# L14 - Last Class Beams shear and moment diagrams(Chapter 5...

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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) normal (due to bending) + 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. V Horizontal plane Longitudinal shearing stress τ xy yx xy = yx xy yx

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Shear on the Horizontal Face of a Beam Element • For equilibrium of a beam element F x = 0 = Δ H + σ C −σ D ( ) dA A Δ H = M D M C I y dA A Horizontal shear force
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## This note was uploaded on 12/14/2010 for the course ENGR 2530 taught by Professor Lindaschadlerfeist during the Fall '08 term at Rensselaer Polytechnic Institute.

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L14 - Last Class Beams shear and moment diagrams(Chapter 5...

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