432. It is often not convenient, or even possible, to sustain a bridge
by the methods we have been considering. It is desirable therefore to
inquire whether we cannot arrange some plan of strengthening a beam, by
giving to it what shall be equivalent to an increase of depth.
433. We shall only be able to describe here some very simple methods
for doing this. Superb examples are to be found in railway bridges
all over the country, but the full investigation of these complex
structures is a problem of no little difficulty, and one into which it
would be quite beyond our province to enter. We shall, however, show
how by a judicious combination of several parts a structure can offer
sufficient resistance. The most complex lattice girder is little more
than a network of ties and struts.
[Illustration: FIG. 61.]
434. Let A B (Fig. 61) be a rod of pine 40" × 0"·5" × 0"·5, secured at
each end. We shall suppose that the load is applied at the two points G
and H, in the manner shown in the figure. The load which a bridge must
bear when a train passes over it is distributed over a distance equal
to the length of the train, and the weight of the bridge itself is of
course arranged along the entire span; hence the load which a bridge
bears is at all times more or less distributed and never entirely
concentrated at the centre in the manner we have been considering. In
the present experiment we shall apply the breaking load at the two
points G and H, as this will be a variation from the mode we have
latterly used. E F is an iron bar supported in the loops E G and F H.
Let us first try what weight will break the beam. Suspending the tray
from E F, I find that a load of 48 lbs. is sufficient; much less would
have done had not the ends been clamped. We have already applied a load
in this manner in Art. 406.
435. You observed that the beam, as usual, deflected before it broke;
if we could prevent deflection we might reasonably expect to increase
the strength. Thus if we support the centre of the beam C, deflection
would be prevented. This can be done very simply. We clamp the pieces D
A, D B, D C, on a similar beam, and it is evident that C cannot descend
so long as the joints at A, B, D, C remain firmly secured. We now find
that even with a weight of 112 lbs. in the tray, the bar is unbroken.
An arrangement of this kind is frequently employed in engineering,
for it seems to be able to bear more than double the load which is
sufficient to break the unsupported beam.
[Illustration: FIG. 62.]
436. Two frames of this kind, with a roadway laid between them, would
form a bridge, or if the frames were turned upside down they would
answer equally well, though of course in this case D A and D B would
become ties, and D C a strut, but a better arrangement for a bridge
will be next described.