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 . t figure will bear vertical press-ures only and they will be the same as in Fig. 368, whilethe tension in the tie-rod will be = On.] 338. Theorem.—The vertical dimensions of any two equili-brium polygons, drawn to the same loads, load-verticals, andabutment-verticals, are inversely proportional to their Hs (orpole distances ). We here regard an equil. polygon andits abutment-line as a closed figure. Thus, in
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 . t figure will bear vertical press-ures only and they will be the same as in Fig. 368, whilethe tension in the tie-rod will be = On.] 338. Theorem.—The vertical dimensions of any two equili-brium polygons, drawn to the same loads, load-verticals, andabutment-verticals, are inversely proportional to their Hs (orpole distances ). We here regard an equil. polygon andits abutment-line as a closed figure. Thus, in Fig. 369,we have two force-diagrams (with a common load-line, forconvenience) and their corresponding equil. polygons, forthe same loads and verticals. From § 337 we know thatOn is || to AB and 00n is || to A0B0. Let CD be any ver-tical cutting the first segments of the two equil. polygons. GRAPHICAL STATICS. 417 Denote the intercepts thus determined by z and zot respect-ively. From theparallelisms justmentioned, andothers more famil-^ iar, we have thetriangle 0 In sim-ilar to the triangleAz (shaded), andthe triangle 0olnsimilar to the tri-angle A0z£, Hence c P, 1 2- z p* y- r. the proportions between j In z bases and altitudes =— and In h ) { H h H0 .. z : z0 : : H0 : H. The same kind of proof may easily be applied to the vertical intercepts in any other segments,e. g., z and z0. Q. E. D. 339. Corollaries to the foregoing. It is evident that:(1.) If the pole of the force-diagram be moved along avertical line, the equilibrium polygon changing its formin a corresponding manner, the vertical dimensions of theequilibrium polygon remain unchanged; and (2.) If the pole move along a straight line which con-tains the point nt the direction of the abutment-lineremains constantly parallel to the former line, while thevertical dimensions of the equilibrium polygon change ininverse proportion to the pole distance, or H, of the force-diagram. [R is the 1 distance of the pole from the
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
