Engineers, called on to advise on the repair of an old building — a cathedral, say
— will usually have learned their skills in the design of modern buildings using
modern materials — steel and reinforced concrete. Care must be taken in transferring
those skills to ancient structures. In particular, the engineer is used to provide precise
answers (for example, values of stresses) in order to satisfy criteria imposed by
accepted practice.
Such an engineer will not have had occasion to consider the fact that a precise
description cannot be given for the behaviour of any structure, modern or ancient.
The states of all structures are critically dependent on unknown, and unknowable,
defects in construction, and, above all, on unknowable movements of the
environment. The footing of a column in a steel skyscraper, and the foundation of a
pier carrying a tower in a cathedral, will in reality not be in the precise
locations assumed by the engineer, and even small “defects” of this sort can
have a very large influence on the structural state of the buildings being
analysed.
Although unequivocal and unique answers cannot be given to questions that arise
in the analysis and repair of old buildings, it is at least possible to calculate
states of equilibrium with which a structure is “comfortable”. Although such
states will not be observed in practice, their existence satisfies one of the
basic theorems of plastic theory — if any one such state can be found, then
this gives assurance that the structure is in fact safe. Further, it may be
possible to calculate minimum and maximum values for important structural
quantities.
Keywords
ancient buildings, limit analysis, geometrical factor of
safety, masonry equilibrium
