Skip to main content
SpringerLink
Log in

Limit equilibrium analysis of masonry buttresses and towers under lateral and gravity loads

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

This paper revisits the fracturing of masonry buttresses and towers when subjected either to a concentrated oblique force at their head or to lateral inertial loading due to ground shaking and presents the corresponding failure criteria in elongation and shear. The loading configurations examined result either from the thrust that an elevated arch exerts on its supporting buttresses or from earthquake shaking on solitary masonry towers. At their limit state, tall, slender masonry buttresses and towers collapse by pivoting about their base corner, whereas less slender masonry structures may collapse by developing a shear failure. Because of the unilateral behavior of masonry, at the initiation of collapse of a slender buttress, the compression-free region separates from the rest of the buttress and reduces the stabilizing moment. As the ratio, base/height or the gravity load, increases, masonry buttresses and towers may fail in shear; therefore, the paper presents envelopes of their limit lateral capacity depending on the aspect ratio, the mechanical properties of masonry and the level of vertical loading. The equivalent static analysis adopted in this paper concludes that in most cases under lateral inertial loading, elongation failure is the lower failure mechanism of a tall masonry tower; nevertheless, a subsequent initiation of rocking that engages the large rotational inertia of the detached portion of the tower attracts additional inertia forces that may induce a follower shear failure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Audoy, M.: Mémoire sur la poussée des voûtes en berceau. Mémorial de l’officier du génie, no 4, 1–96 (1820)

    Google Scholar 

  2. Dupuit, J.: Traité de l’équilibre des voûtes et de la construction des ponts en maçonnerie. Dunod Editeur, Paris (1870)

    Google Scholar 

  3. Heyman, J.: On the rubber vaults of the Middle Ages, and other matters. Gaz. des Beaux-Arts 71, 177–188 (1968)

    Google Scholar 

  4. Heyman, J.: The Masonry Arch. Ellis Horwood, Chichester (1982)

    Google Scholar 

  5. Heyman, J.: The Stone Skeleton. Structural Engineering of Masonry Architecture. Cambridge University Press, New York (1995)

    Google Scholar 

  6. Sanabria, S.L.: The mechanization of design in the 16th century: the structural formulae of Rodrigo Gil de Hontañon. J. Soc. Archit. Hist. 41, 281–293 (1982)

    Google Scholar 

  7. Huerta, S.: The Medieval ‘scientia’ of Structures: The Rules of Rodrigo Gil de Hontañón. Omaggio a Edoardo Benvenuto, University of Genoa, Italy (1999)

    Google Scholar 

  8. Huerta, S.: The safety of masonry buttresses. Proc. ICE Eng. Hist. Herit. 163, 3–24 (2010). doi:10.1680/ehah.2010.163.1.3

    Article  Google Scholar 

  9. Heyman, J.: Leaning Towers. Meccanica 27, 153–159 (1992). doi:10.1007/978-94-017-2188-2_1

  10. Ochsendorf, J.A., Hernando, J.I., Huerta, S.: Collapse of masonry buttresses. J. Archit. Eng. 10, 88–97 (2004). doi:10.1061/(ASCE)1076-0431(2004)10:3(88)

    Article  Google Scholar 

  11. Alexakis, H., Makris, N.: Structural stability and bearing capacity analysis of the tunnel-entrance to the stadium of ancient Nemea. Int. J. Archit. Herit. 7, 673–692 (2013). doi:10.1080/15583058.2012.662262

    Article  Google Scholar 

  12. Alexakis, H., Makris, N.: Minimum thickness of elliptical masonry arches. Acta Mech. 224, 2977–2991 (2013). doi:10.1007/s00707-013-0906-2

    Article  MathSciNet  MATH  Google Scholar 

  13. Alexakis, H., Makris, N.: Limit equilibrium analysis and the minimum thickness of circular masonry arches to withstand lateral inertial loading. Arch. Appl. Mech. 84, 757–772 (2014). doi:10.1007/s00419-014-0831-4

    Article  MATH  Google Scholar 

  14. Alexakis, H., Makris, N.: Limit equilibrium analysis of masonry arches. Arch Appl. Mech. published on line (2014). doi:10.1007/s00419-014-0963-6

  15. Makris, N., Alexakis, H.: The effect of stereotomy on the shape of the thrust-line and the minimum thickness of semicircular masonry arches. Arch Appl. Mech. 83, 1511–1533 (2013). doi:10.1007/s00419-013-0763-4

    Article  MATH  Google Scholar 

  16. Makris, N., Alexakis, H.: From Hooke’s “hanging chain” and Milankovitch’s “druckkurven” to a Variational Formulation: in Search of the Minimum Thickness of Masonry Arches. In: Proceedings of the 10th HSTAM International Congress on Mechanics, Chania, Crete, Greece, paper no. 2 (2013)

