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 . iPj?.-. pc=3/8id=y8w ., ^TFandP0=2JF— 2PC- ? JF The Moment and Shear Diagrams can now be formed since all the external forces arew known. In Fig. 279 meas-ure x from G. Then in anysection n the moment of thestress-couple is. M=y8Wx- wx2 2 (1) which holds good for anyvalue of x on CO, , fromx=0 up to x=l. By inspec-pig. 279. tion it is seen that for x=0, M=0; and also for x=ffl, M=0, at the inflection p
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 . iPj?.-. pc=3/8id=y8w ., ^TFandP0=2JF— 2PC- ? JF The Moment and Shear Diagrams can now be formed since all the external forces arew known. In Fig. 279 meas-ure x from G. Then in anysection n the moment of thestress-couple is. M=y8Wx- wx2 2 (1) which holds good for anyvalue of x on CO, , fromx=0 up to x=l. By inspec-pig. 279. tion it is seen that for x=0, M=0; and also for x=ffl, M=0, at the inflection point G,beyond which, toward 0, the upper fibres are in tension 326 MECHANICS OF ENGINEERING. the lower in compression, whereas between C and G theyare vice versa. As to the greatest moment to be found onCG, put dM^-dx—0 and solve for x. This gives }i W—wx=0 .*. [x for M max.]=^ . (2) which in eq. (1) gives JfH(atJViseefigure)=+£JPZ . (2) But this is numerically less than M0(=—1/& Wl) hence thestress in the outer fibre at 0 being Po=}6-T» ... (3) the equation for safe loading is ^L=y6Wl .... (4) the same as if the beam were cut through at 0, each half,of length I, retaining the same load as before [see § 242 eq.(2)]. Hence making the girder continuous over the mid-dle support does not make it any stronger under a uni-formly distributed load; but it does make it considerablystiffer. As for t
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
