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

^{1}Massimo Corradi

^{1}Dipartimento di Scienze per l’Architettura, Scuola Politecnica - Genova, corradi@arch.unige.it

**Remark**

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?

###
**Bibliography**

- 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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