Triangulation Layout for an Offset Square-to-Round Transition
In a fabrication shop, a 24 ga galvanized transition is to be laid out from a 600 mm × 600 mm square duct to a 400 mm diameter round duct. The vertical height is 500 mm, and the round centreline is offset 150 mm along the x-axis from the square centre. The shop has a 1:1 layout table, dividers, trammel points, and a straightedge; the brake can handle 1.2 m wide sheets. The journeyperson proposes to divide the round opening into 12 equal parts and triangulate from the four square corners. The seam is planned on the side where the transition is shortest. The apprentice asks how to calculate true lengths and how much material to add for the seam and flanges.
1. Outline the triangulation layout and calculate the true length of the element from base corner B (600, 0) to the round division point at θ = 0° (650, 300), with the top at +500 mm.
Read the worked answer
Start with an accurate 1:1 plan: draw the 600 mm square with corners A(0,0), B(600,0), C(600,600), D(0,600). Draw the 400 mm diameter circle with its centre at (450,300), which is offset 150 mm along x. Divide the circle into 12 equal parts at 30° intervals and number the points. Project each division point to the base plane and connect each square corner to each division point. These lines are the triangulation elements.
For corner B to the θ = 0° point at (650,300), first find the plan distance: d = √[(650 − 600)² + (300 − 0)²] = √(50² + 300²) = √(2,500 + 90,000) = √92,500 = 304.1 mm. The true length includes the 500 mm rise: TL = √(304.1² + 500²) = √(92,500 + 250,000) = √342,500 = 585.2 mm.
Repeat this for every corner-to-division pair. Use symmetry to reduce the number of calculations. Develop the pattern by swinging true lengths from the base corners and stepping off the round chord lengths and the square side lengths. The 12-part chord on the 400 mm circle is 2 × 200 × sin(15°) = 103.5 mm. Check the base perimeter of 2,400 mm against the developed base length before cutting.
2. Explain seam allowance and minimum throat check for 24 ga galvanized, and how to verify before cutting.
Read the worked answer
For 24 ga galvanized, the base metal thickness is about 0.64 mm. A practical lap seam allowance is 10 mm plus the material thickness, so add about 10.6 mm; if the shop standard uses a 12 mm lap for handling, use that and record it. Add flange allowance separately if the ends are flanged, for example 25 mm per flanged end. Do not add seam allowance to both sides of a single-piece pattern; add it once at the seam line and mark the seam direction clearly.
Check the throat and slope before cutting. The shortest element in this transition is on the offset side; the calculated shortest true length is about 585 mm. The horizontal offset of 150 mm over a 500 mm rise gives a transition angle of arctan(150/500) = 16.7°, which is acceptable for a gradual transition; verify that the developed pattern does not create a sharp re-entrant angle at the seam. Confirm the longest element is within the sheet size and the brake capacity. For this job, keep the seam on the short side as planned, but check that the seam does not fall on a corner where it would be difficult to dress.
Before cutting, make a half-pattern template, verify the developed base length equals 2,400 mm, verify the round stretchout by stepping 12 chords of 103.5 mm, and trial-fit the pattern to the square and round openings. If the pattern is more than 1 mm out on the diagonal or circumference, correct the layout before cutting.
3. What dimensional checks and fit-up criteria would you use before assembling the transition?
Read the worked answer
Check the base opening for square: both sides should be 600 mm ±1 mm and the diagonals should be 848.5 mm ±2 mm. Check the round opening diameter at 400 mm ±1 mm in two directions and confirm the 150 mm offset from the square centre. Check the vertical height at 500 mm ±2 mm at four points. Verify the seam allowance is present and the seam edges align without a step.
During fit-up, the transition should slip over the square duct and into or over the round duct according to the joint detail, with a uniform lap of at least 25 mm unless the specification says otherwise. The transition should not require forcing; if it does, check the true lengths and the plan layout rather than springing the metal. Check for oil canning or buckling on the flat sides, which indicates an incorrect element length or seam location. Confirm the seam is oriented on the short side and that the joint will be sealed after assembly. Record the checks and correct any pattern error before fastening.