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

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Consequently, in the present work for each offspring (generated by the Crossover operator) an ideal “binary coin” is flipped in order to mutate only those offsprings corresponding to a value of the “binary coin” equal to 1. Moreover, as in the first formulation of the procedure by Falcone (2017), the number of mutated genes is proportional to the mutation rate µ rate ; such variable is gradually increased during the analysis so that at the end of the analyses the mutation rate results to be doubled with respect to its initial value µ rate,ini , assumed equal to the 5%. 3. Application of the GA procedure 3.1 Structure presentation and performance evaluation In order to test the capacity of the proposed Genetic Algorithm in reaching an optimal upgrading solution, in the present application a GLD (Gravitational Load Designed) 4 story RC structure is considered. The structure consists of 4 frames of 5 bays along the X direction and 4 frames of 3 bays along the Y direction, as reported in Fig. 2. The typical cross section of the beams is 35x60 cm 2 , while 35x35 cm 2 is the typical dimension of the columns. With respect to what has been explained in Section 2.1, it is possible to observe that the total number of design variables is equal to 128.

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Fig. 2. (a) 3D model of the structure; (b) Plan view of the typical story.

The structure is ideally located in Sant’Angelo dei Lombardi (AV, Italy), an Italian city characterized by significantly high seismic hazard, as indicated in Table 1. Table 1. Main Hazard parameters for the site of Sant’Angelo dei Lombardi (AV) according to Italian Code (DM 20/02/2018). Limit State a g /g [-] F 0 [-] S [-] (Normalized PGA) (Amplification Factor) (Soil factor) SLD (Damage Limitation) 0.08 2.33 1.50 SLV (Life Safety) 0.27 2.28 1.36 The seismic performance of the structure is determined by means of Pushover (Nonlinear Static) Analyses, having defined a nonlinear model through the OpenSEES (Mazzoni et al., 2006) framework. Both beams and columns are modelled by means of distributed-plasticity “nonlinearBeamColumn” elements with 5 Lobatto integration points per element. Uniaxial “Concrete01” and “Steel01” materials are employed to model the behavior of the fibers used to discretize the cross sections of members. At each step of the procedure each chromosome is decoded in order to modify the “as-built” nonlinear model either introducing the bracing systems or modifying the peak stress and ultimate strain of the “Concrete01” material only for the confined columns, according to the models suggested by the Italian technical document CNR-DT 200 (2013). The estimation of the seismic displacement demand relies on the application of the N2-Method, formulated by Fajfar (1999). The attainment of a certain Limit State is associated to the achievement of some limit values of the interstorey drift ratios, as explained by Falcone et al. (2019). As provided by the Italian Code (DM 20/02/2018), for the Serviceability