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 . , in sucha position that by inspection the segments of the result-ing equil. polygon shall give fair intersections and notpass off the paper. If the given forces are parallel thedevice of introducing the oblique P and P is quite neces-sary. 328.—The result of this construction may be stated asfollows, (regarding Oa and cm as segments of the as well as ab and be): If any tivo segments of anequil
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 . , in sucha position that by inspection the segments of the result-ing equil. polygon shall give fair intersections and notpass off the paper. If the given forces are parallel thedevice of introducing the oblique P and P is quite neces-sary. 328.—The result of this construction may be stated asfollows, (regarding Oa and cm as segments of the as well as ab and be): If any tivo segments of anequil polygon be prolonged, their intersection is a point inthe line of action of the resultant of those forces acting at 404 MECHANICS OF ENGINEERING. the vertices intervening between the given segments. Here,the resultant of Px P2 P3 acts through d. 329. Vertical Reaction of Piers, etc.—Fig. 354. Given thevertical forces or loads Px P2 and P3 acting on a rigid body(beam, or truss) which is supported by two piers havingsmooth horizontal surfaces (so that the reactions must bevertical), required the reactions V0 and Vn of the an instant suppose V0 and VQ known; they are in. Fig. 354. equil. with Px P2 and P3. The introduction of the equaland opposite forces P and P in the same line will not dis-turb the equilibrium. Taking the seven forces in theorder P V0 Pr P2 P3 Vn and P, a force polygon formed withthem will close (see (b) in Fig. where the forces whichreally lie on the same line are slightly separated). With0, the butt of P, as a pole, draw the rays of the force dia-gram OA, OB, etc. The corresponding equil. polygonbegins at. a, the intersection of P and V0 in (a) (the spacediagram), and ends at n the intersection of P and an. Now since P and P act in the same line, anmust be that line and must be || to P and P of the forcediagram. Since the amount and direction of P and P arearbitrary, the position of the pole 0 is arbitrary, whilePi, P2, and P3 are the onl
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
