Kinematic Stability of Masonry Arches


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To quantify the safety of masonry arches and vaults using limit-analysis, various types of safety factors have been devised. The most well-known were introduced by Heyman: a “static factor of safety” (or load factor) assessing how vulnerable the structure is to increases in the living loads and a “geometrical factor of safety” assessing how critical the thickness of the structure is for its stability. In non seismic areas, one of the main risks of total or partial collapse of arches and vaults is excessive displacement of the supports (following walls or soil deformation). Limit analysis technique can be used to analyse this risk, quantifying movements permitted before collapse and evolution of the thrust on the supports. This analysis can be combined with pathological investigations and displacement monitoring to study the evolution of the risk and define a “kinematic factor of safety”. A software program was developed (a) to compute domains of stability for particular mechanisms of deformation, (b) to study possibility of transitions between mechanisms during deformation and (c) to interactively study the influence of movements of the supports on thrust and stability. Scaled physical models are used to validate the limit analysis approach, using an experimental rig where horizontal and vertical displacements are controlled by computer. A high-speed camera is used to study transition between mechanisms. Finally it is referred to techniques integrating this kinematic approach into a more general probabilistic approach, taking into account various uncertainties in the structure (shape, thickness, loads, movements).



Advanced Materials Research (Volumes 133-134)

Edited by:

Xianglin Gu and Xiaobin Song




P. Smars "Kinematic Stability of Masonry Arches", Advanced Materials Research, Vols. 133-134, pp. 429-434, 2010

Online since:

October 2010





[1] Frézier, A F (1737-39). La theorie et la pratique de la coupe des pierres et des bois pour la construction des voutes et autres parties des batiments civils et militaire., Strasbourg, France : J. -D. Doulsseker fils, L. -H. Guérin aîné.

DOI: 10.4000/books.enseditions.7531

[2] Viollet le Duc, E E (1854-1868). Dictionnaire raisonné de l'architecture française du XIe au XVIe siècle., Paris, France : A. Morel.

DOI: 10.17658/issn.2058-5462/issue-06/jillson/figure1

[3] Beranek, W J (1989). Understanding of structures, Stable-Unstable, structural consolidation of ancient buildings, 29-43.

[4] Heyman, J (1966). The stone skeleton., International journal of solids and structures, 2, 249-279.

[5] Briccoli Bati, S, Paradiso, M, and Tempesta, G (1997). Archi in muratura soggetti a carichi e cedimenti delle imposte., Laterizio, 60, 436-443.

[6] Smars, P (2000). Etudes sur la stabilité des arcs et voûtes, confrontation des méthodes de l'analyse limite aux voûtes gothiques en Brabant., PhD thesis, K.U. Leuven, (2000).

[7] Ochsendorf, J A (2002). Collapse of Masonry Structures., PhD thesis, University of Cambridge.

[8] Ochsendorf, J A (2006). The masonry arch on spreading supports., Structural Engineer, 84(2), 129-135.

[9] Mainstone, R J (1997). Structural analysis, structural insights, and historical interpretation, Journal of the society of architectural historians, 56(3), 316-340.

DOI: 10.2307/991244

[10] Smars, P (2008). Influence of friction and tensile resistance on the stability of masonry arches, in Structural Analysis of historical constructions, Bath (UK), 1199-1206.

[11] Calipous website. [Online]. Available: http: /smars. yuntech. edu. tw/calipous.

[12] ICOMOS. (2003). Principles for the analysis, conservation and structural restoration of architectural heritage, ICOMOS Charter.

[13] Livesley, R K (1978). Limit analysis of structures formed from rigid blocks., International journal for numerical methods in engineering, 12, 1853-1871.

DOI: 10.1002/nme.1620121207

[14] Livesley, R K (1992). A computational model for the limit analysis of three-dimensional masonry structures., Meccanica, 27, 161-172.

DOI: 10.1007/bf00430042

[15] Schueremans, L, Smars, P, and Van Gemert, D (2001a). Safety of arches - a probabilistic approach, in 9th Canadian masonry symposium (Spanning the Centuries with Masonry), 12pp.

[16] Schueremans, L, Van Gemert, D, and Smars, P (2001b). Safety assessment of masonry arches using probabilistic methods., International Journal for restoration of buildings and monuments, 7(5), 517-538.

DOI: 10.1515/rbm-2001-5596

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