Abstract
Masonry arch structures, and, more generally, vaulted structures, are traditionally assessed using a well-established approach, such as linear elasticity or limit analysis, whereby system behavior at the intermediate stage—which occurs when the material’s tensile strength has been exceeded but the collapse mechanism has not yet formed—is disregarded. A more accurate interpretation requires a thorough analysis that can take into account the intermediate cracking stage and uses a constitutive law providing a closer approximation to the actual behavior of the material. In this paper, an evolutionary fracturing process analysis for the stability assessment of masonry arches is presented. This method makes it possible to capture the damaging process that takes place when the conditions evaluated by means of linear elastic analysis no longer apply and before the conditions assessed through limit analysis set in. Furthermore, the way the thrust line is affected by the opening of cracks and the redistribution of internal stresses can be checked numerically. Finally, by applying this evolutionary method, a numerical calculation of the arch of the Mosca Bridge over the Dora River in Turin, Italy, is described, and the results are compared with those obtained by Castigliano’s iterative analysis.
Get full access to this article
View all available purchase options and get full access to this article.
References
Benvenuto, E., and Radelet de Grave, P. (1995). Between mechanics and architecture, Birkhäuser, Basel, Switzerland.
Berto, L., Saetta, A., Scotta, R., and Vitaliani, R. (2002). “An orthotropic damage model for masonry structures.” Int. J. Numer. Meth. Eng., 55(2), 127–157.
Bocca, P., Carpinteri, A., and Valente, S. (1989). “Fracture mechanics of brick masonry: Size effect and snap-back analysis.” Mater. Struct., 22(5), 364–373.
Broek, D. (1984). Elementary engineering fracture mechanics, Martinus Nijhoff Publishers, Leiden, Netherlands.
Buyukozturk, O., and Hearing, B. (1998). “Crack propagation in concrete composites influenced by interface fracture parameters.” Int. J. Solids Struct., 35(31–32), 4055–4066.
Carpinteri, A. (1981). “Static and energetic fracture parameters for rocks and concretes.” Mater. Struct., 14(3), 151–162.
Carpinteri, A. (1982). “Application of fracture mechanics to concrete structures.” J. Struct. Div., 108(4), 833–848.
Carpinteri, A. (1983). “Stiffness loss and fracture resistance of a cracked beam with circular cross section.” Meccanica, 18(3), 156–162.
Carpinteri, A. (1992). Meccanica dei materiali e della frattura, Pitagora Editrice, Bologna, Italy (in Italian).
Carpinteri, A., and Carpinteri, An. (1982). “Softening and fracturing process in masonry arches.” Proc., 6th Int. Brick Masonry Conf., Associazione Nazionale degli Industriali dei Laterizi, Ed. Laterconsult, Roma, Italy, 502–510.
Carpinteri, A., Invernizzi, S., and Lacidogna, G. (2007). “Structural assessment of a XVIIth century masonry vault with AE and numerical techniques.” Int. J. Archit. Heritage, 1(2), 214–226.
Castigliano, A. (1879). Théorie de l’equilibre des systèmes elastiques et ses applications, A.F. Negro, Turin, Italy.
Chiorino, M. A., Icardi, A., Rolando, S., and Testa, M. (2001). “Mechanism and finite element failure of Mosca’s Bridge over the Dora in Turin.” Proc., 3rd Int. Arch Bridges Conf. ARCH’01, Présses de l’Ecole Nationale des Ponts et Chaussées, Paris.
Chondros, T., and Dimarogonas, D. (1998). “Vibration of a cracked cantilever beam.” J. Vibr. Acoust., 120(3), 742–746.
Choo, B. S., Coutie, M., and Gong, N. (1991). “The effect of cracks on the behavior of masonry arches.” Proc., 9th Int. Brick/Block Masonry Conf., DgfM, Berlin, Germany, 948–955.
Crisfield, M. A., and Wills, J. (1986). “Nonlinear analysis of concrete and masonry structures.” Finite element methods for nonlinear problems, Springer, Berlin.