  17. Makris, N., Alexakis, H.: The effect of stereotomy on the shape of the thrust-line and the minimum thickness of masonry arches. In: Proceedings of 9th International Masonry Conference, Guimarães, Portugal, paper no. 1461 (2014)

  18. La Hire, P.: Sur la construction des voûtes dans les édifices. Mémoires de l’Académie Royale des Sciences, Paris (1731), pp. 69–77 (1712)

  19. Bélidor, B.F.: La science des ingénieurs dans la conduite des travaux de fortification et d’architecture civile. C-A Jombert, Paris (1729)

  20. Boothby, T.E.: Stability of masonry piers and arches including sliding. J. Eng. Mech. 120, 304–319 (1994). doi:10.1061/(ASCE)0733-9399(1994)120:2(304)

    Article  Google Scholar 

  21. Gilbert, M., Melbourne, C.: Rigid-block analysis of masonry structures. Struct. Eng. 72, 356–361 (1994)

    Google Scholar 

  22. Ochsendorf, J.A., De Lorenzis, L.: Failure of rectangular masonry buttresses under concentrated loading. Proc. ICE Struct. Build. 161, 265–275 (2008). doi:10.1680/stbu.2008.161.5.265

    Article  Google Scholar 

  23. Coulomb, C.A.: Essai sur une application des règles des maximis et minimis à quelques problèmes de statique relatifs à l’arquitecture. Mémoires de mathématique et de physique, présentés à l’académie royal des sciences per divers savants et lus dans ses assemblées, Paris (1776) 7, 343–382 (1773)

    Google Scholar 

  24. Rots, J.G.: Structural Masonry: An Experimental/Numerical Basis for Practical Design Rules. A.A. Balkema, Rotterdam (1997)

    Google Scholar 

  25. Macorini, L., Izzuddin, B.A.: A non-linear interface element for 3D mesoscale analysis of brick-masonry structures. Int. J. Numer. Methods Eng. 85, 1584–1608 (2011). doi:10.1002/nme.3046

    Article  MATH  Google Scholar 

  26. Konstantinidis, D., Makris, N.: Seismic response analysis of multidrum classical columns. Earth Eng. Struct. Dyn. 34, 1243–1270 (2005). doi:10.1002/eqe.478

    Article  Google Scholar 

  27. Konstantinidis, D., Makris, N.: Earthquake analysis of multidrum columns. In: 5th International Conference on Earthquake Resistant Engineering Structures (ERES 2005), Skiathos, Greece (2005)

  28. Alexakis, H., Makris, N.: Stability analysis of the underground masonry tunnel of Ancient Nemea. In: Bilotta, E., Flora, A., Lirer, S., Viggiani, C. (eds.) Geotechnical Engineering for the Preservation of Monuments and Historic Sites. CRC Press, Taylor & Francis Group, London (2013)

    Google Scholar 

  29. Clough, R.W., Penzien, J.: Dynamics of Structures, 2nd edn. McGraw-Hill, New York (1993)

    Google Scholar 

  30. DeJong, M.J., Vibert, C.: Seismic response of stone masonry spires: computational and experimental modeling. Eng. Struct. 40, 566–574 (2012). doi:10.1016/j.engstruct.2012.03.001

    Article  Google Scholar 

  31. Makris, N.: The role of the rotational inertia on the seismic resistance of free-standing rocking columns and articulated frames. Bull. Seismol. Soc. Am. 104, 2226–2239 (2014). doi:10.1785/0120130064

    Article  Google Scholar 

  32. Makris, N.: A Half-Century of Rocking Isolation. Earthquakes and Structures, 7, published online (2014). doi:10.12989/eas.2014.7.6.000

  33. Makris, N., Vassiliou, M.F.: The dynamics of the rocking frame. In: Psycharis, I.N., Pantazopoulou, S.J., Papadrakakis, M. (eds.) Seismic Assessment, Behavior and Retrofit of Heritage Buildings and Monuments. Computational Methods in Applied Sciences. Springer International Publishing, Switzerland (2015). doi:10.1007/978-3-319-16130-3XXUndXX2

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Structures, Department of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL, 32816, USA

    Nicos Makris

  2. Office of Theoretical and Applied Mechanics, Academy of Athens, 10679, Athens, Greece

    Nicos Makris

  3. Division of Structures, Department of Civil Engineering, University of Patras, 26500, Patras, Greece

    Haris Alexakis

Authors
  1. Nicos Makris
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haris Alexakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicos Makris.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Makris, N., Alexakis, H. Limit equilibrium analysis of masonry buttresses and towers under lateral and gravity loads. Arch Appl Mech 85, 1915–1940 (2015). https://doi.org/10.1007/s00419-015-1027-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-015-1027-2

Keywords

Search

Navigation