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 . ly applied, as in thecase of a weight falling upon it, (from the same height,should be added); or if the same weights are used, thelonger beam will not break by the weight falling upon itunless it falls through twice the distance required to frac-ture the shorter beam. 268. Combined Flexure and Torsion. Crank Shafts. Fig. OiB be the crank, and NOi the portion projecting beyond the nearest bearingN. 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 . ly applied, as in thecase of a weight falling upon it, (from the same height,should be added); or if the same weights are used, thelonger beam will not break by the weight falling upon itunless it falls through twice the distance required to frac-ture the shorter beam. 268. Combined Flexure and Torsion. Crank Shafts. Fig. OiB be the crank, and NOi the portion projecting beyond the nearest bearingN. P is the pressure of theconnecting-rod against thecrank-pin at a definite in-stant, the rotary motion be-ing uniform. Let a= theperpendicular dropped fromthe axis 001 of the shaftupon P, and 1= the distanceof P, along the axis 0 0Y fromthe cross-section NmN of theLet NN be a diameter of thisIn considering the portionNO^B free, and thus exposing the circular section NmN,we may assume that the stresses to be put in on the ele-ments of this surface are the tensions (above NN) andthe compressions (below NN) and shears ~| to NN, dueto the bending action of P; and the shearing stress tan-. Fig. 5271. shaft, close to the bearing,section, and parallel to c FLEXURE. SPECIAL PROBLEMS. 315 gent to the circles which have 0 as a common centre, andpass through the respective dFs or elementary areas,these latter stresses being due to the twisting action of the former set of elastic forces let p = the tensilestress per unit of area in the small parallelopipedical ele-ment m of the helix which is furthest from NN (the neu-tral axis) and 1= the moment of inertia of the circle aboutNN\ then taking moments about NN for the free body,(disregarding the motion) we have as in cases of flexure(see §239) pi « .. Plr PI; , p- (a) [None of the shears has a moment about M.] Nexttaking moments about 00u (the flexure elastic forces, bothnormal and shearing, having no moments about 00,) wehave as
Size: 1726px × 1447px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
