Cyclopedia of architecture, carpentry, and building : a general reference work . beam) in a wooden beamon end supports, which is 12 feet long and G X 12 inches incross-section ? (This is the safe load for the beam ; see example1, Art. 65.) The formula for this case (see Table B, page 55) is 5 W/^ 884 EI Here W = 6,400 pounds ; / = 144 inches ; E = 1,800,000pounds per square inch ; and 1 1 I = ^ U^ = .^^ 6 X 12^== 864 inchest Hence the deflection is _ 5 X 6,400 X 144^ _ ~ 384 X 1,800,000 X 864 ^ ^-^^ ^^^• EXAMPLES FOR PRACTICE. 1. Compute the deflection of a timber built-in cantilever8x8 inches
Cyclopedia of architecture, carpentry, and building : a general reference work . beam) in a wooden beamon end supports, which is 12 feet long and G X 12 inches incross-section ? (This is the safe load for the beam ; see example1, Art. 65.) The formula for this case (see Table B, page 55) is 5 W/^ 884 EI Here W = 6,400 pounds ; / = 144 inches ; E = 1,800,000pounds per square inch ; and 1 1 I = ^ U^ = .^^ 6 X 12^== 864 inchest Hence the deflection is _ 5 X 6,400 X 144^ _ ~ 384 X 1,800,000 X 864 ^ ^-^^ ^^^• EXAMPLES FOR PRACTICE. 1. Compute the deflection of a timber built-in cantilever8x8 inches which projects 8 feet from the wall and bears anend load of 900 pounds. (This is the safe load for the cantilever,see example 1, Art. 65.) Ans. incli. 2. Compute the deflection caused by a uniform load of 40,000 127 118 STRENGTH OF MATERIALS pounds on a -ii-pound 15-inch steel I-beam which is 10 feet longand rests on end supports. Ans. inch. 98. Twist of Shafts. Let Fig. 57 represent a portion of a shaft, and suppose that the part represented lies wholly between. Fig. 57. two adjacent pulleys on a shaft to which twisting forces are applied(see Fig. 54). Imagine two radii ma and rib in the ends of theportion, they being parallel as shown when the shaft is not the shaft is twisted they will not be parallel, ma havingmoved to ma^ and nh to nV. The angle between the two linec intheir twisted positions {ina and nV) is called the angle of twist,or angle of torsion, for the length /. If a a is parallel to al>^ thenthe angle anV equals the angle of torsion. If the stresses in the portion of the shaft considered do notexceed the elastic limit, and if the twisting moment is the samefor all sections of the portion, then the angle of torsion a (indegrees) can be computed from the following: For solid circular shafts, 584 TZ 36,800,000 \\l For hollow circular shafts,584 Yld Y} dn 36,800,000 11/ Y (19) J Y}{d-d^)~Y} [d-d;) n Here T, ?, fZ, d^^ II, and n have the
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