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Torsional Deflection Stress Pipe Equation and Calculator

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Torsional Deformation and Stress Concentric Circlar Section Equations and Calculator. Torsional deflection and stress of a pipe.

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Torsional Deformation and Stress Concentric Circlar Section Calculator

K = 0.5 π ( r⁴₀ - r⁴_i )

Angle of Twist under applied Torque Moment

θ = ( T L ) / ( K G )

Shear Stress

τ_max = 2 T / ( π ( r⁴₀ - r⁴_i ) ) at outer boundary

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.