Spiral staircase

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 spiraltrappe: en central søjle (rør) med flade trin-plader fordelt op ad søjlen, hvor hvert trin drejes lidt videre rundt. En sammensat del — søjlerøret og trinnene udvikles hver for sig.

Vindeltrapper, repos- og platforms-spiraltrapper i stål. Pladearbejdet er søjlerøret (udrullet) plus de ens trinflader, der svejses radialt på søjlen.

Smed — vindeltrapper samt repos- og platforms-spiraltrapper i stål.

Konstruktionsstål S235: søjlerør + rifleplade-trin. 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).

Højde — Height

Trappens samlede højde langs søjlen (mm) — også søjlerørets længde og dermed panelets højde ved udrulning.

Søjle-radius — Søjle-radius

Radius på det centrale søjlerør (mm). Udrullet bliver rør-omkredsen 2π × søjle-radius til panelets bredde, og trinnenes inderkant sidder her.

Trin-radius — Trin-radius (ydre)

Afstand fra søjlecentrum til trinnets yderkant (mm). Trin-pladens radiale længde = trin-radius − søjle-radius.

Antal trin — Number of steps

Hvor mange ens trin-plader der fordeles op ad søjlen.

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

1. 01Udvikl søjlerøret som et rektangel: bredden = 2π × søjle-radius (udrullet omkreds), højden = trappens højde — parallel-linje-udrulning af cylinderen.
2. 02Find trin-pladens mål: radial længde = trin-radius − søjle-radius, og dybde ≈ trin-radius × 0,5; aftegn én trinflade som rektangel.
3. 03Aftegn de øvrige ens trin-plader (samme rektangel) — én pr. trin.
4. 04Skær søjle-rektanglet ud, rul det til røret og luk sømmen langs limflappen.
5. 05Skær trin-pladerne ud, fordel dem jævnt i højden og drej hvert trin lidt videre rundt om søjlen til en jævn spiral.
6. 06Fastgør hver trin-plade til søjlen ved den korte inderkant og kontrollér at trinnene står vandret.

Trinnene skal stige lige meget pr. trin (højde ÷ antal trin) og dreje lige meget pr. trin, ellers bliver spiralen ujævn. Marker delepunkterne på søjlen før montering, og kontrollér med vaterpas at hvert trin er vandret.

• ·Bærende trapper er omfattet af EN 1090.
• ·BR18: stigning højst 180 mm på fælles adgangsveje, grunden mindst 250 mm i boliger (280 mm i kontor/institution) — byggetilladelsens konkrete krav går forud.
• ·Pladearbejdet er søjlerøret (udrullet) + ens flade trinplader; 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.

10 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, not statics. A spiral staircase with cantilevered treads carried by one central column is a load-bearing system: each tread is a cantilever, and the column is loaded in torsion and bending. The tread plate's thickness, deflection, the column's buckling and the entire structure must be sized in accordance with EN 1993 (steel) and executed in accordance with EN 1090 — that has not been calculated here.
• The joint between tread and column carries the ENTIRE load and is not drawn or sized. Whether the tread is welded to a collar, slid onto a sleeve or bolted through a flange is a structural detail that must be calculated by a structural engineer.
• Railings, handrail, guarding and headroom are not covered. A staircase is a fall-protected building component — guarding and handrail must be executed in accordance with BR18 and (for industrial staircases) EN ISO 14122-3, and they are not part of this drawing.
• The riser and going dimensions are checked against BR18 §57 as GUIDANCE, not an approval. A spiral staircase has its own rules for clear width and going on the walking line, and the local building-case administration decides whether the staircase may be used as an access route. Secondary/internal staircases have more lenient requirements.
• The material thickness applies to both tread and column. In practice the treads are often thicker (chequer plate, duplex) for reasons of deflection and slip resistance, and the column tube is selected according to statics. The treads' slip protection and drainage are not drawn.
• The contour in the pattern and in the DXF is NOMINAL. The cut width has not been deducted: without kerf compensation, each tread becomes one cut width too small and the tread hole one cut width too large. For plasma in thick sheet that is several millimetres — enough for the tread not to fit over the column.
• The column's top and bottom edges are cut square; base plate, top termination and any division of a tall column into several rolled sections with circumferential seams are not drawn. If the column is longer than a sheet can roll in one piece, the figure states that as information.