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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 Fall '12
 ROSS
 Torsion, Trigraph, Statically Indeterminate Torsion

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