAM is evaluated according to the “conventional method” suggested in the “Annex A” of the Italian DM 65 07/03/2017, having explicitly evaluated the PGA in terms of capacity only for the SLD and the SLV, which represent the two relevant Limit States for existing structures. 3.2 “Optimal” upgrading solution according to the GA, considering different seismic risk target classes The application considered in the present study aims at evaluating the effectiveness of the proposed optimization procedure in figuring out the “optimal” solution, considering as target of the analyses a particular seismic risk class for the structure ideally located in a site characterized by a high value of the seismic hazard. Consequently, the “optimal” solution given by the GA corresponds to a possible seismic upgrading solution, having imposed the constraint represented by Eqn. (3). Fig. 3 (a) represents the conveOrgence process for the two examined cases, having generated a total number of 200 Populations of 40 chromosomes (per population), while Fig. 3 (b) shows a comparison between the pushover curves of the upgraded structures and the “as-built” one, considering only the Y+ direction, highlighting the points corresponding to the attainment of the Damage Limitation LS (SLD) and the Life Safety LS (SLV), as well. Finally, Table 2 reports the values of the PAM and ISV parameters of the “as-built” structure and of the upgraded structures.

3000

As-Built Target B Target A Step SLD Step SLV

2500

2000

1500

V b [kN]

1000

500

0

0.00

0.03

0.06

0.09

0.12

0.15

∆ Top [m]

Fig. 3. (a) Convergence processes (optimization) of the upgrading solution considering two different seismic risk target classes. (b) Pushover curves in the Y+ direction of the “as-built” structure and of the upgraded ones.

Table 2. Values of PAM and ISV parameters of the “as built” structure and for the upgraded structures Direction: X+ X- Y+ Y-

PAM [%]

ISV [%] 67,8 88,4 80,5

PAM [%]

ISV [%] 67,8 86,1 75,8

PAM [%]

ISV [%] 71,8 91,9 82,9

PAM [%]

ISV [%] 71,8 91,5

Structure:

As-built

1,53

1,53 0,75 1,21

1,73 0,75 1,48

1,73 0,75 1,48

Target “A” 0,74

Target “B” 82,9 Since the structure in its “as-built” state belongs to the seismic risk class “C”, the intervention cost – represented by the objective function f(x) – needed to upgrade the structure to the “A” class is much higher than the one needed to achieve the “B” class requirements. “Optimal” upgrading solution for target class “A” The plan distribution of the supplementary bracing systems needed according to the algorithm is reported in Fig. 4. The steel profiles employed for their realization are reported in Table 3 (a), while a description of the (few) local interventions is reported in Table 3 (b). 1,19 3.2.1