Branch Pipe Intersection and Development
A fabricator is producing a welded 90° branch connection between two steel pipes. The main pipe has an outside diameter of 120 mm and a horizontal axis. The branch pipe has an outside diameter of 76 mm and a vertical axis that intersects the main axis at right angles. Both pipes have a 3 mm wall, and the branch is to be cut to sit on the outside surface of the main pipe before welding. The drawing office works in third-angle projection. A junior drafter has shown the branch end as a single straight line in the front view, arguing that the branch is 'cut square' and that the weld preparation hides the curve. The same drafter produced the branch development using only six equally spaced divisions around the circumference, because 'the curve is nearly flat'. Before the cut sheets are released, the checker must decide whether either simplification is acceptable and must give the shop three ordinates for setting out the saddle.
1. Explain, with calculated ordinates at 0°, 90° and 180° around the branch, why the straight-line representation in the front view is not acceptable. State what the front-view intersection actually looks like.
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Set the main-pipe axis along x and the branch axis along z, with the viewer looking along y. The main-pipe outer surface is y² + z² = R² with R = 60 mm. A point on the branch circumference at angle θ from the plane of the axes is (x, y) = (r cos θ, r sin θ) with r = 38 mm. At the intersection, z = √(R² − r² sin²θ). At θ = 0°: z = √(60² − 0) = 60.0 mm, x = 38.0 mm. At θ = 90°: z = √(60² − 38²) = 46.4 mm, x = 0. At θ = 180°: z = 60.0 mm, x = −38.0 mm. So the front-view intersection is a symmetrical saddle curve dropping 13.6 mm at the centre, not a straight line at z = 60 mm. A straight line would leave the branch 13.6 mm too long at the centre, which is more than four times the 3 mm wall thickness. In front view it is a smooth curve, concave downward; in side view it is the complementary curve.
2. The development is to be set out on the branch surface. Determine which generator is longest and which is shortest, and calculate the difference. Explain how this affects the 12-division development and whether six divisions can capture the maximum ordinate.
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The cut is closest to the main axis at θ = 90° (front and back), where z = 46.4 mm. The branch generator from a fixed top reference down to the cut is longest there. The cut is farthest from the axis at θ = 0° and 180°, where z = 60.0 mm, so the generator is shortest there. The difference is 60.0 − 46.4 = 13.6 mm. With six divisions at 60° spacing, samples fall at θ = 0°, 60°, 120°, …; the minimum at 90° is never sampled. At θ = 60°, z = √(3600 − 1444 × 0.75) = 50.2 mm, so the development misses the true extreme by 3.8 mm and flattens the curve between samples. Twelve divisions at 30° include 90° and 270°, so they capture the controlling ordinate. Twelve straight chord segments will still slightly flatten the curve between points, but for a 76 mm branch that is acceptable for layout if the template is checked at the saddle. Six divisions are not acceptable because they miss the extreme.
3. The shop proposes to use the straight-line front view to set the branch length and then grind to fit. Assess this proposal and state two drawing controls that should be added before release.
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Not acceptable. Using the straight-line front view transfers a 13.6 mm error into the weld gap: the gap can vary by more than the wall thickness around the saddle, far beyond a controlled 2–3 mm root gap, and grinding can thin the branch wall. Fit-up depends on the actual saddle curve, not on weld preparation. Add: (1) a true intersection curve in both front and side views, with at least the θ = 0°, 90° and 180° ordinates dimensioned or tabulated; (2) a note that the branch is to be cut from a developed template and first-off checked against the main pipe, with 'grind to fit' prohibited on the saddle. A development table at 30° intervals would also let the shop mark the cut directly.