405. We have up to the present only considered the case where the load
is suspended from the centre of the beam. But in the actual employment
of beams the load is not generally applied in this manner. See in the
rafters which support a roof how every inch in the entire length has
its burden of slates to bear. The beams which support a warehouse floor
have to carry their load in whatever manner the goods are disposed:
sometimes, as for example in a grain-store, the pressure will be
tolerably uniform along the beams, while if the weights be irregularly
scattered on the floor, there will be corresponding inequalities in
the mode in which the loads are distributed over the beams. It will
therefore be useful for us to examine the strength of a beam when its
load is applied otherwise than at the centre.
406. We shall employ, in the first place, a beam 40" span, 0"·5 broad,
and 1" deep; and we shall break it by applying a load simultaneously at
two points, as may be most conveniently done by the contrivance shown
in the diagram, Fig. 53. A B is the beam resting on two supports; C and
D are the points of trisection of the span; from whence loops descend,
which carry an iron bar P Q; at the centre R of which a weight W is
suspended. The load is thus divided equally between the two points C
and D, and we may regard A B as a beam loaded at its two points of
trisection. The tray and weights are employed which we have used in the
apparatus represented in Fig. 58.
[Illustration: FIG. 53.]
407. We proceed to break this beam. Adding weights to the tray, we see
that it yields with 117 lbs., and cracks across between C and D. On
reference to Table XXIV. we find from experiment No. 2 that a similar
bar was broken by 77 lbs. at the centre; now ³/₂ × 77 = 115·5; hence we
may state with sufficient approximation that the bar is half as strong
again when the load is suspended from the two points of trisection as
it is when suspended from the centre. It is remarkable that in breaking
the beam in this manner the fracture is equally likely to occur at any
point between C and D.
408. A beam _uniformly_ loaded requires twice as much load to break
it as would be sufficient if the load were merely suspended from the
centre. The mode of applying a load uniformly is shown in Fig. 54.
[Illustration: FIG. 54.]
In an experiment actually tried, a beam 40" × 0"·5 × 1" placed edgewise
was found to support ten 14 lb. weights ranged as in the figure; one or
two stone more would, however, doubtless produce fracture.
409. We infer from these considerations that beams loaded in the manner
in which they are usually employed are considerably stronger than would
be indicated by the results in Table XXIV.