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 . ched loads sufficientlynumerous to give a close approximation, let us supposethat this has already been done if necessary, and that Px,P2, etc., are the detached loads resting in the span AB inquestion ; see Fig. 447. Since [by (1), § 397] the positive moment-area is thesame as the total moment-area would be if this portion ofthe beam simply rested on the extremities of the span, notextending beyond them, we
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 . ched loads sufficientlynumerous to give a close approximation, let us supposethat this has already been done if necessary, and that Px,P2, etc., are the detached loads resting in the span AB inquestion ; see Fig. 447. Since [by (1), § 397] the positive moment-area is thesame as the total moment-area would be if this portion ofthe beam simply rested on the extremities of the span, notextending beyond them, we may use the construction in §389 for finding it, remembering that in that paragraph the 500 MECHANICS OF ENGINEERING. oblique polygon in the lower part of Fig. 439 will serveas well as the (upper) one whose abutment-line is thebeam itself, as far as moments are concerned. Hence, Fig. 447, lay off the load-line LL9 take any pole0, with any convenient pole-distance H, and draw theequilibrium polygon FWG. After joining FG, FWGFwill be the positive moment-area required. To find its gravity vertical, divide the span AB, or FG\into from ten to twenty equal parts (each = As) and draw a. Pig. 447. vertical through the middle of each. The lengths zlf z2>etc., on these verticals, intercepted in the moment-area,are proportional to the corresponding strips of moment-area, each of width=ds, and of an amount =HzAs. Form a load line, SK, of the successive as, and withany pole 0, draw the equilibrium polygon AB (for thez-verticals). The intersection, B, of the extreme segments,is a point in the required gravity-vertical (§ 336). The amovfnt of the moment-area is (\-=2\_HzAs~] =KAs. Z(z)=(zl+z2+Zs+ . . ) CONTINUOUS GIRDER BY GRAPHICS. 501 For example, with the span =Z=120 in., subdivided intotwelve equal Ass, we have As-10 inches (of actual distance).If H=4 inches of paper and SK=I(z)= inches of paper,the force-scale being 80 lbs. to the inch, and the distance-scale 15 inches
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
