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Cutting

Cutting list: stock lengths needed (first-fit decreasing, with saw kerf)

Lc=n1L1+n2L2+n3L3Nmin=⌈LcS⌉Wst=NS−LcU=LcNS×100
where
Lc
total length of cuts (mm)
n1,n2,n3
quantities of each cut length
L1,L2,L3
cut lengths (mm)
Nmin
theoretical minimum stock lengths, ignoring kerf
S
stock length (mm)
Wst
offcut and kerf waste (mm)
N
stock lengths needed, from first-fit decreasing with saw kerf
U
material utilisation (%)
Explain this equation

Works out how many stock lengths to order for a cutting list, by packing the cuts into bars the way you would on the saw.

N comes from a packing routine rather than a single formula: cuts are sorted longest first and each goes into the first bar with room for it plus a saw kerf. L_c is the total of all the cuts. Dividing by the stock length and rounding up gives the theoretical least, ignoring kerf and awkward leftovers. Waste is the stock bought minus the steel used, and utilisation is used over bought.

Longest-first packing usually gets within a bar of the best possible arrangement.

Sense check: six at 1850, five at 1200 and four at 650 total 19,700 mm, so at least 4 bars of 6 m.

Watch out: allow for squaring the ends and any damaged ends on the stock. Keep useful offcuts for the next job.

How many stock lengths of bar, tube or section to order for a list of cuts, using the first-fit decreasing method and allowing for the saw kerf between pieces.

pieces
pieces
pieces

Enter your values to see the result.

Good to know

The pieces are sorted longest first and each is put in the first stock length it still fits, otherwise a new length is started. A kerf is allowed between neighbouring pieces in a bar. First-fit decreasing is a well-proven method that is never more than about 22% worse than the best possible plan and is usually optimal for short lists. Set unused lines to quantity 0. Allow for squaring a rough mill end by reducing the stock length (e.g. 6000 → 5980).

Common mistake

Ordering by total length alone (the theoretical minimum). Long pieces cannot share bars, so the real number of lengths is often higher. Merchants' "6 m" lengths can also be a little short or long; measure before cutting.

Limits

Up to three different cut lengths. Not a guaranteed optimum. Ignores mitre cuts (add the extra length to the cut length) and the minimum offcut a saw can clamp.

Sources

Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the welding procedure specification (WPS), BS EN ISO 15614/9606, BS EN 1090, BS EN 1993 and manufacturers’ data. Structural welds need qualified welders and engineered designs.

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