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Review Articles

On the Analysis of Minimum Thickness in Circular Masonry Arches

[+] Author and Article Information
Giuseppe Cocchetti

Facoltà di Ingegneria (Dalmine),
Dipartimento di Progettazione e Tecnologie,
Università degli Studi di Bergamo,
viale G. Marconi 5, I-24044 Dalmine (BG), Italy;
Dipartimento di Ingegneria Strutturale,
Politecnico di Milano,
piazza Leonardo da Vinci 32,
I-20133 Milano, Italy

Egidio Rizzi

e-mail: egidio.rizzi@unibg.it
Facoltà di Ingegneria (Dalmine),
Dipartimento di Progettazione e Tecnologie,
Università degli Studi di Bergamo,
viale G. Marconi 5, I-24044 Dalmine (BG), Italy

Throughout the paper, with the purpose of subtle academic comparisons, numerical results will be provided with 6 significative digits.

1Corresponding author.

Manuscript received March 16, 2011; final manuscript received May 21, 2012; published online October 1, 2012. Assoc. Editor: Panos Papadopoulos.

Appl. Mech. Rev 64(5), 050802 (Oct 01, 2012) (27 pages) doi:10.1115/1.4007417 History: Received March 16, 2011; Revised May 21, 2012

In this paper, the so-called Couplet–Heyman problem of finding the minimum thickness necessary for equilibrium of a circular masonry arch, with general opening angle, subjected only to its own weight is reexamined. Classical analytical solutions provided by J. Heyman are first rederived and explored in details. Such derivations make obviously use of equilibrium relations. These are complemented by a tangency condition of the resultant thrust force at the haunches' intrados. Later, given the same basic equilibrium conditions, the tangency condition is more correctly restated explicitly in terms of the true line of thrust, i.e., the locus of the centers of pressure of the resultant internal forces at each theoretical joint of the arch. Explicit solutions are obtained for the unknown position of the intrados hinge at the haunches, the minimum thickness to radius ratio and the nondimensional horizontal thrust. As expected from quoted Coulomb's observations, only the first of these three characteristics is perceptibly influenced, in engineering terms, by the analysis. This occurs more evidently at increasing opening angle of the arch, especially for over-complete arches. On the other hand, the systematic treatment presented here reveals the implications of an important conceptual difference, which appears to be relevant in the statics of masonry arches. Finally, similar trends are confirmed as well for a Milankovitch-type solution that accounts for the true self-weight distribution along the arch.

