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 . position under no strain and ata definite the conditions for locating the special equilibriumpolygon are r^Mds _ 0. s> Myds _ Q . fMxds _ aJo EI Jo ~~E1~ Jo EI In the figure the imaginary rigid prolongations at theends are shown [see § 366]. Other designs than those mentioned are practicable(such as: one end fixed, the other hinged; both ends fixedand one hinge between, etc.), but are of
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 . position under no strain and ata definite the conditions for locating the special equilibriumpolygon are r^Mds _ 0. s> Myds _ Q . fMxds _ aJo EI Jo ~~E1~ Jo EI In the figure the imaginary rigid prolongations at theends are shown [see § 366]. Other designs than those mentioned are practicable(such as: one end fixed, the other hinged; both ends fixedand one hinge between, etc.), but are of unusual occur-rence. Fig. 423. 378a. Rib of Three Hinges. Forces not all Vertical. If thegiven rib of three hinges upholds a roof, the wind-press-ure on which is to be considered as well as the weights ofthe materials composing the roof-covering, the forces willnot all be vertical. To draw the special equil. polygon in such a case the followingconstruction holds: Re-quired to draw an equilib-rium polygon, for anyplane system of forces,through three arbitrarypoints, A, p and B; Find the line ofaction of Bl3 the resultantof all the forces occurringbetween A and p; also,,. Fig. 423a. ARCH-KIBS. 461 that of R2} the resultant of all forces between [p and B ;also the line of action of R, the resultant of Ri and R2) [see§ 328.] Join any point ill in R with A and also with B,and join the intersections N and 0. Then A N will be thedirection of the first segment, 0 B that of the last, andNO itself is the segment corresponding to p (in the dersired polygon) of an equilibrium polygon for the givenforces. See § 328. If A Np 0 B are the correspondingsegments (as yet unknown) of the desired equil. polygon,we note that the two triangles MNO and MN 0\ havingtheir vertices on three lines which meet in a point [, Rmeets i?x and R2 in (7], are homological [see Prop. VII. ofIntroduc. to Modern Geometry, in Chauvenets Geometry,]and that . ?. the three intersections of their corresp
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
