356. We proceed to examine into the capability of timber to resist
forces of longitudinal compression, either as a pillar or in any other
form of “strut,” such for instance, as the jib of the crane represented
in Fig. 17. The use of timber as a strut depends in a great degree upon
the coherence of the fibres to each other, as well as upon their actual
rigidity. The action of timber in resisting forces of compression is
thus very different from its action when resisting forces of extension;
we can examine, by actual experiment, the strength of timber under the
former conditions, as the weights which it will be necessary to employ
are within the capabilities of our lecture room apparatus.
357. The apparatus is shown in Fig. 50. It consists of a lever of
the second order, 10' long, the mechanical advantage of which is
threefold; the resistance of the pillar D E to crushing is the load to
be overcome, and the power consists of weights, to receive which the
tray B is used; every pound placed in the tray produces a compressive
force of 3 lbs. on the pillar at D. The fulcrum is at A and guides at
G. The lever and the tray would somewhat complicate our calculations
unless their weights were counterpoised. A cord attached to the
extremity of the lever passes over a pulley F; at the other end of
this cord, sufficient weights C are attached to neutralize the weight
of the apparatus. In fact, the lever and tray now swing as if they had
no weight, and we may therefore leave them out of consideration. The
pillar to be experimented upon is fitted at its lower end E into a hole
in a cast iron bracket: this bracket can be adjusted so as to take in
pieces of different lengths; the upper end of the pillar passes through
a hole in a second piece of cast iron, which is bolted to the lever:
thus our little experimental column is secured at each end, and the
risk of slipping is avoided. The stands are heavily weighted to secure
the stability of the arrangement
[Illustration: FIG. 50.]
358. The first experiment we shall make with this apparatus is upon a
pine rod 40" long and 0"·5 square; the lower bracket is so placed that
the lever is horizontal when just resting upon the top of the rod.
Weights placed in the tray produce a pressure three times as great
down the rod, the effect of which will first be to bend the rod, and,
when the deflection has reached a certain amount, to break it across.
I place 28 lbs. in the tray: this produces a pressure of 84 lbs. upon
the rod, but the rod still remains perfectly straight, so that it bears
this pressure easily. When the pressure is increased to 96 lbs. a very
slight amount of deflection may be seen. When the strain reaches 114
lbs. the rod begins to bend into a curved form, though the deflection
of the middle of the rod from its original position is still less than
0"·25. Gradually augmenting the pressure, I find that when it reaches
132 lbs. the deviation has reached 0"·5; and finally, when 48 lbs. is
placed in the tray, that is, when the rod is subjected to 144 lbs., it
breaks across the middle. Hence we see that this rod sustained a load
of 96 lbs. without sensibly bending, but that fracture ensued when the
load was increased about half as much again. Another experiment with
a similar rod gave a slightly less value (132 lbs.) for the breaking
load. If I add these results together, and divide the sum by 2, I
find 138 lbs. as the mean value of the breaking load, and this is a
sufficiently exact determination.
359. Let us next try the resistance of a shorter rod of the same
section. I place a piece of pine 20" long and 0"·5 square in the
apparatus, firmly securing each end as in the former case. The
lower bracket is adjusted so as to make the lever horizontal; the
counterpoise, of course, remains the same, and weights are placed in
the tray as before. No deflection is noticed when the rod supports 126
lbs.; a very slight amount of bending is noticeable with 186 lbs.;
with 228 lbs., the amount by which the centre of the rod has deviated
laterally from its original position is about 0"·2; and finally, when
the load reaches 294 lbs., the rod breaks. Fracture first occurs in the
middle, but is immediately followed by other fractures near where the
ends of the rod are secured.
360. Hence the breaking load of a rod 20" long is more than double
the breaking load of a rod of 40" long the same section; from this we
learn that the sections being equal, short pillars are stronger than
long pillars. It has been ascertained by experiment that the strength
of a square pillar to resist compression is proportional to the square
of its sectional area. Hence a rod of pine, 40" long and 1" square,
having four times the section of the rod of the same length we have
experimented on, would be sixteen times as strong, and consequently its
breaking weight would amount to nearly a ton. The strength of a rod
used as a _tie_ depends only on its section, while the strength of a
rod used as a _strut_ depends on its length as well as on its section.