Mechanics of Materials

Shear Stress and Shear FlowIn Beams))

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Shear Stress in Beams

•Transverse Shear•V is the result of transverse shear-stress•There will be Longitudinal shear stress associated with transverse shear stress•Longitudinal shear stresses act along longitudinal planes of the beam

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Proof of Longitudinal stress

•Shear Strain: as a result of shear stress• Distort cross section• Complex distortion• Distortion neglected for slender beams

( small depth compared to its length)

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Shear FormulaRelationship between the shear-stress distribution, acting over the cross section of a beam, and the resultant shear force at the section

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Rectangular cross section:

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Rectangular cross section:

Max shear stress is 50% greater than the average shear stress

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Integration of the shear-stress distribution over the cross section result in the shear force V

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Wide Flange Beam

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