. Graphic statics, with applications to trusses, beams, and arches. ancing forces DE and EA, parallelto AD and passing through the points y and x respectively. Themagnitudes of these balancing forces are found, as in Art. 15, bydrawing the closing string e (.vV) of the funicular polygon andthe corresponding ray E. Now since the forces ABCDEA arebalanced, all funicular polygons drawn for them will close. If,then, we wish the string a of any such polygon to pass through xand the string d through y, the string e must evidently pass throughboth x and v, and the pole P therefore lie somewhere on th
. Graphic statics, with applications to trusses, beams, and arches. ancing forces DE and EA, parallelto AD and passing through the points y and x respectively. Themagnitudes of these balancing forces are found, as in Art. 15, bydrawing the closing string e (.vV) of the funicular polygon andthe corresponding ray E. Now since the forces ABCDEA arebalanced, all funicular polygons drawn for them will close. If,then, we wish the string a of any such polygon to pass through xand the string d through y, the string e must evidently pass throughboth x and v, and the pole P therefore lie somewhere on the raydrawn through E parallel to xy, , parallel to the line joining thetwo given points. GENERAL METHODS. 25 23. Funicular Polygon through Three Points. draw a funicular polygon for a given system of forces, such thatthree designated strings shall pass through three given the forces be ABCDEF (Fig. 18). It is required to draw afunicular polygon such that the string a will pass through O, thestring c through O, and the string / through Fig. 18. Let mn be any funicular polygon for the given forces, with Pfor pole. By means of the construction of Art. 22, we determinePX to be the locus of the poles of all funicular polygons whosestrings a and c pass through O and O respectively. Also, by thesame construction we determine PX to be the locus of the poles ofall funicular polygons whose strings c and / pass through O andO respectively. Hence, in order for both conditions to be satis-fied, the pole must lie on both PX and PX, , at their pointof intersection, P. The required polygon is drawn in full lines. (Note. To secure accuracy, draw the strings a, c, and / first,then draw the intermediate strings closing on the ones midwaybetween the given points.) 24. Funicular Polygon through Three Points. Parallel Forces. A shorter solution than that given in Art. 23 can be made for thiscase. Let AB, BC, CD, and DE (Fig. 19) be the given forces, it 26 GRAPHIC ST
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