Rectangular Tee: flat pattern

A rectangular branch set square onto a rectangular duct, straight or with a shoe, with the hole marked on the duct. A rectangular branch set square onto the side of a rectangular duct, straight or with a shoe, with the hole marked on the duct.

Configurations

• Straight branch. The branch has the same size from the duct to its end.
• Branch with a shoe. The foot of the branch is drawn out toward End A, so that side slopes into the air stream.

A worked example

The straight branch configuration with the sizes SheetMorph opens with, in mm. 8 plates: the four sides of the duct, one with its hole, and the four sides of the branch: 8 parts, 8 seams.

How it is developed

True-shape development of flat sides. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.

• The branch stands on a flat side of the duct, so its foot is a plain rectangle and the hole is the same rectangle, marked on that side of the duct.
• The weight is for the plates with the hole cut out.
• Each side is a separate plate. The four corner edges of a duct are joints between plates, drawn as plain edges without allowance.

Checked before it can be exported

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

• Every station is a rectangle (passed): 4 stations: opposite sides and the two diagonals of each compared (max deviation 0).
• Plates flat, rolled or triangulated (passed): 8 flat, 0 folded or rolled from flat pieces (both develop exactly), 0 twisted and split along a diagonal.
• Surface connectivity (passed): 16 facets form 2 closed ducts, set one onto another: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
• Developed edges equal true 3D lengths (passed): 48 facet edges compared between the 3D surface and the flat pattern (max deviation 1.14e-13).
• Shared edges and seam closure (passed): 8 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 0).
• Cut outlines closed and non-overlapping (passed): 8 closed outline(s); no outline crosses itself or another outline.
• Hole lies within its plate (passed): The hole in P2 has 4 corners and an area of 50451; it is marked where the part set onto the plate meets it.

Assumptions

• The pattern is developed on the mid-thickness surface; inside or outside sizes are converted to it by one thickness across each opening.
• Folds are sharp lines; no bend allowance is applied.
• No seam, lap or weld allowance is added.

Limits of this module

• The branch is square to the duct and on one side only; an angled branch or a second branch is not modelled.
• The branch and the duct are separate parts joined at the hole; no collar, tabs or seam allowance are added there.
• No seam, lap, lock-seam, flange or weld allowance is added unless the module says so; corner joints are drawn as plain edges.
• Bend allowance and springback are not modelled; folds are sharp lines on the mid-thickness surface.
• No stiffening, tie rods, access doors or nesting onto stock sheets.

Conventions

Coordinate system. End A is at Z = 0, centred on the Z axis, with its width along X and its depth along Y. A duct that turns or is offset does so in the XZ plane, toward +X.

Corners and sides. Corners are numbered 0 (-X, -Y), 1 (+X, -Y), 2 (+X, +Y), 3 (-X, +Y), seen from +Z at End A. Rj_c is corner c of station j. Each of the four sides is its own plate; the plates are joined along the four corner edges.

Plates. Plates are drawn outside face up and stacked in the order of their numbers. The blank sizes listed are the bounding rectangle of each plate.

Material thickness. Say whether the sizes are inside, mid-thickness or outside sizes. The pattern is developed on the mid-thickness surface, one thickness larger or smaller across each opening; the views show the sizes as entered.

Branch. The branch stands on the +X side of the duct, its axis square to the duct. Its position is measured from End A to the centre of its opening; its width is along the duct and its depth along Y. A shoe lengthens the foot toward End A, taken as the upstream end. End C is the open end of the branch.

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 intersections

• Tee or Lateral: A branch set onto a run: equal or reducing tees and angled laterals, with the saddle cut and the hole in the run.
• Cross: Two branches set onto opposite sides of a run: equal, reducing or unequal, with both saddle cuts and both holes in the run.
• Manifold: A round run with a row of equal branches at an even pitch: the run unrolled with every hole marked, and the branches with their saddles.
• Cone on Pipe: A cone set onto a round pipe, square as a boot or hopper outlet, or at an angle as a conical lateral, with the hole in the pipe.
• Pipe on Cone: A round branch set square onto a conical shell, such as a nozzle on a hopper, with the hole in the cone.
• Cone on Cone: A cone set square onto a conical shell, such as a reducing branch on a hopper, with the hole in the main cone.
• Rectangle on Round: A rectangular branch set square onto a round run, on its centre or offset: the run with its hole, and the branch folded at its corners.