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References

Heyman, J., 1977, Equilibrium of Shell Structures, Oxford University Press, Oxford, UK.
Heyman, J., 1982, The Masonry Arch, Ellis Horwood Ltd., Chichester, UK.
Heyman, J., 1966, “The Stone Skeleton,” Int. J. Solids Struct., 2(2), pp. 249–279. [CrossRef]
Heyman, J., 1967, “On Shell Solutions for Masonry Domes,” Int. J. Solids Struct., 3(2), pp. 227–241. [CrossRef]
Heyman, J., 1969, “The Safety of Masonry Arches,” Int. J. Mech. Sci., 11(4), pp. 363–385. [CrossRef]
Heyman, J., 1995, The Stone Skeleton—Structural Engineering of Masonry Architecture, Cambridge University Press, Cambridge, UK.
Irvine, H. M., 1979, “The Stability of the Roman Arch,” Int. J. Mech. Sci., 21(8), pp. 467–475. [CrossRef]
Benvenuto, E., 1981, La Scienza delle Costruzioni e il suo Sviluppo Storico, Sansoni, Firenze, Italy.
Sinopoli, A., Corradi, M., and Foce, F., 1997, “Modern Formulation for Preelastic Theories on Masonry Arches,” J. Eng. Mech., ASCE, 123(3), pp. 204–213. [CrossRef]
Sinopoli, A., 2003, “The Role of Geometry in the Theories on Vaulted Structures by Lorenzo Mascheroni (1785),” Proceedings of the 1st International Congress on Construction History, S.Huerta, ed., Madrid, Jan. 20–24, 2003, Madrid Instituto Juan de Herrera, Vol. 1, Paper No. CIHC1_175, pp. 1865–1873.
Huerta, S., 2001, “Mechanics of Masonry Vaults: The Equilibrium Approach,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar, P.B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2003, pp. 47–70.
Huerta, S., 2004, Arcos, Bóvedas y Cúpulas. Geometría y Equilibrio en el Cálculo Tradicional de Estructuras de Fábrica, Instituto Juan de Herrera, Madrid, Spain.
Huerta, S., 2006, “Galileo was Wrong: The Geometrical Design of Masonry Arches,” Nexus Network J., 8(2), pp. 25–52. [CrossRef]
Albuerne, A., and HuertaS., 2010, “Coulomb's Theory of Arches in Spain ca. 1800: The Manuscript of Joaquín Monasterio,” Proceedings of 6th International Conference on Arch Bridges (ARCH’10), B.Chen and J.Wei, eds., Fuzhou, China, Oct. 11–13, 2010, College of Civil Engineering, Fuzhou University, P. R. C., Paper No. 46, pp. 354–362.
Aita, D., Barsotti, R., and Bennati, S., 2003, “Some Explicit Solutions for Flat and Depressed Masonry Arches,” Proceedings of the 1st International Congress on Construction History, S.Huerta ed., Madrid, Spain, Jan. 20–24, 2003, Madrid Instituto Juan de Herrera, Vol. 1, Paper No. CIHC1_018, pp. 171–183.
Becchi, A., 2003, “The Statics of Arches Between France and Italy,” Proceedings of the 1st International Congress on Construction History, S.Huerta ed., Madrid, Spain, Jan. 20–24, 2003, Madrid Instituto Juan de Herrera, Vol. 1, Paper No. CIHC1_034, pp. 353–364.
Foce, F., and Aita, D., 2003, “The Masonry Arch Between «Limit» and «Elastic» Analysis. A Critical Re-Examination of Durand-Claye's Method,” Proceedings of the 1st International Congress on Construction History, S.Huerta, ed., Madrid, Spain, Jan. 20–24, 2003, Madrid Instituto Juan de Herrera, Vol. 1, Paper No. CIHC1_088, pp. 895–908.
Foce, F., 2005, “On the Safety of the Masonry Arch. Different Formulations From the History of Structural Mechanics,” Essays in the History of the Theory of Structures, S.Huerta, ed., Instituto Juan de Herrera, Madrid, Spain, pp. 117–142.
Foce, F., 2007, “Milankovitch's Theorie der Druckkurven: Good Mechanics for Masonry Architecture,” Nexus Network J., 9(2), pp. 185–210. [CrossRef]
Aita, D., 2003, “Between Geometry and Mechanics: A Re-Examination of the Principles of Stereotomy From a Statical Point of View,” Proceedings of the 1st International Congress on Construction History, S.Huerta ed., Madrid, Spain, Jan. 20–24, 2003, Madrid Instituto Juan de Herrera, Vol. 1, Paper No. CIHC1_017, pp. 161–170.
Sakarovitch, J., 2003, “Stereotomy, a Multifaceted Technique,” Proceedings of the 1st International Congress on Construction History, S.Huerta ed., Madrid, Jan. 20–24, 2003, Madrid Instituto Juan de Herrera, Vol. 1, Paper No. CIHC1_008, pp. 69–79.
Heyman, J., 2009, “La Coupe Des Pierres,” Proceedings of the Third International Congress on Construction History, Brandenburg University of Technology, Cottbus, Germany, May 20–24, 2009, Vol. 2, pp. 807–812.
Bičanič, N., Stirling, C., and Pearce, C. J., 2003, “Discontinuous Modelling of Masonry Bridges,” Comput. Mech., 31(1–2), pp. 60–68. [CrossRef]
Thavalingam, A., Bičanič, N., Robinson, J. I., and Ponniah, D. A., 2001, “Computational Framework for Discontinuous Modelling of Masonry Arch Bridges,” Comput. Struct., 79(19), pp. 1821–1830. [CrossRef]
MacLaughlin, M. M., and Doolin, D. M., 2006, “Review of Validation of the Discontinuous Deformation Analysis (DDA) Method,” Int. J. Numer. Anal Methods Geomech., 30(4), pp. 271–305. [CrossRef]
Tóth, A. R., Orbán, Z., and Bagi, K., 2009, “Discrete Element Analysis of a Stone Masonry Arch,” Mech. Res. Commun., 36(4), pp. 469–480. [CrossRef]
Lucchesi, M., Padovani, C., Pasquinelli, G., and Zani, N., 1997, “On the Collapse of Masonry Arches,” Meccanica, 32(4), pp. 327–346. [CrossRef]
