Case Studies
May 11, 2018

Medieval Arch Bridges in the Lanzo Valleys, Italy: Case Studies on Incremental Structural Analysis and Fracturing Benefit

Publication: Journal of Bridge Engineering
Volume 23, Issue 7

Abstract

After presenting a historical overview concerning the masonry arch design, this article proposes a computational procedure that allows the capture of the arch-damaging process, which takes place when the conditions assessed through linear elastic analysis are no longer valid and before the set-in of the conditions established by means of limit analysis. This evolutionary analysis of the fracturing process is then applied to three medieval masonry arch bridges located in the Lanzo Valleys (Italy). Through damage assessment, the present work shows how the arch thrust line is affected by crack formation and the internal stress redistribution; it also shows that the maximum admissible load evaluated by means of linear elastic fracture mechanics is greater than the load predicted by the theory of elasticity. Such an increment in terms of maximum admissible load can be defined as the fracturing benefit, and it is analogous to the plastic benefit of limit analysis.

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Acknowledgments

The authors are grateful to Eng. Alessandro Lano for the collaboration in the analysis of the historical monuments.

References

Accornero, F., Lacidogna, G., and Carpinteri, A. (2016). “Evolutionary fracture analysis of masonry arches: Effects of shallowness ratio and size scale.” C.R. Mec., 344(9), 623–630.
ARCO [Computer software]. University of Brescia, Brescia, Italy.
Becchi, A., and Foce, F. (2002). Degli archi e delle volte. Arte del costruire tra meccanica e stereotomia, Marsilio, Venezia, Italy.
Benvenuto, E., and Radelet de Grave, P. (1995). Between mechanics and architecture, Birkhäuser, Basel, Switzerland.
Betti, M., Drosopoulos, G. A., and Stavroulakis, G. E. (2008). “Two non-linear finite element models developed for the assessment of failure of masonry arches.” C.R. Mec., 336(1-2), 42–53.
Block, P., De Jong, M. J., and Ochsendorf, J. A. (2006). “As hangs the flexible line: Equilibrium of masonry arches.” Nexus Network J., 8(2), 13–24.
Boothby, T. E. (2001). “Analysis of masonry arches and vaults.” Prog. Struct. Eng. Mater., 3(3), 246–256.
Brencich, A., and Morbiducci, R. (2007). “Masonry arches: Historical rules and modern mechanics.” Int. J. Archit. Heritage, 1(2), 165–189.
Carpinteri, A. (1982). “Application of fracture mechanics to concrete structures.” J. Struct. Div., 108(4), 833–848.
Carpinteri, A. (1989a). “Cusp catastrophe interpretation of fracture instability.” J. Mech. Phys. Solids, 37(5), 567–582.
Carpinteri, A. (1989b). “Size effects on strength, toughness, and ductility.” J. Eng. Mech., 1375–1392.
Carpinteri, A., and Accornero, F. (2018). “Multiple snap-back instabilities in progressive microcracking coalescence.” Eng. Fract. Mech., 187, 272–281.
Carpinteri, A., and Carpinteri, An. (1982). “Softening and fracturing process in masonry arches.” Proc., 6th Int. Brick Masonry Conf., International Masonry Society, Whyteleafe, U.K, 502–510.
Carpinteri, A., Lacidogna, G., and Accornero, F. (2015). “Evolution of fracturing process in masonry arches.” J. Struct. Eng., 04014132.
Casapulla, C. (2001). “Dry rigid block masonry: Safe solutions in presence of Coulomb friction.” WIT Trans. Built Environ., 55, 251–261.
Casapulla, C., and Argiento, L. U. (2016). “The comparative role of friction in local out-of-plane mechanisms of masonry buildings. Pushover analysis and experimental investigation.” Eng. Struct., 126, 158–173.
Castigliano, A. (1879). Théorie de l’Equilibre des systèmes elastiques et ses applications, A. F. Negro, Turin, Italy.
Cavallari-Murat, A. (1973). Lungo la Stura di Lanzo, Istituto Bancario San Paolo, Torino, Italy.
Cavicchi, A., and Gambarotta, L. (2007). “Lower bound limit analysis of masonry bridges including arch-fill interaction.” Eng. Struct., 29(11), 3002–3014.
Coulomb, C. (1773). Mémoires de mathématique et de physisque présentés à l’Académie royale des sciences, et lus dans les assemblées, Académie Royale des Sciences, Paris.
Couplet, C. A. (1731). De la poussée des voutes, Académie Royale des Sciences, Paris.
De La Hire, P. (1730). “Traité de mécanique, où l’on explique tout ce qui est necessaire dans la pratique des arts.” Mémoires de l’Académie Royale des Sciences, 9, 1–333.
