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Unformatted text preview: Chapter Six Shearing Stresses in Beams and ThinWalled Members 6.1 Introduction In a long beam, the dominating design factor: m Mc I = ( ) xy V average A = Primary design factor Minor design factor In a short beam, the dominating design factor: 3 2 max V A = [due to transverse loading] y component: xy dA V =  z component: xz dA = Equation of equilibrium: Shear stress xy is induced by transverse loading. In pure bending  no shear stress (6.1) (6.2) Materials weak in shear resistance shear failure could occur. 6.2 Shear on the Horizontal Face of a Beam Element : ( ) x D C F H dA + = + = A My I = C D I I I = = Knowing and D C M M H ydA I = A We have (6.3) Since dM V dx = ( / ) D C M M M dM dx x V x  = = = VQ H x I = H VQ q x I = = Therefore, and (6.4) (6.5) Defining Q ydA = = shear flow = horizontal shear/length here Q = the first moment w.t.to the neutral axis Q = max at y = 0 6.3 Determination of the Shearing Stresses in a Beam ave H VQ x A I t x = = ave VQ It = VQ H x I = (6.6) = ave. shear stress...
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 Fall '11
 Wu

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