Pipe Bend Minimum Wall Thickness Calculator (B31.3 ¶304.2.1) — Sample Report

ProjectSample Project — Demonstration Only	Job No.SAMPLE-001	Client—
CalculationPipe Bend Minimum Wall Thickness Calculator (B31.3 ¶304.2.1)	Calc byPiping Toolset (calc-core)	Checked byUNCHECKED — sample
Date2026-09-03	Rev0	BasisASME B31.3 ¶304.2.1 / B31.1 ¶102.4.5 (I-factor)

1 · Design inputs

NPS 8 (8.625 in OD) bent at R = 12 in (≈1.4D), P = 1,000 psi, S = 20,000 psi, E = 1, y = 0.4, allowance 0.065 in.

Pressure P	1,000	psi
OD D	8.625	in
Bend radius R	12	in
S / E / y	20,000 / 1 / 0.4	psi, —, —
Allowance A	0.065	in

2 · Method

With R the bend radius to centerline and D the OD:

I_intrados = (4(R/D) − 1) / (4(R/D) − 2) I_extrados = (4(R/D) + 1) / (4(R/D) + 2)

t_m(I) = P·D / ( 2( S·E/I + P·y ) ) + A

The I factor works by scaling the allowable stress inside the straight-pipe relation: at the intrados I > 1 divides S·E down, demanding more wall, while at the extrados I < 1 credits the lower hoop stress on the outside of a torus with a thinner requirement. Both factors are pure functions of the radius ratio R/D — a tighter bend pushes them further from 1 in both directions. The calculator computes R/D, evaluates I at each surface, and solves the corrected thickness equation three times: intrados, extrados, and centerline, where I = 1 and the result reproduces the straight-pipe value as a built-in sanity anchor. The allowance A is added to each. The same form is referenced by B31.1 ¶102.4.5 and the B31.4/B31.12 bend rules, so one card serves the process, power and pipeline bend checks with the appropriate user-supplied S, E and y. Because the correction rides on the allowable rather than the geometry, every input keeps the same meaning it has in the straight-pipe calculation — the bend check adds exactly one new piece of information, the radius, and reports exactly what it costs.

3 · Calculation

R/D = 12/8.625 = 1.39130 → 4(R/D) = 5.56522.
I_intrados = (5.56522−1)/(5.56522−2) = 4.56522/3.56522 = 1.28049; I_extrados = 6.56522/7.56522 = 0.86782.
Intrados: t_m = 1,000·8.625 / (2·(20,000/1.28049 + 400)) + 0.065 = 8,625/32,038 + 0.065 = 0.33421 in.
Extrados: 8,625/46,893 + 0.065 = 0.24893 in; centerline: 8,625/40,800 + 0.065 = 0.27640 in.

4 · Results COMPUTED

I intrados / extrados	1.28049 / 0.86782	—
tm — intrados (governs)	0.33421	in
tm — extrados	0.24893	in
tm — centerline	0.27640	in

5 · Verification statement

The result values above are locked as fixture bend-thickness.json, case “NPS 8, R=12 in, P=1000, S=20000, E=1, y=0.4, A=0.065”, tolerance 0.0001, 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 — ¶304.2.1, pressure design of bends. · ASME B31.1, Power Piping — ¶102.4.5 (same I-factor form on the Power line card).

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.