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 . ^icl. 243. Prismatic Beam Supported at its Extremities and Loadedin any Manner. Equation for Safe Loading.—Fig. 236. Given the loads Plt P2, and P3, whosedistances from the right sup-^h Fi EW-J-H Por* are t ha and l3; ,required —p the equation for safe loading ;, find 3Im and write it =Rl+e. If the moment curve werecontinuous, , if M were acontinuous function of x fromend to end of the beam, wecould e
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 . ^icl. 243. Prismatic Beam Supported at its Extremities and Loadedin any Manner. Equation for Safe Loading.—Fig. 236. Given the loads Plt P2, and P3, whosedistances from the right sup-^h Fi EW-J-H Por* are t ha and l3; ,required —p the equation for safe loading ;, find 3Im and write it =Rl+e. If the moment curve werecontinuous, , if M were acontinuous function of x fromend to end of the beam, wecould easily find Mm by makingdJl-:rdx=0, , J=0, and sub-stitute the resulting value of x in the expression for in the present case of detached loads, J is not zero,necessarily, at any section of the beam. Still there issome one section where it changes sign, , passes sud-denly through the value zero, and this will be the sectionof greatest moment (though not a maximum in the strictsense used in calculus). By considering any portion n Oas free, J is found equal to the Reaction at 0 Diminished bythe Loads Occuring Between n and 0. The reaction at B is r r r. Fig. 236. 270 MECHANICS OF ENGINEERING. obtained by treating the whole beam as free (in which caseno elastic forces come into play) and putting ^( O)=0; while that at 0,=PQ=P1+P2+Pir-PBIf n is taken anywhere between 0 and E, J=P0 E FfJ=P0-PlF H,J=P0-P1-P2H B, J=P0-P1-P2-P3This last value of J also = the reaction at the othersupport, B. Accordingly, the shear diagram is seen toconsist of a number of horizontal steps. The relationJ—dM-r-dx is such that the slope of the moment curve isproportional to the ordinate of the shear diagram, andthat for a sudden change in the slope of the moment curvethere is a sudden change in the shear ordinate. Hence inthe present instance, J being constant between any twoconsecutive loads, the moment curve reduces to a straightline between the same loads, this line having a
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
