Civil Engineering Reference
In-Depth Information
the voussoirs comprising a vault. However whereas a vault is set directly on any
rectilinear plan, a dome can only be raised on a curvilinear base (almost always a
circle, but it is possible to build domes over an, e.g. elliptical plan—although there
is little evidence of such construction in the ancient world). h erefore since the
great majority of domes were raised over a rectilinear (square) plan, the question
arose of accommodating the circular base of the dome to the square plan of the
underlying chamber.
h e construction of the dome proper will be dealt with i rst.
In dealing with Graeco-Roman ashlar stone domes attempted analysis of stresses
will be avoided. h e roughest rule of thumb guide to design is that deforming
stresses in a dome (e.g. outward thrust at the haunches) increase according to the
square of the span and diminish directly according to the height (the “rise”). It is
thus not possible to identify an optimum geometrical form which is applicable to
all domes irrespective of scale—i.e. if the span to be covered is doubled, the rise
should be increased fourfold to maintain the same statical properties. h is can be
put in categorical terms as follows. h e thrust in a dome is directly proportional
to the load (dead weight of the construction) and to the square of the span; and is
inversely proportional to the rise. h us to minimise the thrust for a dome of given
span it must be as light as possible and have the maximum rise feasible.
Statical information of this and more detailed nature was not available at the
time. h e architects and builders then had at their disposal knowledge of solid
geometry necessary to set out any curved form, and they had possibilities of refer-
ence to experience in other regions of the construction and behaviour of domes
out of materials other than stone. In this way they knew that the greater the span
the more dii cult it was to construct a stable dome; and they knew that a dome
tended to push outwards at its haunches involving vertical cracks and i ssures in
this region (signs of “hoop tension”). To minimize this behaviour they knew of
two obvious measures, constructionwise. h e dome should be as light as possible
and as tall as possible relative to the span.
h ese simple considerations, however, had complications in practice. To gain
overall lightness meant dif erentially reducing the weight of the upper registers of
the dome, since here the self load was much less than at the base. h is could be
ef ected in two ways: using lighter material at the crown, or reducing the thickness
of the wall section at the crown. Both devices were practiced in domes constructed
from other materials (e.g. clay), and both could be incorporated in stone domes.
h e thickness of the wall section was progressively reduced by striking the curves
of the extrados and the intrados of the dome from dif erent centres (that of the
extrados from a centre below that of the intrados). It was also possible, though
unusual, to build the upper part of the dome from the lightest possible stone—e.g.
pumice. However when consideration was directed to the optimum tall proi le, it
h e Dome
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