From the several calculations made, it will be seen that if two beams or joists are of the same length and sectional area, the one of greater depth will be the stronger of the two.
This can readily be seen by taking as examples two joists of the same sectional area, but of dif ferent dimensions. A piece of 12-inch by inch, another 10 inches by 3 inches, have the same sectional area (30 square inches); but their relative strength when placed on edge is as 360 to 300. The rule stated covering this, is that the strength of a beam is as the square of its depth—that is, the depth must be multiplied by itself; 12X 12X 21/2=360, and 10 X10 X 3= 300, or a proportion of strength between the two as 6 is to 5.
There is, of course, a limitation in the prac tical application of this; for if a beam be made very deep in relation to its breadth, it will buckle and twist when loaded. In the case of floor joists, the disproportion of depth to breadth is very marked; but their tendency to buckle is overcome by strutting, either with solid blocks the same depth as the joists cut in between each pair, or with herring-bone strutting cut from narrow battens.
Many experiments have been made to find the best proportion for the breadth and depth of wood beams, and it has been laid down that a ratio of 5 to 7 gives the best section. This is a useful thing to remember and easily kept in mind.
In concluding our discussion of the strength of beams, the writer trusts that some of the readers who may have been deterred from going into the matter of calculating the strength of materials will be in some measure led to see that a formula is only a simple way of putting down a rule for some arithmetical process that would take a long time to describe in words. The strength of beams is a question that is so often cropping up that this discussion may be directly valuable in showing how to find it in any given case; but the writer also hopes that the discussion may lead many readers to take up other lines of calculation equally simple and useful to the practical man.