BIZOMAT MAKEOS · Springs
Torsion Bar Spring
What rate, twist and shear stress does this torsion bar spring have?
Torsional rate, angle of twist, arm-tip deflection and shear stress of a solid round torsion bar loaded through a lever arm.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bar diameter | mm | Diameter of the active (twisting) part of the bar. |
| Active length | mm | Length between the fixed end and the arm. |
| Shear modulus | GPa | Shear modulus of the bar steel. |
| Force at arm | N | Force at the end of the lever arm. |
| Arm length | mm | Lever arm length from the bar axis. |
| Allowable shear stress | MPa | Allowable shear stress for the spring steel and duty. |
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: Bar diameter
- What it is
- The diameter of the active, twisting part of the solid round bar, not of the enlarged ends or splines.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 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.
- Effect on the result
- Stress falls with the cube of diameter and twist with its fourth power, so small changes matter.
- Get it right
- Use the diameter of the working length; end fittings are not modelled.
What this means: Active length
- What it is
- The active length of bar that twists, between the fixed anchor and the point where the lever arm is attached.
- 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 800 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Twist and arm-tip deflection rise in 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 bar steel, which sets its torsional stiffness.
- 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 lowers the twist and raises the rate; stress does not change.
- Get it right
- Enter gigapascals, not megapascals.
What this means: Force at arm
- What it is
- The force applied at the end of the lever arm, at right angles to it, which twists the bar.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Torque, twist and stress all rise in proportion to force.
- Get it right
- Enter newtons; the torque is this force times the arm length.
What this means: Arm length
- What it is
- The length of the lever arm, measured from the bar’s axis to the line of action of the force.
- 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 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer arm increases the torque and so twist and stress; the tip deflection rises with the square of the arm.
- Get it right
- Measure from the bar centreline, not from the bar surface.
What this means: Allowable shear stress
- What it is
- The highest shear stress permitted for the bar steel and its duty, from the spring maker, material data or your standard.
- 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 600 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Cyclic loading needs a fatigue-based allowable, lower than the static value.
Method and formulas
- T = F × arm; J = π d⁴ ÷ 32.
- Twist θ = T L ÷ (G J); rate = G J ÷ L.
- τ = 16T ÷ π d³; arm-tip deflection ≈ arm × θ (small angles).
- Example: 1000 N on a 200 mm arm twists the default bar 7.3595° with τ = 127.32 MPa.
Limitations
- Solid round bar; end fittings and transitions add stress concentrations.
- Small-angle arm deflection approximation.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a torsion bar for a counterbalance or suspension
- Check stress at maximum twist
- Find arm deflection
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Torque and twist
- Torsional rate and linear rate at the arm
- Shear stress
Interpreting the result
- Preset (scragging) and shot peening raise the usable stress of torsion bars.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 295–303, 344. 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
Torsion bars and flat springs
What it covers: How to size a torsion bar for stress and twist and balance a heavy panel with it, and how to check flat cantilever springs, with their limits at the ends and in large deflection.
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