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Torsional Deformation Circular Section Torsional Deformation Stress Equation and Calculator

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Preview Torsional Deformation and Stress Solid Circular Section Calculator

θ = TL / KG

K = 0.5 π r⁴

τ_max = 2 T / π r³ at Boundary

Where:

θ - angle of twist (radians)
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 circular section
Q = Length cubed (in³, mm³)
R = Radius (in, mm)

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