SAMPLE
Piping Toolset — Calculation Report
generated by calc-core · 2026-07-21
ProjectSample Project — Demonstration Only Job No.SAMPLE-001 Client—
CalculationMitered Elbow Allowable Pressure Calculator (ASME B31.3 ¶304.2.3) Calc byPiping Toolset (calc-core) Checked byUNCHECKED — sample
Date2026-07-21 Rev0 BasisASME B31.3 ¶304.2.3 Eq. (4a)/(4b)/(4c)

1 · Design inputs

3-cut miter, half-angle 15°, S = 20,000 psi, E = 1.0, available wall Tc = 0.25 in, mean radius r2 = 4.1515 in, effective bend radius R1 = 12 in.

Allowable stress S20,000psi
Quality factor E1.0—
Available wall Tc0.25in
Mean radius r24.1515in
Bend radius R112in
Half-angle θ15deg
Miter cuts3—

2 · Method

Pm1 = (S·E·Tc/r2) · Tc / ( Tc + 0.643·tan θ·√(r2·Tc) )  (Eq. 4a)

Pm2 = (S·E·Tc/r2) · (R1 − r2) / (R1 − r2/2)  (Eq. 4b)

Single miter with θ > 22.5° replaces the 0.643 coefficient with 1.25 (Eq. 4c). Tc is the wall available after tolerances and allowances, r2 the mean pipe radius, R1 the effective bend radius, θ the miter half-angle.

3 · Calculation

  1. Base term: S·E·Tc/r2 = 20,000·0.25/4.1515 = 1,204.4 psi.
  2. Eq. (4a): 0.643·tan15°·√(4.1515·0.25) = 0.643·0.26795·1.01876 = 0.17551; Pm1 = 1,204.4 · 0.25/(0.25+0.17551) = 1,204.4·0.58752 = 707.6 psi.
  3. Eq. (4b): Pm2 = 1,204.4 · (12−4.1515)/(12−2.0758) = 1,204.4·0.79084 = 952.5 psi.
  4. Governing: min(707.6, 952.5) = 707.6 psi — Eq. (4a) governs.

4 · Results COMPUTED

Pm1 (Eq. 4a)707.6psi
Pm2 (Eq. 4b)952.5psi
Governing allowable707.6psi

5 · Verification statement

The result values above are locked as fixture miter-allowable-pressure.json, case “3-miter, theta=15deg, Tc=0.25, r2=4.1515, R1=12, S=20000”, tolerance 0.001, 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 — ¶304.2.3 Eq. (4a), (4b), (4c) and Eq. (5) minimum miter radius.

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.