Abstract
The role played by inclination in both the load carrying capacity and seismic assessment of masonry bell towers is investigated through the results obtained from different analyses on three case studies. The Italian Code for the built heritage is not explicit about the influence of inclination on the seismic assessment of towers, leaving to practitioners the task to properly consider it, potentially leading to both an overestimation of the capacity and an underestimation of the horizontal actions. The case studies investigated in this paper are three leaning masonry bell towers, all exhibiting a quite meaningful inclination and all located in Emilia-Romagna region (Italy), recently (2012) stricken by a moderate/high intensity seismic sequence. This study compares the procedure provided by the Italian Code with the finite element (FE) results obtained through non-linear static analyses and proposes a modification of the Italian code simplified mechanical model (SMM), which explicitly accounts for the actual inclination of the towers within a cantilever beam approach. The FE results show that inclination may considerably reduce the load carrying capacity, increasing the seismic vulnerability of the structures. The SMM approach proposed properly takes into account the role played by inclination, always providing results on the safe side with respect to FEM.
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References
Abruzzese D, Miccoli L, Yuan J (2009) Mechanical behavior of leaning masonry Huzhu Pagoda. J Cult Herit 10:480–486
Anzani A, Binda L, Carpinteri A, Invernizzi S, Lacidogna G (2010) A multilevel approach for the damage assessment of historic masonry towers. J Cult Herit 11:459–470
Bartoli G, Betti M, Vignoli A (2016) A numerical study on seismic risk assessment of historic masonry towers: a case study in San Gimignano. Bull Earthq Eng 14:1475
Bayraktar A, Sahin A, Özcan M, Yildirim F (2010) Numerical damage assessment of Haghia Sophia bell tower by nonlinear FE modeling. Appl Math Model 34:92–121
Bernardeschi K, Padovani C, Pasquinelli G (2004) Numerical modelling of the structural behaviour of Buti’s bell tower. J Cult Herit 5:371–378
Binda L, Zanzi L, Lualdi M, Condoleo P (2005) The use of georadar to assess damage to a masonry bell tower in Cremona, Italy. NDT & E Int 38:171–179
Camata G, Cifelli L, Spacone R, Conte J, Torrese P (2008) Safety analysis of the bell tower of S. Maria Maggiore Cathedral in Guardiagrele (Italy). In: 14th World conference on earthquake engineering, Beijing
Carpinteri A, Invernizzi S, Lacidogna G (2006) Numerical assessment of three medieval masonry towers subjected to different loading conditions. Mason Int 19:65–75
Casolo S (1998) A three dimensional model for vulnerability analyses of slender masonry medieval towers. J Earthq Eng 2(4):487–512
Casolo S (2001) Significant ground motion parameters for evaluation of the seismic performance of slender masonry towers. J Earthq Eng 5(2):187–204
Casolo S, Milani G, Uva G, Alessandri C (2013) Comparative seismic vulnerability analysis on ten masonry towers in the coastal Po Valley in Italy. Eng Struct 49:465–490
Chopra AK, Goel RK (1999) Capacity-demand-diagram methods for estimating seismic deformation of inelastic structures: SDF systems. Pacific Earthquake Engineering Research Center College of Engineering University of California. Report No. PEER-1999/02. University of California, Berkeley
Circolare 617 2009 (Explicative Notes of Italian National Technical Code) (2009) Istruzioni Per L’applicazione Delle «Nuove Norme Tecniche Per Le Costruzioni» Di Cui Al Decreto Ministeriale 14 Gennaio 2008, CIRCOLARE 2 Febbraio 2009, Gazzetta Ufficiale n. 47, 26 Febbraio 2009 (in Italian)
CSI, Computers and Structures Inc. (2013) CSi Analysis Reference Manual for SAP2000, ETABS, SAFE and CSiBridge, Berkeley
DPCM (Direttiva del Presidente del Consiglio dei Ministri) (2011) Linee Guida Per La Valutazione E La Riduzione Del Rischio Sismico Del Patrimonio Culturale Con Riferimento Alle Norme Tecniche Per Le Costruzioni Di Cui Al Decreto Del Ministero Delle Infrastrutture E Dei Trasporti Del 14 Gennaio 2008 [Guidelines for assessment and sesimic risk reduction of cultural heritage], Rome (in Italian)
