Truncated Rectangular Tube development

What it is

The rectangular-section duct that ends on a tilted plane — a roof, a sloping wall, the bottom of a funnel. It is to the rectangular section what the truncated cylinder is to the round shell, and the catalogue had one without the other. Rolled flat, the mouth becomes a line of four runs: straight on the low and high faces, sloping on the two sides.

Where it is used

Ducts dying into a roof or a sloping wall, intakes beside a graded floor, duct connections to equipment with a tilted face.

Measurements the calculation needs

• X Side along the tilt
• Y Side across the tilt
• H Height of the low side
• ANG Cut angle from square
• THK Plate thickness
• R Bend radius

Worked example

The values the form comes pre-filled with, run through the tool itself:

Side along the tilt	500 mm
Side across the tilt	300 mm
Height of the low side	400 mm
Cut angle from square	30°
Plate thickness	1.5 mm
Bend radius	0 mm
The flat pattern fits a plate of	1594 × 688 mm

Result of the example

Plate	1594 × 688 mm

Assembly notes

The pattern develops the SHARP CORNER, on the mean line — the theoretical layout, which is what gets delivered. If you fold it on a press brake with an inside radius, the blank comes out LONG: each fold needs the deduction 2*(r+t)*tan(a/2) − a*(r + k*t), with r the inside radius, a the bend angle in radians, and your tooling's k. On a 500x300 tube in 1.5 mm sheet with four 90° folds that is 3.5 mm at radius 0.75 and 9.0 mm at radius 4.5 — always to be taken off. A welded corner from separate plates needs no deduction at all.

Fold to an angle of 90° BETWEEN THE TWO FACES — what a protractor reads on the finished part, not the press stroke angle. Every crease on this part has the same angle.

Frequently asked questions

Are all four faces cut the same?

No, and it is the same trap as the rectangular bend. The low and high faces come out RECTANGULAR, cut square: each lies wholly at one distance from the axis, so the cut does not vary along it. Only the two side faces come out trapezoidal.

Which side is the height given for?

The LOW side. The high side follows from the arithmetic — it is the given height plus the width times the tangent of the angle. Same convention as the truncated cylinder.

Why can't the angle reach 90 degrees?

Because at 90 the plane runs parallel to the tube's axis and cuts no mouth at all — it slides down the side instead of crossing. And at zero the part is a straight tube, with no cut.

Where does the seam go?

In the middle of the low face, which is the shortest generator and so the shortest weld. And on a straight line, which closes better than a corner.