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Mechanics of engineering. Comprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc (1888)

Church, Irving P[orter], 1851- [from old catalog] · New York, J. Wiley & sons · leaf 249

An illustration from Mechanics of engineering. Comprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc, 1888, leaf 249
couplesand considering the left hand portion as a free body, theforces holding it in equilibrium are the two forces P ofthe left-hand couple and an infinite number of shearingforces, each tangent to its circle of radius z, on the crosssection exposed by the removal of the right-hand portion.The… … Each elementary shearing force = -± p^dF, and z is itslever arm about the axis Oo. Eor equilibrium, I (mom.)about the axis Oo must =0; i.e. in detail —Py2a—Py2a+ J ( S pHdF)z=0 or, reducing, ^s Cz2dF=Pa ; or, PJi *L=Pa (3) Eq. (3) relates to torsional strength, since it contains ps, thegreatest…

Mechanics, Applied · Engineering · Strength of materials

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