5a. Torsion Members: Circular Cross-sections (SSES Ch. 5.1-5.3, 5.5) Thin-Walled Shafts Solid/Thick-Walled Shafts Discretely and Continually Varying Shafts Power Transmission |
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Thin-Walled Torsion Member
If the torque, cross-section 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. |
Thin-walled circular shaft |
Solid and Thick-walled 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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