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 . he lower outer fibre at L, Fig. 298,where x is as great as possible, =1; and will be a compres-sion, viz.: fo+ft] rcosg+;(sinq)e-| _ _ (4) .*. the equation for Safe Loading is N/ = pf cosa +Z(sin«)e~| ^ . _ ^ since with e^e, as will be assumed here,[p— —p2] max. FLEXURE. OBLIQUE FORCES. 355 can not exceed, numerically, [pi+p2~\ max. The stress-intensity in the outer fibres along the upper edge of thebe
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 . he lower outer fibre at L, Fig. 298,where x is as great as possible, =1; and will be a compres-sion, viz.: fo+ft] rcosg+;(sinq)e-| _ _ (4) .*. the equation for Safe Loading is N/ = pf cosa +Z(sin«)e~| ^ . _ ^ since with e^e, as will be assumed here,[p— —p2] max. FLEXURE. OBLIQUE FORCES. 355 can not exceed, numerically, [pi+p2~\ max. The stress-intensity in the outer fibres along the upper edge of thebeam, being =pv—p2 (supposing el=e) will be compressiveat the upper end near 0, since there p2 is small, x beingsmall; but lower down as x grows larger, p2 increasing, asection may be found (before reaching the point L) wherep2=Pi and where consequently the stress in the outer fibreis zero, or in other words the neutral axis of that sectionpasses through the outer fibre. In any section above thatsection the neutral axis is imaginary, , is altogether out-side the section, while below it, it is within the section, butcannot pass beyond the gravity axis. Thus in Fig. 300, OU. Fig. 300. Fig. 301. is the locus of the positions of the neutral axis for successivesections, while OL the axis of the beam is the locus of thegravity axes (or rather of the centres of gravity) of thesections, this latter line forming the elastic curve un-der flexure. As already stated, however, the flexure is tobe but slight, and a must not be very small. For in-stance, if the deflection of 0 from its position before flex-ure is of such an amount as to cause the lever-arm OR ofP about L to be greater by 10 per cent, than its value(=1 sin a) before flexure, the value of p2 as computed fromeq. (3) (with x=l) will be less than its true value in thesame proportion. The deflection of 0 from the tangent at L, by § 237, (a) is d=(P sin a)P-^3EI, approximately, putting P sin a 356 MECHANICS OF ENGIN
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
