PSI - Issue 29

Mario De Stefano et al. / Procedia Structural Integrity 29 (2020) 71–78 De Stefano and Cristofaro/ Structural Integrity Procedia 00 (2019) 000 – 000

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of vibrating characterized by a frequency equa l to 6.5 Hz, which affects a ll the blocks of the model. For the moda l ana lysis with response spectrum, the ana lyses were performed on both models and the relative assessments consideringmultiple limit sta tes and spectra

spectrum on soil B (SLV)

Site spectrum (SLVSITE)

Site spectrum SLV (Soil B)

Capacity/Demand

Block A Block E Block G Block H Block L Block M

Block L Block M

Block A Block E Block G Block H

(a) (c) Fig. 6. (a) Site spectrum (SLVSITE) and elastic spectrum on soil B (SLV); (b) Risk index for individual block; (c) Capacity/demand ratio for all block analyzed. (b)

Fig. 7. East view. (a) Maximum principal stresses; (b) Minimum principal stresses.

Dynamic moda l analysis was performed on two models, one more rigid and one more deformable, useful for defining a sort of "band criterion". Model 1, rigid model, same as that used for linear static ana lysis; Model 2, deformable model without horizonta ls. As regards Model 1, Fig 8a shows a moda l deformation relating to a more significant way of vibrating. With regard to Model 2, Fig. 8b shows the moda l deformation relating to a more significant way of vibrating. As it can be seen, the areas that undergo the grea test displacements are distributed over a large part of the building complex and, particularly in block G ( Sala dei Prigioni ) and block D ( Sala del Colosso ). Fina lly, some spectra l forms consistent with the range (6.3 Hz - 7.5 Hz) observed in the instrumenta l seismometric measurements performed by the research group of the the Department of Earth Sciences of University of Florence on a ll the bodies of the architectura l complex were identified AA.VV. (2017). In Fig. 8d is represented, the stress sta te resulting from the analysis assumingclass of use CU= III, nominal life VN = 50 years and site spectrum.

(a) (d) Fig. 8. (a) Mode of vibration model 1; (b) Mode of vibration model 2; (c) Mode of vibration n. 134; (d) Analysis CU III, VN 50 years, site, direction x, principal maximum forces, model 2. It should be noted that the grey areas, where the tensile strength limit of 0.2 MPa is exceeded, are widespread. More specifica lly, the areas where tensile stresses exceed the limit va lue are more present in model 2. In no case, however, compression stresses greater than 3.0 MPa were found throughout the buildingmodels. 4. Conclusions The high exposure to which Ita lian monuments are subjected requires a careful eva luation of their seismic performance. This is necessary both for the protection of human lives and to preserve the artistic heritage from irreversible damage. In 2009 MIBACT through the Tuscan Direction of Cultura l Heritage and Landscape launched a (b) (c)