transversal and torsional stiffness, and significant out-of-plane deformations of the elements. Furthermore the plan deformed configurations of the structure confirm that the seismic loads acting along the church transversal direction involve remarkable out of plane deformations of the orthogonal structural elements.
The study of the seismic behavior has been made using a non-linear static analysis method. Seismic loads are evaluated with respect to the New Italian rule (DM 14/09/05 & OPCM 3274) using a pushover analysis (Galasco et al. 2006, Kim & D'Amore 1999). Based on this analysis method, the effects of the seismic loads are evaluated through the application of two systems of horizontal forces perpendicular to one another. These forces, not acting simultaneously, are evaluated taking into account two load distributions. The first load distribution is directly proportional to building's masses
(uniform); the second load distribution is proportional to the product of the masses for the displacements of the corresponding first buildings modal shape. These load distributions could be considered as two limit states for the building's capacity. The first distributions assume that the horizontal loads representative of inertia seismic forces are constant with respect to the building's height. This means that the displacements on the lower level of the building are overestimated, while the opposite happens on the displacement on the top level. On the contrary the second distributions overvalue the displacements on top level. In this study a conventional pushover is assumed, i.e. loads applied on the building don't change with progressive degradation of the buildings during loading. This means that the conventional pushover does not account for the progressive changes in modal frequencies due to yielding and cracking on the structure during loading. This is a critical point for the application of conventional pushover to the analysis of historic masonry buildings, because it is predictable that the progressive damage of the building may also lead to period elongation, and therefore to different spectral amplifications (Antoniou & Pinho 2004). Hence the hypothesis of invariance of static loads could cause an overestima-tion in the analysis of masonry building especially when a non uniform damage on the buildings or a high level of cracking are expected. Further studies will be devoted to the investigation ofthis point. However, also in its conventional form, the pushover provides an efficient alternative to expensive computational inelastic dynamic analyses.
The seismic loads to apply to the building have been evaluated through modal analysis with the elastic response spectrum. For the case study the Class 1 spectrum as reported in the New Italian Rule (DM 14/09/05), with a ground type A corresponding to rock or other rock-like geological formation, is assumed. Following expressions are derived:
The peak ground acceleration (PGA) for the reference return period is denoted by ag and for the case study is assumed equal to 0.35 g. S is a factor depending on the ground type that in this case (ground type A) is equal to 1.0. Next, results concerning church behavior are detailed. The critical load distribution is the one acting on the y-direction (direction perpendicular to main nave direction). This is quite expected due to the fact that the transversal direction of the church involves remarkable out of plane deformations of the orthogonal structural elements.
Figure 8 reports the displacements on the transversal direction at the end of the analysis; Figure 9 reports the corresponding crack pattern. The capacity curve is reported in Figure 10 with the corresponding behavior of the equivalent bilinear systems. For this system it has been obtained, by eq. (2) (see DM 14/09/05 for more details), that the seismic displacement demand is dmax = 89 mm against the building displacement capacity that is equal to 88 mm.
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