Blasi, C., and Foraboschi, P., 1994, “Analytical Approach to Collapse Mechanisms of Circular Masonry Arch,” J. Struct. Eng., ASCE, 120(8), pp. 2288–2309. [CrossRef]
Boothby, T. E., 1996, “Discussion: Analytical Approach to Collapse Mechanisms of Circular Masonry Arch,” J Struct. Eng., 122(8), pp. 978–980. [CrossRef]
Ochsendorf, J., 2006, “The Masonry Arch on Spreading Supports,” Struct. Eng., 84(2), pp. 29–36. Available at http://www.istructe.org/journal/ volumes/volume-84-%28published-in-2006%29/issues/issue-2/articles/the-masonry-arch-on-spreading-supports
Block, P., DeJong, M., and Ochsendorf, J., 2006, “As Hangs the Flexible Line: Equilibrium of Masonry Arches,” Nexus Network J., 8(2), pp. 13–24. [CrossRef]
Ochsendorf, J., 2002, “Collapse of Masonry Structures,” Ph.D. thesis, University of Cambridge, King's College, UK.
Milankovitch, M., 1904, “Beitrag zur Theorie der Druckkurven,” Ph.D. thesis, K. K. Technische Hochschule, Vienna, Austria.
Milankovitch, M., 1907, “Theorie der Druckkurven,” Z. Math. Phys., 55, pp. 1–27.
Romano, A., and Ochsendorf, J., 2009, “The Mechanics of Gothic Masonry Arches,” Int. J. Archit. Heritage, 4(1), pp. 59–82. [CrossRef]
Martinez Martinez, J. A., Moreno Revilla, J., and Aragon Torre, A., 2001, “Critical Thickness Criteria on Stone Arch Bridges With Low Rise/Span Ratio and Current Traffic Loads,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar, P. B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2001, pp. 609–616.
Block, P., 2005, “Equilibrium System. Studies in Masonry Structures,” M.S. thesis, Massachusetts Institute of Technology, Department of Architecture, Cambridge, MA.
Block, P., Ciblac, T., and Ochsendorf, J., 2006, “Real-Time Limit Analysis of Vaulted Masonry Buildings,” Comput. Struct., 84(29–30), pp. 1841–1852. [CrossRef]
DeJong, M., and Ochsendorf, J. A., 2006, “Analysis of Vaulted Masonry Structures Subjected to Horizontal Ground Motion,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06), P. B.Lourenço, P.Roca, C.Modena, and S.Agrawal, eds., New Delhi, India, Nov. 6–8, 2006, Macmillan Advanced Research Series, pp. 973–980.
O'Dwyer, D., 1999, “Funicular Analysis of Masonry Vaults,” Comput. Struct., 73(1–5), pp. 187–197. [CrossRef]
Andreu, A., Gil, L., and Roca, P., 2007, “Computational Analysis of Masonry Structures With a Funicular Model,” J. Eng. Mech., ASCE, 133(4), pp. 473–480. [CrossRef]
Gilbert, M., 2007, “Limit Analysis Applied to Masonry Arch Bridges: State-of-the-Art and Recent Developments,” Proceedings of 5th International Conference on Arch Bridges (ARCH’07), P. B.Lourenço, D. B.Oliveira, and A.Portela, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007, Multicomp, Lda Publishers, Madeira, Portugal, pp. 13–28.
Oikonomopoulou, A., Ciblac, T., and Guéna, F., 2009, “Modelling Tools for the Mechanical Behaviour of Historic Masonry Structures,” Proceedings of the 3rd International Congress on Construction History, Brandenburg University of Technology, Cottbus, Germany, May 20–24, 2009, Vol. 3, pp. 1097–1104.
Varma, M., Jangid, R. S., and Ghosh, S., 2010, “Thrust Line Using Linear Elastic Finite Element Analysis for Masonry Structures,” Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China, Oct. 6–8, 2010, Advanced Materials Research, Trans Tech Publications, Vols. 133–134, pp. 503–508.
Antunes, G. J. J., 2010, “Comportamento Estrutural de Edifícios Antigos. Estruturas Arqueadas Planas,” M.S. thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa.
Gago, A. S., Alfaiate, J., and Lamas, A., 2011, “The Effect of the Infill in Arched Structures: Analytical and Numerical Modelling,” Eng. Struct., 33(5), pp. 1450–1458. [CrossRef]
Gago, A. S., 2004, “Análise Estrutural de Arcos, Abóbadas e Cúpulas—Contributo para o Estudo do Património Construído,” Ph.D. thesis, Universidade Técnica de Lisboa, Instituto Superior Técnico, IST-UTL.
Colasante, G., 2007, “Sui Meccanismi di Collasso degli Archi in Muratura Secondo l'Analisi Limite,” B.S. thesis, Università di Bergamo, Italy.
Rusconi, F., 2008, “Analisi Numerica per Elementi Discreti dei Meccanismi di Collasso degli Archi in Muratura,” B.S. thesis, Università di Bergamo, Italy.
Rizzi, E., Cocchetti, G., Colasante, G., and Rusconi, F., 2010, “Analytical and Numerical Analysis on the Collapse Mode of Circular Masonry Arches,” Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China, Oct. 6–8, 2010, Advanced Materials Research, Trans Tech Publications, Vols. 133–134, pp. 467–472.
Rizzi, E., Rusconi, F., and Cocchetti, G., 2011, “Numerical DEM (DDA) Analysis on the Collapse Mode of Circular Masonry Arches,” University of Bergamo, Technical Report No. SdC2011/02.
Kooharian, A., 1952, “Limit Analysis of Voussoir (Segmental) and Concrete Arches,” J. Proc. Am. Concr. Inst., 49(12), pp. 317–328. Available at http://www.concrete.org/PUBS/JOURNALS/OLJDetails.asp?Home=JP&ID=11822
