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 . ntercepts forming thewedge MMGC form a system of graded stresses*whose combination (algebraic) with those of the thrustshows the two sets of normal stresses to be equivalent tothe actual system of normal stresses represented by thesmall prisms forming the imaginary solid AMT .. AMT\It will be shown that these graded stresses constitute a stress-couple. Analytically, the object of this classification of the no
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 . ntercepts forming thewedge MMGC form a system of graded stresses*whose combination (algebraic) with those of the thrustshows the two sets of normal stresses to be equivalent tothe actual system of normal stresses represented by thesmall prisms forming the imaginary solid AMT .. AMT\It will be shown that these graded stresses constitute a stress-couple. Analytically, the object of this classification of the nor-mal stresses into a thrust and a stress-couple, may be madeapparent as follows: In dealing with the free body KAM Fig. 296, we shallhave occasion to sum the components, parallel to the beam,of all forces acting (externaland elastic), also those 1 tothe beam; and also sum theirmoments about some axis ~Jto the force plane. Let thisaxis of moments be GG thegravity-axis of the section(and not the neutral axis);also take the axis X || to thebeam and FT to it (and inforce-plane). Let us seewhat part the elastic forceswill play in these three summations,gives merely a side view. p2dF-^. -ipJF Fig. 297. See Fig. 297, whichReferring to eq. (2) we see that elastic! n a a [see eq. (4) § 23]. But as the as are measured from G agravity axis, z must be zero. Hence [The IX of the Elastic forces] =p,F^E j ^ ^^ j (4) FLEXURE. OBLIQUE FORCES. 351 Also, [The lYoi the Elastic forces] = J= the shear; . (5)while for moments about G [see eq. (1)][The I () of the elastic forces] = f\pldF)z^f(z^p2dF)zei \ =p1fzdF+SLfzidF and hence finally e where IGi — C z2dF, is the moment of inertia ofithe section about the gravity axis G, (not the neutral axis).The expression in (6) may be called the moment of thestress-couple, understanding by stress-couple a couple towhich the graded stresses of Fig. 297 are equivalent. Thatthese graded stresses are equivalent to a couple is shownby the fact that althou
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
