Analysis Sets: Multi-Code Piping Stress Comparison Calculator — Sample Report

1 · Design inputs

NPS 8 Sch 40 line (8.625 in OD × 0.322 in wall, Z = 16.81 in³) carrying 600 psi, evaluated against all four codes at once. Moment range resultants of 50,000 / 30,000 / 20,000 in·lbf (in-plane / out-plane / torsional) with SIFs ii = 2.27, io = 1.89; Sc = 20,000 psi, Sh = 17,300 psi; SL = 8,000 psi; SMYS = 35,000 psi with the default design factor F = 0.72.

2 · Method

Same geometry and load case evaluated by each selected code's own screening check, with allowables entered by the user rather than embedded:

hoop = P·Do / (2·t)

S_b = √((i_i·Mi)² + (i_o·Mo)²) / Z (shared bending term, both rows)

S_a = i_a·Fa / Ap (axial term, both rows; Fa defaults to 0, which zeroes S_a; i_a = 1.0, the code's own default for elbows/bends/miters)

B31.1 (current editions, 2020–2024 unchanged) SE = √{[|S_a| + S_b]² + (i_t·Mt / Z)²} vs SA = f·(1.25·Sc + 0.25·Sh) — Figure 104.8-1 Eq. (17)

B31.3 S_t = Mt / (2·Z), SE = √((|S_a| + S_b)² + (2·S_t)²) vs SA (same form as B31.1) — ¶319.4.4 Eq. (17)

B31.4 hoop vs F·SMYS; longitudinal SL vs 0.75·F·SMYS

B31.8 hoop vs F·E·T·SMYS; combined (SL + SE_B31.1) vs 0.90·T·SMYS

B31.1 and B31.3 sustained rows both compare the same user-supplied sustained longitudinal stress SL against the hot allowable Sh — the two rows diverge only in how they combine the expansion-case moments into SE. Both rows now run their code's current-edition Eq. (17): B31.1's has read this direction-split form since the 2020 edition (unchanged through 2024, which additionally deleted Mandatory Appendix D but left the equation itself alone); the single-i-on-resultant-moment form this card used to implement for B31.1 is the 2018-and-earlier form, not a current one. In the current editions the two expansion equations are the same expression written two ways: B31.3-2024 ¶319.4.4 defines S_t = i_t·M_t/2Z and squares 2S_t, while B31.1-2024 Figure 104.8-1 squares i_t·M_t/Z directly, and both add the axial term to the bending term before squaring. With the same inputs the two expansion rows therefore return the same S_E; the rows differ in the allowables and sustained stress the user enters for each code, which is where the comparison earns its place. Defaults when not entered: f = 1.0, F = 0.72, E = 1.0, T = 1.0, i_t = 1.0, Fa = 0.

3 · Calculation

1. Hoop stress: hoop = P·Do/(2·t) = 600·8.625/(2·0.322) = 5,175/0.644 = 8,035.71 psi — feeds both the B31.4 and B31.8 hoop checks.
2. Shared bending term: S_b = √((2.27·50,000)² + (1.89·30,000)²)/16.81 = √(113,500² + 56,700²)/16.81 = 7,547.56 psi — used by both the B31.1 and B31.3 rows. Axial term S_a = i_a·Fa/Ap = 0 (Fa not entered here — see Example 3 for a case with Fa ≠ 0).
3. B31.1 expansion stress (Figure 104.8-1 Eq. (17), current since the 2020 edition): SE = √{[|S_a| + S_b]² + (i_t·Mt/Z)²} = √{7,547.56² + (1.0·20,000/16.81)²} = √{7,547.56² + 1,189.77²} = 7,640.76 psi (i_t = 1.0 default).
4. B31.1/B31.3 allowable: SA = f·(1.25·Sc + 0.25·Sh) = 1.0·(1.25·20,000 + 0.25·17,300) = 25,000 + 4,325 = 29,325 psi.
5. B31.1: sustained unity = SL/Sh = 8,000/17,300 = 0.46243; expansion unity = SE/SA = 7,640.76/29,325 = 0.26055.
6. B31.3 expansion stress (¶319.4.4 Eq. (17)): S_t = 20,000/(2·16.81) = 594.88 psi; SE = √((S_a + S_b)² + (2·S_t)²) = √(7,547.56² + 1,189.77²) = 7,640.76 psi — identical to the B31.1 value here, because B31.3's 2·S_t reduces to the same Mt/Z that B31.1's i_t·Mt/Z gives at the default i_t = 1.0.
7. B31.3: sustained unity matches B31.1 at 0.46243 (same SL/Sh); expansion unity = 7,640.76/29,325 = 0.26055.
8. B31.4: hoop unity = 8,035.71/(0.72·35,000) = 8,035.71/25,200 = 0.31888; longitudinal unity = SL/(0.75·0.72·35,000) = 8,000/18,900 = 0.42328.
9. B31.8: hoop unity = 8,035.71/(0.72·1.0·1.0·35,000) = 0.31888 (E = T = 1.0 default); combined unity = (SL + SE_B31.1)/(0.9·1.0·35,000) = (8,000 + 7,640.76)/31,500 = 15,640.76/31,500 = 0.49653.
10. Governing row across all eight checks: B31.8 combined at 0.49653 — the highest unity in the set, still ≤ 1.0 → ALL PASS.

4 · Results PASS

5 · Verification statement

The result values above are locked as fixture analysis-set.json, case “NPS8 sch40 all four codes, moderate loads -> governing B31.8 combined 0.49653, ALL PASS”, 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 B31.1 — Power Piping, ¶104.8.1 (sustained) and Figure 104.8-1 Eq. (17) (expansion, current since the 2020 edition). · ASME B31.3 — Process Piping, ¶302.3.5 (sustained) and ¶319.4.4 Eq. (17) (expansion). · ASME B31.4 — Pipeline Transportation Systems for Liquids and Slurries, Design chapter. · ASME B31.8 — Gas Transmission and Distribution Piping Systems, Design chapter.