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 . ee pieces, A, B and 0, the total com- *The St Louis Bridge is not strictly of constant moment of inertia, being somewhatstrengthened near each pier ARCH-RIBS. 479 pressions (or tensions) in which are thus found : For thepoint ra, of rib-axis, there is a certain moment = Hz, athrust = Th, and a shear = J, obtained as previously ex-plained. We may then write P sin ft = J (1) and thus determine whether P is a te
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 . ee pieces, A, B and 0, the total com- *The St Louis Bridge is not strictly of constant moment of inertia, being somewhatstrengthened near each pier ARCH-RIBS. 479 pressions (or tensions) in which are thus found : For thepoint ra, of rib-axis, there is a certain moment = Hz, athrust = Th, and a shear = J, obtained as previously ex-plained. We may then write P sin ft = J (1) and thus determine whether P is a tension or compres-sion ; then putting P+P ± P cos fi = Th . . . 2(in which P is taken with a plus sign if a compression, andminus if tension); and {Pr-P)\=Hz (3) A we compute F and P, which are assumed to be both com-pressions here, /? is the angle between the web memberand the tangent to rib-axis at ra, the middle of the Fig. 406, as an explanation of the method justadopted. HORIZONTAL, STRAIGHT GIRDERS. 389. Ends Free to Turn.—This corresponds to an arch-rib with hinged ends, but it must be understood that thereis no hindrance to horizontal motion. (Fig. 439.) In. Fig 439. treating a straight beam, slightly bent under vertical forcesonly (as in this case with no horizontal constraint), as a 480 MECHANICS OF ENGINEERING. particular case of an arch-rib, it is evident that since thepole distance must be zero, the special equil. polygon willhave all its segments vertical, and the corresponding forcediagram reduces to a single vertical line (the load line).The first and last segments must pass through A and B(points of no moment) respectively, but being vertical willnot intersect Px and P2; , the remainder of the specialequilibrium polygon lies at an infinite distance above thespan AB. Hence the actual spec, equil. pol. is useless. However, knowing that the shear, J, and the momentM (of stress couple) are the only quantities pertaining toany section ra (Fig. 439) w
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
