Torsion Notes

# 8and49canbe appliedtononuniformcircular

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Unformatted text preview: T= Jτ max a Tρ τ= J J is the polar moment of inertia. J is the polar moment of inertia. J = ∫ ρ 2 dA Derivation of the Torsion Formula Derivation of the Torsion Formula ► For a circular rod, π4 a 2 ► For a hollow shaft, J= J= ► The shear strain γ can be can be related to T by, ► π44 (a − b ) 2 γ= Tρ GJ γ max = Ta GJ Eqns (4.8) and (4.9) can be applied to non­uniform circular bars and bars subjected to varying torques along the length. Angular Twist of a Circular Bar Angular Twist of a Circular Bar Recall from the geometry, φa γ max = L ► Substitution of τ = G γ in the above equation together with ► γ max = results in, ► φ= Ta GJ TL GJ The angle of twist is proportional to the applied torque T and provides the basis for determining the modulus of rigidity (shear modulus) of a given material. Composite Shafts Composite Shafts Notes on Power Transmission Notes on Power Transmission Power units is work/unit time. 1 Watt = 1 N *1m/1s ► Torque is a force couple (N­m) so rot...
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