Livesley, R. K., 1978, “Limit Analysis of Structures Formed From Rigid Blocks,” Int. J. Numer. Anal. Methods Eng., 12(12), pp. 1853–1871. [CrossRef]
Livesley, R. K., 1992, “A Computational Model for the Limit Analysis of Three-Dimensional Masonry Structures,” Meccanica, 27(3), pp. 161–172. [CrossRef]
Boothby, T. E., and Brown, C. B., 1992, “Stability of Masonry Piers and Arches,” J. Eng. Mech., ASCE, 118(2), pp. 367–383. [CrossRef]
Boothby, T. E., 1994, “Stability of Masonry Piers and Arches Including Sliding,” J. Eng. Mech., ASCE, 120(2), pp. 304–319. [CrossRef]
Boothby, T. E., 1995, “Collapse Modes of Masonry Arch Bridges,” Masonry Int., 9(2), pp. 62–69. Available at http://www.masonry.org.uk/masonry/ publications/masonry_international/masonry_international_papers/volume_09/ collapse_modes_of_masonry_arch_bridges
Boothby, T. E., 2001, “Analysis of Masonry Arches and Vaults,” Prog. Struct. Eng. Mater., 3(3), pp. 246–256. [CrossRef]
Como, M., 1992, “Equilibrium and Collapse Analysis of Masonry Bodies,” Meccanica, 27(3), pp. 185–194. [CrossRef]
Clemente, P., Occhiuzzi, A., and Raihtel, A., 1995, “Limit Behaviour of Stone Arch Bridges,” J. Struct. Eng., ASCE, 121(7), pp. 1045–1050. [CrossRef]
DelPiero, G., 1998, “Limit Analysis and No-Tension Materials,” Int. J. Plast., 14(1–3), pp. 259–271. [CrossRef]
Gilbert, M., Casapulla, C., and Ahmed, H. M., 2006, “Limit Analysis of Masonry Block Structures With Non-Associative Frictional Joints Using Linear Programming,” Comput. Struct., 84(13–14), pp. 873–887. [CrossRef]
Cavicchi, A., and Gambarotta, L., 2006, “Two-Dimensional Finite Element Upper Bound Limit Analysis of Masonry Bridges,” Comput. Struct., 84(31–32), pp. 2316–2328. [CrossRef]
Cavicchi, A., and Gambarotta, L., 2007, “Lower Bound Limit Analysis of Masonry Bridges Including Arch–Fill Interaction,” Eng. Struct., 29(11), pp. 3002–3014. [CrossRef]
Chen, Y., Ashour, A. F., and Garrity, S. W., 2007, “Modified Four-Hinge Mechanism Analysis for Masonry Arches Strengthened With Near-Surface Reinforcement,” Eng. Struct., 29(8), pp. 1864–1871. [CrossRef]
Smars, P., 2000, “Etudes sur la Stabilité des Arcs et Voûtes, Confrontation des Méthodes de l'Analyse Limite aux Voûtes Gothiques en Brabant,” Ph.D. thesis, Catholic University of Leuven, Belgium.
Smars, P., 2008, “Influence of Friction and Tensile Resistance on the Stability of Masonry Arches,” Proceedings of the 6th International Conference on Structural Analysis of Historic Construction, D.D'Ayala and E.Fodde, eds., Bath (UK), July 2–4, 2008, Taylor & Francis Group, London, pp. 1199–1206.
Smars, P., 2010, “Kinematic Stability of Masonry Arches,” Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China, Oct. 6–8, 2010, Advanced Materials Research, Trans Tech Publications, Vols. 133–134, pp. 429–434.
Lucchesi, M., Šilhavý, M., and Zani, N., 2012, “Equilibrium Problems and Limit Analysis of Masonry Beams,” J. Elast., 106(2), pp. 165–188. [CrossRef]
Baratta, A., and Corbi, O., 2010, “An Approach to Masonry Structural Analysis by the No-Tension Assumption—Part I: Material Modeling, Theoretical Setup, and Closed Form Solutions,” Appl. Mech. Rev., 63(4), p. 040802. [CrossRef]
Baratta, A., and Corbi, O., 2010, “An Approach to Masonry Structural Analysis by the No-Tension Assumption—Part II: Load Singularities, Numerical Implementation and Applications,” Appl. Mech. Rev., 63(4), p. 040803. [CrossRef]
Bednarz, L., Górski, A., Jasienko, J., and Rusinski, E., 2011, “Simulations and Analyses of Arched Brick Structures,” Autom. Constr., 20(7), pp. 741–754. [CrossRef]
Fanning, P. J., and Boothby, T. E., 2001, “Three-Dimensional Modelling and Full-Scale Testing of Stone Arch Bridges,” Comput. Struct., 79(29–30), pp. 2645–2662. [CrossRef]
Vermeltfoort, A. T., 2001, “Analysis and Experiments of Masonry Arches,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar, P. B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2001, pp. 489–498.
Brencich, A., and Morbiducci, R., 2007, “Masonry Arches: Historical Rules and Modern Mechanics,” Int. J. Archit. Heritage, 1(2), pp. 165–189. [CrossRef]
de Arteaga, I., and Morer, P., 2012, “The Effect of Geometry on the Structural Capacity of Masonry Arch Bridges,” Constr. Build. Mater., 34, pp. 97–106. [CrossRef]
Armesto, J., Roca-Pardiñas, J., Lorenzo, H., and Arias, P., 2010, “Modelling Masonry Arches Shape Using Terrestrial Laser Scanning Data and Nonparametric Methods,” Eng. Struct., 32(2), pp. 607–615. [CrossRef]
Morer, P., de Arteaga, I., Armesto, J., and Arias, P., 2011, “Comparative Structural Analyses of Masonry Bridges: An Application to the Cernadela Bridge,” J. Cult. Heritage, 12(3), pp. 300–309. [CrossRef]
Riveiro, B., Morer, P., Arias, P., and de Arteaga, I., 2011, “Terrestrial Laser Scanning and Limit Analysis of Masonry Arch Bridges,” Constr. Build. Mater., 25(4), pp. 1726–1735. [CrossRef]
Riveiro, B., Caamaño, J. C., Arias, P., and Sanz, E., 2011, “Photogrammetric 3D Modelling and Mechanical Analysis of Masonry Arches: An Approach Based on a Discontinuous Model of Voussoirs,” Autom. Constr., 20(4), pp. 380–388. [CrossRef]
