L15 - Longitudinal Shear on a Beam Element of Arbitrary...

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Longitudinal Shear on a Beam Element of Arbitrary Shape • Last class: vertical components τ xy on a transverse section of a beam. • This class: horizontal components xz of the stresses. Transverse Section (plane) Horizontal plane
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First moment of the area of interest above/below neutral axis VQ Hx I HV Q q shear flow xI Δ= Δ Δ == = Δ Horizontal force Vertical shear loading Moment of inertia for the entire cross sectional area
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Determination of the Shearing Stress in a Beam ave VQ It τ = •T h e average shearing stress on the horizontal face of the element: ave H qx V Q x A AI t x Δ ΔΔ == = Δ Area of interest thickness
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Shearing Stresses in Thin-Walled Members • The longitudinal shear force on the element is x I VQ H Δ = Δ • shearing stress in the web It VQ xy = τ τ xz τ xy
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zx xz HV Q tx I t ττ Δ =≈ =
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L15 - Longitudinal Shear on a Beam Element of Arbitrary...

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