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 . so many lbs. or tons to the inch of paper ; inthe space-diagram we deal with a scale of so many feet tothe inch of paper. We have found, then, that if any vertex or corner of theclosed force polygon be taken as a pole, and rays drawnfrom it to all the other corners of the polygon, and a cor-responding equil. polygon drawn in the space diagram, and last segments of the latter polygon must co-ineidewi
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 . so many lbs. or tons to the inch of paper ; inthe space-diagram we deal with a scale of so many feet tothe inch of paper. We have found, then, that if any vertex or corner of theclosed force polygon be taken as a pole, and rays drawnfrom it to all the other corners of the polygon, and a cor-responding equil. polygon drawn in the space diagram, and last segments of the latter polygon must co-ineidewith the first and last forces according to the orderadopted (or with the resultants of the first two and lasttwo, if more convenient to classify them thus). It remains,to utilize this principle. 327. To Pind the Resultant of Several Forces in a Plane.—Thismight be done as in § 326, but since frequently a given setof forces are parallel, or nearly so, a special method willnow be given, of great convenience in such cases. Fig. 352. Let Pl P2 andP3 be the givenforces whoseresultant is re-quired. Let usfirst find theiran^i - resultant,,or force whichfig. 352. Fig. 353. will balance. GRAPHICAL STATICS. 40 3 them. This anti-resultant may be conceived as decom-posed into two components P and P one of which, say P,is arbitrary in amount and position. Assuming P, then,at convenience, in the space diagram, it is required to findP. The five forces must form a balanced system; henceif beginning at Ol9 Fig. 353, we lay off a line OxA = P byscale, then A\ = and || to P{, and so on (point to butt), theline BOx necessary to close the force polygon is = P re-quired. Now form the corresponding equil. polygon inthe space diagram in the usual way, viz.: through a theintersection of P and P1 draw ab || to the ray 0L . . 1(which connects the pole Ox with the point of the last forcementioned). From b, where ab intersects the line of P2,draw be, || to the ray 0L . 2, till it intersects the line of P
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
