ASME BPE Fitting Dimensions Lookup (Part DT-4.1) — Sample Report

1 · Design inputs

A 2 in hygienic transfer line turns two 90° corners in the same plane. The isometric shows the two elbow centerline intersections 24 in apart. The fabricator needs the cut length of the straight between the elbows and the length of tube the orbital head will clamp on at each elbow end.

2 · Method

weld elbow tangent = A − R·tan(θ/2) (θ = 90° → A − R; θ = 45° → A − 0.4142·R)

eccentric reducer centerline offset = (OD_large − OD_small) / 2 (BPE tube OD = nominal size)

The lookup is a direct table read, and it is deliberately not more than that: the fitting type selects the DT-4.1 table, the size selects the row, and every dimension the row carries is returned with the table id so the number can be traced to its source line. Equal fittings — elbows, tees, crosses, ferrules, caps — are tabulated by a single tube size from 1/2 in to 6 in; reducers and instrument tees are tabulated as run × branch pairs, entered exactly as the table designates them. The elbow tangent is derived from the geometry of a bend: a centerline arc of radius R turning through θ reaches the tangent point R·tan(θ/2) short of the centerline intersection, so whatever remains of the center-to-end dimension beyond that is straight tube. For a 90° elbow that is simply A − R; for a 45° elbow the bend takes only 0.4142·R of the length, which is why the 45° A is so much shorter than the 90° A at the same radius while the tangent lands in the same neighbourhood. The two tables carry independent A values rather than a shared formula, so the 45° and 90° tangents agree to a few hundredths of an inch at most sizes and differ by about 0.13 in at 1 in nominal — comparable, not identical. The eccentric offset follows from BPE tubing being an OD-based product: a 2 × 1 reducer joins a 2.000 in OD to a 1.000 in OD, so with both tubes tangent on one side the centerlines sit 0.500 in apart. The card reports COMPUTED rather than PASS/FAIL — there is no acceptance criterion in a dimension lookup — and an unlisted size returns a failure that names the sizes the table does carry.

3 · Calculation

1. Table DT-4.1.1-1, 2 in row: center-to-end A = 4.75 in, centerline radius R = 3.0 in.
2. Weld tangent = A − R·tan(45°) = 4.75 − 3.0 = 1.75 in of straight tube beyond the bend at each weld end.
3. Straight between the elbows = 24 − 2 × 4.75 = 14.5 in, before any fit-up allowance the WPS calls for.

4 · Results COMPUTED

5 · Verification statement

The result values above are locked as fixture bpe-fitting-dimensions.json, case “90 deg weld elbow 2 in: A 4.75 center-to-end, R 3.0, tangent A - R = 1.75 (DT-4.1.1-1)”, tolerance 0.000001, in the calc-core continuous verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are user-supplied inputs; citations: ASME BPE-2026 — Part DT-4.1 fitting-dimension tables: DT-4.1.1-1 / -3 / -4 / -6 (90° and 45° elbows, weld and clamp ends), DT-4.1.2-1 (tees, crosses), DT-4.1.2-10 (instrument tees), DT-4.1.3-1 (concentric and eccentric reducers), DT-4.1.4-1 (weld-end ferrules), DT-4.1.5-2 (solid end caps); centerline radius R per Part DT-3.