Essentials in the theory of framed structures . ues in (20),(21) and (22) AP + 2BI = 6,0002AP + iBP = 550,8008,273,664^ + 824,0405 = 43,416,000whence P —. ^ -(- 13, — 209, = oor I = or or ft. Sec. V RESTRAINED AND CONTINUOUS BEAMS 279 If ft. is taken, then A = — 5= 55-98and Al + B = Hence the intensity of the soil pressure is tons per linearfoot at the left end; and decreases uniformly to tons at theright end. Since a = 6 ft., and I = ft., the foundationextends b = ft. beyond the right column. Since the quantity
Essentials in the theory of framed structures . ues in (20),(21) and (22) AP + 2BI = 6,0002AP + iBP = 550,8008,273,664^ + 824,0405 = 43,416,000whence P —. ^ -(- 13, — 209, = oor I = or or ft. Sec. V RESTRAINED AND CONTINUOUS BEAMS 279 If ft. is taken, then A = — 5= 55-98and Al + B = Hence the intensity of the soil pressure is tons per linearfoot at the left end; and decreases uniformly to tons at theright end. Since a = 6 ft., and I = ft., the foundationextends b = ft. beyond the right column. Since the quantity b does not appear in Eqs. (20), (21) and(22), it will be found advantageous in any numerical problemto arrange the nomenclature so that P may represent the endcolumn beyond which the length of the foundation is Kmited;and assign a numerical value to a. When no extension of thefoundation beyond P is allowed, a = o. Vj*j. Case III. Both Projections Limited by Site.—In thecase illustrated by Fig. 174, where both a and b are fixed or equal. Pig. 174. zero; the footing may be so proportioned as to produce anintensity of soil pressure per linear foot, which varies accordingto the ordinates of a parabolic curve. The soil pressure persquare foot may be made uniform by varying the length of thecross-beams accordingly. The dimensions a, b, c and d, and theloads P, Q and R will be known; while the three constants whichdetermine the intensity of the soil pressure are to be found bysolution. Let the intensity of the soil pressure per linear foot at adistance x from the left end be Wx = Ax^ + Bx + C 28o THEORY OF FRAMED STRUCTURES Chap. VI SO that the soil pressure at the left end will have the intensity Cper linear foot, and at the right end the intensity Al^ + Bl + Cper linear static equations are SF = 2AP + sBP + 6CI- 6{P + Q + R) -= o (23) SM = sAl^ + 4BP + 6CP - 120^ - 12(0 + c)Q - i2(a + c + d)R = o (24) The elastic Eq. (17) when developed, may be written in theform c[
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