sabato 13 giugno 2015

Collapse of masonry domes

Mechanical collapse of masonry domes: the Lamé-Clapeyron’s Mémoire and the case of St. Isaac in Saint Petersburg

1Massimo Corradi
1Dipartimento di Scienze per l’Architettura, Scuola Politecnica - Genova,


The Mechanics of arches, vaults and domes is a topic of Structural Mechanics that starts his history from XVIII century starting from de La Hire, Couplet, Bélidor to Bouguer, Bossut, Coulomb and Mascheroni (Benvenuto, 1991). Only at the beginning of XIX century the contributions of Persy, Audoy, Navier, Mery and the Coulomb’s theory (Coulomb, 1773; Heyman, J.,1972) have permitted to establish a general theory for collapse of masonry arch with, friction and cohesion, formed by a system of voussoirs with unilateral constraints (Heyman, 1969; Sinopoli, Corradi & Foce, 1997).
In this complex and tortuous path, after the great debates on the dome of Santa Maria del Fiore in Florence and on the dome of S. Peter in Rome, we remark the important contribution to develop a general theory for domes published by Lamé and Clapeyron in regards the dome of S. Isaac in Saint Petersburg (Lamé & Clapeyron, 1823).

Fig. 1 - From Lamé, G. and B.P.E. Clapeyron, 1823.

The question around this subject is to establish what is the most agreeable method to determine the line of thrust before that dome collapses. The argument proposed by Lamé and Clapeyron – at this time working at Science Academy of Saint Petersburg - is very interesting and it opened a three new paths of research. The first is to define the line thrust for masonry arch, the second is to define the collapse of masonry domes according to Poleni’s theory (Poleni, 1748) and the third is to define a method to increase structural strength and the more appropriate method to strengthen St. Isaac masonry dome.
The aim is to show as Lamé and Clapeyron’s theory is today still present and the strengthening methods (traditional building techniques and methods, and also static reinforcement systems) proposed in the XIX and XX centuries are more compatible with old materials and structures with respect to new material, concrete and steel.
In fact, over the past few years, the restoration work done on monumental architecture has brought out a disagreement between the rationale for static and the reasoning behind conservation. This disagreement has highlighted how the “need” for strengthening often moves away from the search for mechanical models that more closely approach the extensive and masterly rules of “good building”. These rules have always been set down by relying on skillful mastery that has matured over centuries of careful empiricism, to follow the safe and unfailing path laid down by the theory of elasticity that was first set forth during the past century, and has now been consolidated through the use of precisely elaborated instruments and methods of calculation. In this sense, we will attempt to clarify the reasoning underlying the question posed by the title. In other words, when we analyze the structural behaviour of monumental architecture, is it better to proceed using the tools of elastic calculation or is it best to rely on the new models proposed by limit design principles, retracing the steps that were already taken by the scientific culture of the nineteenth century, particularly for calculating masonry arches, vaults and domes?


  • 1748 Poleni, G. Memorie istoriche della gran cupola, del Tempio Vaticano, e dé danni di essa, e dé ristoramenti loro. Padova: nella stamperia del Seminario [Giovanni Manfrè].
  • 1773 Coulomb, C.A. “Essai sur une application des Règles de Maximis & Minimis à quelques Problèmes de Statique, relatifs à l’Architecture”, Mémoires de Mathématique et de Physique, présentés à l’Académie Royale des Sciences, par divers Savans, Année 1773, 7 (1773), pp. 343-382, Paris, impr. Royale 1776.
  • 1823 Lamé, G. and B.P.E. Clapeyron, “Mémoire sur la stabilité des voûtes”. Annales des Mines, vol. 8, pp. 789-818.
  • 1969 Heyman, J. “The safety of masonry arches”, Int. J. Mech. Sci, Vol. 11, pp. 363-385.
  • 1972 Heyman, J. (1972). Coulomb’s memoir on statics. An essay on the history of civil engineering, Cambridge University Press, Cambridge.
  • 1988 Heyman, J. “Poleni’s problem”, Proc. Instn. Civ. Engrs, London, Part I, Vol. 84, pp. 737-759.
  • 1991 Benvenuto, E. An Introduction to the History of Structural Mechanics. New York, Springer-Verlag, 1991.
  • 1997 Sinopoli, A., Corradi, M. & F. Foce. “A Modern Formulation for Pre-Elastic Theories on Masonry Arches”. Journal of Engineering Mechanics, vol. 123, n. 3 (march 1997), pp. 204-213.

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