Displacement Stress Range Check (ASME B31.3 ¶319.4.4)
Compares the displacement stress range SE = √(Sb² + 4St²) of ASME B31.3 ¶319.4.4 Eq. (17) with the allowable SA = f(1.25Sc + 0.25Sh) of ¶302.3.5(d) Eq. (1a), returning both plus the utilization ratio and a PASS/FAIL verdict. Moment ranges come from your flexibility analysis.
The thermal-expansion acceptance check of B31.3: the computed displacement stress range SE from an analysis' moment ranges must not exceed the allowable SA. Enter the SIF-intensified moments at the point of interest (from your flexibility analysis or hand layout), the section modulus, and the cold/hot allowables.
Method
Sb = √( (ii·Mi)² + (io·Mo)² ) / Z St = Mt / (2Z)
SE = √( Sb² + 4·St² ) (Eq. 17)
SA = f · (1.25·Sc + 0.25·Sh) (Eq. 1a)
PASS when SE ≤ SA. The cyclic factor f comes from the Fatigue Factor card (f = 1.0 up to 7,000 equivalent cycles).
| Inputs | ||
|---|---|---|
| ii, io | In-plane / out-of-plane SIFs (from the SIF card) | — |
| Mi, Mo, Mt | In-plane, out-of-plane, torsional moment ranges | in·lb |
| Z | Section modulus | in³ |
| Sc, Sh | Allowable stress cold / hot (user-supplied) | psi |
| f | Cyclic stress-range factor | — |
| Outputs | ||
| Sb, St | Resultant bending and torsional stress | psi |
| SE | Displacement stress range | psi |
| SA | Allowable stress range | psi |
| ratio | SE / SA utilization | — |
Limitations — what this calculator is not
- This is the acceptance check, not the flexibility analysis: moment ranges Mi/Mo/Mt must come from your own analysis (or a validated hand method). The tool deliberately does not solve piping systems — that remains CAESAR II / AutoPIPE territory.
- Eq. (1a) allowable; the liberal allowance of Eq. (1b) (adding unused sustained margin) is not applied.
- Single-point check with one Z — evaluate each candidate governing point separately.
Worked example — fixture-verified
NPS 6 Sch 40 point (Z = 8.49575 in³) with a pure in-plane moment range of 44,139 in·lb intensified by ii = 2.26557 (the Appendix D elbow above); A106-B allowables Sc = 20,000, Sh = 17,300 psi, f = 1.0.
| Given | ||
|---|---|---|
| ii / io | 2.26557 / 1.0 | — |
| Mi | 44,139 | in·lb |
| Mo, Mt | 0 | in·lb |
| Z | 8.49575 | in³ |
| Sc / Sh | 20,000 / 17,300 | psi |
| f | 1.0 | — |
Step by step
- Bending: Sb = 2.26557·44,139 / 8.49575 = 100,000 / 8.49575 = 11,770.6 psi; St = 0.
- Stress range: SE = √(11,770.6² + 0) = 11,770.6 psi.
- Allowable: SA = 1.0·(1.25·20,000 + 0.25·17,300) = 25,000 + 4,325 = 29,325 psi.
- Utilization: 11,770.6 / 29,325 = 0.40 → PASS.
| Result PASS | ||
|---|---|---|
| SE — displacement stress range | 11,770.6 | psi |
| SA — allowable range | 29,325 | psi |
| Utilization | 0.40 | — |
| Verdict | PASS | — |
SE and SA here reproduce the PVP Suite selftest values (11,770.588 / 29,325) — the fixture holds them to 0.01 psi.
displacement-stress.json — case “PVP: pure in-plane SE + SA” (tolerance 0.01) — in the
calc-core release gate. It re-runs on every commit; a red fixture blocks deployment.
See the validation methodology.Sources & citations
- ASME B31.3, Process Piping — ¶319.4.4 Eq. (17); ¶302.3.5(d) Eq. (1a) allowable stress range.
Per the source & citation policy, allowable-stress and factor table values are user-supplied — this page and the app cite paragraph numbers and never reproduce ASME table data.
FAQ
Where do the moment ranges come from?
From a flexibility analysis of the operating-to-cold displacement cycle — a pipe stress program, or a validated simplified method for simple layouts. This card is the transparent acceptance math you can put in a calculation report and check by hand.
What if my system cycles more than 7,000 times?
Compute f = 6·N^(−0.2) with the Fatigue Factor card (¶302.3.5(d)), including equivalent cycles from partial-range operation, and enter it here — SA scales down accordingly.
Related calculators
- Stress Intensification & Flexibility Factor Calculator (B31.3 Appendix D) — Source of the ii and io this check requires
- Expansion Loop / Leg Sizing Calculator (Guided Cantilever) — Add flexibility when SE exceeds the allowable SA
- Pipe Thermal Growth Calculator (in / 100 ft) — Growth driving the moment ranges entered here
- ASME B31.3 Pipe Wall Thickness Calculator — Pressure design precedes the displacement stress check