Читать книгу Inventors at Work, with Chapters on Discovery - George Iles - Страница 7

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Forms of this kind, well exemplified in the steel columns and girders of to-day, have been arrived at by pursuing a path opened long ago by some shrewd observer. This man noticed that a plank laid flatwise bent much beneath a load, but that when the plank rested on its narrow edge, joist fashion, it curved much less, or hardly at all. Thus simply by changing the position of his plank he in effect altered its form with reference to the strain to be borne, securing a decided gain in rigidity. Let us repeat his experiment, using material much more yielding than wood. We take a piece of rubber eight inches long, one inch wide and one quarter of an inch thick. Placing it flatwise on supports close to its ends we find that its own weight causes a decided sag. We next place it edgewise, taking care to keep it perpendicular throughout its length, when it sags very little. Why? Because now the rubber has to bend through an arc four times greater in radius than in the first experiment. Suppose we had a large board yielding enough to be bent double, we can see that there would be much more work in doubling it edgewise than flatwise. The rule for joists is that breadth for breadth their stiffness varies as the square of their depth, because the circle through which the bending takes place varies in area as the square of its radius. In our experiment with the rubber strip by increasing depth four-fold, we accordingly increased stiffness sixteen-fold; but the breadth of our rubber when laid as a joist is only one-fourth of its breadth taken flatwise, so we must divide four into sixteen and find that our net gain in stiffness is in this case four-fold.

Telegraph poles under compression. Wires under tension.