PSI - Issue 78

Matteo Calzolari et al. / Procedia Structural Integrity 78 (2026) 1119–1125

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Table 2. Kinematic analysis results.

a 0 [g] 0.060 0.209 0.521

a z [g] 0.118 0.214 0.118

a 0 /a z

Mechanism

(a)

0.508

(b) (c)

0.977 4.415

a 0 spectral acceleration of activation; a z peak floor acceleration. The seismic action was calculated using a PGA of 0.076 g, consistent with the values recorded near the building. Since all the mechanisms involve hinges at height, accelerations amplified by floor spectra were considered, as prescribed by section §C7.2.3 of the Italian Ministry of Infrastructure and Transport (2019). Overturning mechanisms were analyzed taking account of hinge setback, based on the average compressive strength of the masonry. The floor support was assumed to be equal to half of the wall thickness, with a linear distribution of pressures. The results of the kinematic analyses are reported in Table 2. As could be seen from results, the overall overturning mechanism (a) would have been activated if tie rods would not have been installed. Considering the post-installation condition of tie rods, the only active mechanism is the overturning of the upper portion (b), since the expulsion of the lower level is prevented (c). This mechanism is confirmed by the crack pattern: during the seismic event, the lower level did not mobilize, whereas the overturning mechanism of the upper level was activated, as confirmed by the opening of the crack recorded on the wall orthogonal to the facade during the seismic sequence. 5. Conclusion The study enables a detailed analysis of the current crack pattern of a Renaissance-era historic building representative of the urban fabric of Ferrara, identifying the most significant cracks and their underlying causes. The crack pattern reveals an interaction between in-plane and out-of-plane mechanisms within the structure, consistent with the direction of the main shock of the 2012 earthquake. Once the most vulnerable portion of the building was identified, the main structural modifications carried out over time have been examined, allowing the identification of the interventions that contributed to defining the building’s current configuration. Kinematic analysis, performed for both pre- and post-installation configurations of the tie rods, highlighted how this intervention effectively prevented the mobilization of the lower portion of the facade, leaving active only the overturning mechanism of the upper level. Thus, it could be concluded that the installed tie rods are a crucial and effective measure: in their absence, during the 2012 seismic sequence, the overall mechanism (a) shown in Fig. 5 and characterized by a significantly lower activation acceleration compared to mechanism (b), would have been activated. Future works will involve the analysis of structural behaviour, taking account of the in-plane action of masonry piers, and adopting different assumptions regarding floor stiffness, in order to assess the safety level associated with the presence of rigid or deformable diaphragms. Acknowledgements The present investigation was developed in the framework of the Research Program FAR 2024 of the University of Ferrara. Moreover, the analyses were developed within the activities of the (Italian) University Network of Seismic Engineering Laboratories (ReLUIS) in the research program funded by the (Italian) National Civil Protection (DPC) – Progetto DPC-ReLUIS 2024/26 – WP4. References

Alessandri, C., Garutti, M., Mallardo, V., & Milani, G. (2015). Crack patterns induced by foundation settlements: integrated analysis on a renaissance masonry palace in Italy. International Journal of Architectural Heritage 9(2): 111-129.