Formula used
For a closed, thin-walled, single-cell section under torque T:
- Shear flow: q = T / (2Am)
- Torsion constant: J = 4Am2 / \u∮(ds/t)
- Twist rate: d\uθ/dx = T / (GJ)
- Shear stress: \uτ = q/t (uniform) or \uτi = q/ti (segmented)
Use Am and perimeter/segments along the wall centerline (mean geometry).
How to use this calculator
- Select Uniform thickness for constant wall thickness.
- Select Segmented wall list
- Enter the applied torque, enclosed area, member length, and shear modulus.
- Provide perimeter and thickness, or fill the segment table.
- Press Calculate
- Use Download CSV or Download PDF for reporting.
Example data table
Sample inputs and typical outputs for a thin-walled closed section.
| Case | T (N\u00b7m) | Am (m\u00b2) | P (m) | t (mm) | G (GPa) | L (m) | q (N/m) | \uτ (MPa) | \uθ (deg) |
|---|---|---|---|---|---|---|---|---|---|
| Example | 250 | 0.004 | 0.35 | 2.0 | 26 | 1.2 | 31250 | 15.625 | 0.096 |
Example values are illustrative; validate assumptions for your geometry.
Thin wall torsion in practice
1) Why thin-wall theory matters
Thin-walled closed sections deliver high torsional efficiency because material is placed far from the centerline. For many tubes, box beams, and stiffened skins, the thickness is small compared with the perimeter dimensions, so shear stress is nearly uniform through the thickness and can be treated with shear flow.
2) Mean area and shear flow
The Bredt-Batho relation links torque and shear flow: q = T/(2Am). The mean enclosed area Am is measured along the wall centerline. Doubling Am halves q, which directly reduces stress at a fixed thickness.
3) How thickness drives stress
Shear stress follows τ = q/t. For a uniform wall, a 10% reduction in thickness increases stress by about 11%. If thickness varies, the same q circulates around the cell, so the thinnest segment governs peak stress and fatigue sensitivity.
4) Torsion constant and stiffness
The torsion constant is J = 4Am2/∮(ds/t). Larger area increases J quadratically, while a larger perimeter-to-thickness ratio increases ∮(ds/t) and reduces stiffness. This calculator evaluates ∮(ds/t) using either P/t or a segmented sum.
5) Twist rate and service limits
Twist per length is dθ/dx = T/(GJ), and total twist is that rate times length. In design, twist limits often control for driveline shafts, aerospace control surfaces, and thin box beams where small angular errors affect alignment, vibration, and clearances.
6) When segmented input is worth it
Segmented input is useful when the wall is made from different gauges, has local reinforcements, or includes bonded joints. Enter each side length and thickness to compute Σ(si/ti). This improves J and stress estimates without requiring a full finite element model.
7) Common sources of error
Results are sensitive to the mean geometry. Use centerline dimensions, not outer dimensions. Ensure units are consistent, and avoid applying this single-cell model to open sections, multi-cell boxes, or thick-walled parts where shear distribution and warping become important. For high accuracy, confirm the section behaves as a single cell.
8) Interpreting exported results
Use the CSV for spreadsheets and the PDF for reports and design reviews. Record the assumed mode, geometry basis, and material G. Add the torque case name, operating temperature, and any safety factors used. When comparing designs, track how changes in Am, thickness, or G shift q, J, and twist so decisions remain traceable.
FAQs
1) What is mean enclosed area Am?
Am is the area enclosed by the wall centerline. For thin walls, using the centerline area gives better shear flow and stiffness predictions than using the outer boundary.
2) Why does every segment share the same shear flow?
For a single closed cell under torque, equilibrium requires a constant circulating shear flow around the perimeter. Thickness changes alter shear stress, not the shear flow.
3) Can I use this for an open channel section?
No. Open sections do not develop a closed shear-flow path, and their torsion behavior is governed by St. Venant torsion with significant warping. Use an open-section torsion approach instead.
4) How do I choose shear modulus G?
Use material data from a datasheet. If you only know Young’s modulus E and Poisson’s ratio ν, estimate G ≈ E/[2(1+ν)]. Keep units consistent with your inputs.
5) What thickness should I enter for tapered walls?
Use the mean thickness along the shear path for a quick estimate. If thickness varies by side or panel, switch to segmented mode and represent each panel with its own thickness.
6) What does ∮(ds/t) represent physically?
It measures how “perimeter-heavy” the section is relative to thickness. Larger ∮(ds/t) lowers the torsion constant J, increasing twist and stresses for the same torque.
7) Are warping and multi-cell effects included?
No. This tool assumes a single closed cell with thin walls. Multi-cell boxes require compatibility between cells, and warping restraint can change stresses. Use specialized multi-cell methods when needed.