Essentials in the theory of framed structures . uilibrium. Any line in the equilibrium polygon, or as it is sometimescalled, the funicular polygon or string polygon, also represents but two of thethree elements of a force, viz., location and direction. Hereafter, we shall usethe distinctive terms, magnitude-direction diagram and location-directiondiagram. The lines in the first diagram will be called magnitude-directions;in the second, location-directions. The two diagrams have nothing in commonexcept the element of direction and the sense, which are registered in is nothing pertain
Essentials in the theory of framed structures . uilibrium. Any line in the equilibrium polygon, or as it is sometimescalled, the funicular polygon or string polygon, also represents but two of thethree elements of a force, viz., location and direction. Hereafter, we shall usethe distinctive terms, magnitude-direction diagram and location-directiondiagram. The lines in the first diagram will be called magnitude-directions;in the second, location-directions. The two diagrams have nothing in commonexcept the element of direction and the sense, which are registered in is nothing pertaining to locations in the first, and nothing pertaining to 42 THEORY OF FRAMED STRUCTURES Chap. I The closing of the magnitude-direction diagram in the graphicmethod corresponds to the solution of LH = o and ZF = oin the algebraic method; while the drawing of a location-direc-tion diagram corresponds to the solution of ZM = o. The body in Fig. 21a is re-drawn to scale (Fig. 21/) and fulllines are added to represent known location-directions. The. lengths of these Hues have no significance whatever, since theydo not represent magnitudes in any particular. The magni-tude-direction diagram is now constructed (Fig. 2 ig) from a toe by laying off to scale the known magnitude-directions in anyorder and in the same manner as for a concurrent system. Thediagram is closed by drawing the magnitude-direction ea which magnitudes in the second. There is no connection between the scale ratiosused in laying off the elements in the two diagrams; for in the first the scale ratiois pounds-to-the-inch, in the second, feet-to-the-inch. Sec. VI EQUILIBRIUM OF COPLANAR FORCES 43 gives the magnitude, direction and sense of the equilibrant location of the equilibrant with reference to the body () remains to be determined. This may be accomplished bydrawing the location-direction diagram in one of two ways: (a) By combining the forces in pairs and drawing the location-directions of t
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