BIZOMAT 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). |
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: Working load limit
- What it is
- The rated load the hook is designed to lift in service, acting along the line through the centre of curvature of the throat.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All the stresses rise in direct proportion to the load.
- Get it right
- Enter kN, not tonnes: 1 tonne of mass weighs about 9.81 kN.
What this means: Proof load ÷ working load
- What it is
- The proof test load divided by the working load. The inner stress at the proof load is checked against yield.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger multiple raises the stress at the proof load in direct proportion.
- Get it right
- Take the multiple from the lifting standard you follow.
What this means: Inner radius of the throat
- What it is
- The radius from the centre of curvature of the hook throat to the inside edge of the critical section, where the load sits.
- 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.
- Effect on the result
- A tighter inner radius raises the inner fibre stress.
- Get it right
- This is a radius from the centre of the curve, not the throat opening width.
What this means: Section depth (radial)
- What it is
- The depth of the critical section measured radially, from the inside edge of the throat to the outside of the hook.
- 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 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A deeper section lowers the stresses strongly.
- Get it right
- Measure along the radius through the deepest part of the bend, usually directly below the load.
What this means: Section width
- What it is
- The width of the critical section across the hook, at right angles to the plane of the curve. The tool treats the section as a 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 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider section lowers the stresses in direct proportion.
- Get it right
- Real hooks are trapezoidal; using the widest part overstates the strength, so use an average width or check with the true shape.
What this means: Allowable stress at the working load
- What it is
- The highest inner fibre stress you accept at the working load, your design value for the hook material.
- 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 200 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Base it on the material and the safety margin the lifting standard requires.
What this means: Yield strength
- What it is
- The yield strength of the hook material. The inner fibre stress at the proof load must stay below it.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 350 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the yield strength for the heat-treated condition of the finished hook.
What this means: Shank thread diameter
- What it is
- The nominal diameter of the thread on the hook shank that carries the load into the nut or block.
- 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 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger thread lowers the shank stress.
- Get it right
- Use the nominal thread size; the tool works out the stress area from it and the pitch.
What this means: Shank thread pitch
- What it is
- The pitch of the shank thread, used with the nominal diameter to find the tensile stress area.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For an inch thread, pitch = 25.4 ÷ threads per inch.
What this means: Allowable shank tensile stress
- What it is
- The tensile stress you allow in the shank thread at the working load, your design value.
- 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 120 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Allow for the stress concentration at the thread root in your choice.
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.
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Open the Crane Hook Design (Curved-Beam Stress, Proof Load and Shank) calculator