PSI - Issue 44

Maria Teresa De Risi et al. / Procedia Structural Integrity 44 (2023) 958–965 De Risi, Del Gaudio, Scala, Verderame/ Structural Integrity Procedia 00 (2022) 000–000

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3.1. Nonlinear modelling and analyses Only the flexural response of RC beams and columns is modelled, as common in design practice. A lumped plasticity approach is adopted, by means of Verderame and Ricci (2018)’s moment-chord rotation relationship, specifically calibrated for RC elements with plain bars. Joints are considered as rigid. Eventual shear failures in columns/beams or joints have been detected by means of a post-processing of the static pushover results. For each building, nonlinear static pushover analyses have been performed in both (longitudinal and transverse) directions and with two lateral Load Distributions (LD): (i) “modal” LD, proportional to the first vibration mode in each direction; (ii) “uniform” LD, proportional to the story accelerations (D.M., 2018). Resulting capacity curves, obtained as suggested by code (D.M. 2018, CEN, 2005), are shown in Fig. 3, in terms of first period (T)-spectral displacement (S d ) – spectral acceleration (S a ), along with the corresponding collapse mechanisms. 3.2. Safety check results Based on pushover results, safety checks are performed. First, a “Full Knowledge Level” (KL3) (CEN, 2005) has been assumed, and, thus, the mean values of the mechanical properties of existing materials used in the capacity calculation have been not further reduced (confidence factor, FC =1). Then, two performance levels have been analyzed for this code-based assessment: “Damage Limitation” (DL), and “Life Safety” or “Severe Damage” (SD) limit states, corresponding to seismic actions with a return period of 50 and 475 years, respectively (D.M., 2018). The building capacity at DL limit state is assumed to be achieved when for the first time an inter-story drift ratio (IDR) equal to 0.5% is achieved. Building capacity at SD LS is reached at the first ductile (DF) or shear (SF) failure. Ductile members reach their DF when their chord rotation demand reaches ¾ of the ultimate chord rotation capacity (θ u ), estimated according to Biskinis and Fardis (2010), as suggested by the Eurocode 8 and the Italian prescriptions. On the other hand, about shear-sensitive elements:  Beam-column joints (BCJs) shear failure occurs when its principal compressive stress, p c , overcomes 0.5f c (compressive joint failure, JF, “C”), or if the principal tensile stress, p t , overcomes 0.3√f c (tensile JF “T”);  columns/beams SF occurs when the shear demand overcomes for the first time the shear strength, the latter evaluated according to the model by D.M. 2018 and Circolare C7/2019, and thus depending on the inelastic displacement demand. The achievement of the first DF, beam or column SF and “C” and “T” JF are shown in Fig.3.

Fig. 3. Static pushover curves and “1 st failure mapping”: a) 2-storey and b) 4-storey-building.

The number of failing elements in each pushover analysis is summarized in Table 1, considering together both directions and lateral load shapes, for three “characteristic conditions”, very important for the adopted retrofitting strategy (as explained in the next section): (i) the 1 st “compressive” shear failure, which is a JF “C” (no beams or columns fail in compression due to shear loads in these cases); (ii) the first DF; and (iii) the pushover end. Obtained capacity curves have been finally bi-linearized according to D.M. 2018 aiming at the assessment of displacement