Torsion Notes

# From1 and max ga l g l max a shearstressdistribution

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Unformatted text preview: = a). outer Shear Stress Distribution Shear Stress Distribution ► As long as material remains elastic, the shear stress τ can be can be related to shear strain as, τ = Gγ where G is the shear modulus. ► From (1) τ= and τ max = Gφa L Gφρ L τ = τ max ρ a Shear Stress Distribution Shear Stress Distribution ► An internal torque develops a linear distribution of shear stress along each radial line in the cross sectional plane as well as an associated shear stress in the axial plane. ► This axial stress causes shafts to split. Derivation of the Torsion Formula Derivation of the Torsion Formula ► The moment produced by shear stress τ about the longitudinal about the longitudinal axis of the bar must be equal to the applied torque T. T = ∫ ρ τ dA dA T= τ max ρ 2 dA a∫...
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