If such a beam, instead of resting flatwise, were placed edgewise, its strength would be increased in the ratio of its depth to its breadth—that is, it would be increased d-fold—and would therefore amount to
| 6080 | |
| ————— | × d². |
| l |
We thus learn the strength of a beam 1" broad, d" deep, and l" span. The strength of b of these beams placed side by side, would be the same as the strength of one beam b" broad, d" deep, and l" span, and thus we finally obtain
| 6080 | |
| ————— | × d² × b. |
| l |
Since b d is the area of the section, we can express this result conveniently by saying that the breaking load in lbs. of a rectangular pine beam is equal to
| 6080 × | area of section × depth |
| span |
the depth and span being expressed in inches linear measure, and the section in square inches.
400. In order to test this formula, we have calculated from it the breaking loads of all the ten beams given in [Table XXIV]. and the results are given in the sixth column. The difference between the amount calculated and the observed mean breaking weight is shown in the last column.
401. Thus, for example, in experiment No. 7 the span is 20", breadth, 1", depth 0"·5; the formula gives, since the area is 0"·5,
| 0·5 × 0·5 | ||
| P = 6080 | ————— | = 76 |
| 20 |