KEVOS® MAKEOS · Strength
Crane Hook Design (Curved-Beam Stress, Proof Load and Shank)
Is this lifting hook strong enough at its working load and proof load, allowing for the curvature, and is the threaded shank strong enough?
Check of a hook or curved lifting member with a rectangular critical section: inner and outer fibre stresses by the curved-beam (Winkler–Bach) method at the working load limit (as the curved beam tool), the same stress at the proof load against yield, the straight-beam stress for comparison, and the tensile stress in the threaded shank at the thread stress area.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Working load limit | kN | Rated working load of the hook. |
| Proof load ÷ working load | Proof test load as a multiple of the working load (from the lifting standard you follow). | |
| Inner radius of the throat | mm | Radius from the centre of curvature to the inside of the critical section. |
| Section depth (radial) | mm | Radial depth of the critical section. |
| Section width | mm | Width of the critical section (a rectangle approximates the real trapezoid). |
| Allowable stress at the working load | MPa | Allowable stress at the working load (your design value). |
| Yield strength | MPa | Yield strength; the proof load must not exceed it. |
| Shank thread diameter | mm | Nominal diameter of the shank thread. |
| Shank thread pitch | mm | Pitch of the shank thread. |
| Allowable shank tensile stress | MPa | Allowable tensile stress in the shank thread (your design value). |
Method and formulas
- Neutral axis r_n = h ÷ ln(r_o ÷ r_i); eccentricity e = r_c − r_n; moment M = P r_c (as the curved beam tool).
- Inner fibre σ_i = P ÷ A + M (r_n − r_i) ÷ (A e r_i); outer σ_o = P ÷ A − M (r_o − r_n) ÷ (A e r_o).
- Proof check: σ_i at the proof load against S_y.
- Shank: σ = W ÷ A_s, A_s = π ÷ 4 (d − 0.9382p)².
- Example: 20 kN gives 120.76 MPa at the throat (1.4098× the straight-beam bending), 241.53 MPa at proof, and 35.677 MPa in the shank.
Limitations
- Rectangular section approximation; the trapezoidal hook section has a different neutral axis.
- Hooks must be rated and proof tested to the applicable lifting standard.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a fabricated or forged hook for a load rating
- Compare a curved member with straight-beam theory
- Check the shank thread of a hook
Who it is for
- Design engineers
- Rigging supervisors
- Structural engineers
What you get
- Curved-beam stresses at the working load
- Inner fibre stress at the proof load
- Shank thread stress
Interpreting the result
- Curvature concentrates stress on the inside of the throat: the straight-beam formula would underestimate it.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 274–276, 1521–1535. Topic reference; no source tables or recommended settings are reproduced.
WORKOS 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.
Open the Crane Hook Design (Curved-Beam Stress, Proof Load and Shank) calculator
