PSI - Issue 64

Maria Teresa De Risi et al. / Procedia Structural Integrity 64 (2024) 959–967 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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MPa for concrete (depending on compressive loads or bending actions, respectively), and 140 MPa for reinforcing plain bars. Note that no transverse reinforcement is present in beam-column joints, since not required at that time. For more information about the buildings features, refer to De Risi et al. (2023). Nowadays, the entire Italian territory is classified as a seismic-prone zone according to a classification into 4 seismic zones. This means that all municipalities (around 6700) that were not classified as seismic risk until the 1970s can be considered as possible locations of the analyzed RC GLD buildings. Currently, about the 2% of considered municipalities are in the first (at the highest hazard) seismic zone, the 23% in the second, about the 60% in the third and the 17% in the fourth. Considering the current soil typology (Mori et al., 2020) according to the Italian classification (DM, 2018), about 75% of considered municipalities are in B-soil typology, about the 24% in C, and only the 1% in D.

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Fig. 1. (a) Plan (a) and (b) 3D views of the case-study buildings (dimensions in centimeters)

3.1. Modelling strategy Each building is modeled in OpenSees platform (McKenna, 2011) as a 3D bare model, without considering the numerical modeling of masonry infills and neglecting the nonlinear response of beam-column joints, as common among practitioners for code-based safety check. Infills are only considered in terms of masses and loads, while the joints are assumed to be rigid elements. Lastly, the floors are assumed to be stiff in their own plane. Beams and columns are modeled as ductile elements using a lumped plasticity approach to simulate their flexural response. Specifically, this approach is implemented in OpenSees by employing elastic BeamColumn Elements in series with Zero-Length Elements positioned at each end of beams/columns. The flexural response adopted is a moment (M)- chord rotation (θ) relationship that has been specifically calibrated for RC elements with plain bars (Verderame and Ricci, 2018); it is characterized by a four-point envelope defined by the yielding point, the capping point, the intersection of the softening branches, and the zero-strength condition. An additional point corresponding to the first cracking is also included herein. In the perspective of a code-based practice-oriented assessment, potential shear failures are identified via post-processing the static pushover results by using all the capacity models described in the previous section. 4. Nonlinear analyses and assessment According to DM 2018, the code-based assessment at a given limit state can be expressed through the capacity-to demand ratio (ζ e ), calculated in terms of PGA. The demand is related to the considered limit state (LS) and construction’s site. Conversely, the capacity also depends on the first failure attained by the building. To obtain PGA C at the Severe Damage (SD) LS, nonlinear pushover (PO) analyses are carried out, considering a lateral load distribution proportional to the first modal shape in both directions. Then, for a given direction, each capacity curve is bi-linearized by means of the equal-energy approach, obtaining an Elastic-Perfectly-Plastic curve. Starting from the inelastic displacement of a given capacity point (i.e., the attainment of the first failure), the corresponding elastic capacity point is obtained via R- μ -T relationships (Vidic et al., 1994). Thus, the spectrum passing through such point provides its corresponding PGA value. This procedure is applied in both the X and Y directions, thus providing two capacity values, the minimum of which finally represents the PGA C .