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 . Deter-mine the sum T2 ofthe broken ordi- IFig. 418. nates (between v2G2 ana F2G2) and its vertical line of ap-plication, precisely as in dealing with R; also T2 that ofthe dotted ordinates (five) and its vertical. Now the trueT=Rt+(s+t) and the true T=Bs+(s+t). Hence com-pute vF=(T-r-T2) v2F2 and ^G=(T+T2) ~m~G2, and bylaying them off vertically upward from F and G respec-tively we determine v and m, , th
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 . Deter-mine the sum T2 ofthe broken ordi- IFig. 418. nates (between v2G2 ana F2G2) and its vertical line of ap-plication, precisely as in dealing with R; also T2 that ofthe dotted ordinates (five) and its vertical. Now the trueT=Rt+(s+t) and the true T=Bs+(s+t). Hence com-pute vF=(T-r-T2) v2F2 and ^G=(T+T2) ~m~G2, and bylaying them off vertically upward from F and G respec-tively we determine v and m, , the line vm to fulfil theconditions imposed at the beginning of this article, rela-ting to the vertical ordinates intercepted between vm andgiven points on the perimeter of a polygon or curve. Note (a). If the verticals in which the intercepts lie areequidistant and quite numerous, then the lines of actionof T2 and T2 will divide the horizontal distance betweenF and G into three equal parts. This will be exactly truein the application of this construction to § 390. Note (b). Also, if the verticals are symmetrically placedabout a vertical line, (as will usually be the case) v2m2 is. 458 MECHANICS OF ENGINEERING. best drawn parallel to FG, for then T2 and T\ will beequal and equi-distant from said vertical line. 378. Classification of Arch-Ribs, or Elastic Arches, accordingto continuity and modes of support. In the accompany-ing figures the full curves show the unstrained form of therib (before any load, even its own weight, is permitted tocome upon it) ;the dotted curve shows its shape (much ex-aggerated) when bearing a load. For a given loadingThree Conditions must be given to determine the specialequilibrium polygon (§§ 366 and 367). Class A.—Continuous rib, free to slip laterally on thepiers, which have smooth horizontal surfaces, Fig. 420. This is chiefly of theoretic interest, its considerationbeing therefore omitted. The pier reactions are neces-sarily vertical, just as
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
