Shaft Shear Stress due to Torsion
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Shear Stress in the Shaft
When a shaft is subjected to a torque or twisting, a shearing stress is produced in the shaft. The shear stress varies from zero in the axis to a maximum at the outside surface of the shaft.
The shear stress in a solid circular shaft in a given position can be expressed as:
σ = T r / Ip
where
σ = shear stress (MPa, psi)
T = twisting moment (Nmm, in lb)
r = distance from center to stressed surface in the given position (mm, in)
Ip = "polar moment of inertia" of cross section (mm4, in4)
Note
• the "Polar Moment of Inertia" is a measure of a beam’s ability to resist torsion. The "Polar Moment of Inertia" is defined with respect to an axis...More

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