Drosopoulos, G. A., Stavroulakis, G. E., and Massalas, C. V. (2006). “Limit analysis of a single span masonry bridge with unilateral frictional contact interfaces.” Eng. Struct., 28(13), 1864–1873.
Fett, T. (2001). “Mixed mode stress intensity factor for partially opened cracks.” Int. J. Fract., 111(4), 67–72.
Fuller, G. (1875). “Curve of equilibrium for a rigid arch under vertical forces.” Minutes Proc. Inst. Civ. Eng., 40(1875), 143–149.
Gilbert, M., and Melbourne, C. (1994). “Rigid block analysis of masonry structures.” Struct. Eng., 72(21), 356–361.
Heyman, J. (1966). “The stone skeleton.” Int. J. Solids Struct., 2(2), 249–279.
Heyman, J. (1982). The masonry arch, Ellis Horwood, Chichester, U.K.
Heyman, J. (1998). Structural analysis: A historical approach, Cambridge University Press, Cambridge, U.K.
Hooke, R. (1675). A description of helioscopes, and some other instruments, T.R. for John Martyn, London.
Karnowsky, I. (2012). Theory of arched structures, Springer, New York.
Kooharian, A. (1953). “Limit analysis of voussoir (segmental) and concrete arches.” J. Am. Concr. Inst., 89, 317–328.
Lacidogna, G., and Accornero, F. (2018). “Elastic, plastic, fracture analysis of masonry arches: A multi-span bridge case study.” Curved Layered Struct., 5(1), 1–9.
Lacidogna, G., Accornero, F., Corrado, M., and Carpinteri, A. (2013). “Crushing and fracture energies in concrete specimens monitored by Acoustic Emission.” Proc., 8th Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures, FraMCos 2013, International Center for Numerical Methods in Engineering, Barcelona, Spain, 1726–1736.
Lourenço, P. (2000). “Anisotropic softening model for masonry plates and shells.” J. Struct.Eng., 1008–1015.
Mascheroni, L. (1785). Nuove ricerche sull'Equilibrio delle volte, Locatelli, Bergamo.
Mery, E. (1840). “Équilibre des voûtes en berceau.” Annales des Ponts et Chaussées, 1, 50–70.
Milani, G., and Lourenço, P. B. (2012). “3D non-linear behavior of masonry arch bridges.” Comput. Struct., 110–111, 133–150.
Navier, C. L. (1833). Résumé des leçons données à l'École des ponts et chaussées sur l'Application de la mécanique à l'Établissement des constructions et des machines, Paris.
Orduña, A., and Lourenço, P. B. (2005). “Three-dimensional limit analysis of rigid blocks assemblages. Part I: Torsion failure on frictional interfaces and limit analysis formulation.” Int. J. Solids Struct., 42(18–19), 5140–5160.
Page, J. (1993). Masonry arch bridges, Her Majesty’s Stationery Office, London.
Paradiso, M., Tempesta, G., Galassi, S., and Pugi, F. (2007). Sistemi voltati in muratura, DEI, Rome, Italy.
Pippard, A. J. S. (1948). “The approximate estimation of safe loads on masonry bridges.” The civil engineer in war: A symposium of paper on war-time engineering problems, Thomas Telford, London, 365–372.
Poleni, G. (1748). Memorie istoriche della gran cupola del tempio vaticano, Stamperia del Seminario, Padova, Italy.
Poncelet, J. V. (1852). “Examen critique et historique des principales théories ou solutions concernant l'équilibre des voûtes.” C.R. Acad. Sci., 35, 494–587.
Tada, H., Paris, P. C., and Irwin, G. R. (1985). The stress analysis of crack handbook, Paris Productions, St. Louis.
Taylor, N., and Mallinder, P. (1993). “The brittle hinge in masonry arch mechanisms.” Struct. Eng., 71(20), 359–366.
Tóth, A. R., Orbán, Z., and Bagi, K. (2009). “Discrete element analysis of a stone masonry arch.” Mech. Res. Commun., 36(4), 469–480.
Vitruvius Pollio, M. (1914). De Architectura, Harvard University Press, Cambridge, MA.
Vittone, B. A. (1766). Istruzioni diverse concernenti l'officio dell'Architetto civile, Agnelli, Lugano, Switzerland.

Information & Authors

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Published In

Go to Journal of Bridge Engineering
Journal of Bridge Engineering
Volume 23Issue 7July 2018

History

Received: Sep 13, 2017
Accepted: Jan 8, 2018
Published online: May 11, 2018
Published in print: Jul 1, 2018
Discussion open until: Oct 11, 2018

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Authors

Affiliations

Federico Accornero [email protected]
Research Assistant, Dept. of Structural Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy (corresponding author). E-mail: [email protected]
Giuseppe Lacidogna
Associate Professor, Dept. of Structural Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy.
Alberto Carpinteri, F.ASCE
Full Professor, Dept. of Structural Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy.

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