L15 - = = NOTE: xy xz in the flanges in the web Shearing...

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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 H x I H VQ q shear flow x I 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 = • The average shearing stress on the horizontal face of the element: ave H q x VQ x A A I t x Δ Δ Δ = = = Δ Δ 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 H VQ t x It τ Δ
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Unformatted text preview: = = NOTE: xy xz in the flanges in the web Shearing Stresses in Thin-Walled Members The variation of shear flow across the section depends only on the variation of the first moment. I VQ t q = = For a box beam, q grows smoothly from zero at A to a maximum at C and C and then decreases back to zero at E . Shearing Stresses in Thin-Walled Members For a wide-flange beam, the shear flow increases symmetrically from zero at A and A , reaches a maximum at C and the decreases to zero at E and E . The continuity of the variation in q and the merging of q from section branches suggests an analogy to fluid flow....
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L15 - = = NOTE: xy xz in the flanges in the web Shearing...

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