Encyclopaedia Britannica > Volume 3, Anatomy-Astronomy

ARCH.
Process of
the break¬
ing of an
arch.
only by loading that part more than is requisite for equi¬
librium. It would be prudent to do this to a certain de¬
gree, because it is by this cohesion that the crown always
becomes the weakest part of the arch, and suffers more
by any occasional load.
We expect that it will be said in answer to all this,
that the cohesion given by the strongest cement that we
can employ, nay the cohesion of the stone itself, is a mere
nothing in comparison with the enormous thrusts that are
in a state of continual exertion in the different parts of an
arch. This is very true; but there is another force which
produces the same effect, and which increases nearly in
the proportion that those thrusts increase, because it
arises from them. This is the friction of the stones on
each other. In dry freestone this friction considerably
exceeds one half of the mutual pressure. The reflecting
reader will see that this produces the same effect, in the
case under consideration, that cohesion would do; for
while the arch is in the act of failing, the mutual pressure
of the arch-stones is acting with full force, and thus pro¬
duces a friction more than adequate to all the effects we
have been speaking of.
30. When these circumstances are considered, we ima¬
gine that it will appear that an arch, when exposed to a
great overload on the crown (or indeed on any part), di¬
vides of itself into a number of parts, each of which con¬
tains as many arch-stones as can be pierced (so to speak)
by one straight line, and that it may then be considered
as nearly in the same situation with a polygonal arch of
long stones abutting on each other like so many beams
in a Norman roof, but without their braces and ties. It
tends to break at all those angles; and it is not suffi¬
ciently resisted there, because the materials with which
the flanks are filled up have so little cohesion, that the
angle feels no load except what is immediately above
it; whereas it should be immediately loaded with all
the weight which is diffused over the adjoining side
of the polygon. This will be the case, even though
the curvilinear arch be perfectly equilibrated. We re¬
collect some circumstances in the failure of a consider¬
able arch, which may be worth mentioning. It had been
built of an exceedingly soft and friable stone, and the
arch-stones were too short. About a fortnight before it
fell, chips were observed to be dropping off from the joints
of the arch-stones, about ten feet on each side of the mid¬
dle, and also from another place on one side of the arch,
about twenty feet from its middle. The masons in the
neighbourhood prognosticated its speedy downfall, and
said that it would separate in those places where the chips
were breaking off. At length it fell; but it first split in
the middle, and about fifteen or sixteen feet on each side,
and also at the very springing of the arch. Immediately
before the fall a shivering or crackling noise was heard,
and a great many chips dropped down from the middle,
between the two places from whence they had dropped a
fortnight before. The joints opened above at those new
places above two inches, and in the middle of the arch the
joints opened below, and in about five minutes after this
the whole came down. Even this movement was plainly
distinguishable into two parts. The crown sunk a little,
and the haunches rose very sensibly, and in this state it
hung for about half a minute. The arch-stones of the
crown wrere hanging by their upper corners : when these
splintered off, the whole fell down.
We apprehend that the procedure of nature was some¬
what in this manner. Straight lines can be drawn within
the arch-stones from A (Plate XLIX. fig. 8) to B andD, and
from these points to C and E. Each of the portions ED,
DA, AB, BC, resist as if they were of one stone, composing
a polygonal vault ED ABC. When this is overloaded at A,
A can descend in no other way than by pushing the an-
gles B and D outwards, causing the portions BC, DE, to
turn round C and E. This motion must raise the points
B and D, and cause the arch-stones to press on each other
at their iwwer joints b and d. This produced the copious
splintering at those joints immediately preceding the total
downfall. The splintering which happened a fortnight
before arose from this circumstance, that the lines AB
and AD, along which the pressure of the overload was
propagated, were tangents to the soffit of the arch in the
points F, H, and G, and therefore the strain lay all on those
corners of the arch-stones, and splintered a little from off
them till the whole took a firmer oed. The subsequent
phenomena are evident consequences of this distribution
and modification of pressure, and can hardly be explained
in any other way, at least not on the theoretical principles
already set forth; for in this bridge the loads at B and D
were very considerably greater than what the equilibrium
required; and we think that the first observed splintering
at H, F, and G, was most instructive, showing that there
was an extraordinary pressure at the inner joints in those
places, which cannot be explained by the usual theory.
Not satisfied with this single observation after this way
of explaining it occurred to us, and not being able to find
any similar fact on record, the writer of this article got
some small models of arches executed in chalk, and sub¬
jected them to many trials, in hopes of collecting some
general laws of the internal workings of arches which
finally produce their downfall. He had the pleasure of
observing the above-mentioned circumstances take place
very regularly and uniformly when he overloaded the
models at A. The arch always broke at some place B
considerably beyond another point F, where the first chip¬
ping had been observed. This is a method of trial that
deserves the attention both of the speculatist and the
practitioner.
If these reflections are any thing like a just account of
the procedure of nature in the failure of an arch, it is
evident that the ingenious mathematical theory of equili¬
brated arches is of little value to the engineer. We ven¬
tured to say as much already, and we rested a good deal
on the authority of Sir Christopher Wren. He was a
good mathematician, and delighted in the application of
this science to the arts. He was a celebrated architect,
and his reports on the various works committed to his
charge show that he was in the continued habit of mak¬
ing this application. Several specimens remain of his
own methods of applying them. Ihe roof of the theatre
of Oxford, the roof of the cupola of St Paul s, and in par¬
ticular the mould on which he turned the inner dome of
that cathedral, are proofs of his having studied this theory
most attentively. He flourished at the very time that it
occupied the attention of the greatest mechanicians of
Europe; but there is nothing to be found among his pa¬
pers which shows that he had paid much regard to it.
On the contrary, when he has occasion to deliver his
opinion for the instruction of others, and to explain to the
dean and chapter of Westminster his operations in repair¬
ing that collegiate church, this great architect considers
an arch just as a sensible and sagacious mason would do,
and very much in the way that we have just now been
treating it. (See Account of the Family of Wren, p. 356.)
Supported therefore by such authority, we would recom¬
mend this way of considering an arch to the study of
the mathematician; and we would desire the experien¬
ced mason to think of the most efficacious methods for re¬
sisting this tendency of arches to rise in the flanks. Un¬
fortunately there seems to be no precise principle to point
out the place where this tendency is most remarkable.
31. We are therefore highly pleased with the ingenious
Arch.