Stair stringer

The surface is developable and the flat pattern is solved in closed form. Cut the part to the drawing and it fits — the whole uncertainty sits in the K-factor, which belongs to the material and the machine, not to the geometry.

Dimensions are entered as: Outside dimensions. The flat pattern itself is always computed on the neutral fibre — at Ø800 in 3 mm sheet the difference between the inside and the outside dimension is 18.8 mm of developed width, and then the seam does not meet.

En lige trappe hvor hvert trin er en kasse, der forskydes både opad og fremad. Selve plade-arbejdet er trinfladerne — ens flade rektangler, ét pr. trin.

Lige stål-trapper, lejder- og platformstrapper. Trinfladerne skæres som ens rektangler og monteres på vanger eller kantede sider med fast stigning og fremspring.

Smed — lige stål-, lejder- og platformstrapper.

Konstruktionsstål S235: vanger + rifleplade-/gittertrin. Bærende → EN 1090.

Source: Bærende stål: EN 1090 (smede-artikel i src/lib/skoler/indhold/data.ts + kilder.ts). Materialer/tykkelser: src/lib/kasse/materialer.ts (DIN 6935 for stål; massefylder og handelstykkelser; springback).

Antal trin — Number of steps

Hvor mange ens trinflader trappen har.

Bredde — Trinflade-bredde

Trinnets bredde på tværs af gangretningen (mm) — den lange side af trinflade-rektanglet.

Trin-højde — Trin-højde (stigning)

Hvor meget hvert trin stiger opad i forhold til det forrige (mm). Samlet stigning = antal × trin-højde.

Trin-dybde — Trin-dybde (grund)

Trinnets dybde i gangretningen (mm) — den korte side af trinflade-rektanglet. Samlet løbelængde = antal × trin-dybde.

Step by step with compass and square — in cardboard first, in sheet metal after.

1. 01Aftegn én trinflade som et rektangel: bredde × trin-dybde i 1:1.
2. 02Aftegn de øvrige ens trinflader (samme rektangel) — i alt 'antal trin' stykker, gerne lagt i et gitter på pladen.
3. 03Skær alle trinflade-rektangler ud langs konturen.
4. 04Sæt hvert trin op ad de bærende vanger, forskudt 'trin-højde' opad og 'trin-dybde' fremad i forhold til det forrige.
5. 05Kontrollér at alle trinflader er vandrette og i flugt, før de svejses/nittes fast.

Stigningsvinklen følger af trin-højde og trin-dybde (tan = højde ÷ dybde). Hold stigning og dybde konstante hele vejen op — ujævne trin er både ubehagelige og farlige at gå på.

• ·Bærende trapper er omfattet af EN 1090.
• ·BR18: stigning ≤ 180 mm, grund ≥ 250 mm (bolig) / 280 mm (kontor/institution) — hold samme stigning hele vejen.
• ·Trinfladerne er ens rektangler; illustration uden DXF-udfoldning.

The words and formulas the trade uses for a flat pattern. The symbols are the same throughout Discebo: α is the bend angle in degrees, R the inside bend radius, t the sheet thickness and K the K-factor — all in millimetres.

Flat pattern (development)

The part's surface laid out flat as one continuous cutting outline — the way the sheet looks BEFORE it is bent or rolled. Only a developable surface can be unfolded exactly; a doubly curved surface cannot be laid flat without stretching the material.

Flat length

The flat length the part must be cut to so the dimensions come out right once it is bent. It is either the sum of the outside dimensions minus the bend deductions, or the sum of the flat legs plus the bend allowances — both routes must give the same number.L = Σ(udvendige mål) − Σ(BD) = Σ(flade ben) + Σ(BA)

Bend allowance

The length of material that sits in the bend itself, measured along the neutral fibre. The bend allowance is always positive and is added to the flat legs.BA = (π/180) · α · (R + K · t)

Bend deduction

The amount subtracted from the sum of the outside dimensions, because the two outside dimensions between them count the corner twice. Here the bend deduction is taken as POSITIVE and subtracted; DIN 6935 writes the same quantity as the compensation value v with the opposite sign.BD = 2 · OSSB − BA

Outside setback

The distance from the theoretical outside corner point in to where the bend starts. Above 90°, tan(α/2) is clamped to at most 1 per DIN 6935, so the number does not explode towards 180°.OSSB = tan(α/2) · (R + t)

