By J. S. C. Browne, N. Hiller and G. E. Walker (Auth.)
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Diagram, Fig. m. m. at mid-span is equal to (B—A). As the latter must also be equal to A9 then B = 2A. l. m. FIG. 12 Position of supports for least bending areas must be proportional to the squares of their bases. Hence, as the triangle A has a base of length x, the base of the triangle B must be J2x. v = / 2(1+Λ/2) 0-207/. 6. A uniform beam 10 ft long, and weighing 401bf per ft, is pinned to a rigid support at the left-hand end, and rests on a smooth roller, placed 2 ft from the other end. A load of 500 lbf, inclined at 30° to the vertical, is applied to the beam 6 ft from the pinned end.
Diagram, Fig. 7c, is a parabola over the left-hand half, where the uniform load is applied, and straight over the right-hand half. f. m. at D and C. f. diagram, between A and D, is equal to the difference between the bending moments at A and D. m. m. at D is equal to j^g w-72. m. f. f. ;';;;(®':;:. m. f. m. m. (c) Cantilever with uniform loading (d) Simple beam with uniform loading FIG. f. m. f. m. m. at B. f. m. are a maximum. f. m. diagrams for some common loadings on simple beams and cantilevers are given in Fig.
If a vertical load of 6 lbf is applied at the free end B, determine completely the reactions at A and C. Ans: Reaction at peg = 15-6 lbf Vertical reaction at A = 4-5 lbf Horizontal reaction at A — 7-8 lbf 2. Three forces act on a body and maintain it in equilibrium. State the conditions that they must satisfy (a) if the forces are parallel, (b) if the forces are not parallel. A uniform ladder rests on rough horizontal ground and leans against a smooth vertical wall. If the coefficient of friction between the ground and the ladder is μ show that the greatest inclination that the ladder can have to the vertical, without slipping, is tan _ 1 2μ.