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 . ty Vertical.—From the same construction inFig. 415 we can determine the line of action (or gravityvertical) of the resultant of the parallel vertical forces zlfz2, etc. (or loads); by prolonging the first and last segments to their intersection at0. The resultant of thesystem of forces or loadsacts through C and isvertical in this case ; itsvalue being = I (z),that is, it = the length1 ... 7 in the force dia-
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 . ty Vertical.—From the same construction inFig. 415 we can determine the line of action (or gravityvertical) of the resultant of the parallel vertical forces zlfz2, etc. (or loads); by prolonging the first and last segments to their intersection at0. The resultant of thesystem of forces or loadsacts through C and isvertical in this case ; itsvalue being = I (z),that is, it = the length1 ... 7 in the force dia-gram, interpreted by theproper scale. It is nowsupposed that the zsrepresent forces, the #sbeing their respectivelever arms about F. Ifthe zs represent theareas of small finite por-tions of a large planefigure, we may find agravity-line (through C)of that figure by theabove construction; eachz being-applied throughthe centre of gravity ofits own portion. Calling the distance x between the verticals through C and F, we k3 have also x . I (z) = I (xz) because I (z) is the resultant of the || zs. ki This is also evident from the proportion (similar triangles) H : (1 . 7) :: x : h. 454 MECHANICS OF ENGINEERING. 376 a. Moment of Inertia (of Plane Figure) by Graphics.— a. IN = ? First, for the portion on right. Divide OBmto equal parts each = Ax. Let zu z2} etc., be the middleordinates of the strips thus obtained, and xly etc. theirabscissas (of middle points). Then we have approximately 7N for OB={\- =Jx[(zlx1)xl-\-(z2x2)x2+ ...].. (1) But by §375 we may construct the products zlx1,z2x2, etc.,taking a convenient H, (see Fig. 416, (&)), and obtain klt k2,etc., such that ZyXx = Hk^ z2x2 = Hk2, etc. Hence eq. (1)becomes: iNfor OB [&1a;1+&2^2+ ...]... (2) By a second use of § 375 (see Fig. 416 c) we construct I,such that A^ + k2x2 + ....= Hl [H taken at con-venience]. .*. from eq. (2) we have finally, (approx.), IN for OB=BHlAx (3) For exampl
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
