Issue 45

F. Brandão et alii, Frattura ed Integrità Strutturale, 45 (2018) 14-32; DOI: 10.3221/IGF-ESIS.45.02 21 Figure 8 : First three modal shapes of the Nossa Senhora das Dores Church. In literature is rather usual the use of ambient vibration testing information for calibration of numerical models, summa- rizing the natural frequencies information about the modal parameters of the structure [34, 35, 36, 37, 38, 39]; usually, an error between experimental and numerical results up to about 5 % is considered acceptable. In the present calibration the biggest error - obtained as the difference between the natural frequency of the structure extracted by ambient vibration test and the natural frequency extracted by numerical analysis - was 2.6 %, therefore the calibration has been considered successful (taking into account both the aim of the numerical model and its refinement). The elastic mechanical properties of the clay brick masonry after model updating are summarized in Tab. 4. E (GPa) W (kN/m 3 ) f c (MPa) f t (MPa) ν 1.70 18.00 3.20 0.16 0.20 Table 4 : Mechanical properties adopted in the calibrated numerical model Analyzing the numerical modal shapes of the church (Fig. 8), it is possible to observe that the first mode shape involves the translation in the weakest transversal direction (X direction) of the wall of the North lateral façade, with significant out-of-plane deformation (out-of-plane mode of the longitudinal wall). The second and third modal shapes are still local modes, involving out-of-plane deformation of the façade, of the lateral walls and the central arches and the lateral tower. The distribution of the mode shapes demonstrates that the church displays low transversal and torsional stiffness, with significant out-of-plane deformations of the elements. This demonstrates that the dynamic response of the Church is strongly affected by the local behavior of elementary macro-elements. It is possible to observe that the participating mass- es of each mode of vibration are affected by high dispersion: the distribution of the first 100 vibration modes (in the lon- gitudinal and transversal direction) is reported in Figure 9.(a). (a) (b) Figure 9 : (a) Modal participating mass ratios vs. main periods and (b) cumulative modal mass ratio (CMF). The modal participating mass ratios (ME) is plotted as a function of the corresponding period (T), and it is possible to ob- serve that almost all vibration modes have modal participating mass ratio less than 10-15%. As the participating mass ratio