When a uniformly loaded beam is supported at each end on level bearings (the beam itself being either horizontal or inclined), the amount of pressure caused by the load on each point of support is equal to one half the load; and this is also the ase when the load is concentrated at the middle of the beam, or has its centre of gravity at the middle of the beam; but when the load is unequally distributed, or concentrated so that its centre of gravity occurs at some other point than the middle of the beam, then the amount of pressure caused by the load on one of the points of support is unequal to that on the other. The precise amount on each may be ascertained by the following rule.
Rule. - Multiply the weight W (Fig. 35) by its distance, CB, from its nearest point of support, B, and divide the pro-duct by the length, A B, of the beam, and the quotient will be the amount of pressure on the remote point of support, A. Again, deduct this amount from the weight W, and the remainder will be the amount of pressure on the near point of support, B; or, multiply the weight W by its distance, A C, from the remote point of support, A, and divide the product by the length, A B, and the quotient will be the amount of pressure on the near point of support, B.
When l equals the length between the bearings A and B, n - AC, m = C B, and W = the load; then
Wm/1 = A = the amount of pressure at A, and Wn/l== B = the amount of pressure at B.
Example. - A beam 20 feet long between the bearings has a load of 100 pounds concentrated at 3 feet from one of the bearings: what is the portion of this weight sustained by each bearing?
Here W = 100; n, 17; m, 3; and l, 20.
Hence A = Wm = 100x3 = 15
And B= Wn/l = 100x17/20 = 85.
Load on A == 15 pounds. Load on B =85 pounds. Total weight = 100 pounds.
Preliminary to designing a roof-truss or other piece of framing, a knowledge of two subjects is essential: one is, the effect of gravity acting upon the various parts of the intended structure; the other, the power of resistance possessed by the materials of which the framing is to be constructed. The former subject having been treated of in the preceding pages, it remains now to call attention to the latter.