Elementary lessons in the physics of agriculture elementarylesson01king Year: 1894 41 When a board, in every respect like the one in A, Fig. 19, is placed under the conditions represented in either B or C, Fig. 19, it should require just four times the load to break it, because the board is practically converted into two levers whose power-arms remain the same, but whose weight-arms are only one-half as long each. 73. The Transverse Strength of Timbers Propor- tional to the Squares of their Vertical Thicknesses.— Common experience demonstrates that a joist resting on edge is able to carry a
Elementary lessons in the physics of agriculture elementarylesson01king Year: 1894 41 When a board, in every respect like the one in A, Fig. 19, is placed under the conditions represented in either B or C, Fig. 19, it should require just four times the load to break it, because the board is practically converted into two levers whose power-arms remain the same, but whose weight-arms are only one-half as long each. 73. The Transverse Strength of Timbers Propor- tional to the Squares of their Vertical Thicknesses.— Common experience demonstrates that a joist resting on edge is able to carry a much greater load than when laying fiat- wise. If we place a 2 x 4 and a 2 x 8, which differ only in thickness, on edge, their relative strengths are to each other as the squares of 4 and 8, or as 16 to 64. That is, the 2x8, con- taining only twice the amount of lumber as the 2x4, will, under the conditions named, sustain four times the load. The reason for this is as follows: In Fig. 20 let A represent a 2 x 4 and B a 2 X 8. In each of these cases the load draws lengthwise upon the upper half of the joist, acting through a weight-arm F. W. ten inches in length, to overcome the force of cohesion at the fixed ends, whose strength, according to 70, is ten thousand pounds per square inch, or a total of 2 X2 X 10,000 ,000 lbs. in the 2x4 joist, and of 2x4x 10,000 ,000 lbs. in the 2x8 joist. These two total strengths become powers acting through their respective power-arms F. P., whose mean lengths are, in the 2x4 joist, one inch, and in the 2x8 joist, two inches. Now we have, from 30, A,,
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