Strength of Timbers

STRENGTH OF TIMBERS.

Strength of Beams Supported at Both Ends. "Will you decide a little argument which my mate and I have been having?" said a carpenter friend of mine as he and his mate came into the office the other morning. "We want to know which is the stronger of two pitch pine beams we have outside here. One is 9 inches by 6 inches, and the other 8 inches by 7 inches; and both are to be used over openings of 12-feet span. My mate thinks the 9 by 6 is the stronger of the two, but I hold that the 8 by 7 will carry more weight." "I shall be very pleased to work it out for you, and can tell you the result in about a min ute;" said I, "but if you have half an hour to spare, I should prefer to show you how I arrive at my figures, and thus enable you to make the necessary calculations for yourselves whenever you desire." As work was not very pressing that morn ing, they readily agreed to take a lesson, and I proceeded somewhat as follows: A piece of wood 1 inch square placed on bearings one foot apart, will break under a cer tain weight. This wieght varies with different woods and with specimens of the same wood; but most authorities have agreed to re Bard certain average weights as standards. These averages were obtained from hundreds of experiments, and are therefore fairly reliable. The following table deals with a few woods only, but is sufficient for our present purpose.

Breaking weights of wood beams 1 foot long, 1 inch broad, and 1 inch deep, loaded in the cen ter and supported at both ends (the length means the span of the opening—that is, the dis tance in clear of bearings), are as follows: Ash 7 cwt.

White oak 51 Georgia pitch pine 5 Norway red pine 4 " Spruce Teak 8 (1 ewt.=112 pounds.) Referring to the illustration, Fig. 161, we find at A, that, taking pitch pine as our wood, a piece 1 inch by 1 inch, on bearings 1 foot apart, will break with a central load of 5 cwt. Now, it is quite clear that if we increase the breadth to 3 inches, as at B, it will take three times five, or 15 cwt., to break the piece.

But suppose that we put this piece of 3 by 1 pitch pine on edge and see what it takes to break it. Instead of 15 cwt., we shall find that it takes no less than 45 cwt. to do so. Or, as the books put it, the strength of a beam is as the square of its depth. That means that instead of saying, as in B, three times five, we square the three, and say three times 3 are nine, and nine times 5 cwt. is 45 cwt., which is the breaking weight (approximately) of a piece of 1 by 3 pitch pine on edge over a 12-inch bearing.

But suppose, further, that instead of the bearings being 12 inches apart the distance be tween them had been 2 feet. It is clear that the beam would only carry half as much, and we should have to divide our answer by two. And as the longer the beam, the less it will bear, this gives us another rule which will be referred to later.

The diagrams, A, B, and C, represent in a pictorial and striking way one of the most useful formulas or rules which a carpenter can carry in his head. By it he can calculate the strength of any beam in a couple of minutes.

"But," objected my friend, the seeker after information, "you haven't answered our ques tion yet. And, as for making calculations, I haven't done any arithmetic since I left school, and know just about enough of it to reckon up my pay when pay-day comes round." While bound to admit that his case was not uncommon amongst many first-class craftsmen, I pointed out that the necessary calculations for finding the strength of a beam do not call for more than the very simplest operations in multi plying and dividing, and thereupon proceeded to work out, as shown at D and E, the problem propounded by him at the outset of this article. The diagrams explain themselves fairly well; and, as will be seen from them, the 9 by 6 man was the winner, presuming that the beams had been placed (as they should be) with their great est dimensions upright.