Spiral Stair Stringer: flat pattern

The stringer of a spiral or helical stair: a plate rolled to stand on a cylinder as it climbs, alone or as a pair, with a line for every tread. The stringer of a spiral or helical stair: a plate rolled to stand on a cylinder as it climbs, alone or as an inner and outer pair, with a line for every tread.

Configurations

• One stringer. A single stringer at the radius entered, as round a centre column or on the outside of the stair.
• Inner and outer pair. Two stringers, the outer one the width of the stair outside the inner one.

A worked example

The one stringer configuration with the sizes SheetMorph opens with, in mm. One plate: a straight strip that slopes at the angle of the stair: 1 part, 0 seams.

How it is developed

Parallel-line development (unrolled cylinder). This is a triangulated approximation: the curved surface is divided into small flat triangles, each laid out at its true size. The finer the division, the closer the pattern is to the surface; SheetMorph states the deviation it found.

• A stringer stands on a cylinder, so it unrolls to a straight strip: as long as its edge truly is, and sloping across the sheet at the angle of the stair there. Its upright ends become slanting cuts.
• The lines across the plate are upright in the stair, one at each riser. Roll the plate with the lines square to the rolls’ feed turned by the slope, to the rolling radius and not to the radius of the stair.

Checked before it can be exported

Every pattern SheetMorph draws is checked against the 3D part it comes from. For this example:

• Surface connectivity (passed): 30 facets form one open sheet: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 1).
• Developed edges equal true 3D lengths (passed): 90 facet edges compared between the 3D surface and the flat pattern (max deviation 7.96e-13).
• Shared edges and seam closure (passed): 29 internal edges are shared vertex-for-vertex between adjacent facets; 0 seam(s) have mating edges of equal true length (max deviation 0).
• Developed facets consistently oriented (passed): All developed facets are counter-clockwise (outside face up); none is mirrored or degenerate.
• Developed area equals surface area (passed): Facet area in 3D and in the flat pattern agree (difference 2.33e-10).
• Cut outlines closed and non-overlapping (passed): 1 closed outline(s); no outline crosses itself or another outline.

Assumptions

• The pattern is developed on the mid-thickness surface; inside or outside sizes are converted to it by the thickness.
• Curves are chains of chords between division points.
• No seam, lap, weld-preparation or pressing allowance is added.

Limits of this module

• A stringer lies on a cylinder, so it unrolls exactly, to a straight strip that slopes at the angle of the stair. It is rolled on the skew, to the rolling radius listed, which is larger than the radius of the stair.
• The stringer is of constant depth with upright ends; shaped ends, landings and returns are not drawn.
• Treads, risers and their fixings are not developed: only their positions along the stringer are marked. Sizes are those of the surface the sheet lies on; the thickness is used for the weight only.
• Curves are chains of straight chords between division points.
• No seam, lap, weld-preparation or pressing allowance is added, and plates are not nested onto stock sheets.

Conventions

Coordinate system. The part stands on the Z axis with End A at Z = 0. Angles round the axis are measured from +X toward +Y, counter-clockwise seen from +Z.

Divisions and thickness. A circle is divided into 4N equal chords. Sizes are inside, mid-thickness or outside sizes; the pattern is developed on the mid-thickness surface and the views show the sizes as entered.

Stair. The stair winds round the Z axis, counter-clockwise seen from above, from the +X side at Z = 0, and rises the height entered over the turn angle. For a stair that winds the other way, turn the pattern over. The radius is that of the surface the plate lies on.

Stringer. A stringer stands upright on its cylinder: its depth is measured upright, and its ends are upright cuts. End A is its lower edge and End B its upper edge; of a pair, End A is the lower edge of the inner stringer and End B that of the outer one. The inner stringer, or the only one, is drawn as seen from the axis, and the outer one as seen from outside the stair.

Treads. The stair is divided into equal treads. Each has a line across the plate, upright in the stair, where its riser stands; the points on the lower edge are numbered from the bottom.

Change the sizes to your own in SheetMorph, check the drawing, add seam and flange allowances, and export DXF, PDF, SVG, CSV or G-code. Check every pattern against your own standards before cutting.

Other rings and helicals

• Segmented Flange: A flat ring, as a flange, a stiffener or a base ring, made in equal segments so that it nests on the plate, with or without its bolt holes.
• Rolled Bar: A ring, a hoop or part of one rolled from flat bar or strip: the length to cut on the neutral line, with the gap for the weld and the flat ends.
• Screw Flight: One flight of a screw conveyor or auger, right or left hand: standard, tapered or ribbon, as the flat blank that is pulled out to one pitch.
• Spiral Chute: A spiral chute: a floor that winds round an axis as it falls, with or without walls on its edges.