BIZOMAT MAKEOS · Fabrication
Segmented Flange Ring Plan (Segment Size, Plate Fit, Yield, Welds)
If I make this large flange ring from segments cut out of plate, how big is each segment’s rectangle, will it fit my plate, and how much plate is wasted?
Plan for a large flat ring (flange, stiffener or base ring) welded from equal segments cut from plate: the area of each ring-sector segment (as the plane area tool for a ring sector), the bounding rectangle each segment needs (chord of the outside edge by the width from the outside edge to the inside chord), whether it fits the plate size, material yield, ring mass and the length of butt welds, checked against the plate size and your least yield.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Ring outside diameter | mm | Outside diameter of the finished ring. |
| Ring inside diameter | mm | Inside diameter of the finished ring. |
| Number of segments | Number of equal segments welded together. | |
| Plate thickness | mm | Thickness of the plate. |
| Density | kg/m³ | Density of the plate. |
| Cutting allowance around each segment | mm | Extra added around each segment for cutting. |
| Plate and limits | ||
| Plate width | mm | Width of the plate available. |
| Plate length | mm | Length of the plate available. |
| Least yield of a segment rectangle | % | Least share of each rectangle used by its segment. |
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: Ring outside diameter
- What it is
- The outside diameter of the finished flat ring after welding the segments together.
- 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 3000 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 outside diameter makes each segment longer and wider and raises ring mass.
- Get it right
- Enter the finished size; the cutting allowance is entered separately.
What this means: Ring inside diameter
- What it is
- The inside diameter of the finished ring.
- 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 2600 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 inside diameter narrows the ring, lowering segment area and ring mass.
- Get it right
- It must be smaller than the outside diameter.
What this means: Number of segments
- What it is
- The number of equal ring segments welded together to make the full ring.
- Units and format
- Enter a plain number with no unit. The form accepts 2 to 72. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More segments shorten each rectangle and add butt weld length in proportion.
- Get it right
- More segments fit narrower plate but add butt welds.
What this means: Plate thickness
- What it is
- The thickness of the plate the segments are cut from, equal to the ring thickness.
- 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 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Ring mass rises in direct proportion to thickness.
What this means: Density
- What it is
- The density of the plate material, used to work out the ring mass.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 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
- Ring mass rises in direct proportion to density.
What this means: Cutting allowance around each segment
- What it is
- The extra added to both the length and the width of each segment’s rectangle for cutting kerf and edge clearance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 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 allowance enlarges each rectangle and lowers yield.
- Get it right
- It is added once to each dimension of the rectangle, not to every edge.
Plate and limits
What this means: Plate width
- What it is
- The width of the plate you have or can buy for cutting the segments.
- 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 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the usable width after any edge trim.
What this means: Plate length
- What it is
- The length of the plate you have or can buy for cutting the segments.
- 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 6000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the usable length after any end trim.
What this means: Least yield of a segment rectangle
- What it is
- The smallest share of each segment’s bounding rectangle that the segment itself must use for the plan to be acceptable.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself (50 for 50 %).
Method and formulas
- Segment area = (R² − r²) θ ÷ 2 with θ = 360° ÷ n (as the plane area tool for a ring sector).
- Rectangle length = 2R sin(θ ÷ 2) + allowance; width = R − r cos(θ ÷ 2) + allowance.
- Yield = segment area ÷ rectangle area; ring mass = n × area × thickness × density; welds = n × (R − r).
- Example: each of 6 segments needs 1,510 × 384.17 mm (50.546% yield); the ring weighs 276.21 kg with 1.2 m of butt weld.
Limitations
- Rectangles nested one per space; staggering segments head-to-tail on the plate improves yield.
- Weld shrinkage and machining allowance on the faces are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan a large flange or base ring from plate
- Choose the number of segments for a plate size
- Estimate plate and welding for a ring
Who it is for
- Boilermakers
- Fabrication supervisors
- Estimators
What you get
- Segment area and bounding rectangle
- Plate fit and yield
- Ring mass and butt weld length
Interpreting the result
- More segments improve yield and fit smaller plate, but add welds: balance plate cost against welding.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 66–81. Topic reference; no source tables or recommended settings are reproduced.
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Open the Segmented Flange Ring Plan (Segment Size, Plate Fit, Yield, Welds) calculator