Solla, M., Caamaño, J. C., Riveiro, B., and Arias, P., 2012, “A Novel Methodology for the Structural Assessment of Stone Arches Based on Geometric Data by Integration of Photogrammetry and Ground-Penetrating Radar,” Eng. Struct., 35, pp. 296–306. [CrossRef]
Solla, M., Lorenzo, H., Rial, F. I., and Novo, A., 2012, “Ground-Penetrating Radar for the Structural Evaluation of Masonry Bridges: Results and Interpretational Tools,” Constr. Build. Mater., 29, pp. 458–465. [CrossRef]
Oliveira, D.V., Lourenço, P. B., and Lemos, C., 2010, “Geometric Issues and Ultimate Load Capacity of Masonry Arch Bridges From the Northwest Iberian Peninsula,” Eng. Struct., 32(12), pp. 3955–3965. [CrossRef]
Roca, P., Cervera, M., Gariup, G., and Pelá, L., 2010, “Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches,” Arch. Comput. Methods Eng., 17(3), pp. 299–325. [CrossRef]
Atamturktur, S., and Laman, J. A., 2012, “Finite Element Model Correlation and Calibration of Historic Masonry Monuments: Review,” Struct. Des. Tall Build., 21(2), pp. 96–113. [CrossRef]
Lourenço, P. B., 2001, “Analysis of Historical Constructions: From Thrust-Lines to Advanced Simulations,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd Internaional Seminar, P. B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2001, pp. 91–116.
Dede, T., and Ural, A., 2007, “A Finite Element Program for Historical Stone Arch Bridges,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07), P. B.Lourenço, D. B.Oliveira, and A.Portela, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007, Multicomp, Lda Publishers, Madeira, Portugal, pp. 533–541.
Melbourne, C., Wang, J., and Tomor, A., 2007, “A New Masonry Arch Bridge Assessment Strategy (SMART),” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07), P. B.Lourenço, D. B.Oliveira, and A.Portela, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007, Multicomp, Lda Publishers, Madeira, Portugal, pp. 227–236.
Gibbons, N., and Fanning, P. J., 2010, “Ten Stone Masonry Arch Bridges and Five Different Assessment Approaches,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10), B.Chen and J.Wei, eds., Fuzhou, China, Oct. 11–13, 2010, College of Civil Engineering, Fuzhou University, Paper No. 63, pp. 482–489.
Kumar, P., 2010, “Performance Assessment and Maintenance of Masonry Arch Bridges,” 34th IABSE Symposium on Large Structures and Infrastructures for Environmentally Constrained and Urbanised Areas, Venice, Sept. 22–24, 2010, International Association for Bridge and Structural Engineering, pp. 818–826.
Casas, J. R., 2011, “Reliability-Based Assessment of Masonry Arch Bridges,” Constr. Build. Mater., 25(4), pp. 1621–1631. [CrossRef]
Harvey, W. J., 1988, “Application of the Mechanism Analysis to Masonry Arches,” Struct. Eng., 66(5), pp. 77–84. Available at http://www.istructe.org/Journal/Volumes/Volume-66-%28Published-in-1988%29/Issues/Issue-5/Articles/Application-of-the-Mechanism-Analysis-to-Masonry-A
Smith, F. W., Harvey, W. J., and Vardy, A. E., 1990, “Three-Hinge Analysis of Masonry Arches,” Struct. Eng., 68(11), pp. 203–213. Available at http://www.istructe.org/Journal/Volumes/Volume-68-%28Published-in-1990%29/Issues/Issue-11/Articles/Three-Hinge-Analysis-of-Masonry-Arches
Harvey, B., and Maunder, E., 2001, “Thrust Line Analysis of Complex Masonry Structures Using Spreadsheets,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar, P. B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2001, pp. 521–528.
Harvey, B., 2009, “Interactive Analysis of Arching Masonry Structures,” Proceedings of the 3rd Australasian Engineering Heritage Conference, Engineering in the Development of a Region—Heritage and History, Salmond College, University of Otago, Dunedin, New Zealand, Nov. 22–25, 2009.
Hughes, T. G., and Blackler, M., 1997, “A Review of the UK Masonry Arch Assessment Methods,” Proceedings of the Institution of Civil Engineers—Structures and Buildings, 122(3), Paper No.11302, pp. 305–315. [CrossRef]
Hughes, T. G., Hee, S. C., and Soms, E., 2002, “Mechanism Analysis of Single Span Masonry Arch Bridges Using a Spreadsheet,” Proceedings of the Institution of Civil Engineers—Structures and Buildings, 152(4), Paper No. 12710, pp. 341–350. [CrossRef]
Miri, M., and Hughes, T. G., 2006, “The Physical and Numerical Modelling of a Repaired Masonry Arch Bridge,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06), P. B.Lourenço, P.Roca, C.Modena, and S.Agrawal, eds., New Delhi, India, Nov. 6–8, 2006, Macmillan Advanced Research Series, pp. 1255–1262.
Molins, C., and Roca, P., 1998, “Capacity of Masonry Arches and Spatial Frames,” J. Struct. Eng., ASCE, 124(6), pp. 653–663. [CrossRef]
Ponterosso, P., Fishwick, R. J., Fox, D.St.J., Liu, X. L., and Begg, D. W., 2000, “Masonry Arch Collapse Loads and Mechanisms by Heuristically Seeded Genetic Algorithm,” Comput. Methods Appl. Mech. Eng., 190(8–10), pp. 1233–1243. [CrossRef]
