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 . IQUE FORCES. 353 elastic curve, of which G0G is an element, is G0B insteadof G0B. But the difference between G0B and GQB is verysmall, being the same, relatively, as the difference betweenGQG and G0G; for instance, with wrought-iron, even Upl9the intensity of the uniform pull, were as high as 22,000lbs. per sq. in. [see § 203] G0G would exceed G0G by onlyyi2 of one per cent. (=); hence by using GB inste
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 . IQUE FORCES. 353 elastic curve, of which G0G is an element, is G0B insteadof G0B. But the difference between G0B and GQB is verysmall, being the same, relatively, as the difference betweenGQG and G0G; for instance, with wrought-iron, even Upl9the intensity of the uniform pull, were as high as 22,000lbs. per sq. in. [see § 203] G0G would exceed G0G by onlyyi2 of one per cent. (=); hence by using GB insteadof GB as the radius of curvature p, an error is introducedof so small an amount as to be neglected. But from § 231, eqs. (6) and (7), — Pthe sum of the moments of the external forces; hence for prismatic beams under oblique forces we may still use dxr ±M%{=M) (1) as one form for the -(moms.) of the elastic forces of thesection about the gravity-axis ; remembering that the axisX must be taken parallel to beam. 296. Oblique Cantilever with Terminal Load.—Fig. 298. LetI = length. The fixing of the lower end of the beam isits only support. Measure x along the beam from 0. Let. Fig. 298. Fig. 299. n be the gravity axis of any section and nT, =x sin a, thelength of the perpendicular let fall from n on the line ofaction of the force P (load). The flexure is so slight thatnT is considered to be the same as before the load is al- 354 MECHANICS OF ENGINEERING. lowed to act. [If a were very small, however, it is evidentthat this assumption would be inadmissible, since then alarge proportion of nT would be due to the flexure causedby the load.] Consider nO free, Fig. 299. In accordance with the pre-ceding paragraph (see eqs. (4), (5), and (6)) the elasticforces of the section consist of a shear J, whose value maybe obtained by writing 17=0 whence J=P sin a; . . (1) of a uniform thrust =piF, obtained from 2X=0, viz: P cos a—plF=0 .. p1F=P cos a ; . (2) and of a stress-couple whos
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
