418. We begin with the study of a very simple contrivance, represented
in Fig. 57.
A B is a rod of pine 20" long. In the diagram it is represented, for
simplicity, imbedded at the end A in the support. In reality, however,
it is clamped to the support, and the same remark may be made about
some other diagrams used in this lecture. Were A B unsupported except
at its end A, it would of course break when a weight of 10 lbs. was
suspended at B, as we have already found in Art. 414.
419. We must ascertain whether the transverse force on A B cannot
be changed into forces of tension and compression. The tie B C is
attached by means of clamps; A B is sustained by this tie; it cannot
bend downwards under the action of the weight W, because we should
then require to have on the same base and on the same side of it two
triangles having their conterminous sides equal, but this we know from
Euclid (I. 7) is impossible. Hence B is supported, and we find that
112 lbs. may be safely suspended, so that the strength is enormously
increased. In fact the transverse force is changed into a compressive
force or thrust down A B, and a tensile force on B C.
[Illustration: FIG. 57.]
420. The actual magnitudes of these can be computed. Draw the
parallelogram C D E B; if B D represent the weight W, it may be
resolved into two forces,—one, B C, a force of extension on the tie;
the other, B E, a compressive force on A B, which is therefore a strut.
Hence the forces are proportional to the sides of the triangle, A B C.
In the present case