Fajfar P (2000) A nonlinear analysis method for performance based seismic design. Earthq Spectra 16(3):573–592
Heyman J (1992) Leaning towers. Meccanica 27(3):153–159
Heyman J (1995) The stone skeleton: structural engineering of masonry architecture. Cambridge University Press, Cambridge
Ivorra S, Pallares FJ (2006) Dynamic investigations on a masonry bell tower. Eng Struct 28:660–667
Lourenço PB, de Borst R, Rots J (1997) A plane stress softening plasticity model for orthotropic materials. Int J Numer Methods Eng 40:4033–4057
Luciano R, Sacco E (1998) Damage of masonry panels reinforced by FRP sheets. Int J Solids Struct 35(15):1723–1741
Milani G, Valente M (2015a) Comparative pushover and limit analyses on seven masonry churches damaged by the 2012 Emilia-Romagna (Italy) seismic events: possibilities of non-linear Finite Elements compared with pre-assigned failure mechanisms. Eng Fail Anal 47:129–161
Milani G, Valente M (2015b) Failure analysis of seven masonry churches severely damaged during the 2012 Emilia-Romagna (Italy) earthquake: non-linear dynamic analyses vs conventional static approaches. Eng Fail Anal 54:13–56
Milani G, Lourenço PB, Tralli A (2006a) Homogenised limit analysis of masonry walls, Part I: failure surfaces. Comput Struct 84(3–4):166–180
Milani G, Lourenço PB, Tralli A (2006b) Homogenised limit analysis of masonry walls, Part II: structural examples. Comput Struct 84(3–4):181–195
Milani G, Casolo S, Naliato A, Tralli A (2012) Seismic assessment of a medieval masonry tower in northern Italy by limit, nonlinear static, and full dynamic analyses. Int J Archit Herit 6(5):489–524
Modena C, Valluzzi MR, Tongini FR, Binda L (2002) Design choices and intervention techniques for repairing and strengthening of the Monza cathedral bell-tower. Constr Build Mater 16:385–395
NTC 2008 (New Technical Norms on Constructions) (2008) Decreto Ministeriale 14 Gennaio 2008, Nuove norme tecniche per le costruzioni. Ministero delle Infrastrutture (GU n.29 04/02/2008), Rome (in Italian)
Pena F, Lourenço PB, Mendez N, Oliveira D (2010) Numerical models for the seismic assessment of an old masonry tower. Eng Struct 32:1466–1478
Pintucchi B, Zani N (2014) Effectiveness of nonlinear static procedures for slender masonry towers. Bull Earthq Eng 12:2531
Riva P, Perotti F, Guidoboni E, Boschi E (1998) Seismic analysis of the Asinelli Tower and earthquakes in Bologna. Soil Dyn Earthq Eng 17:525–550
Russo G, Bergamo O, Damiani L, Lugato D (2010) Experimental analysis of the Saint Andrea Masonry Bell Tower in Venice. A new method for the determination of Tower Global Young’s Modulus E. Eng Struct 32:353–360
Timoshenko S (1938) Vibration problems in engineering. D. Van Nostrand, Inc., New York, pp 307–317
Valente M, Milani G (2016a) Non-linear dynamic and static analyses on eight historical masonry towers in the North-East of Italy. Eng Struct 114:241–270
Valente M, Milani G (2016b) Seismic assessment of historical masonry towers by means of simplified approaches and standard FEM. Constr Build Mater 108:74–104
Vanmarcke EH, Fenton GA, Heredia-Zavoni E (1999) SIMQKE-II, conditioned earthquake ground motion simulator. User’s manual. Princeton University, Princeton
Zalka KA (2002) Global structural analysis of buildings. Taylor & Francis E-Library, London, pp 43–60
Zanotti Fragonara L, Boscato G, Ceravolo R et al (2016) Dynamic investigation on the Mirandola bell tower in post-earthquake scenarios. Bull Earthq Eng. doi:10.1007/s10518-016-9970-z
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Milani, G., Shehu, R. & Valente, M. Role of inclination in the seismic vulnerability of bell towers: FE models and simplified approaches. Bull Earthquake Eng 15, 1707–1737 (2017). https://doi.org/10.1007/s10518-016-0043-0
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DOI: https://doi.org/10.1007/s10518-016-0043-0