De La Hire, P. (1731). “Memoires de l’Academie Royale des Sciences.” 1719, 69.
Giambanco, G., Failla, A., and Cucchiara, C. (2000). “Numerical modelling of masonry arches via interface models.” Proc., 12th Int. Brick/Block Masonry Conf., Madrid, 449–463.
Heyman, J. (1966). “The stone skeleton.” Int. J. Solids Struct., 2(2), 255–296.
Heyman, J. (1969). “The safety of masonry arches.” Int. J. Mech. Sci., 11(4), 363–385.
Heyman, J. (1982). The masonry arch, Ellis Horwood, Chichester, U.K.
Hillerborg, A., Modéer, M., and Petersson, P. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res., 6(6), 773–782.
International Union of Railways (UIC). (1995). “Recommendations for the assessment of the load carrying capacity of existing masonry and mass-concrete arch bridges.”, Paris.
Invernizzi, S., Lacidogna, G., Manuello, A., and Carpinteri, A. (2011). “AE monitoring and numerical simulation of a two-span model masonry arch bridge subjected to pier scour.” Strain, 47(2), 158–169.
Irwin, G. (1957). “Analysis of stresses and strains near the end of a crack traversing a plate.” J. Appl. Mech., 24(3), 361–364.
Karnovsky, I. (2012). Theory of arched structures, Springer, Bosten, MA.
Kooharian, A. (1952). “Limit analysis of voussoir (segmental) and concrete arches.” J. Am. Concr. Inst., 24(12), 317–328.
Krawczuk, M., Zak, A., and Ostachowicz, W. (2000). “Elastic beam finite element with a transverse elasto-plastic crack.” Finite Elem. Anal. Des., 34(1), 61–73.
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.” Bergamo.
Méry, E. (1840). “Sur l' équilibre des voutes en berceau.” Annales des Ponts et Chaussées, Vol. 19, 50–70.
Milne, I., Ritchie, R., and Karihaloo, B. (2003). Comprehensive structural integrity: Fracture of materials from nano to macro, Elsevier, Amsterdam, Netherlands.
Murakami, Y. (1987). Stress intensity factors handbook, Pergamon Press, Oxford, U.K.
Navier, C. L. (1939). “Résumé des leçons données à l'École des Ponts et Chaussées.” Bruxelles.
Okamura, H., Watanabe, K., and Takano, T. (1975). “Deformation and strength of cracked member under bending moment and axial force.” Eng. Fract. Mech., 7(3), 531–539.
Orduna, A., and Lourenço, P. (2001). “Limit analysis as a tool for the simplified assessment of ancient masonry structures.” Proc., Historical Construction, P. B. Lourenço, and P. Roca, eds., Univ. of Minho Press, Guimarães, Portugal.
Page, J. (1993). Masonry arch bridges, HMSO, London.
Paradiso, M., Tempesta, G., Galassi, S., and Pugi, F. (2007). Sistemi voltati in muratura: Teoria e applicazioni, DEI, Roma, Italy (Italian).
Parmerter, R. (1976). “A method for calculating the reduction in stress intensity factor due to an elastic foundation.” Eng. Fract. Mech., 8(3), 539–546.
Pippard, A., and Baker, J. (1962). The analysis of engineering structures, Edward Arnold, London.
Tada, H., Paris, P. C., and Irwin, G. R. (1985). The stress analysis of crack handbook, Paris Productions, St. Louis, MO.
Towler, K., and Sawko, F. (1982). “Limit state behavior of brickwork arches.” Proc., 6th Int. Brick Masonry Conf., Associazione Nazionale degli Industriali dei Laterizi, Ed. Laterconsult, Roma, Italy, 422–429.
Zucchini, A., and Lourenço, P. (2002). “A micro-mechanical model for the homogenization of masonry.” Int. J. Solids Struct., 39(12), 3233–3255.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 141 • Issue 5 • May 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Sep 16, 2012
Accepted: Mar 6, 2014
Published online: Jul 17, 2014
Discussion open until: Dec 17, 2014
Published in print: May 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.