Bar cutting plan
Enter the part lengths and quantities — the plan lays them out on stock bars, collapses identical bars into one row and shows how many bars to order and how much really goes to scrap. It downloads as a table and goes straight to the saw.
Short answer
The offcut does not depend on how much steel you need but on how the lengths fall on a bar. Six 2400 mm parts out of six-metre bars leave 20 % waste; the same 2400s paired with an 1190 leave almost none (with a 3 mm saw kerf). That is why an allowance percentage is guesswork and a cutting plan is arithmetic: the calculator lays the parts out on bars and tells you how many bars to buy and how much really goes to scrap.
| No. | Part length, mm | Quantity |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
How the layout is worked out
Fitting parts into stock bars is the bin packing problem, and it has no exact solution: trying every arrangement of forty parts will not finish in any useful time. So the plan uses First Fit Decreasing — the parts are sorted longest first and each goes into the first bar it fits.
The order is not a formality. Long parts go down first so that short ones can fill the remainders afterwards; laid out in the order you typed them, the same list takes noticeably more bars. One kerf is allowed for every part cut off — three millimetres across forty parts is twelve centimetres: not decisive, but not nothing either.
Finished bars are collapsed by identical layout, which is how a cutting card is written in a shop: “six bars, cut like this”, not six identical rows one under another.
The optimum: FFD gives a good plan, not the best one. A usable remnant: a 1.7 m offcut is counted as waste because the plan cannot know whether it goes in the corner or into the next job — and that is the foreman’s call, not the arithmetic’s. And a single stock length: if the yard carries both six- and twelve-metre bars, run both and compare.
What to do with the result
First, replace the percentage. The bill of materials takes an allowance blind, 5 % by default; here you get the real figure, and it is worth carrying back to where the mass and the cost are worked out.
Second, hand the card to the saw as it stands. A line reading “2 × 2400 + 1 × 1190” can be measured off without recalculating, and the bar count in the next column says how many times to repeat it.
First Fit Decreasing in plain words
Picture a pile of parts and an empty rack for bars. The algorithm does three things:
- Sorts the parts from longest to shortest. The order you typed them in does not matter.
- Takes the next part and tries it against the bars in turn, starting with the first. It goes into the first bar with room for the part plus the kerf.
- If it fits nowhere — a new bar is started.
That is all. It does not try every combination, so it answers instantly even for dozens of parts. The price is that the result can be a little worse than the best possible, but it has a guaranteed upper bound (see the questions below), and “longest first” is exactly what an experienced saw operator does by eye.
Worked example: why the order matters
Bar 6000 mm, kerf 3 mm. Parts: 4 × 3200, 6 × 1300, 2 × 500 — 21.60 m in total.
| Method | Layout | Bars | Waste |
|---|---|---|---|
| FFD (longest first) | 3 bars: 3200 + 2 × 1300 (191 mm left); 1 bar: 3200 + 2 × 500 (1791 mm left) | 4 | 2400 mm, 10.0 % |
| Shortest first | 2 × 500 + 3 × 1300; 3 × 1300; then each 3200 on a bar of its own | 6 | 14 400 mm, 40.0 % |
Step by step for FFD: the first 3200 goes into bar 1 (2797 mm left), the second does not fit beside it — new bar, four times over. Then the 1300s: one fits into bar 1 (2797 ≥ 1303), so does a second (191 mm left), the third goes into bar 2, and so on. Finally the two 500s go into bar 4, the only one with room. In the reverse order the short parts take the start of the bars and every 3200 needs its own — two more bars for the same list.
How to read the plan
The line “3200 + 2 × 1300” with the number 3 means: cut three bars the same way — one 3200 part and two 1300s. The “Used” column is the length of the parts with kerfs (5809 mm), “Left” is what remains at the end of the bar (191 mm). The summary gives the net length needed, the length bought (bars × bar length), and the waste in millimetres and per cent. That percentage is what goes into the bill of materials instead of the default 5 %.
The plan counts the 1791 mm offcut as waste, but in the shop it is often perfectly good stock for short parts on the next job. Mark it with chalk and rack it — then the real waste will be closer to the sum of the small offcuts than to the figure on the plan.
How to cut waste
- Check whether a part exceeds half a bar by a few millimetres. 3000 mm with kerf is two bars, 2997 mm is one.
- Work out both bar lengths. With long parts 12 m often wins, with short ones not necessarily (see the questions).
- Combine jobs on the same section. Short parts from another item fill the offcuts — FFD does this by itself if you enter them together.
- Enter the real kerf. A band saw and a cut-off saw take different amounts; 3 mm is a default, not a standard.
Section masses for costing are in the steel section weight table or the metal weight calculator, and the welds on the same item are counted by the weld schedule.
Common mistakes
- Drawing dimension instead of cut length. If a part has mitred ends or overlaps, its cut length differs from its centreline dimension.
- Different sections on one plan. The plan does not know it is another material.
- Kerf set to 0. The plan will show a layout that cannot be cut.
- A part longer than the bar. The plan skips it and lists it separately — it has to be spliced by welding or a longer bar ordered.
Frequently asked questions
Why is this not the optimal cutting plan?
Because there is nothing to find the optimum with: bin packing is NP-hard, and an exhaustive search over a real parts list does not terminate. FFD guarantees a result no worse than 11/9 of the best plus one bar — in practice usually a difference of one bar, and in exchange the plan can be read by eye and reproduced with a tape.
Why are the long parts placed first?
Because a short part can always be tucked in somewhere, and a long one cannot. Start with the short ones and they take up the starts of the bars, leaving the long parts to open new ones. “Longest first” is not decoration on the method; it is the method.
Why is the remainder of a bar counted as waste?
Because the plan does not know your yard. A 1.7 m offcut is rarely thrown away in a real shop; it is put aside for the next job, and then the actual waste is lower than the calculation. But that call belongs to the person who can see what is stacked in the corner, not to a calculator.
How much does the kerf matter?
Less than people expect, but not so little that it can be dropped. Three millimetres across forty parts is twelve centimetres — a quarter of an average part. One kerf is allowed per part cut off; if your blade is thicker, change the figure in the field.
Why don’t two 3000 mm parts fit into a 6000 mm bar?
Because the plan adds a kerf to every part: 3000 + 3 and again 3000 + 3 make 6006 mm. The shop floor is the same — the bar end has to be squared and the bar cut in half, and the saw takes metal. If the drawing allows it, a 2997 mm part fits twice with nothing left over.
Do 12 m bars waste less than 6 m bars?
Not always. For the default parts list the plan gives three 6 m bars and 18.3 % waste, and with 12 m bars two bars and 38.8 %, because the second one is almost empty. A longer bar pays when the offcut goes into another job or when the parts are long.
Can I enter parts of different sections on one plan?
No — one plan is one section and one bar length. An angle and a channel will not go into the same bar, but the plan would lay them out that way. Make a separate plan for each section in the bill of materials.
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