Alfaiate, J., and Gallardo, A., 2001, “Numerical Simulations of a Full Scale Load Test on a Stone Masonry Arch Bridge,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar, P. B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2001, pp. 739–748.
Roeder-Carbo, G. M., and Ayala, A. G., 2001, “An Evaluation of Methods for the Determination of the Structural Stability of Historic Masonry Arches,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar, P. B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2001, pp. 557–566.
Giordano, A., Mele, E., and De Luca, A., 2002, “Modelling of Historical Masonry Structures: Comparison of Different Approaches Through a Case Study,” Eng. Struct., 24(8), pp. 1057–1069. [CrossRef]
Giordano, A., De Luca, A., Mele, E., and Romano, A., 2006, “Simplified Evaluation of the Horizontal Capacity of Masonry Arches,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06), P. B.Lourenço, P.Roca, C.Modena, and S.Agrawal, eds., New Delhi, India, Nov. 6–8, 2006, Macmillan Advanced Research Series, pp. 1221–1229.
Ford, T. E., Augarde, C. E., and Tuxford, S. S., 2003, “Modelling Masonry Arch Bridges Using Commercial Finite Element Software,” Proceedings of the 9th International Conference on Civil and Structural Engineering Computing, B. H. V.Topping, ed., The Netherlands, Sept. 2–4, 2003, Civil-Comp Press, Stirlingshire, UK, Paper No. 101.
Ng, K.-H., and Fairfield, C. A., 2004, “Modifying the Mechanism Method of Masonry Arch Bridge Analysis,” Constr. Build. Mater., 18(2), pp. 91–97. [CrossRef]
Toker, S., and Ünay, A., 2004, “Mathematical Modeling and Finite Element Analysis of Masonry Arch Bridges,” GU J. Sci., 17(2), pp. 129–139. Available at http://194.27.18.47/dergi/ojs/index.php/GUJS/article/viewFile/414/212
Kumar, P., and Bhandari, N. M., 2005, “Non-Linear Finite Element Analysis of Masonry Arches for Prediction of Collapse Load,” Struct. Eng. Int. (IABSE, Zurich, Switzerland), 15(3), pp. 166–174. [CrossRef]
Kumar, P., and Bhandari, N. M., 2006, “Mechanism Based Assessment of Masonry Arch Bridges,” Struct. Eng. Int. (IABSE, Zurich, Switzerland), 16(3), pp. 226–234. [CrossRef]
Migliore, M. R., Letizia, F. S., and Ruocco, E., 2006, “On the Stability of Masonry Arches,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06), P. B.Lourenço, P.Roca, C.Modena, and S.Agrawal, eds., New Delhi, India, Nov. 6–8, 2006, Macmillan Advanced Research Series, pp. 965–972.
Audenaert, A., Peremans, H., and Reniers, G., 2007, “An Analytical Model to Determine the Ultimate Load on Masonry Arch Bridges,” J. Eng. Math., 59(3), pp. 323–336. [CrossRef]
Audenaert, A., Fanning, P., Sobczak, L., and Peremans, H., 2008, “2-D Analysis of Arch Bridges Using an Elasto-Plastic Material Model,” Eng. Struct., 30(3), pp. 845–855. [CrossRef]
Betti, M., Drosopoulos, G. A., and Stavroulakis, G. E., 2007, “On the Collapse Analysis of Single Span Masonry/Stone Arch Bridges With Fill Interaction,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07), P. B.Lourenço, D. B.Oliveira, and A.Portela, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007, Multicomp, Lda Publishers, Madeira, pp. 617–624.
Campo, M., Drosopoulos, G. A., Fernández, J. R., and Stavroulakis, G. E., 2007, “Unilateral Contact and Damage Analysis in Masonry Arches,” IUTAM Symposium on Computational Contact Mechanics, P.Wriggers and U.Nackenhorst, eds., Springer, New York, pp. 357–363 [CrossRef].
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), pp. 1864–1873. [CrossRef]
Drosopoulos, G. A., Stavroulakis, G. E., and Massalas, C. V., 2008, “Influence of the Geometry and the Abutments Movement on the Collapse of Stone Arch Bridges,” Constr. Build. Mater., 22(3), pp. 200–210. [CrossRef]
Ainsworth, M., and Mihai, L. A., 2007, “Modeling and Numerical Analysis of Masonry Structures,” Numer. Methods Partial Differ. Equ., 23(4), pp. 798–816. [CrossRef]
Mihai, L. A., and Ainsworth, M., 2009, “An Adaptive Multi-Scale Computational Modelling of Clare College Bridge,” Comput. Methods Appl. Mech. Eng., 198(21–26), pp. 1839–1847. [CrossRef]
Viola, E., Panzacchi, L., and Tornabene, F., 2007, “General Analysis and Application to Redundant Arches Under Static Loading,” Constr. Build. Mater., 21(5), pp. 1129–1143. [CrossRef]
Oikonomopoulou, A., 2009, “Approches Numériques pour l’Étude du Comportement des Structures Maçonnées Anciennes: un Outil Basé sur le Calcul à la Rupture et la Visualisation Graphique,” Ph.D. thesis, Université Paris Est et de l'Ecole Nationale Supérieure d'Architecture de Paris la Villette, Paris, France.
Pintucchi, B., and Zani, N., 2009, “Effects of Material and Geometric Non-Linearities on the Collapse Load of Masonry Arches,” Eur. J. Mech. A/Solids, 28(1), pp. 45–61. [CrossRef]
Vares, R. J., 2009, “Avaliação de Segurança de Pontes Existentes de Alvenaria de Pedra com Recurso a Métodos Simplificados,” M.S. thesis, Universidade do Porto.
Grandjean, A., 2010, “Capacité Portante de Ponts en Arc en Maçonnerie de Pierre Naturelle—Modèle d’Évaluation Intégrant le Niveau d'Endommagement,” Ph.D. thesis, École Polytechnique Fédérale de Lausanne (EPFL), Suisse, Février.
