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### Circular Section Deformation and Stress Torsional Deformation Stress Equation and Calculator

Beam Deflection and Stress Equation and Calculators

Torsional Deformation and Stress Circular Section Equations and Calculator. ALL calculators require a Premium Membership

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Torsional Deformation and Stress Solid Circular Sector Calculator

K = Cr4 where C varies with α / π as follows:

For 0 ≤ α / π ≤ 2.0

C = 0.0034 - 0.0697 (α / π) + 0.5825 (α / π)2 - 0.2950 (α / π)3 + 0.0874 (α / π)4 - 0.0111 (α / π)5

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress

For 0 ≤ α / π ≤ 1.0

B = 0.0117 - 0.2137 (α / π) + 2.2475 (α / π)2 - 4.6709 (α / π)3 + 5.1764 (α / π)4 - 2.2000 (α / π)5

τmax = T / B r3 on a radial boundary

Where:

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