Stress Intensification & Flexibility Factor Calculator (B31.3 Appendix D) — Sample Report

ProjectSample Project — Demonstration Only	Job No.SAMPLE-001	Client—
CalculationStress Intensification & Flexibility Factor Calculator (B31.3 Appendix D)	Calc byPiping Toolset (calc-core)	Checked byUNCHECKED — sample
Date2026-09-03	Rev0	BasisASME B31.3 Appendix D Table D300 closed forms (elbow: ii=0.9/h^⅔, io=0.75/h^⅔; welding tee: io=0.9/h^⅔, ii=0.75·io+0.25)

1 · Design inputs

NPS 6 Sch 40 long-radius elbow: D = 6.625 in, T = 0.28 in, R1 = 9 in — the PVP Suite selftest case.

Component	LR elbow	—
Outside diameter D	6.625	in
Wall T	0.28	in
Bend radius R1	9	in

2 · Method

Elbow (bend radius R₁, mean radius r₂ = (D−T)/2):

h = T·R₁ / r₂² k = 1.65/h

Welding tee (B16.9): h = 4.4·T/r₂, k = 1, with the Table D300 assignment reversed — i_o = 0.9/h^2/3 and i_i = 0.75·i_o + 0.25 (each ≥ 1.0).

Elbow: i_i = 0.9 / h^2/3 i_o = 0.75 / h^2/3 (each ≥ 1.0)

The calculator works from geometry inward: the mean radius r₂ comes from the entered OD and nominal wall, h follows from the component form — thin wall and large mean radius drive h down — k is derived from h for the elbow (welding tees take k = 1), and the SIFs are the h^−2/3 closed forms floored at 1.0. All four values are reported together because they travel together: k softens the component in a flexibility model, changing the moments the system delivers, while i_i and i_o then intensify those moments in the stress-range check. Table D300 is the source of every form used; nothing here depends on a material property or an allowable stress, which is why the outputs can be verified to five decimals against published validation sets — the worked example reproduces the PVP Suite elbow case exactly.

3 · Calculation

Mean radius: r₂ = (6.625 − 0.28)/2 = 3.1725 in.
Flexibility characteristic: h = 0.28·9 / 3.1725² = 2.52 / 10.0648 = 0.25038.
Flexibility factor: k = 1.65 / 0.25038 = 6.590.
SIFs: h^2/3 = 0.39725 → i_i = 0.9/0.39725 = 2.2656; i_o = 0.75/0.39725 = 1.8880.

4 · Results COMPUTED

h — flexibility characteristic	0.25038	—
k — flexibility factor	6.590	—
ii — in-plane SIF	2.2656	—
io — out-of-plane SIF	1.8880	—

5 · Verification statement

The result values above are locked as fixture b31-sif.json, case “PVP: 6in sch40 LR elbow (R1=9)”, 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 flexibility and stress intensification factors. · ASME B31J — more-accurate SIF/k data (planned as a mode-gated dataset, not embedded).

SAMPLE REPORT — auto-generated from a verification fixture to show the report format. Not a project calculation. ⚠ Engineering-aid tool. Public code equations; allowable-stress and factor data are user-supplied. Results MUST be independently verified and reviewed by a qualified/licensed engineer before any design, fabrication, or operation decision.