Peng, D. M., Chen, Y. Y., Jiang, R. J., and Fairfield, C. A., 2010, “Optimal Design of Masonry Arch Bridges,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10), B.Chen and J.Wei, eds., Fuzhou, China, Oct. 11–13, 2010, College of Civil Engineering, Fuzhou University, Paper No. 87, pp. 674–682.
Tsutsui, M., Mizuta, Y., and Sakata, T., 2010, “Line of Thrust and Theoretical Load of Masonry Arch Bridge,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10), B.Chen and J.Wei, eds., Fuzhou, China, Oct. 11–13, 2010, College of Civil Engineering, Fuzhou University, Paper No. 43, pp. 332–337.
Yamao, T., Yamamoto, K., Kudo, T., Ogami, K., and Nakamura, H., 2010, “Development of Static Analytical Method for Mechanical Behavior of Stone Arch Bridges,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10), B.Chen and J.Wei, eds., Fuzhou, China, Oct. 11–13, 2010, College of Civil Engineering, Fuzhou University, Paper No. 48, pp. 370–378.
Manrique Hoyos, C., 2010, “Limit Analysis: Collection of Examples of Applications,” M.S. thesis, UPC Barcelona, Spain.
Cai, Y., 2011, “Detailed Numerical Simulation of Experiments on Masonry Arch Bridges by Using 3D FE,” M.S. thesis, UPC Barcelona, Spain.
Koltsida Spyridoula, I., 2011, “Detailed Numerical Simulation of Experiments on Masonry Arch Bridges by Using 3D FE,” M.S. thesis, UPC Barcelona, Spain.
Sinopoli, A., Aita, D., and Foce, F., 2007, “Further Remarks on the Collapse Mode of Masonry Arches With Coulomb Friction,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07), P. B.Lourenço, D. B.Oliveira, and A.Portela, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007, Multicomp, Lda Publishers, Madeira, Portugal, pp. 649–657.
Casapulla, C., and Lauro, F., 2000, “A Simple Computation Tool for the Limit-State Analysis of Masonry Arches,” Proceedings of the 5th International Congress on Restoration of Architectural Heritage (Firenze 2000), Università di Firenze, Sept. 17–24, 2000, pp. 2056–2064 (CDROM).
Casapulla, C., and D'Ayala, D., 2001, “Lower Bound Approach to the Limit Analysis of 3D Vaulted Block Masonry Structures,” Proceedings of the 5th International Symposium on Computer Methods in Structural Masonry ( STRUMAS V), Roma, Italy, p. 28–36.
D'Ayala, D., and Casapulla, C., 2001, “Limit State Analysis of Hemisferical Domes with Finite Friction,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar, P. B.Lourenço and P.Roca, eds., Guimarães, Portugal, University of Minho, Nov. 7–9, 2001, Paper No. 056, pp. 617–626.
D'Ayala, D., and Tomasoni, E., 2011, “Three-Dimensional Analysis of Masonry Vaults Using Limit State Analysis With Finite Friction,” Int. J. Archit. Heritage, 5(2), pp. 140–171. [CrossRef]
Frigerio, A., 2010, “Sul Meccanismo di Collasso Misto negli Archi Semicircolari in Muratura,” B.S. thesis, Università di Bergamo, Italy.
Colasante, G., 2010, “Sul Ruolo dell'Attrito nei Meccanismi di Collasso degli Archi Circolari in Muratura,” M.S. thesis, Università di Bergamo, Italy.
Rizzi, E., Colasante, G., Frigerio, A., and Cocchetti, G., 2012, “On the Mixed Collapse Mechanism of Semi-Circular Masonry Arches,” Proceedings of the 8th International Conference on Structural Analysis of Historical Constructions ( SAHC 2012), J. Jasiénko, ed., Wroclaw, Poland, Oct. 15–17, DWE, Vol. 1, pp. 541–549.
Aita, D., Barsotti, R., and Bennati, S., 2012, “Equilibrium of Pointed, Circular and Elliptical Masonry Arches Bearing Vertical Walls,” J. Struct. Eng. ASCE, 138(7), pp. 880–888. [CrossRef]
Romano, A., 2005, “Modelling, Analysis and Testing of Masonry Structures,” Ph.D. thesis, Università degli Studi di Napoli Federico II, Italy.
Romano, A., and Ochsendorf, J., 2006, “Circular, Pointed and Basket-Handle Arches: A Comparison of Structural Behavior of Masonry Spans,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06), P. B.Lourenço, P.Roca, C.Modena, and S.Agrawal, eds., New Delhi, India, Nov. 6–8, 2006, Macmillan Advanced Research Series, pp. 1205–1212.
De Rosa, E., and Galizia, F., 2007, “Evaluation of Safety of Pointed Masonry Arches Through the Static Theorem of Limit Analysis,” Proceedings of 5th International Conference on Arch Bridges (ARCH’07), P. B.Lourenço, D. B.Oliveira, and A.Portela, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007, Multicomp, Lda Publishers, Portugal, pp. 659–668.
Hejazi, M., and Jafari, F., 2010, “Structural Effects of Brick Arrangement and Span Length on Mid-Pointed Arches,” Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China, Oct. 6–8, 2010, Advanced Materials Research, Trans Tech Publications, Vols. 133–134, pp. 411–416.
Aita, D., Foce, F., Barsotti, R., and Bennati, S., 2007, “Collapse of Masonry Arches in Romanesque and Gothic Constructions,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07), P. B.Lourenço, D. B.Oliveira, and A.Portela, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007, Multicomp, Lda Publishers, Madeira, Portugal, pp. 625–632.

