BIZOMAT MAKEOS · Mechanics
Shear Legs (A-Frame) Check (Geometry, Leg Force, Foot Thrust, Buckling)
For a pair of shear legs (an A-frame) lifting this load, what is the head height and leg angle, what force does each leg carry, how hard do the feet push apart, and will the tube legs buckle?
Check of shear legs or an A-frame of two equal legs with the load hung from the apex: the triangle of legs and foot spread, apex angle and head height (as the triangle solver tool), the compression in each leg and the outward thrust at each foot, and Euler or Johnson buckling of each round-tube leg (as the column buckling tool), checked against your factor of safety and the foot tie or anchor capacity.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Leg length (foot to head) | mm | Length of each leg from foot to the head pin. |
| Spread between the feet | mm | Distance between the two feet. |
| Load at the head (with hook block) | kN | Load hung from the head, including the hook block and slings. |
| Leg tube | ||
| Tube outside diameter | mm | Outside diameter of the tube legs. |
| Wall thickness | mm | Wall thickness of the legs. |
| Elastic modulus | GPa | Elastic modulus. |
| Yield strength | MPa | Yield strength of the tube. |
| Effective length factor | Effective length factor for the leg ends (1 for pinned). | |
| Required safety factor on buckling | Factor against buckling you need. | |
| Foot tie or anchor capacity | kN | Capacity of the tie between the feet, or of each foot anchor against sliding outwards. |
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: Leg length (foot to head)
- What it is
- The length of each of the two equal legs, from the foot to the pin at the head where the load hangs.
- 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 4000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer legs raise the head and lower the leg angle, but increase slenderness and reduce the buckling load.
- Get it right
- Measure from the foot bearing point to the head pin centre, not the overall tube length.
What this means: Spread between the feet
- What it is
- The distance between the two feet of the shear legs, measured along the ground between the bearing points.
- 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 2400 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 spread increases the leg angle, so both the leg force and the outward foot thrust rise.
- Get it right
- It must be less than twice the leg length.
What this means: Load at the head (with hook block)
- What it is
- The total load hung from the head: the lifted item plus the hook block, slings and shackles.
- 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 10 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Leg force and foot thrust rise in direct proportion to the load.
- Get it right
- Enter kilonewtons, not kilograms (1 tonne weighs about 9.81 kN), and include all rigging below the head.
Leg tube
What this means: Tube outside diameter
- What it is
- The outside diameter of the round tube used for each leg.
- 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 76.1 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 tube raises the radius of gyration and the buckling load strongly.
- Get it right
- Use the actual tube outside diameter from the tube standard, not the nominal bore size.
What this means: Wall thickness
- What it is
- The wall thickness of each leg tube.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker wall adds section area and raises the buckling load.
- Get it right
- Use the minimum wall thickness allowing for any corrosion; twice the wall must be less than the outside diameter.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the leg material, used in the Euler and Johnson buckling formulas.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For slender legs (Euler range) the buckling load rises in direct proportion to the modulus.
- Get it right
- Enter gigapascals, not megapascals.
What this means: Yield strength
- What it is
- The yield strength of the leg tube material, from the tube standard or mill certificate, used in the Johnson formula for stockier legs.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It raises the buckling load of short legs; slender legs in the Euler range are not affected.
- Get it right
- Use the minimum specified yield strength for the tube grade.
What this means: Effective length factor
- What it is
- The effective length factor for the leg ends, which converts the leg length to its buckling length.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger factor increases slenderness and lowers the buckling load.
- Get it right
- Choose it for the real end fixity from your structural code; pinned feet and head pin give 1.
What this means: Required safety factor on buckling
- What it is
- The factor of safety against leg buckling that your lifting standard, code or company rule requires.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the standard that applies to the lift; it is compared with buckling load ÷ leg force.
What this means: Foot tie or anchor capacity
- What it is
- The capacity of the tie joining the two feet, or of each foot anchor, to resist the outward thrust that tries to spread the feet.
- 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 5 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter kilonewtons; it is compared with the thrust at each foot, so check the anchor or tie and its connections.
Method and formulas
- Triangle with sides L, L and s: apex angle and base angles by the law of cosines (as the triangle solver tool); head height = √(L² − (s ÷ 2)²).
- Each leg carries W ÷ (2 cos θ) with θ the half apex angle; thrust at each foot = W tan θ ÷ 2.
- Leg buckling by Euler or Johnson for the tube section (as the column buckling tool).
- Example: the head stands 3,815.8 mm high; each leg carries 5.2414 kN and the feet push out with 1.5724 kN; buckling factor 13.9.
Limitations
- Load hung centrally at the apex in the plane of the legs; shear legs also need back guys against falling over.
- Pinned leg ends; foot slipping and ground bearing are checked separately.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check improvised lifting shear legs
- Size the tube for an A-frame hoist
- Find the foot tie force
Who it is for
- Riggers
- Maintenance engineers
- Lifting supervisors
What you get
- Apex angle, leg angle and head height
- Leg force and foot thrust
- Leg buckling factor
Interpreting the result
- Spreading the feet wider lowers the head and raises both the leg force and the foot thrust.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 95–102, 281–287. 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
Temporary frames and shear legs
What it covers: Buckling and stability of temporary lifting frames: leg forces, foot thrust and leg buckling of shear legs, why an A-frame has no stiffness out of its plane, and a lift that swung.
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Open the Shear Legs (A-Frame) Check (Geometry, Leg Force, Foot Thrust, Buckling) calculator