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 . nging to any joint inwhich that piece terminates; the stress in the piece FGby the force fg in the proper force polygon, and so on. In Fig. 356 the whole truss is shown free, in equili-brium under the external forces. To find the pulls orthrusts (, tensions or compressions) in the pieces, con-sider that if all but two of the forces of a closed forcepolygon are known in magnitude and direction, while thedi
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 . nging to any joint inwhich that piece terminates; the stress in the piece FGby the force fg in the proper force polygon, and so on. In Fig. 356 the whole truss is shown free, in equili-brium under the external forces. To find the pulls orthrusts (, tensions or compressions) in the pieces, con-sider that if all but two of the forces of a closed forcepolygon are known in magnitude and direction, while thedirections, only, of those two are known, the tcJiole forcepolygon may be drawn, thus determining the amounts ofthose two forces by the lengths of the correspondingsides. We begin with a joint where no more than twopieces meet, as at a; [call the joints a, /9, r, d, and the cor-corresponding force polygons a, /3 etc. Fig. 356.] Henceat a (anywhere on the paper) make ah || and = (by scale)to the known force AB (, V0) pointing it at the upper end,and from this end draw be = and || to the known force BC(, Wx) pointing this at the lower end. 408 MECHANICS OF Fig. 356. To close the polygon draw through c a || to the pieceCD, and through a a || to AD; their intersection deter-mines d, and the polygon is closed. Since the arrowsmust be point to butt round the periphery, the force withwhich the piece CD acts on the pin of the joint a is aforce of an amount = cd and in a direction from c towardd; hence the piece CD is in compression ; whereas theaction of the piece DA upon the pin at a is from d towarda (direction of arrow) and hence DA is in tension. Noticethat in constructing the force polygon « a right-handed(or clock-wise) rotation has been observed in consideringin turn the spaces ABC and D, round the joint a. Asimilar order will be found convenient in each of the otherjoints. Knowing now the stress in the piece CD, (as well as inDA) all but two of the
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
