429. The same principles that we have employed in the construction of
the bridge of Fig. 58 may be extended further, as shown in the diagram
of Fig. 59.
[Illustration: FIG. 59.]
We have here two horizontal rods, 48" × 0"·5 × 0"·5, each end being
secured to the supports; one of these rods is shown in the figure. It
is divided into five equal parts in the points B, C, C´, B´. We support
the rod in these four points by struts, the other extremities of which
are fastened to the framework. The points B, C, C´, B´ are fixed, as
they are sustained by the struts: hence a weight suspended from P,
which is to break the bridge, must be sufficiently strong to break a
piece C C´, which is secured at the ends; the rod A A´ would have been
broken with 38 lbs., hence 190 lbs. would be necessary to break C C´.
There is a similar beam on the other side of the bridge, and therefore
to break the bridge 380 lbs. would be necessary, but this force must
be applied exactly at the centre of C C´; and if the weights be spread
over any considerable length, a heavier load will be necessary. In
fact, if I were to distribute the weight uniformly over the distance C
C´, it appears from Art. 408 that double the load would be necessary to
produce fracture.
430. We shall now break this model. I place 18 stone upon it ranged
uniformly, and the cathetometer tells me that the bridge only deflects
0"·1, and that its elasticity is not injured. Placing the tray in
position, and loading the bridge by this means, I find with a weight of
2 cwt. that there is a deflection of 0"·15; with 4 cwt. the deflection
amounts to 0'·72. We therefore infer that the bridge is beginning to
yield, and the clamps give way when the load is increased to 500 lbs.