KEVOS® MAKEOS · Strength
Curved Beam and Hook Stress
What are the inner and outer fibre stresses in this curved beam or hook section?
Stresses at the inner and outer fibres of a curved rectangular section (crane hook, C-frame, ring) by the Winkler–Bach theory, with the straight-beam comparison.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load (line of action through the centre of curvature) | N | Load pulling the section apart, acting along a line through the centre of curvature (as on a hook). |
| Inner radius | mm | Radius from the centre of curvature to the inside face. |
| Section depth (radial) | mm | Radial depth of the rectangular section. |
| Section width | mm | Width of the section. |
| Allowable stress | MPa | Allowable stress from your design code or lifting standard. |
Method and formulas
- ro = ri + h; centroid radius rc = ri + h/2; neutral radius rn = h ÷ ln(ro/ri); e = rc − rn.
- Moment M = P rc. Inner σ = P/A + M(rn − ri) ÷ (A e ri); outer σ = P/A − M(ro − rn) ÷ (A e ro).
- Straight beam: σ = P/A ± 6M ÷ (b h²).
- Example: 20000 N on the default hook section gives 120.76 MPa at the inner fibre against 88.889 MPa by straight-beam theory.
Limitations
- Rectangular section; hooks with trapezoidal or round sections need their own section integrals.
- Elastic theory; lifting hooks must follow their standard and proof testing.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check hooks, clamp frames and C-frame presses
- See how curvature raises inner-fibre stress
- Size a curved bracket
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Inner fibre stress
- Outer fibre stress
- Neutral axis shift
- Straight-beam stress and curvature factor
Interpreting the result
- The inner fibre governs: curvature raises its stress above the straight-beam value.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 212–218, 257–260. Topic reference; no source tables or recommended settings are reproduced.
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