Safety assessment of historic masonry structures is a complex problem mainly due to the mechanical characteristics of their material. In the 50’s it was shown that Standard Limit Analysis is suitable for that type of structures and has proven effectiveness for simplified assessment as long as sliding collapse does not occur. This can be formulated as an optimization problem with the intention of calculating the bounds of the load factor, the maximum for static formulations and the minimum for kinematics. In the static case, it is generally assumed that a load factor lower than the referred of the onset of collapse is a safe load factor, but this assumption is false. The collapse due to the lack of stability may occur by increase or decrease of the load factor. This work presents an alternative to load factor determination to evaluate the safety of masonry structures. The possibility to incorporate one or more safety coefficients is presented applying a deterministic partial safety factor method. An important difficulty for this purpose is that usually these partial coefficients are applied to variables that are referred to the origin of coordinates. This would be appropriate for materials with similar mechanical behaviour under tension and compression stresses, but it is not the case for the typical materials employed in masonry structures like stones, bricks or similar. Materials with non-symmetric tension-compression behaviour have the origin of coordinates over the yield surface or very close to it. For this reason, the origin can hardly be considered as a safe reference point. The method proposed in this work consists of the calculation of the interior point further of the yield surface and considers it as the safest point. Considering that point as the origin of coordinates, the deterministic partial safety factors can be calculated.
 A. Kooharian, “Limit Analysis of Voussoir (segmental) and Concrete Arches”, Proceedings of the American Concrete Institute, 49 (12): 317-328, (1953)
 Drucker, D.C. (1953). Coulomb friction, plasticity and limit loads. Transations of American Society of MechanicalEngineers. 76, 71-74.
 A.Orduña, P.B. Lourenço, “Limit analysis as a tool for the simplified assessment of ancient masonry structures”, Historical Constructions, 511-520. Guimarães: University of Minho(2001)
 Charnes, A., Greenberg, H.J. (1951). Plastic collapse and linear programming.Bull. Amer. Math. Soo.. 57, 480.
 Dorn, W. S. (1955). On the Plastic Collapse of Structures and Linear Programming. Dissertations. Carnegie MellonUniversity. Paper 85.
 Charnes, A., Lemke, C. E., Zienkiewiz, O. C. (1959). Virtual Work, Linear Programming and Plastic Limit Analysis. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. Vol. 251, No. 1264, 110-116.
 Anderheggen, E., Knopfel, H. (1972). Finite element limit analysis using linear programming. Int. J. Solids Structures. 8, 1413-1431.
 Livesley, R.K. (1978). Limit analysis of structures formed from rigid blocks. Int. Journal for Numerical Methods in Engineering. 12, 1853-1871.
 Gilbert, M., Melbourne, C. (1994). Rigid block analysis of masonry structures. The Structural Engineer. 72, 356-361.
 Heyman, J. (1966) The stone skeleton. International Journal of Solids and Structures, 2, 249-279
 Delbecq, Jean-Michel (1982). Les ponts en maçonnerie. Evaluation de la stabilité. SETRA Ministère des transports.
 Magdalena, F. (2013) El problema del rozamiento en el análisis de estructuras de fábrica mediante modelos de sólidos rígidos. Tesis de Doctorado. Universidad Politécnica de Madrid.
 Magdalena, F.; García, J.; Hernando, J.I.; Magdalena, E. (2017). Safety assessment of masonry structures using ordinal optimization. Proceedings of the 4th WTA International PhD Symposium. Ed. WTA Nederland.
 Magdalena,;Aznar, A.; Hernando, J.I.; F.; García, J.(2014). Linear programming as a tool to study the stability of masonry arch bridges Report 37th IABSE Symposium Madrid 2014. International Association for Bridge and Structural Engineering
 S.Boyd, L.Vanderberghe, Convex Optimization. Cambridge University Press. (2004)
 Cervera, J. (2010). Un criterio robusto para la medida del margen -coeficiente- de seguridad. Informes de la Construcción. Vol.62, 518, 33-42.
 O. Ditlevsen, H.O. Madsen, Structural Reliability Methods, Internet edition 2.3.7,http://odwebsite.dk/books/OD-HOM-StrucRelMeth-Ed2.3.7.pdf, (2007)
Are you one of the authors of this document?