What is Torsion in Shafts?
Torsion occurs when a shaft is twisted by torque, causing shear stress and deformation. Understanding torsion is essential for designing durable shafts in machinery, motors, and vehicles. The angle of twist and shear stress depend on the applied torque, shaft length, and material properties.
Torsion is the twisting of a shaft under torque. Shear stress τ and angle of twist θ are calculated using τ = Tr/J and θ = TL/GJ.
Try it: interactive calculator
Step-by-step worked examples
Solid shaft radius 0.05 m, polar moment J = 4.9×10⁻⁵ m⁴, torque 500 N·m. Max shear stress?
τ_max = T·r/J τ_max = (500 × 0.05)/(4.9×10⁻⁵) τ_max = 25/(4.9×10⁻⁵) = 510,204 Pa ≈ 51 MPa
Steel shaft 2 m long (G = 80 GPa, J = 1×10⁻⁴ m⁴), torque 300 N·m. Angle of twist?
θ = TL/(GJ) θ = (300 × 2)/(80×10⁹ × 1×10⁻⁴) θ = 600/(8×10⁶) = 7.5×10⁻⁵ rad ≈ 0.0043°
Hollow shaft inner 0.04 m, outer 0.06 m, torque 800 N·m. J = π(r_o⁴−r_i⁴)/32. τ_max?
J = π(0.06⁴−0.04⁴)/32 ≈ 1.16×10⁻⁵ m⁴ τ_max = (800 × 0.06)/(1.16×10⁻⁵) ≈ 4.14 MPa
Flashcards
Quick quiz
Q1.Shear stress is proportional to…
Q2.Polar moment J for solid circular shaft?
Q3.Larger shear modulus G means…
Q4.Unit of polar moment J?
The full card deck, worked steps and AI-tutor support for “What is Torsion in Shafts?” are in Notek — study by hand before your exam.
Common mistakes
Shear stress is uniform across shaft radius. — Correct: Shear stress increases linearly from center to outer surface.
Angle of twist is independent of shaft length. — Correct: Longer shafts twist more (θ ∝ L).
Solid and hollow shafts have same J. — Correct: Hollow shafts have much smaller J.
Shear modulus G is same for all materials. — Correct: G varies; steel ~80 GPa, aluminum ~25 GPa.
FAQ
What is the torsion formula?
τ = Tr/J for shear stress, θ = TL/(GJ) for angle of twist.
Why do hollow shafts reduce torsion?
Material near center contributes little to J; removing it saves weight without much strength loss.
What is polar moment of inertia?
J measures resistance to torsional deformation — higher J means less twist for same torque.
Can torsion cause failure?
Yes — if shear stress exceeds material's shear yield strength, shaft fails.