Journal of Engineering Mathematics

, Volume 59, Issue 3, pp 323–336 | Cite as

An analytical model to determine the ultimate load on masonry arch bridges.

  • Amaryllis Audenaert
  • Herbert Peremans
  • Genserik Reniers


This paper proposes an analytical elasto–plastic model to describe the behavior of arches. The modeling is carried out using the equations of (i) horizontal equilibrium, (ii) vertical equilibrium and (iii) equilibrium of moments. The latter equations of equilibrium are ordinary differential equations which can easily be solved by adding boundary conditions, imposing restrictions on the horizontal and vertical movement and on the rotation in the abutments of the arch. For masonry arches, including material properties allowing the occurrence of cracks and the subsequent formation of hinges is required. The latter theory has been implemented in a computer program (Matlab), offering numerical simulations. The software was used to illustrate two case-studies, i.e., the assessment of an arch loaded with a vertical point load and one with a horizontal point load.


Collapse load Masonry arches Numerical simulation Ordinary differential equations 


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  1. 1.
    Woolfenden PA (1993) Modeling the masonry arch: Improving modern arch bridge assessment using nonlinear finite element software package (MAFEA). Bridge Managment, vol. 2. Thomas Telford, London, pp 254–263Google Scholar
  2. 2.
    Boothby T (1995) Collapse modes of masonry arch bridges. J Brit. Masonry Soc 9(2):62–69Google Scholar
  3. 3.
    Gilbert M, Melbourne C (1994) Rigid-block analysis to masonry arches. Struct Engng 72:356–361Google Scholar
  4. 4.
    Hughes TG, Blackler MJ (1995) A review of the UK masonry assessment methods. Proc Inst Civil Eng 110:373–382Google Scholar
  5. 5.
    Choo BS, Coutie MG, Gong NG (1991) Finite-element analysis of masonry arch bridges using tapered elements. Proc Inst Civil Eng 91:755–770Google Scholar
  6. 6.
    Mollins C, Roca P (1998) Capacity of masonry arches and spatial frames. J Struct Engng 124:653–663CrossRefGoogle Scholar
  7. 7.
    Boothby TE, Domalik DE, Dalal VA (1998) Service load response of masonry arch bridges. J Struct Engng 124:17–23CrossRefGoogle Scholar
  8. 8.
    Lourenço PB, Rots JG (2000) Failure criterion for masonry suitable for numerical implementation. The Masonry Soc J 18:11–18Google Scholar
  9. 9.
    Ng KH, Fairfield CA, Sibbad A (1999) Finite-element analysis of masonry arch bridges. Proc Inst Civil Eng: Structs Build 134:119–127Google Scholar
  10. 10.
    Fanning PJ, Boothby TE, Roberts BJ (2001) Longitudinal and transverse effects in masonry arch assessment. Construction Build Mater 15:51–60CrossRefGoogle Scholar
  11. 11.
    Hendry AW, Davies SR, Royles R (1985) Test on a Stone Masonry Arch at Bridgemill-Girvan. Transport and Road REsearch Lab, Contractors Report 7 United KingdomGoogle Scholar
  12. 12.
    Audenaert A, Peremans H, De Wilde WP (2004) Static determination of the internal forces and displacements in arch bridges. The Masonry Soc J 22(1):97–109Google Scholar
  13. 13.
    Timoshenko SP (1983) History of strength of materials. Dover PublicationsGoogle Scholar
  14. 14.
    Lourenço PB (1996) Computational strategies for masonry structures. Delft University PressGoogle Scholar
  15. 15.
    Heyman J (1966) The stone skeleton. Int J Solids Struct 2:249–279CrossRefGoogle Scholar
  16. 16.
    Kachanov LM (2004) Fundamentals of the theory of placticity. Dover PublicationsGoogle Scholar
  17. 17.
    Brencich A, De Francesco U, Gambarotta L (2001) Elastic no tensil resistant-plastic analysis of masonry arch bridges as an extension of Castigliano’s method. The Ninth Canadian masonry symposium at New Brunswich, on 4–6 June 2001Google Scholar
  18. 18.
    RING (2003) The University of Sheffield,, 2003Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Amaryllis Audenaert
    • 1
  • Herbert Peremans
    • 1
  • Genserik Reniers
    • 1
  1. 1.Department of Environment, Technology and Technology ManagementUniversity AntwerpAntwerpenBelgium

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