Abstract
Following Méry’s thrust line approach, this paper presents an alternative method to define the structural safety of masonry arches, based on admissible geometrical domains. These are implemented in a parametric model built on the reciprocal diagrams of graphic statics. The application to a case study – a semi-circular masonry arch loaded by a central point load – helps drawing a comparison with the classical geometric safety factor as defined by Jacques Heyman. The model is also used to evaluate the impact of geometrical as well as resistance hypotheses on the structural safety level. Analyses first confirm that stereotomy only slightly influences the load bearing capacity of the arch. They also validate the common use of an infinite compressive strength for arches’ constitutive material, since considering a typical value of 10 MPa reduces structural performances by less than 2%. Finally, a methodology using admissible geometrical domains is suggested to get insights on the robustness of masonry arches.
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References
Ochsendorf J (2002) Collapse of masonry structures. PhD dissertation, University of Cambridge
Huerta S (2001) Mechanics of masonry vaults: the equilibrium approach. In: Lourengo P, Roca P (eds) Historical constructions, pp 47–69
Méry E-H-F (1840) Equilibre des voûtes en berceau. In: Carilian-Goeury, Dalmont (eds) Annales des ponts et chaussées 1er semestre, pp 51–70
Moseley H (1833) On a new principle in statics, called the principle of least pressure. Phil Mag 3:285–288
Dermot O (1999) Funicular analysis of masonry vaults. Comput Struct 73(1–5):187–197
Ochsendorf J, Hernando JI, Huerta S (2004) Collapse of masonry buttresses. J Archit Eng 10(3):88–97
Block P, Ciblac T, Ochsendorf J (2006) Real-time limit analysis of vaulted masonry buildings. Comput Struct 84:1841–1852
Milankovitch M (1907) Theorie der Druckkurven. Zeitschrift für Mathematik und Physik 55:1–27
Makris N, Alexakis H (2013) The effect of stereotomy on the shape of the thrust-line and the minimum thickness of semicircular masonry arches. Arch Appl Mech 83(10):1511–1533
Heyman J (1995) The stone skeleton: structural engineering of masonry architecture. Cambridge University Press, Cambridge
Zalewski W, Allen E (1998) Shaping structures: statics. Wiley, New York
Fivet C (2013) Constraint-based graphic statics, a geometrical support for computer-aided structural equilibrium design. PhD dissertation, Université catholique de Louvain
Rondeaux J-F, Zastavni D (2017) A fully graphical approach for limit state analysis of existing structures: application to plane elastic-plastic bended structures and to plane masonry arches. International J Archit Heritage Conserv Anal Restor 12(3):1–23
Eurocode 1 - actions on structures. Part 1–7 General actions - accidental actions EN 1991-1-7
Zastavni D, Deschuyteneer A, Fivet C (2016) Admissible geometrical domains and graphic statics to evaluate constitutive elements of structural robustness. Int J Space Struct 31(2–4):165–176
Frangopol D, Curley J (1987) Effects of damage and redundancy on structural reliability. J Struct Eng 113(7):1533–1549
Muttoni A, Fernandez Ruiz M (2007) Champs de contraintes pour le béton structural. Tracés 5:17–21
Trautz M (1998) Zur Entwicklung von Form und Struktur historischer Gewölbe aus der Sicht der Statik. PhD dissertation, Institut für Baustatik der Universität Stuttgart
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Deschuyteneer, A., Rondeaux, JF., Zastavni, D. (2019). Structural Assessment of Masonry Arches Using Admissible Geometrical Domains. In: Aguilar, R., Torrealva, D., Moreira, S., Pando, M.A., Ramos, L.F. (eds) Structural Analysis of Historical Constructions. RILEM Bookseries, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-99441-3_116
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DOI: https://doi.org/10.1007/978-3-319-99441-3_116
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