5a. Torsion Members: Circular Crosssections (SSES Ch. 5.15.3, 5.5) • ThinWalled Shafts • Solid/ThickWalled Shafts • Discretely and Continually Varying Shafts • Power Transmission 
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ThinWalled Torsion Member
If the torque, crosssection and material are all constant over the length, then the following relationships hold for shear strain and shear stress: Combining the above equations with Hooke's law:
t = Gg give the angle of twist: J is the Polar Moment of Inertia. 
Thinwalled circular shaft 
Solid and Thickwalled Torsion Members
and Combining gives: The maximum shear stress is: J is the Polar Moment of Inertia 
Variation of shear stress in solid circular shaft. 
Power Transmission
Power is often transmitted through rotating shafts. The power transmitted by a shaft is given by the torque multiplied by the shaft's angular velocity w:

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