GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 2.2 441 Table 1 - Summary results of PAs in terms of safety and behavior factors. Load direction BCP F S = d C * / d D * q * a * = F * / m * C1 0.23 2.69 2.56 +X C2 0.27 2.32 2.97 C3 0.38 2.20 3.14 C1 0.31 2.17 3.18 -X C2 0.38 2.15 3.20 C3 0.35 2.38 2.89 C1 0.19 2.86 2.40 +Y C2 0.23 2.66 2.59 C3 0.22 2.68 2.57 C1 0.34 2.03 3.39 -Y C2 0.28 2.02 3.41 C3 0.26 2.17 3.17 Limit analysis with kinematic approach. The previous seismic analyses highlighted the onset of out-of-plane mechanisms which occur on the perimeter walls denoting the lack of box- like-behavior. In order to compare the spectral acceleration provided by the different approaches (PAs, RHAs, and KAs), two out-of-plane mechanisms were analyzed: Simple Overturning (SO) and Vertical Overturning with 2 side wings (VO) (Fig. 3). These mechanisms refer to the rocking west tower of the north front which collapses firstly in the +Y PA and reaches higher displacements than all other simulations. The BCP C2 is placed above this structural element, and the detrimental effect of the static thrust of a masonry vault was considered. At the first stage, two linear kinematic analyses were carried out in order to evaluate the corresponding multiplier at collapse α 0 by using the Virtual Work Theorem (VWT) (Betti and Galano, 2012, Olivito et al. , 2019). In the calculation, masonry walls are considered as an assemblage of macro-elements made of a no-tension material with an infinite compressive strength. In the next stage, according to NTC 2018, the nonlinear kinematic analysis was used in order to calculate the spectral acceleration values a * of the SDOF system. Comparison of spectral acceleration values. With regard to the spectral acceleration, a comparison among all types of analyses is reported in Table 2. In numerical analyses, the values concerning node C2 are taken into account along the +Y load direction in PAs as well as the Y direction in RHAs. In the case of KAs, the spectral accelerations are calculated on Fig. 2 - Results of RHA for Y direction in terms of top displacements of BCPs.