377. In the preceding lecture we have examined some general
circumstances in connection with the condition of a beam acted on
by a transverse force; we proceed in the present to inquire more
particularly into the strength under these conditions. We shall, as
before, use for our experiments rods of pine only, as we wish rather to
illustrate the general laws than to determine the strength of different
materials. The strength of a beam depends upon its length, breadth,
and thickness; we must endeavour to distinguish the effects of each of
these elements on the capacity of the beam to sustain its load.
We shall only employ beams of rectangular section; this being
generally the form in which beams of wood are used. Beams of iron,
when large, are usually not rectangular, as the material can be more
effectively disposed in sections of a different form. It is important
to distinguish between the _stiffness_ of a beam in its capacity to
resist flexure, and the _strength_ of a beam in its capacity to resist
fracture. Thus the stiffest beam which can be made from the cylindrical
trunk of a tree 1' in diameter is 6" broad and 10"·5 deep, while the
strongest beam is 7" broad and 9"·75 deep. We are now discussing the
strength (not the stiffness) of beams.
378. We shall commence the inquiry by making a number of experiments:
these we shall record in a table, and then we shall endeavour to see
what we can learn from an examination of this table. I have here
ten pieces of pine, of lengths varying from 1' to 4', and of three
different sections, viz. 1" × 1", 1" × 0"·5, and 0"·5 × 0"·5. I have
arranged four different stands, on which we can break these pieces: on
the first stand the distance between the points of support is 40", and
on the other stands the distances are 30," 20", and 10" respectively;
the pieces being 4', 3', 2', and 1' long, will just be conveniently
held on the supports.
379. The mode of breaking is as follows:—The beam being laid upon the
supports, an S hook is placed at its middle point, and from this S hook
the tray is suspended. Weights are then carefully added to the tray
until the beam breaks; the load in the tray, together with the weight
of the tray, is recorded in the table as the breaking load.
380. In order to guard as much as possible against error, I have here
another set of ten pieces of pine, duplicates of the former. I shall
also break these; and whenever I find any difference between the
breaking loads of two similar beams, I shall record in the table the
mean between the two loads. The results are shown in Table XXIV.