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 . pressed in the fig-ure, the following results may be obtained, after havingdivided the length of the beam into three parts for sepa-rate treatment as necessitated by the external forces, whichare the distributed load W, andand the two reactions, each =]/2 W. The moment curve ismade up of parts of three dis-tinct parabolas, each with itsaxis vertical. The central par-abola may sink below the hori-zontal axis o
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 . pressed in the fig-ure, the following results may be obtained, after havingdivided the length of the beam into three parts for sepa-rate treatment as necessitated by the external forces, whichare the distributed load W, andand the two reactions, each =]/2 W. The moment curve ismade up of parts of three dis-tinct parabolas, each with itsaxis vertical. The central par-abola may sink below the hori-zontal axis of reference if thesupports are far enough apart,in which case (see Fig.) the elas-tic curve of the beam itself becomes concave upward be-tween the points E and F of contrary flexure. At eachof these points the moment must be zero, since the radiusof curvature is oo and M= EI?+ p (see § 231) at any sec-tion ; that is, at these points the moment curve crosses itshorizontal axis. As to the location and amount of the max. moment the diagram we see that it will be either at H,the middle, or at both of the supports B and G (which fromsymmetry have equal moments), ,. Fig. 267. w. Mm\ — \=\ * I -El? at B and C or according to which is the greater in any given case; as l2 is > or < \ ^/§t The shear close on the left of B = wl1} while close to theright oi Bit= y2 W - w\. (It will be noticed that in this,case since the beam overhangs, beyond the support, the:shear near the support is not equal to the reaction there,as it was in some preceding cases.) 308 MECHANICS OF ENGINEERING. Hence J„ { y2 w-wl, } according as h ^ 264, Hydrostatic Pressure Against a Vertical Plank.— Fromelementary hydrostatics we know that the pressure, perunit area, of quiescent water against the vertical side of atank, varies directly with the depth, x, below the surface,and equals the weight of a prism of water whose altitude= x, and whose sectional area is u
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
