BIZOMAT MAKEOS · Strength
Torsion Member Comparison (Solid Bar, Tube or Rectangle)
For this torque, how do a solid round bar, a round tube and a rectangular bar compare in shear stress, twist and weight, and does the one I chose pass?
Side-by-side check of three shaft or link sections under the same torque: a solid round bar and a round tube by the exact polar moment (as the shaft torsion tool), and a solid rectangle by the handbook rectangular-section formulas (as the rectangular bar torsion tool), giving shear stress, twist over the length, twist per metre and mass per metre, with the chosen section checked against your allowable stress and twist limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Torque | N·m | Torque applied. |
| Length | mm | Length between the torque inputs. |
| Shear modulus | GPa | Shear modulus of the material. |
| Density | kg/m³ | Density for the mass per metre. |
| Allowable shear stress | MPa | Allowable shear stress (your design value). |
| Largest twist per metre | °/m | Largest twist per metre of length you accept (stiffness requirement). |
| Section chosen | choice | Which section to check. |
| Sections | ||
| Solid bar diameter | mm | Diameter of the solid bar. |
| Tube outside diameter | mm | Outside diameter of the tube. |
| Tube wall thickness | mm | Wall thickness of the tube. |
| Rectangle long side | mm | Longer side of the rectangle. |
| Rectangle short side | mm | Shorter side of the rectangle. |
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: Torque
- What it is
- The twisting moment applied to the member. The same torque is applied to all three sections so they can be compared directly.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress and twist rise in direct proportion to torque.
What this means: Length
- What it is
- The length of member between the point where the torque goes in and the point where it is reacted, over which the twist builds up.
- 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 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Twist per metre does not depend on this length; only the total twist does.
What this means: Shear modulus
- What it is
- The shear modulus (modulus of rigidity) of the member material, from its data sheet. It sets how far the section twists, not how highly it is stressed.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 200 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
- Twist is inversely proportional to G; shear stress is unaffected.
- Get it right
- Shear modulus G, not Young’s modulus E, and in GPa.
What this means: Density
- What it is
- The density of the member material, used only to work out the mass per metre of each section for the weight comparison.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Allowable shear stress
- What it is
- The largest shear stress you accept in the chosen section, from the material strength and your design margin.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 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.
What this means: Largest twist per metre
- What it is
- Your stiffness limit: the largest angle of twist per metre of member length you accept, for example to keep driven parts in step.
- Units and format
- Enter a number in °/m: °/m. The form accepts 0.01 °/m to 90 °/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 °/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Degrees per metre of length, not total degrees over the member.
What this means: Section chosen
- What it is
- Which of the three sections receives the pass or fail verdict against the allowable stress and twist limit; all three are still listed in the comparison.
- Units and format
- Choose one of 3 options from the list: Round tube; Solid round bar; Rectangular bar.
- Example
- The form opens with “Round tube” selected as a worked example. Choose the option that matches your case.
Sections
What this means: Solid bar diameter
- What it is
- The outside diameter of the solid round bar in the comparison.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 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 in the bar falls with the cube of its diameter.
What this means: Tube outside diameter
- What it is
- The outside diameter of the round tube in the comparison; its bore is this diameter less twice the wall thickness.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Tube wall thickness
- What it is
- The wall thickness of the round tube, measured radially from the bore to the outside surface.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Twice the wall must be less than the outside diameter, or the tool rejects the inputs.
What this means: Rectangle long side
- What it is
- The longer side of the solid rectangular section, measured across the cross-section.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If the two sides are swapped, the tool sorts them and always treats the larger as the long side.
What this means: Rectangle short side
- What it is
- The shorter side of the solid rectangular section. The torsion constant depends on its cube, so it controls the twist of the rectangle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Round sections: J = π (D⁴ − d⁴) ÷ 32; τ = T (D ÷ 2) ÷ J; twist = T L ÷ (G J) (as the shaft torsion tool).
- Rectangle: τ = T (3b + 1.8c) ÷ (b² c²); K = b c³ [⅓ − 0.21 (c ÷ b)(1 − c⁴ ÷ 12b⁴)]; twist = T L ÷ (K G) (as the rectangular bar torsion tool).
- Mass per metre = density × area.
- Example: solid 37.726 MPa, tube 33.296 MPa, rectangle 48.75 MPa; the tube weighs 2.7374 kg/m against 5.5488 for the bar.
Limitations
- Elastic, uniform torsion away from ends and fittings; warping of open sections is not covered.
- Stress concentrations at keyways and holes are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a section for a torque tube or drive link
- Show the weight saved by a tube
- Check a rectangular bar used as a torsion member
Who it is for
- Design engineers
- Machine designers
- Structural engineers
What you get
- Stress, twist and mass for each section
- Chosen section checks
- Lightest section that passes
Interpreting the result
- Open and rectangular sections are poor in torsion; closed round tubes give the most stiffness per kilogram.
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.
Worked example · BIZOMAT original book
Stress at a point
In Stress Transformation by the Numbers
What it covers: What stress at a point means, how a small element describes it with normal and shear components, and how pressure, axial load, bending and torque on a hollow spindle turn into those components.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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