PSI - Issue 44

Elena Michelini et al. / Procedia Structural Integrity 44 (2023) 1530–1537 Elena Michelini et al / Structural Integrity Procedia 00 (2022) 000 – 000

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Fig. 5. (a) General view of the FE model; (b) example of vaulted floor in the numerical model.

Loads were defined according to the Italian design code (NTC 2018), by dividing floor areas into different categories according to their use (the most of them are public offices). Loads acting on floors and stairs were firstly applied onto the corresponding bearing walls - depending on their tributary area - and subsequently transformed into masses by means of the “load to mass” MIDAS option. Since the numerical model is functional to the dynamic identification of the Town Hall building, a macro-modelling approach was adopted, and masonry was treated as an isotropic continuum material with linear elastic behavior. As a first attempt, the values of elastic modulus E and weight per unit volume w suggested by the Italian Code (NTC 2018, Circ. N.7, 2019) for barely cut stone masonry, properly dressed, were adopted. Based on the available documentation relative to the vulnerability assessment of the Town Hall, an intermediate level of knowledge was assumed according to the Italian Code (NTC 2018) and to the Guidelines for the assessment and reduction of seismic risk for cultural heritage according to the Italian Standard (2011). The elastic modulus was then set equal to the central value of the interval reported in the Italian code, multiplied by an improvement coefficient equal to 1.3 suggested from the Italian Code in case of good quality mortar, as also assumed in the available documentation concerning the vulnerability assessment. Consequently, the following values were initially adopted for masonry walls in the numerical model: E = 2262 MPa, w = 21 kg/m 3 ,  = 0.3. The shear modulus of the masonry, G , was directly derived from the software, based on the chosen values of E and  . It should be noted that the same parameters were also applied for masonry vaults and flights of stairs, but due to the widespread crack pattern that could be observed on site a reduced stiffness was assumed for these elements, by simply halving the elastic modulus value. 5. Calibration of the numerical model and comparison with experimental measurements The dynamic properties and mode shapes of the structure obtained from the FE model are summarized in Fig. 6 and Table 3, where they are also compared to experimental results in terms of natural frequencies. From the analysis of the obtained results, it can be observed that numerical frequencies are quite similar to the experimental ones even before the calibration process (with a maximum scatter lower than 13%). The first two numerical mode shapes, which are decoupled and almost translational in Y and X directions, are however inverted with respect to those obtained from AVT. On this point, it should be remarked that the first two experimental modes have very similar natural frequencies and that all the measurements were carried out during the same day, without further reps over time. However, a reduced stiffness in X direction seems plausible, as already discussed in Section 3. The 3 rd , 4 th and 5 th modes show instead a good correlation with the experimental ones. In order to improve the match between numerical and experimental results, the FE model was manually updated by iteratively changing some selected parameters influencing the structural response, following the “compare -alter- check” procedure discussed in Pierdicca et al. (2016). Among the many factors that can be considered to the purpose (i.e. geometry, boundary conditions, walls current state – with or without cracks – and continuity, floor stiffness, masonry weight per unit volume, elastic modulus, etc.), it has been chosen herein to simply alter the elastic modulus of the masonry E . Basically, a trial and error approach was followed: at each iteration, the experimental and numerical results are first compared to each other in terms of modes shapes and frequencies, and subsequently a new iteration is performed by altering E . Finally, the