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 . dxP. Fig. 220. TORSION. 24,6 a small cube, of edge — dx, (taken from the outer helix ofFig. 215,) free and in equilibrium, the plane of the paperbeing tangent to the cylinder ; while 220 shows the portionBD C, also free, with the unknown total tensile stresspdx2^/2acting on the newly exposed rectangle of area =dxxdx^2,p being the unknown stress per unit of area. From sym-metry the stress on this diagonal plan
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 . dxP. Fig. 220. TORSION. 24,6 a small cube, of edge — dx, (taken from the outer helix ofFig. 215,) free and in equilibrium, the plane of the paperbeing tangent to the cylinder ; while 220 shows the portionBD C, also free, with the unknown total tensile stresspdx2^/2acting on the newly exposed rectangle of area =dxxdx^2,p being the unknown stress per unit of area. From sym-metry the stress on this diagonal plane has no shearingcomponent. Putting I [components normal to BD]=0,we have pdx2,\/2=2dx2p!icos4:50=dx2ps^/2 , . (1) That is, a normal tensile stress exists in the diagonalplane BD of the cubical element equal in intensity to theshearing stress on one of the faces, , =2,930 lbs. per in this case. Similarly in the plane AC will be found a compressivestress of 2,930 lbs. per sq. in. If a plane surface had beenexposed making any other angle than 45° with the face ofthe cube in Fig. 219, we should have found shearing andnormal stresses each less than ps per sq. inch.
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
