BIZOMAT MAKEOS · Mechanics
Plate Lift Plan (Shape Area, Mass, Centre of Gravity, Two-Point Lift Loads)
For a flat plate of any straight-sided shape lifted from two points, what does it weigh, where is its centre of gravity, and how much load does each lift point take?
Lift plan for a cut plate or flat panel: the area, perimeter and centroid of the outline from its corner coordinates (as the polygon area tool), the mass from thickness and density, and the load on each of two lift points from where the centre of gravity falls along the line joining them, with the sideways offset that makes the plate hang tilted, against the working load limit of each lift point.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of corners | corners | Number of corners of the outline (the first n are used, in order round the shape). |
| Corner 1 | ||
| X | mm | X of corner 1. |
| Y | mm | Y of corner 1. |
| Corner 2 | ||
| X | mm | X of corner 2. |
| Y | mm | Y of corner 2. |
| Corner 3 | ||
| X | mm | X of corner 3. |
| Y | mm | Y of corner 3. |
| Corner 4 | ||
| X | mm | X of corner 4. |
| Y | mm | Y of corner 4. |
| Corner 5 | ||
| X | mm | X of corner 5. |
| Y | mm | Y of corner 5. |
| Corner 6 | ||
| X | mm | X of corner 6. |
| Y | mm | Y of corner 6. |
| Corner 7 | ||
| X | mm | X of corner 7. |
| Y | mm | Y of corner 7. |
| Corner 8 | ||
| X | mm | X of corner 8. |
| Y | mm | Y of corner 8. |
| Plate and lift points | ||
| Plate thickness | mm | Thickness of the plate. |
| Density | kg/m³ | Density of the plate material (7850 for steel). |
| Lift point A X | mm | X of lift point A. |
| Lift point A Y | mm | Y of lift point A. |
| Lift point B X | mm | X of lift point B. |
| Lift point B Y | mm | Y of lift point B. |
| Working load limit of each lift point | kN | Rated load of each lug, shackle or clamp. |
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: Number of corners
- What it is
- How many corners the plate outline has. The first this many corner pairs are joined in order, and the last corner joins back to the first; later corners are ignored.
- Units and format
- Enter a number in corners: corners. The form accepts 3 corners to 8 corners. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 corners as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the corners in order round the outline; jumping across the shape gives a wrong area and centre of gravity.
Corner 1
What this means: X
- What it is
- The X coordinate of the first corner of the plate outline, measured from any datum you choose on the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Use the same datum and axes for every corner and for both lift points.
What this means: Y
- What it is
- The Y coordinate of the first corner of the plate outline, measured at right angles to X from the same datum.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Use the same datum and axes for every corner and for both lift points.
Corner 2
What this means: X
- What it is
- The X coordinate of the second corner, the next corner round the outline after corner 1.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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.
- Get it right
- Keep going round the outline in one direction.
What this means: Y
- What it is
- The Y coordinate of the second corner, the next corner round the outline after corner 1.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Keep going round the outline in one direction.
Corner 3
What this means: X
- What it is
- The X coordinate of the third corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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.
- Get it right
- Keep going round the outline in one direction.
What this means: Y
- What it is
- The Y coordinate of the third corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep going round the outline in one direction.
Corner 4
What this means: X
- What it is
- The X coordinate of the fourth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of corners is less than 4.
What this means: Y
- What it is
- The Y coordinate of the fourth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1800 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of corners is less than 4.
Corner 5
What this means: X
- What it is
- The X coordinate of the fifth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Ignored when the number of corners is less than 5.
What this means: Y
- What it is
- The Y coordinate of the fifth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the number of corners is less than 5.
Corner 6
What this means: X
- What it is
- The X coordinate of the sixth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Ignored when the number of corners is less than 6.
What this means: Y
- What it is
- The Y coordinate of the sixth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Ignored when the number of corners is less than 6.
Corner 7
What this means: X
- What it is
- The X coordinate of the seventh corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Ignored when the number of corners is less than 7.
What this means: Y
- What it is
- The Y coordinate of the seventh corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Ignored when the number of corners is less than 7.
Corner 8
What this means: X
- What it is
- The X coordinate of the eighth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Ignored when the number of corners is less than 8.
What this means: Y
- What it is
- The Y coordinate of the eighth corner round the outline.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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
- Ignored when the number of corners is less than 8.
Plate and lift points
What this means: Plate thickness
- What it is
- The thickness of the plate or panel, taken as uniform over the whole outline. Mass is area times thickness times density.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass and both lift point loads rise in direct proportion to thickness.
- Get it right
- Holes and cut-outs are not deducted; the outline is treated as solid.
What this means: Density
- What it is
- The density of the plate material, from the material data sheet. It turns the plate volume into mass.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass and both lift point loads rise in direct proportion to density.
- Get it right
- Enter it in kg/m³; a value in g/cm³ must be multiplied by 1000.
What this means: Lift point A X
- What it is
- The X coordinate of lift point A, such as a lug, clamp or eye, using the same datum as the corners.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure to the point where the sling actually attaches, not to the edge of the lug plate.
What this means: Lift point A Y
- What it is
- The Y coordinate of lift point A, using the same datum as the corners.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure to the point where the sling actually attaches.
What this means: Lift point B X
- What it is
- The X coordinate of lift point B, the second lug, clamp or eye, using the same datum as the corners.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1900 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A and B must be at different positions, or the tool rejects the inputs.
What this means: Lift point B Y
- What it is
- The Y coordinate of lift point B, using the same datum as the corners.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure to the point where the sling actually attaches.
What this means: Working load limit of each lift point
- What it is
- The rated working load limit of each lift point (the lug, shackle or plate clamp), from its marking or certificate. The load at A and at B is compared with it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in kN; a rating marked in tonnes must be converted. Sling angle effects are not included.
Method and formulas
- Shoelace area and centroid from the corners (as the polygon area tool).
- Mass = area × thickness × density; weight = mass × g.
- Share at B = projection of the CG along A→B ÷ |AB|; A takes the rest; the perpendicular offset of the CG from AB is how far the plate swings to hang.
- Example: the plate weighs 565.2 kg with its CG at X 1,200, Y 760; A takes 2.4249 kN and B 3.1178 kN.
Limitations
- Flat plate of uniform thickness without holes; subtract cut-outs as separate shapes.
- Vertical lift from both points; inclined slings add load and need the sling tools.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan a lift of a profile-cut plate
- Place lifting lugs so the load shares evenly
- Check shackle and lug ratings on a panel lift
Who it is for
- Riggers
- Fabrication supervisors
- Lifting engineers
What you get
- Area, perimeter and centre of gravity
- Mass and weight
- Load on each lift point and the hang offset
Interpreting the result
- With only two lift points the plate always hangs with its CG under the line between them; a large offset means it hangs steeply tilted.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 40–48, 66–76, 221–227. 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
Lifting magnets
In Magnetic Workholding by the Numbers
What it covers: Plan a lift with lifting magnets: rated loads and their conditions, derating for thickness, surface and material, plate mass and centre of gravity, lifting beams, plate flex and safe use.
BIZOMAT 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 Plate Lift Plan (Shape Area, Mass, Centre of Gravity, Two-Point Lift Loads) calculator