BIZOMAT MAKEOS · Mechanics
Two-Point Lift with an Off-Centre Load (Centre of Gravity, Leg Loads, Angles)
Where is the centre of gravity of this combined load, how is the weight shared between the two lifting points, and what does each sling leg carry at its angle?
Planning check for lifting a load made of several items from two lifting points on a line: combined mass and centre of gravity along the line (as the combined centre of gravity tool), the share of weight at each lifting point by moments, the sling leg angles and tensions with the hook placed above the centre of gravity at a given height, leg lengths, and checks of leg load against the working load limit and leg angle against your limit (for a central load the leg tensions match the sling tension tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Items (position along the lifting line) | ||
| Item 1 mass | kg | Mass of item 1 (0 if not used). |
| Item 1 centre position | mm | Position of item 1’s centre of gravity along the line of the lifting points. |
| Item 2 mass | kg | Mass of item 2 (0 if not used). |
| Item 2 centre position | mm | Position of item 2’s centre of gravity along the line of the lifting points. |
| Item 3 mass | kg | Mass of item 3 (0 if not used). |
| Item 3 centre position | mm | Position of item 3’s centre of gravity along the line of the lifting points. |
| Rigging | ||
| Lifting point A position | mm | Position of the first lifting point. |
| Lifting point B position | mm | Position of the second lifting point. |
| Hook height above the lifting points | mm | Height of the hook above the lifting points (sets the sling angles). |
| Working load limit per leg | kg | Working load limit of each sling leg at its rating (your value; reduce for the hitch type). |
| Largest leg angle from vertical | ° | Largest leg angle from vertical your lifting procedure allows. |
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.
Items (position along the lifting line)
What this means: Item 1 mass
- What it is
- The mass of one item that makes up the combined load; zero leaves the item out.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Item 1 centre position
- What it is
- Where this item’s centre of gravity lies along the line through the two lifting points, measured from a datum you choose.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure every position, including both lifting points, from the same datum.
What this means: Item 2 mass
- What it is
- The mass of one item that makes up the combined load; zero leaves the item out.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 450 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Item 2 centre position
- What it is
- Where this item’s centre of gravity lies along the line through the two lifting points, measured from a datum you choose.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure every position, including both lifting points, from the same datum.
What this means: Item 3 mass
- What it is
- The mass of one item that makes up the combined load; zero leaves the item out.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Item 3 centre position
- What it is
- Where this item’s centre of gravity lies along the line through the two lifting points, measured from a datum you choose.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure every position, including both lifting points, from the same datum.
Rigging
What this means: Lifting point A position
- What it is
- The position of the first lifting point along the same line, measured from the same datum as the items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Lifting point B position
- What it is
- The position of the second lifting point; it must lie further along the line than lifting point A.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The combined centre of gravity must fall between A and B or the load will tip.
What this means: Hook height above the lifting points
- What it is
- The vertical height of the crane hook above the lifting points, with the hook assumed directly over the combined centre of gravity.
- 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 1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher hook makes the legs steeper, lowering the leg angles and tensions.
What this means: Working load limit per leg
- What it is
- The working load limit of each sling leg for the way it is used, from its tag or certificate.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Reduce it for the hitch type as your rigging tables require; leg tension is compared with it in kg.
What this means: Largest leg angle from vertical
- What it is
- The largest angle between a sling leg and the vertical that your lifting procedure allows.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 60°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measured from the vertical, not from the horizontal.
Method and formulas
- Centre of gravity X = Σ m x ÷ Σ m (as the combined centre of gravity tool).
- Point loads by moments: R_A = W (x_B − X) ÷ (x_B − x_A), R_B = W − R_A.
- With the hook vertically above X at height h: leg angle θ = tan⁻¹(|X − x| ÷ h); leg tension = R ÷ cos θ; leg length = √[(X − x)² + h²].
- Example: the centre of gravity is 615.38 mm along; leg A carries 1,459.2 kg at 22.306° and leg B 816.54 kg at 42.709°.
Limitations
- Rigid load and planar geometry; a third dimension or a flexible load needs a full lift plan.
- Dynamic factors for the crane and the load are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan a lift of an assembly with an off-centre heavy part
- Choose sling lengths so the load hangs level
- Check each leg against its rating
Who it is for
- Rigging supervisors
- Lifting engineers
- Maintenance planners
What you get
- Combined mass and centre of gravity
- Weight at each lifting point
- Leg angles, tensions and lengths with checks
Interpreting the result
- The leg nearer the centre of gravity carries more and hangs more vertical; the far leg is longer and more inclined.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2613–2650, 221–227. Topic reference; no source tables or recommended settings are reproduced.
- AS 3775 and AS 1418 series, or your national lifting standards
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Open the Two-Point Lift with an Off-Centre Load (Centre of Gravity, Leg Loads, Angles) calculator