PSI - Issue 11

Siro Casolo et al. / Procedia Structural Integrity 11 (2018) 20–27 Siro Casolo & Giuseppina Uva / Structural Integrity Procedia 00 (2018) 000–000

27

8

loading, even in the presence of a lesser destructive potential. Figure 8 shows the variation of damage consequent to the application of a pair of ground motions, the first of which is the fixed reference shock while the second is one of the 24 recordings at turn. It is interesting to note that these aftershocks are clearly irrelevant if their intensity in terms of SI is much lower (about 70% to 80%) than the one of the reference ground motion. It is quite evident that the threshold of irrelevance is SI ≈ 60 cm, below which the effect of an aftershock is negligible. References Addessi, D. & Sacco, E. 2016. Enriched plane state formulation for nonlinear homogenization of in-plane masonry wall. Meccanica 51: 2891 2907. Bacigalupo, A. & Gambarotta, L. 2012. Computational two-scale homogenization of periodic masonry: Characteristic lengths and dispersive waves. Computer Methods in Applied Mechanics and Engineering, volume 213–216, 16-28. Bertolesi, E., Milani, G., & Casolo, S. 2018. Homogenization towards a mechanistic rigid body and spring model (HRBSM) for the non-linear dynamic analysis of 3D masonry structures. Meccanica, 53(7), 1819-1855. Bertolesi, E., Milani, G., & Casolo, S. 2017. Homogenized rigid body and spring model (RBSM) for the non-linear dynamic analysis of historic masonry church facades. Paper presented at the COMPDYN 2017 – Proc. of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, 1 2282-2289. Bertolesi, E., Milani, G., & Casolo, S. 2016. Non-linear dynamic analyses of 3D masonry structures by means of a homogenized rigid body and spring model (HRBSM). AIP Conference Proceedings. Betti M., Bartoli M., Orlando M., 2010. Evaluation study on structural fault of a Renaissance Italian palace, Engineering Structures, 32(7), pp.1801 1813, Casolo, S. 1999. Rigid element model for non-linear analysis of masonry façades subjected to out-of-plane loading. Communications in Numerical Methods in Engineering, 15(7), 457-468. Casolo, S. 2000. Modelling the out-of-plane seismic behaviour of masonry walls by rigid elements. Earthquake Engineering and Structural Dynamics, 29(12), 1797-1813. Casolo, S. 2006. Macroscopic modelling of structured materials: Relationship between orthotropic Cosserat continuum and rigid elements. International Journal of Solids and Structures, 43(3-4), 475-496. Casolo, S. 2009. Macroscale modelling of microstructure damage evolution by a rigid body and spring model. Journal of Mechanics of Materials and Structures, 4(3), 551-570. Casolo, S. 2017. A numerical study on the cumulative out-of-plane damage to church masonry façades due to a sequence of strong ground motions. Earthquake Engineering and Structural Dynamics, 46(15), 2717-2737. Casolo, S., Neumair, S., Parisi, M. A., & Petrini, V. (2000). Analysis of seismic damage patterns in old masonry church facades. Earthquake Spectra, 16(4), 757-773. doi:10.1193/1.1586138 Casolo, S., & Milani, G. 2010. A simplified homogenization-discrete element model for the non-linear static analysis of masonry walls out-of plane loaded. Engineering Structures, 32(8), 2352-2366. Casolo, S., & Milani, G. 2013. Simplified out-of-plane modelling of three-leaf masonry walls accounting for the material texture. Construction and Building Materials, 40, 330-351. Casolo, S., & Uva, G. 2010. Out-of-plane seismic response of masonry façades some comparisons among full dynamic and pushover analysis. [Risposta sismica fuori del piano di facciate in muratura: Confronto tra analisi dinamiche non-lineari e analisi pushover] Ingegneria Sismica, 27(3), 33-54. Casolo, S., & Uva, G. 2013. Nonlinear analysis of out-of-plane masonry façades: Full dynamic versus pushover methods by rigid body and spring model. Earthquake Engineering and Structural Dynamics, 42(4), 499-521. Doglioni, F., Moretti A, Petrini V. 1994. Le Chiese e il Terremoto. Lint press: Trieste. In Italian. Giuffré, A. 1993. Sicurezza e conservazione dei centri storici, il caso di Ortigia. Ed. Laterza (1993) Giuffré, A. 1999. A mechanical model for statics and dynamics of historical masonry buildings. Protection of the architectural heritage against earthquakes. No. 359 in CISM courses and lectures. Wien: Springer-Verlag; 1996. Pantò, B., Cannizzaro, F., Caliò, I., & Lourenço, P. B. 2017. Numerical and experimental validation of a 3D macro-model for the in-plane and out of-plane behavior of unreinforced masonry walls. International Journal of Architectural Heritage, 11(7), 946-964. Peña, F. & García, N. 2016. Numerical evaluation of the seismic behavior of façades of Mexican colonial churches. Engineering Failure Analysis, 62, 164-177. Petracca, M., Pelà, L., Rossi, R., Oller, S., Camata, G., Spacone, E. 2017. Multiscale computational first order homogenization of thick shells for the analysis of out-of-plane loaded masonry walls. Computer Methods in Applied Mechanics and Engineering, 315, 273–301. Pietruszczak, S., Ushaksarei, R. 2003. Description of inelastic behaviour of structural masonry. Int J Solids Struct; 40(15), 4003–4019. Preciado, A., Orduña A., Bartoli G., Budelmann H., 2015. Façade seismic failure simulation of an old Cathedral in Colima, Mexico by 3D Limit Analysis and nonlinear Finite Element Method, Engineering Failure Analysis, Volume 49, pp. 20-30. Uang C, Bertero V. 1990. Evaluation of seismic energy in structures. Earthq Eng Struct Dynam; 19(1):77–90. Uva, G. & Salerno, G. 2006. Towards a multiscale analysis of periodic masonry brickwork: A FEM algorithm with damage and friction. International Journal of Solids and Structures, 43(13), 3739-3769. Vitruvius Pollio Marcus, De Architectura libri decem (The Ten Books on Architecture), Roma, 1st century BC.