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Solid Circular Segmental Section Torsional Deformation Stress Equation and Calculator

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Torsional Deformation and Stress Circular Segmental Section Equations and Calculator Equations and Calculator.

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Torsional Deformation and Stress Solid Circular Segmental Section Calculator

h = r ( 1 - cosα)

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

For 0 ≤ h/r ≤ 1.0

C = 0.7854 - 0.0333 (h/r) - 2.6183 (h/r)² + 4.1595 (h/r)³ - 3.0769 (h/r)⁴ + 0.9299 (h/r)⁵

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress

For 0 ≤ h/r ≤ 1.0

B = 0.6366 + 1.7598 (h/r) - 5.4897 (h/r)² + 14.062 (h/r)³ - 14.510 (h/r)⁴ + 6.434 (h/r)⁵

τ_max = TB / r³ where B varies with h / r

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.