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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It should be noted that for the same building (or equivalently the same PO curve), the use of a different capacity model could lead to a different PGA C and, thus, a different ζ e ratio with the same demand. Therefore, in this section, the first achievement of brittle failures at SD LS will be illustrated, using the shear capacity models described in the previous section. Then, the influence of shear strength model on the PGA C will be analyzed, assuming as building location all Italian municipalities seismically classified after the 1970 (about 6700 municipalities mentioned before). The resulting capacity curves, obtained following Italian code approach (DM 2018), are depicted in Fig. 2, showing spectral displacement (S d ) - pseudo-spectral acceleration (S a (T)) for each building and direction, up to the occurrence of the first ductile failure (DF) at SD LS. As suggested by the Italian code, DF is assumed to always occur when the demand in terms of chord rotation θ reaches ¾ of the capacity calculated according to Biskinis and Fardis (2010). The collapse mechanisms are also shown in Fig. 2: A global collapse mechanism is observed in the transverse direction for all the case-study buildings, whereas local mechanisms are observed in the longitudinal direction. Each capacity curve in Fig. 2 shows the achievement of the first joint failure (JF), and the first shear failure (SF) in beams or columns, according to the three considered code-based capacity models. Moreover, the percentage of failing elements is provided in each step of the pushover analysis, for both directions. About SFs (which occur only in the X direction), it should be noted that the most conservative capacity model for the analysed case-study buildings is the one proposed by EC8 2005. Furthermore, only according to this model, even the 2-story building exhibits SFs. Considering then the other two code models, the ASCE/SEI model is less conservative, causing not SFs in the analysed cases. As explained in Section 2, European technical regulations (DM 2018, EN 1998-3, 2008) requires a double safety check for beam-column joints. The first one, related to the diagonal cracking of the concrete, leads to a tension failure, referred to as JF(T); the second one results in a compression failure, i.e. JF(C). According to DM 2018, for all the case studies considered, JF(T) is observed in both directions and a maximum percentage of failing elements in direction X that far exceeds 50% of the elements. The number of failures is about the same moving from the DM 2018 to the EC8 2005 model. JF(C) failure, which could represent a more appropriate failure criterion even for unreinforced joints (Hakuto et al., 2000), involves few joints (i.e., less than 10% of all the joints) for the tallest buildings only, both according to DM 2018 and EC8-2005 models. The joints exhibiting this type of failure typically are interior joints subjected to high axial loads. For this type of joint, the compressive capacity prescribed by EC8-2005 is higher than that of DM 2018, thus reaching the first JF(C) failure later. Lastly, according to the American code, only one safety check is needed. Therefore, the relevant failure mapping is plotted together with JF(T) ones of European codes, resulting less conservative. In fact, the capacity provided by ASCE/SEI is generally higher than the JF(T) one, especially for the interior joints. It should be also noted that the proposal by ASCE, despite its very simple equation, when applied without any reduction of concrete strength, generally provide a quite good estimation, on average, of experimental joint strength, as highlighted in the literature by Jeon et al. (2014), De Risi et al. (2016). For each building under study, starting from the point of inelastic capacity (coincident with the attainment of the first failure at the SD LS on the elasto-plastic bilinear capacity curve), the corresponding elastic capacity is derived. Thus, the elastic spectral acceleration Sa C (T eff ) (at the effective period, T eff ) is derived in each direction of the building by means of Vidic et al. (1994 )’s relationships. The latter provides two different R- μ -T relations based on the ratio between the effective period T eff and the corner period T c (depending on the considered site). In Figure 3(a) for each building (i.e., for each Ns reported on the x-axis), the median Sa C (T eff ) and the corresponding minimum and maximum values (among all the considered sites) are provided, according to the three codes discussed before. Furthermore, the type of failure (e.g., DF, JF(T), SF, etc.) that was reached first and that, thus, limits the building capacity at the SD LS, is specified. Note that in almost all cases, there is no variability around the median Sa C (T eff ) (except for the two story building in the X direction evaluated according to ASCE/SEI), since T eff is generally higher than T c values for all the considered sites. For 2-story building in the X direction, in a small percentage of municipalities, T eff < T c , thus introducing a small variability of Sa C (T eff ) around the median value, only in the ASCE/SEI case, for which the capacity point is beyond the elastic branch. 4.1. As-built assessment depending by codes