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 . to P sin «, and P to Pcos a. p-i qx ~qx constant factors we now write y = -^,x-\-me —n« • • the equation required . (10) To determine the constants m andn(m— C+2q2; n= C-*-2Cq4) we first find dy+dx, dv v2 $x —Qx by differentiating (10) -^r-~2+ymen +fl^«n .... (11) z=0fory=0 0 0 .. (10) gives . . 0—0-{-men— neQ =0 m—n=0 .. m=n . (12) Also for x=l dv p2 & —of\ -^-= (11) gives 0=~f q ^n +nen • • (1
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 . to P sin «, and P to Pcos a. p-i qx ~qx constant factors we now write y = -^,x-\-me —n« • • the equation required . (10) To determine the constants m andn(m— C+2q2; n= C-*-2Cq4) we first find dy+dx, dv v2 $x —Qx by differentiating (10) -^r-~2+ymen +fl^«n .... (11) z=0fory=0 0 0 .. (10) gives . . 0—0-{-men— neQ =0 m—n=0 .. m=n . (12) Also for x=l dv p2 & —of\ -^-= (11) gives 0=~f q ^n +nen • • (13); . n=m we have m=n= r & -^i ?i-q3 «n-Hn • • -(14). The equation of the curve, then, substituting (14) in -P qx —qx (10) isy=^x—P- -L—-?__ . (15) .-., Substituting for p and q we have. /Pcosa T & —Ql~\ I r Qx —Qx 1 (as in §297) EI en+en xsina—ycosa =sin« e —en FLEXURE. OBLIQUE FORCES. 359 298. Inclined Beam with Hinge at One End.—Fig. 304 Let«e = ex. Required the equation for safe loading ; also themaximum shear, there being but one load, P, and that inthe middle, The vertical wall being smooth, its reaction,. H, at 0 is horizontal, while that of the hinge-pin being un-known, both in amount and direction, is best replaced byits horizontal and vertical components B0 and V0, unknownin amount only. Supposing the flexure slight, we findthese external forces in the same manner as in Prob. 1 §37, by considering the whole beam free, and obtain H=~ cota ; H0 also = £. cot« ; V0 a) For any section n between 0 and B, we have, from thefree body nO, Fig. 305, uniform thrust = pYF =5cosaand from I () = 0, ±—- =Hx sin a e ? (2) (3) and the shear = J = Hsin a = }4 P cos a (4) The max. (Pi+p2) to be found on OB is .*. close above B,where x = % I, and is 360 MECHANICS OF ENGINEERING. H cos a , Hie sin a -, . -, „ rcot a , le F esma i . , „ rcot a . ten /irs -— which = P cos a\ +_ (o) 21 I 2F 4/J V In examining sections o
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
