The compression on the top chord is evidently the sum of the compressions of the separate systems; the compression from any one system is as follows, fig. 102.
Fig. 102.
Let a d, c d be the rods, and a b c the chord; also b d, the post; now if d b represents the weight, e h shows the tension on a lower, or the compression on an upper chord; the triangles a c d and a b e are similar; as also e b h and d b c; whence
be = ab × cd
ac;
and
eh = cb × be
dc compression.
Numerically we have the following figures:—
In the first system,
be = 15 × 77.6
90 = 13,