Welding Tee Stress Intensification Factor Calculator (B31.3 App. D / B31J) — Sample Report

1 · Design inputs

NPS 6 Sch 40 welding tee (6.625 in OD × 0.28 in nominal wall) per ASME B16.9 — the same pipe size the App D closed form is validated against in the PVP-parity test suite.

2 · Method

Closed-form welding-tee relations, evaluated in sequence from the pipe geometry:

r₂ = (D − T) / 2

h = 3.1·T / r₂ (Table D300 entry) or h = 4.4·T / r₂ (Note (7): r_x ≥ D_b/8 and T_c ≥ 1.5T)

i_o = max( 0.9 / h^2/3 , 1 ) i_i = max( 0.75·i_o + 0.25 , 1 ) k = 1

The tee-form input selects the coefficient. The 4.4 form is Table D300's Note (7) alternative for a tee whose crotch radius r_x ≥ D_b/8 and crotch thickness T_c ≥ 1.5T (B31.1's legacy Table D-1 Note (7) is the same form) and is the default, because the PVP-parity value this module was validated against was computed on it; the 3.1 form is the table's unconditional entry for any B16.9 welding tee, and because i_o varies as h^−2/3 it returns SIFs about 26 % higher — (4.4/3.1)^2/3 = 1.263 on i_o. The result names the form applied so the calculation sheet carries it. Here D is the pipe outside diameter, T the nominal (mean) wall thickness, and r₂ the mean pipe radius. The bend-radius input that the elbow closed form needs is not used here — a welding tee has no bend radius. i_o is computed first from h; i_i is then derived from i_o by Table D300's fixed linear relation rather than from its own independent formula, and k is taken as 1 outright because a tee's branch does not gain the flexibility credit a curved bend does. Both SIFs are floored at 1 — a computed value below 1 (heavy wall relative to radius) is reported as 1, matching the Code's floor. The calculator also flags h < 0.05 as outside the closed form's validated range, where B31J tabular data should be used instead of the formula.

3 · Calculation

1. Mean radius: r₂ = (D − T)/2 = (6.625 − 0.28)/2 = 6.345/2 = 3.1725 in.
2. Flexibility characteristic: h = 4.4·T/r₂ = 4.4·0.28/3.1725 = 1.232/3.1725 = 0.38834.
3. Out-of-plane SIF: i_o = 0.9/h^2/3 = 0.9/0.38834^2/3 = 1.69084 (above the 1.0 floor, so no clamping applied).
4. In-plane SIF: i_i = 0.75·i_o + 0.25 = 0.75·1.69084 + 0.25 = 1.26813 + 0.25 = 1.51813.
5. Flexibility factor: k = 1 — fixed for a welding tee, unlike an elbow's 1.65/h.

4 · Results COMPUTED

5 · Verification statement

The result values above are locked as fixture b31-sif.json, case “PVP: 6in sch40 welding tee”, tolerance 0.00001, 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 B31.3, Process Piping — Appendix D, Table D300, stress intensification and flexibility factors for welding tees. · ASME B31J, Standard Test Method for Determining Stress Intensification Factors (i-Factors) for Metallic Piping Components — the tabular dataset these closed forms approximate absent Code Data Service tables. · ASME B16.9, Factory-Made Wrought Buttwelding Fittings — the welding-tee dimensional standard the closed form's geometry assumes.