Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . onnecting C and p, we determine N and 0. JoiningNA and OB, the first ray of the required force diagram willbe || to NA, while the last ray will be || to OB, and thusthe pole of that diagram can easily be found and the cor-responding equilibrium polygon, beginning at A, will passthrough p and B. (This general case includes those of §§ 341 and 342.) 379. Arch-Rib of two Hinges; by Prof. Eddys Method.*[It is und
Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . onnecting C and p, we determine N and 0. JoiningNA and OB, the first ray of the required force diagram willbe || to NA, while the last ray will be || to OB, and thusthe pole of that diagram can easily be found and the cor-responding equilibrium polygon, beginning at A, will passthrough p and B. (This general case includes those of §§ 341 and 342.) 379. Arch-Rib of two Hinges; by Prof. Eddys Method.*[It is understood that the hinges are at the ends.] Re-quired the location of the special equilibrium polygon. Wehere suppose the rib homogeneous (, the modulus ofElasticity E is the same throughout), that it is a curvedprism (, that the moment of inertia I of the cross-section is constant), that the piers are on a level, and thatthe rib-curve is symmetrical about a vertical line. Fig. 424. For each point m of the ribcurve we have an x and y (bothknown, being the co-ordinates ofthe point), and also a z (interceptt- between rib and special equilib-^ rium polygon) and a z (intercept. * P. 25 of Prof. Eddys book ; see reference in preface of this work. 4G2 MECHANICS OF ENGENEEKING. between the spec. eq. pol. and the axis X (which is OB),The first condition given in § 378 for Class C may betransformed as follows, remembering [§ 367 eq. (3)] thatM — Hz at any point m of the rib (and that EI is con-stant). *. £ Myds = 0, , .g j\yds = 0. •. j\yds = 0 EI butz =y - }B B B • • I (y — z)yds=0; , f yyds = f yzds . (1) In practical graphics we can not deal with infinitesimals;hence we must substitute As a small finite portion of therib-curve for ds; eq. (1) now reads 2* yy As = 20B yz if we take all the Ass equal, As is a common factorand cancels out, leaving as a final form for eq. (1) Z0\yy) = I*{yz) . . (1) The other two conditions are that the special equilib
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