Issue 45

F. Brandão et alii, Frattura ed Integrità Strutturale, 45 (2018) 14-32; DOI: 10.3221/IGF-ESIS.45.02 20 The mechanical properties of the masonry are - obviously - key parameters, being the performance of the numerical mod- el closely connected to their value. Concerning the estimation of the mechanical properties of the clay brick, the values reported in the literature due to the impossibility to proceed with experimental in situ characterization were preliminarily considered. The Young’s modulus (E), the specific weight (W) and the compressive strength (f c ) were obtained by the Ital- ian recommendation “ Norme Tecniche per le Costruzioni (NTC2008) ” [31], taking into account as masonry type “ Muratura in mattoni pieni e malta di calce ” (full brick masonry with lime mortar). The tensile strength of the masonry (f t ), was assumed as 5% of the compressive strength (f c ). For the Poisson coefficient (ν), a value of 0.20 was considered, as commonly adopted in many studies [29, 32, 33]. Tab. 2 reports the mechanical properties of the clay brick masonry adopted in the numerical model. Calibration of the mechanical properties The numerical model of the Nossa Senhora das Dores Church was subsequently calibrated based on the experimental re- sults obtained by performing environmental vibration tests (EVT). From the EVT, three testing positions were recorded and the Fourier Spectrum on the two principal directions of the Church was calculated. The obtained results are shown in Fig. 7.(a) for the X direction (the transversal one) and in Fig. 7.(b) for the Y direction (the longitudinal one). Analyzing the two spectra, it can be inferred that the first 3 natural frequencies of the church are included in the range between 2.00 Hz and 3.50 Hz. Analyzing the frequencies with the highest amplitude with respect to each main direction of the church, the first fundamental frequency resulted 2.391 Hz in the X direction, the second was 2.880 Hz also in the X direction since the amplitude of the first two peaks in the X direction is greater than in Y direction. The third natural frequency was obtained in the Y direction, with the third peak of the spectrum in Fig. 7.(b), and was characterized as 3.125 Hz because in this direction its amplitude is greater than the third peak of spectrum in Fig. 7.(a). (a) (b) Figure 7 : Fourier spectrum in (a) X direction and (b) in Y for the three points tested. The elastic parameters of the FE model were hence calibrated in order to fit the natural frequencies obtained by the EVT, assuming as starting values the ones estimated in accordance with the Italian recommendation [31]. The specific weight and the masses have been keeping constant, and the Young's Modulus has been iteratively updated (within the range from 1.50 GPa to 1.75 GPa) in order to fit the experimental values. The first three natural frequencies were assumed sufficient for the calibration. It is worth noting that, after calibrating the Young's Modulus in order to reproduce the first numerical natural frequency, a good adherence between experimental and numerical results was also obtained for the second and third frequency, denoting that the numerical model reproduces correctly stiffness and masses of the church. The final identified Young's Modulus was equal to 1.70 GPa. With this fitting, based only on the first frequency, the results and the errors associated with each frequency are shown in Tab. 3, while the first three numerical modal shapes are shown in Fig. 8. Mode Exp. Frequency (Hz) Ansys Frequency (Hz) Error (%) Mode Type 1 2.391 2.403 0.502 Transversal bending (X direction) 2 2.880 2.806 2.637 Transversal bending (X and Y direction) 3 3.125 3.084 1.329 Longitudinal bending (Y direction) Table 3 : Comparison between the experimental and numerical frequencies.