Compensation value v to DIN 6935

The standard's own way of writing the same corner loss: the flat length is a + b + v, where v is negative. Our bend deduction is therefore the same quantity with the opposite sign — never flip one without the other.L = a + b + v ⇒ v = −BD

K-factor

Where the neutral fibre sits in the sheet, given as a fraction of the sheet thickness. DIN 6935 writes the correction factor k, which applies to the neutral line in the form (R + t·k/2); the American CAD convention writes (R + K·t), so K = k/2.k = 0,65 + 0,5 · log₁₀(R/t), k ≤ 1,0 ⇒ K = k/2

Neutral fibre

The layer in the sheet that is neither stretched nor compressed when the part is bent. The flat pattern is always computed on the neutral fibre — which is why it matters whether the drawing's dimensions are inside or outside.

Bend angle

The angle the material is turned through, not the angle between the legs. The bend angle is 180° minus the included angle, so a square corner is 90° and a seam fold is 180°.α = 180° − åbningsvinklen

Inside bend radius

The radius on the inside of the bend. It is set by the tooling and the material, not by the drawing — too small a radius cracks the part in the outer fibre.

Sheet thickness

The thickness of the material. It enters every single bend allowance, so sheet delivered 0.2 mm thicker than ordered shifts the flat length at every bend.

Fold line

The line on the flat pattern where the part is to be bent. It is drawn but never cut through — in a laser file it therefore sits on its own layer.

Test bend

A strip of known raw length, bent in the material and the tooling that production will use. Measure the two outside legs afterwards and the bend deduction and K-factor can be worked back. The machine's own measured bend table beats any table.BD_målt = (A + B) − L₀

DIN 6935 covers only cold bending of flat products in structural steel. Stainless, aluminium, copper, brass and titanium zinc are not included — there the formulas are an extrapolation, and a test bend in the actual material settles it.

25 fields. The starting values belong to the figure itself — they live in one place in the code, so the tool, the share link and the smoke test can never disagree about what «default» means.

A preset sets every dimension at once. The name is often the word the part goes by in the workshop — the library's search knows them all.

Read them before the part is cut. They are here because they cannot be calculated away — not as legal text, but as craft.

• The figure draws GEOMETRY. Load capacity is NOT calculated: the stringer's bending and shear capacity, the remaining cross-section under the notches, deflection, vibrations and the joints' capacity belong under EN 1993-1-1 and EN 1993-1-8. A load-bearing steel staircase is also a construction product and must be executed in accordance with EN 1090-2 with CE marking, execution class (EXC) and welding coordination.
• Guarding and railings are not part of the figure. BR18 §58–59 requires guarding of at least 1.0 m, designed so children can neither climb it nor squeeze through it — in practice a clear opening under approx. 89 mm. Handrail height, baluster spacing and the guarding's fixing to the stringer must be designed separately.
• Fire requirements are not covered. If the staircase is an escape route, BR18 sets requirements for load capacity during fire (R-class), for the surfaces' contribution to fire development and for the escape route remaining usable throughout the entire evacuation. Unprotected steel loses load capacity long before it melts.
• Riser, going and clear width are checked against the BR18 GUIDANCE §57 as it is reproduced in the repo's calculator ‘Steel staircase: riser and going’: riser ≤ 180 mm, going ≥ 280 mm (≥ 250 mm in dwellings), clear width ≥ 1.0 m on shared escape routes. The building permit for the specific building takes precedence over the guidance, and spiral and quarter-turn staircases are measured on the walking line and have their own requirements.
• The tread is not a sub-part here. The tread plate's thickness is included ONLY as the deduction that lowers the notch faces; the tread's own load capacity, slip resistance, nosing projection and fixing have not been calculated. Any nosing has not been added to the base.
• Corner relief, edge distance (1.5 · d for cutting), ligament (≥ 1 · d) and the distance from hole edge to bend line (2.5 · t + R) are WORKSHOP PRACTICE, not standards. The relief radius ≥ t is taken from the repo's own hjoerneUdskaering(); for a fatigue-loaded detail, EN 1993-1-9's notch classes apply instead, and they are stricter.
• The contour in the pattern and in the DXF is NOMINAL. The cut width has not been deducted: without kerf compensation on the machine, the stringer becomes one cut width too small and each hole one cut width too large. For plasma in 20 mm sheet that is 3.6 mm.
• The sheet-format check calculates against the commercial formats in the repo's SHEET FORMATS, which are GUIDANCE ONLY. If the stringer must be split, the splice seam is a fully welded butt seam that must be sized and placed by the structural engineer — never at a notch corner.