BIZOMAT MAKEOS · Strength
Thin-Walled Closed Tube in Torsion
What shear stress and twist does torque cause in this thin-walled round or rectangular tube?
Shear stress (Bredt’s formula), torsional constant and twist of a closed thin-walled round or rectangular tube under torque.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Section | choice | Round or rectangular hollow section. |
| Outside diameter or width | mm | Outside diameter (round) or outside width (rectangular). |
| Outside height (rectangular only) | mm | Outside height (rectangular only). |
| Wall thickness | mm | Wall thickness. |
| Torque | N·m | Torque. |
| Length | mm | Length for twist. |
| Shear modulus | GPa | Shear modulus. |
| Allowable shear stress | MPa | Allowable shear stress from your design code. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Section
- What it is
- Whether the closed thin-walled section is a round tube or a rectangular hollow section (RHS).
- Units and format
- Choose one of 2 options from the list: Round tube; Rectangular tube (RHS).
- Example
- The form opens with “Rectangular tube (RHS)” selected as a worked example. Choose the option that matches your case.
- Get it right
- The method suits closed sections only; a slit or open seam makes the section far weaker.
What this means: Outside diameter or width
- What it is
- For a round tube, its outside diameter; for a rectangular tube, its outside width.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter outside dimensions; the tool subtracts the wall thickness to get the mid-line size.
What this means: Outside height (rectangular only)
- What it is
- The outside height of a rectangular hollow section, measured across the other pair of walls from the width.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used for the rectangular tube only; it is ignored for a round tube.
What this means: Wall thickness
- What it is
- The thickness of the tube wall, assumed uniform all round the section.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shear stress falls roughly in inverse proportion to wall thickness.
- Get it right
- The formula assumes the wall is thin compared with the section size; very thick walls give less accurate results.
What this means: Torque
- What it is
- The twisting moment applied about the tube’s axis, for example by a drive shaft, frame member or torque arm.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shear stress and twist both rise in direct proportion to torque.
- Get it right
- Enter newton-metres; the tool converts to N·mm.
What this means: Length
- What it is
- The length of tube between the torque input and the reaction, over which the angle of twist is calculated.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Twist rises in direct proportion to length; stress does not depend on it.
What this means: Shear modulus
- What it is
- The shear modulus (modulus of rigidity) of the tube material, which sets how much the section twists.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 79.3 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher modulus reduces twist; it does not change the shear stress.
- Get it right
- Enter gigapascals, not megapascals.
What this means: Allowable shear stress
- What it is
- The highest shear stress your design code permits in the tube wall; the calculated wall shear stress is compared with it.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use a shear allowable, and reduce it for fatigue if the torque reverses or cycles.
Method and formulas
- Mid-line dimensions: outside minus t. Enclosed area Am; mid-line perimeter s.
- Bredt: τ = T ÷ (2 Am t).
- J = 4 Am² t ÷ s; twist θ = T L ÷ (G J).
- Example: 1500 N·m on a 100 × 50 × 4 RHS gives τ = 42.459 MPa.
Limitations
- Thin walls (t well under a tenth of the size); corner radii ignored.
- Open sections (with a slit) are far weaker and need a different method.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check RHS and box frames in torsion
- Compare open and closed sections
- Size a torque tube
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Enclosed mid-line area
- Shear stress
- Torsional constant J
- Angle of twist
Interpreting the result
- Closing a section (welding a slit shut) multiplies torsional stiffness many times.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 295–303. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Bound the answer by hand before you mesh
In Design Simulation by the Numbers
What it covers: Use beam theory, section properties, mass and a one-mass frequency estimate to predict each result, reject a weak design early and catch unit errors.
Useful alongside · BIZOMAT original book
Tubes under pressure, thrust and torque
In Stress Transformation by the Numbers
What it covers: How to check a thin-walled tube or hollow shaft under pressure, axial load and torque together, what the pressurised tube tool leaves out, and how to add bending and exact torsion.
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