KEVOS® MAKEOS · Strength
Rectangular Bar in Torsion
What shear stress and twist does torque cause in this rectangular or square bar?
Maximum shear stress, angle of twist and torsional constant of a solid rectangular bar under torque, using Roark’s approximations.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Torque | N·m | Torque transmitted. |
| Long side | mm | Longer side of the section. |
| Short side | mm | Shorter side (equal to b for a square). |
| Length | mm | Length over which twist is wanted. |
| Shear modulus | GPa | Shear modulus (steel about 79 GPa, aluminium about 26 GPa). |
| Allowable shear stress | MPa | Allowable shear stress from your design code. |
Method and formulas
- τmax ≈ T(3b + 1.8c) ÷ (b² c²).
- K = b c³ [1/3 − 0.21 (c/b)(1 − c⁴ ÷ 12b⁴)].
- Twist θ = T L ÷ (K G).
- Example: 200 N·m on a 40 × 20 mm bar gives τmax = 48.75 MPa and 0.98649° of twist over 500 mm.
Limitations
- Approximate formulas (within a few per cent); stress concentrations at re-entrant corners are not included.
- The bar ends are assumed able to warp.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check square drive shafts and flat bars in torsion
- Compare a flat bar with a round shaft
- Estimate twist of a torsion arm
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Maximum shear stress (mid-point of the long side)
- Torsional constant K
- Angle of twist
Interpreting the result
- A rectangular section is much less stiff in torsion than a round or closed tube of the same area.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 295–303. Topic reference; no source tables or recommended settings are reproduced.
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