361. We next come to the important practical subject of the strength
of timber when supporting a transverse strain; that is, when used as
a beam. The nature of a transverse strain may be understood from Fig.
51, which represents a small beam, strained by a load at its centre.
Fig. 52 shows two supports 40" apart, across which a rod of pine
48" × 1" × 1" is laid; at the middle of this rod a hook is placed, from
which a tray for the reception of weights is suspended. A rod thus
supported, and bearing weights, is said to be strained transversely. A
rafter of a roof, the flooring of a room, a gangway from the wharf to
a ship, many forms of bridge, and innumerable other examples, might be
given of beams strained in this manner. To this important subject we
shall devote the remainder of this lecture and the whole of the next.
362. The first point to be noticed is the deflection of the beam from
which a weight is suspended. The beam is at first horizontal; but
as the weight in the tray is augmented, the beam gradually curves
downwards until, when the weight reaches a certain amount, the beam
breaks across in the middle and the tray falls.
[Illustration: FIG. 51.]
For convenience in recording the experiments the tray chain and hooks
have been adjusted to weigh exactly 14 lbs. (Fig. 52). A B is a cord
which is kept stretched by the little weights D: this cord gives
a rough measure of the deflection of the beam from its horizontal
position when strained by a load in the tray. In order to observe the
deflection accurately an instrument is used called the cathetometer
(G). It consists of a small telescope, always directed horizontally,
though capable of being moved up and down a vertical triangular pillar;
on one of the sides of the pillar a scale is engraved, so that the
height of the telescope in any position can be accurately determined.
The cathetometer is levelled by means of the screws H H, so that the
triangular pillar on which the telescope slides is accurately vertical:
the dotted line shows the direction of the visual ray when the centre C
of the beam is seen by the observer through the telescope.
[Illustration: FIG. 52.]
Inside the telescope and at its focus a line of spider’s web is fixed
horizontally; on the bar to be observed, and near its middle point
C, a cross of two fine lines is marked. The tray being removed, the
beam becomes horizontal; the telescope of the cathetometer is then
directed towards the beam, so that the lines marked upon it can be seen
distinctly. By means of a screw the telescope may be raised or lowered
until the spider’s web inside the telescope is observed to pass through
the image of the intersection of the lines. The scale then indicates
precisely how high the telescope is on the pillar.
363. While I look through the telescope my assistant suspends the tray
from the beam. Instantly I see the cross descend in the field of view.
I lower the telescope until the spider’s web again passes through the
image of the intersection of the lines, and then by looking at the
scale I see that the telescope has been moved down 0"·19, that is,
about one-fifth of an inch: this is, therefore, the distance by which
the cross lines on the beam, and therefore the centre of the beam
itself, must have descended. Indeed, even a simpler apparatus would
be competent to measure the amount of deflection with some degree of
precision. By placing successively one stone after another upon the
tray, the beam is seen to deflect more and more, until even without the
telescope you see the beam has deviated from the horizontal.
364. By carefully observing with the telescope, and measuring in the
way already described, the deflections shown in Table XXIII. were
determined. The scale along the vertical pillar was read after the
spider’s web had been adjusted for each increase in the weight. The
movement from the original position is recorded as the deflection for
each load.