Thin-Walled Torsion Calculator
A closed thin-walled tube enclosing 20,000 mm² with 2 mm walls carries 1 kN·m of torque at a shear stress of 12.5 MPa.
Aluminium alloys about 26–28 GPa, steel about 79 GPa.
12.5 MPa
- Torsion constant J
- 5333333.333 mm⁴
- Angle of twist θ = TL/(GJ)
- 0.3978873577 °
- Twist per unit length
- 0.3978873577 °/m
- Torsional stiffness GJ/L
- 144000 N·m/rad
Step-by-step solution
- Shear flow q = T ÷ 2A = 1000 ÷ (2 × 0.02) = 25000 N/m
- τ = q ÷ t = 12.5 MPa
- J = 4A²t ÷ ∮ds = 0.000005333333333 m⁴
- θ = TL ÷ (GJ) = 0.006944444444 rad = 0.3978873577°
Thin-Walled Torsion Formula
q = T / (2A), τ = q/t, J = 4A²t / ∮ds
open section J = Σ bt³/3, τ_max = Tt/J; twist θ = TL/(GJ)
Worked Example
A closed aluminium tube enclosing 20,000 mm² with 2 mm walls and 600 mm perimeter under 1 kN·m:
- Shear flow q = T ÷ 2A = 1000 ÷ (2 × 0.02) = 25000 N/m
- τ = q ÷ t = 12.5 MPa
- J = 4A²t ÷ ∮ds = 0.000005333333333 m⁴
- θ = TL ÷ (GJ) = 0.006944444444 rad = 0.3978873577°
Angle of twist θ = TL/(GJ): 0.3978873577 ° · Twist per unit length: 0.3978873577 °/m · Torsional stiffness GJ/L: 144000 N·m/rad
GATE tip
For walls of varying thickness, ∮ds/t replaces s/t, and the maximum shear stress occurs where t is smallest because q is constant.
More Structures Calculators
-
Von Mises Stress Calculator
σ_v = √(½[(σ₁ − σ₂)² + (σ₂ − σ₃)² + (σ₃ − σ₁)²])
plane stress: σ_v = √(σx² − σxσy + σy² + 3τxy²); Tresca σ₁ − σ₃
Example: A plane stress state of σx = 100 MPa and τxy = 50 MPa: von Mises stress σ_v = 132.288 MPa.
Frequently asked questions
Why are closed sections so much stiffer?
Shear flow circulates around the whole cell, so J goes with A²t. Slitting the same tube makes J go with bt³/3, often hundreds of times smaller.
What is shear flow?
Shear force per unit length of wall, q = τt. In a single closed cell under pure torsion it is constant around the section.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Thin-Walled Torsion Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/thin-walled-torsion-calculator/
IEEE
Scientific Converters, "Thin-Walled Torsion Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/thin-walled-torsion-calculator/