Displacement Stress Range Check (ASME B31.3 ¶319.4.4) — Sample Report

1 · Design inputs

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.

2 · Method

S_b = √( (i_i·M_i)² + (i_o·M_o)² ) / Z   S_t = M_t / (2Z)

S_E = √( S_b² + 4·S_t² )   (Eq. 17)

S_A = f · (1.25·S_c + 0.25·S_h)   (Eq. 1a)

PASS when S_E ≤ S_A. The card works the chain in order: the in-plane and out-of-plane moment ranges are intensified by their SIFs and combined into the resultant bending stress S_b over the section modulus; the torsional range produces S_t on 2Z; Eq. (17) combines bending and torsion into the displacement stress range; and Eq. (1a) builds the allowable from the cold and hot allowable stresses S_c and S_h, scaled by the cyclic factor f. The utilization S_E/S_A is reported alongside the verdict so the margin is visible, not just the outcome. The cyclic factor comes from the Fatigue Factor card (f = 1.0 up to 7,000 equivalent cycles, falling for higher cycle counts); every stress input — moments, SIFs, Z, allowables — is yours, so the same card checks any point of any system regardless of which tool produced the analysis.

3 · Calculation

1. Bending: S_b = 2.26557·44,139 / 8.49575 = 100,000 / 8.49575 = 11,770.6 psi; S_t = 0.
2. Stress range: S_E = √(11,770.6² + 0) = 11,770.6 psi.
3. Allowable: S_A = 1.0·(1.25·20,000 + 0.25·17,300) = 25,000 + 4,325 = 29,325 psi.
4. Utilization: 11,770.6 / 29,325 = 0.40 → PASS.

4 · Results PASS

5 · Verification statement

The result values above are locked as fixture displacement-stress.json, case “PVP: pure in-plane SE + SA”, tolerance 0.01, 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 — ¶319.4.4 Eq. (17); ¶302.3.5(d) Eq. (1a) allowable stress range.