L14 - Last Class: Beams shear and moment diagrams (Chapter...

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Last Class: Beams – shear and moment diagrams (Chapter 5) Moment + Shear Force Normal stress (Chapter 4) Shear stress (Chapter 6)

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Chapter 6: Shearing stress in beams ( ) () 0 0 0 0 0 = = = = = = = = = = = = x z xz z x y xy y xy xz x x x y M dA F dA z M V dA F dA z y M dA F σ τ • Distribution of normal and shearing stresses satisfies • Transverse (vertical) loading applied to a beam (V) Î normal + shearing stresses in transverse sections. Transverse Section (plane)
When shearing stresses are exerted on the vertical faces of an element ( ), equal stresses must be exerted on the horizontal faces ( ). • Longitudinal (horizontal) shearing stresses must exist in any member subjected to transverse loading. xy τ yx xy yx = V Î xy Î yx Horizontal plane Longitudinal shearing stress

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Shear on the Horizontal Face of a Beam Element • For equilibrium of beam element F x = 0 H + σ C −σ D ( ) dA A Δ H = M D M C I ydA A Horizontal shear force
x V x dx dM M M dA y Q C D A Δ = Δ = = First moment of the area

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This note was uploaded on 04/20/2008 for the course ENGR 2530 taught by Professor Lindaschadlerfeist during the Spring '08 term at Rensselaer Polytechnic Institute.

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L14 - Last Class: Beams shear and moment diagrams (Chapter...

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