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Circular Shaft Opposite Sides flattened Torsional Deformation Stress Equation and Calculator

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Torsional Deformation and Stress Circular shaft with opposite sides flattened Equations and Calculator.

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Torsional Deformation and Stress Circular shaft with opposite sides flattened Calculator

h = r - w

K = 2Cr⁴ where C varies with h / r as follows:

For two flat sides 0 ≤ h / r ≤ 0.8

C = .7854 - 0.4053 (h / r) - 3.5810 (h / r)² + 5.2708 (h / r)³ - 2.0772 (h / r)⁴

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress

For 0 ≤ h / r ≤ 0.6

B = 0.6366 + 2.5303 (h / r) - 11.157 (h / r)² + 49.568 (h / r)³ - 85.886 (h / r)⁴ + 69.849 (h / r)⁵

τ_max = T B / r³

Where:

θ = angle of twist (radians)
α = degrees
T = Twisting or torque moment force-length, (in-lbs, N-mm)
L = Length (in, mm)
r = Radius (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.