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Shaft with Keyway Torque Applied Deformation and Stress Equations and Calculator

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Torque Applied Deformation and Stress of a Shaft with Keyway Equations and Calculator

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Torque Applied Deformation and Stress of a Shaft with Keyway Section Calculator

K = 2Cr⁴

Varies with b / r as follows

For:

0   ≤   b / r ≤   0.5

Where 0.3   ≤   a / b   ≤   1.5

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

---

Shear Stress Maximum

At M:

Where B varies with b / r as follows:

for 0.5 ≤ a / b ≤ 1.5

Where:

θ = angle of twist (radians),
T = Twisting or torque moment force-length, (in-lbs, N-mm),
L = Length of Section (in, mm),
h = Length as Indicated (in, mm),
r = radius (in, mm),
a,b = Distance as shown (in, mm),
τ = Unit shear stress force / area (lbs/in², N/mm²),
G = Modulus of rigidity force / area (lbs/in², N/mm²),
K = Polar Moment of Inertia (in⁴, mm⁴) for section

Reference:
Roarks Formulas for Stress and Strain, 7th Edition, Table 10.1 Formulas for torsional deformation and stress.

Related:

The Shaft Design Book (Design Charts and Calculations for Torsional Properties of Non-Circular Shafts)