Essentials in the theory of framed structures . Q - c^P)b + (-sc + 3^ - ?>cH)P + 3(c« + d^)(2 + (-5^ + 3^ - 8crf^)P = 0 (19) Sec. V RESTRAINED AND CONTINUOUS BEAMS 277 Illustrative Problem.—^Let c = 12 ft., d = 30 ft., P = 60° tons, Q = 900 tons and R = 1,500 tons. Substituting the numerical values in Eqs. (18) and (19), and reducing & = a + loff^ + 256^ — 372fl + 4686 = 10,374 whence a = ft., and & = 15 ft. The length of the base is 42 + ft. or ft., and the soil pressure per linear foot is 3,000 , .w = ^—- = If the allowable bearing pressure on the soil is
Essentials in the theory of framed structures . Q - c^P)b + (-sc + 3^ - ?>cH)P + 3(c« + d^)(2 + (-5^ + 3^ - 8crf^)P = 0 (19) Sec. V RESTRAINED AND CONTINUOUS BEAMS 277 Illustrative Problem.—^Let c = 12 ft., d = 30 ft., P = 60° tons, Q = 900 tons and R = 1,500 tons. Substituting the numerical values in Eqs. (18) and (19), and reducing & = a + loff^ + 256^ — 372fl + 4686 = 10,374 whence a = ft., and & = 15 ft. The length of the base is 42 + ft. or ft., and the soil pressure per linear foot is 3,000 , .w = ^—- = If the allowable bearing pressure on the soil is 5 tons persquare foot, the foundation should have a width of -f = ? ? Thus, in Figs. 170 or 172, the girders should be about 65 ; extending approximately 8 ft. beyond the left column and15 ft. beyond the right column. The beams in the lower tierof grillage should have a length of about ft. 176. Case II. Projection at One End Limited by Site.—Archi-tectural features frequently fix the length to which the footing. may extend beyond one of the end columns. Sometimes it isnecessary to allow no extension whatever at one end. When-ever either of these two limitations arises, the footing may be soarranged that its pressure per foot of length varies uniformlyfrom one to the other; as shown in Fig. 173. This may beaccomplished by a variation in the lengths of the cross-beams,resulting in a trapezoidal area for the footing. Care should be 278 THEORY OF FRAMED STRUCTURES Chap. VI exercised in the choice and spacing of the cross-beams in orderthat equal deflections at their centers may be assured. Let the intensity of the soil pressure per linear foot, at a dis-tance X from the left end be, Wx = Ax + Bso that the soil pressure at the left end will have the intensity Bper linear foot, and at the right end the intensity Al + B perlinear foot. The static equations are2F = AP + 2BI- 2{P+Q + R) =0 (20) SM = 2AI + sBP - 6aP - 6(0 + c)Q - 6(a + c + d) R = o (21) The elastic E
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