Issue 45

F. Brandão et alii, Frattura ed Integrità Strutturale, 45 (2018) 14-32; DOI: 10.3221/IGF-ESIS.45.02 22 of each vibration mode is small, it is necessary to take into account about the first 100 modes to describe the dynamic be- havior of the Church: the cumulative modal mass ratio is reported in Figure 9.(b). In general, it is possible to observe that the first mode associated with not negligible participating mass is a transversal mode, namely the first out-of-plane mode of the longitudinal walls of the main nave. Dispersion of vibration modes for such typology of structures has been already observed by other authors [40, 41, 42] and this can be considered a specific structural characteristic of these structures, in contrast with ordinary or modern buildings where the modal participating mass is generally greater than 70% and the first three modes give a cumulative mass generally greater than 85%. In addi- tion, the results shown by the modal analyses are in agreement with the observation of the systematic analysis of the dam- age suffered by the churches after major earthquakes, that highlight that the church seismic behavior is predominantly ruled by the activation of local collapse mechanisms on several macro-elements [41, 43, 44, 45, 46]. As a consequence, on- ly in the case of churches with symmetric plan layout and with effective connections between the various macro-elements, it could be significant to perform the safety checks with a pushover approach. The results of the modal analysis, in addition, show that no one of the first modes activates a relevant mass percentage, thus making doubtful the evaluation of the equivalent single-degree-of-freedom (SDOF) oscillator needed to perform the seismic check. Moreover, since the structure did not show a global box-behavior, it is not possible to identify a single control point representative of the whole model, which might uniquely define the structural capacity [47, 48]. Taking into account these remarks, which sub- stantially highlight the criticism of the pushover approach for such structural typology, linear time-history analyses have been herein performed to have a preliminary evaluation of the potential effects induced by seismic loading. Static analysis The identified numerical model has been preliminarily employed to perform a static analysis under dead and live loads. The stress maps are shown in Fig. 10, where both the maximum principal stress (Figs. 10.(a) and 10.(b)) and the vertical stresses (Figs. 10.(c) and 10.(d)) are reported. The maximum tensile stress is about 0.14 MPa and was found in many re- gions of the structure such as: in the center of the arch facing the altar; in the openings of the Lateral Façade west; in the openings of the Lateral Tower and the connection between the central arches and the Lateral Tower. This value is lower than the maximum admissible value assumed for the tensile strength (0.16 MPa). Figure 10 : Results from the static analysis of the Nossa Senhora das Dores Church: (a) and (b) maximum principal; (c) and (d) vertical stress. Unit in MPa. Positive values of normal stress can be mainly identified in the surrounding opened regions, like the arches in the doors and the windows. In the main façades, positive values of normal stress indicated the existence of tensile stresses especially between the top of the arches of the doors and the bottom of the windows, while negative values of normal stress are re- lated to compression. However, 0.69 MPa was the maximum value of the compressive stress, while the maximum value of (a) (b) (c) (d)