437. An instructive bridge was erected by the late Sir I. Brunel over
the Wye, for the purpose of carrying a railway. The essential parts
of the bridge are represented in the model shown in Fig. 62, which as
before is made of slips of pine clamped together.
438. Our model is composed of two similar frames, one of which we shall
describe, A B is a rod of pine 48" × 0"·5 × 0"·5, supported at each
extremity. This rod is sustained at its points of trisection D, C by
the uprights D E and C F, while E and F are supported by the rods B E,
F E, and A F; the rectangle D E F C is stiffened by the piece C E, and
it would be proper in an actual structure to have a piece connecting D
and F, but it has not been introduced into the model.
[Illustration: FIG. 63.]
439. We shall understand the use of the diagonal C E by an inspection
of Fig. 63. Suppose the quadrilateral A B C D be formed of four pieces
of wood hinged at the corners. It is evident that this quadrilateral
can be deformed by pressing A and C together, or by pulling them
asunder. Even if there were actual joints at the corners, it would be
almost impossible to make the quadrilateral stiff by the strength of
the joints. You see this by the frame which I hold in my hand; the
pieces are clamped together at the corners, but no matter how tightly
I compress the clamps, I am able with the slightest exertion to deform
the figure.
440. We must therefore look for some method of stiffening the frame. I
have here a triangle of three pieces, which have been simply clamped
together at the corners; this triangle is unalterable in form; in fact,
since it is impossible to make two different triangles with the same
three sides, it is evident the triangle cannot be deformed. This points
to a guiding principle in all bridgework. The quadrilateral is not
stiff because innumerable different quadrilaterals can be made with the
same four sides. But if we draw the diagonal A C of the quadrilateral
it is divided into two triangles, and hence when we attach to the
quadrilateral, which has been clamped at the four corners, an
additional piece in the direction of one of the diagonals, it becomes
unalterable in shape.
441. In Fig. 63 we have drawn the two diagonals A C and B D: one would
be theoretically sufficient, but it is desirable to have both, and for
the following reason. If I pull A and C apart, I stretch the diagonal
A C and compress B D. If I compress A and C together, I compress the
line A C and extend B D; hence in one of these cases A C is a tie, and
in the other it is a strut. It therefore follows that in all cases one
of the diagonals is a tie, and the other a strut. If then we have only
one diagonal, it is called upon to perform alternately the functions of
a tie and of a strut. This is not desirable, because it is evident that
a piece which may act perfectly as a tie may be very unsuitable for a
strut, and _vice versâ_. But if we insert both diagonals we may make
both of them ties, or both of them struts, and the frame must be rigid.
Thus for example, I might make A C and B D slender bars of wrought
iron, which form admirable ties, though quite incapable of acting as
struts.
442. What we have said with reference to the necessity for dividing a
quadrilateral figure into triangles applies still more to a polygon
with a large number of sides, and we may lay down the general principle
that every such piece of framework should be composed of triangles.
443. Returning to Fig. 62, we see the reason why the rectangle E D C F
should have one or both of its diagonals introduced. A load placed, for
example, at D would tend to depress the piece D E, and thus deform the
rectangle, but when the diagonals are introduced this deformation is
impossible.
444. Hence one of these frames is almost as strong as a beam supported
at the points C and D, and therefore, from the principles of Art. 388,
its strength is three times as great as that of an unsupported beam.
445. The two frames placed side by side and carrying a roadway form an
admirable bridge, quite independent of any external support, except
that given by the piers upon which the extremities of the frames rest.
It would be proper to connect the frames together by means of braces,
which are not, however, shown in the figure. The model is represented
as carrying a uniform load in contradistinction to Fig. 58, where the
weight is applied at a single point.
446. With eight stone ranged along it, the bridge of Fig. 62 did not
indicate an appreciable deflection.
LECTURE XIV.
_THE MECHANICS OF A BRIDGE._
Introduction.—The Girder.—The Tubular Bridge.—The
Suspension Bridge.