Ch6ShearingStressesinBeamsandThinWalledMembers

Ch6ShearingStressesinBeamsandThinWalledMembers - Chapter...

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Unformatted text preview: Chapter Six Shearing Stresses in Beams and Thin-Walled 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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Ch6ShearingStressesinBeamsandThinWalledMembers - Chapter...

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