SAMPLE
Piping Toolset — Calculation Report
generated by calc-core · 2026-09-03

Mitered Elbow Allowable Pressure Calculator (ASME B31.3 ¶304.2.3) — Sample Report

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
Date2026-09-03 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 for pressure after tolerances and allowances, r2 the mean pipe radius, R1 the effective bend radius of the miter, and θ the miter half-angle. The two equations bound different failure concerns: Eq. (4a) knocks the straight-pipe capacity down for the angular discontinuity at each joint — the 0.643·tan θ·√(r2·Tc) term grows with cut angle and pipe size — while Eq. (4b) limits the bend as a whole through its radius geometry, tightening as R1 approaches the pipe radius. The calculator evaluates whichever forms apply to the entered miter count and half-angle, reports Pm1 and Pm2 individually, takes the lesser as the governing allowable, and names the controlling equation so the margin driver is explicit in the calculation report. The base term S·E·Tc/r2 in both equations is the straight-pipe hoop relation, which makes the knockdown easy to read: whatever fraction of it survives the geometry factors is the fraction of straight-pipe capacity the miter keeps.

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.