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Shaft Torsion

J = π(D⁴−d⁴)/32, τ = T·r/J, twist θ = T·L/(J·G). Combined bending + torsion uses max-shear theory. Units: mm, N·mm, MPa. Torque from power: T(N·m) = 9550·kW/rpm.

Calculator

Outer Ø (mm)

Bore Ø (mm, 0 = solid)

Torque T (N·mm)

Length L (mm)

G (MPa)

Bending M (N·mm, optional)

Stress-concentration Kt (shoulder / keyway / groove)

Polar J

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Nominal shear

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Peak shear (×Kt)

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Angle of twist

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Combined max shear

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Power (kW)

Speed (rpm)

Torque from power

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Elastic, uniform circular section. A helper, not a substitute for engineering judgment.