Figures

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Fig. 1

Sketch of a symmetric circular arch subjected only to its own weight (of specific weight γ) with all characteristic parameters involved (d: out-of-plane depth)

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Fig. 2

Five-hinge rotational collapse mechanism of a symmetric circular arch

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Fig. 3

Statics and kinematics of a symmetric rotational collapse mechanism of a circular arch supporting only its own weight

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Fig. 4

Equilibrium of the upper portion of the arch and Heyman's tangency condition of the resultant thrust at the haunches

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Fig. 5

Heyman solution. Fit βfit of β as a function of A.

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Fig. 6

Heyman solution. Fit βfit of β as a function of α.

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Fig. 7

Heyman solution. Fit ηfit of η as a function of α.

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Fig. 8

Heyman solution. Fit hfit of h as a function of α.

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Fig. 9

Eccentricity of the line of thrust with respect to the geometrical centerline of the arch

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Fig. 10

Qualitative representation of the line of thrust at the critical condition of minimum arch thickness

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Fig. 11

CCR solution. Functional dependence of A, η, h on β.

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Fig. 12

CCR solution. Fit βfit = a (A − 2/3)1/b (2 − A)1/cof β as a function of A.

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Fig. 13

CCR solution. Fit βfit = a (A(α) − 2/3)1/b (2 − A(α))1/cof β as a function of α.

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Fig. 14

CCR solution. Fit ηfit of η as a function of α.

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Fig. 15

CCR solution. Fit hfit of h as a function of α.

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Fig. 16

Plot of the eccentricity of the line of thrust for CCR (line tangent to the intrados) and Heyman solutions (line going out of the arch thickness), α = π / 2

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Fig. 17

Plot of the eccentricity of the line of thrust for CCR (line tangent to the intrados) and Heyman solutions (line going out of the arch thickness), α = 7 π/9

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Fig. 18

Analytical plots of the line of thrust for CCR solution, for α = π/2 = 90 deg (A = π/2) and α = 7π/9 = 140 deg (A = 0.889347)

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Fig. 19

Comparison between Heyman, CCR and Milankovitch solutions in terms of the solution couples (β,η), (β, h), (η, h)

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Fig. 20

Comparison between Heyman, CCR, and Milankovitch solutions in terms of A

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Fig. 21

Comparison between Heyman, CCR, and Milankovitch solutions in terms of α

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Fig. 22

Comparison between Heyman, CCR, and Milankovitch solutions for the horizontal nondimensional thrust h∧ = ηh in terms of A

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Fig. 23

Comparison between Heyman, CCR, and Milankovitch solutions for the horizontal nondimensional thrust h∧ = ηh in terms of α

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Fig. 24

Milankovitch solution. Fit βfit M= a(A−(✓31))1/b (2−A)1/c of β as a function of A.

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Fig. 25

Milankovitch solution. Fit βfit M= a (A(α) − (✓31))1/b (2 − A(α))1/cof β as a function of α.

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Fig. 26

Milankovitch solution. Fit ηfit M of η as a function of α.

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Fig. 27

Milankovitch solution. Fit hfit M of h as a function of α.

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