The App 13 check on the box page is a closed-form calculation. Beside it the page can run a shell finite-element model of the same header and compare the stress at the same locations. The FE result never changes the code verdict. It is an early-access check, under verification, and it is a diagnostic: a disagreement means look at the case, not that the code value is wrong.
How the model is built
- A structured quad shell mesh of the box, on the plate mid-surfaces (or on the inside surfaces in an inside-offset mode), quarter model with symmetry cuts and an auxiliary node for the rigid motions.
- Uniform internal pressure on every wetted part, along the outward normal. Operating and test cases are two meshes, corroded and new thickness.
- Readings: at each read line, an exact linearisation across the line gives the membrane Sm, the bending Sb on each face and the total ST, taken at mid-length. This is the same decomposition App 13 uses.
- Equilibrium is checked and reported: auxiliary reactions near zero, pair B membrane forces adding up to P·H', and the symmetry reactions equal to the pressure resultant.
Why the reference is App 13 at FE dimensions
App 13 works on inside spans. A mid-surface shell model has centreline spans, so its moments are larger. The comparison therefore uses App 13 evaluated at the FE geometry: H' = H + (t2 + t22)/2, h' = h + t1 in mid-surface mode, gross plates and no corrosion allowance.
Span effect, E4.12.1 box (V-PTB-1), no holes, P = 400 psi, t = 0.875 in
| Inside spans, H = 7.375, h = 9.5 | F = 0.82635, M_Q = 2485.9, Sb at Q = 19481.6 psi |
| Mid-surface spans, H' = 8.25, h' = 10.375 | F = 0.83713, M_Q = 3003.6, Sb at Q = 23538.8 psi |
| Difference | +20.8 % |
A shell model that reads 23.5 ksi at the corner is in agreement with the code at its own dimensions. Compared with 19.5 ksi it would look 21 % high.
Tolerances of the comparison table, on the FE aspect r = Lv'/max(H', h'): mid-surface, r ≥ 8, membrane 1 % and bending or total 2 %; 2 < r < 8, 3 %; inside-offset model, 5 %; r ≤ 2, recorded only, with J2 and J3 shown beside. A difference within a tenth of the largest App 13 total stress in the table is not flagged, so a bending value near an inflection point does not fail on noise.
What is verified against what
- Engine against published or printed values: PTB-4 E4.12.1 (sketch 1 with ligaments, V-PTB-1), E4.6.2 (end plate, V-PTB-3), E4.12.2 (sketch 4 reinforced box, V-PTB-2), and COMPRESS job 50183 (hot corroded V-C1, hydrotest V-C2, end plate V-C3). The fixtures hold the printed values and full-precision recomputations.
- Engine against an independent rigid-frame solver (V-OR-1 to V-OR-6): sketches 1 to 3, 7 and 8. This is also how the corrections to the printed sketch (2) equations were confirmed.
- Tank module against its reference calculation sheet (V-T1 to V-T4). This is the Roark and Moss rectangular atmospheric tank, not App 13.
- FE model against App 13 at FE dimensions (FV1, FV2, FV4, FV5, FV6) and against CalculiX 2.22 on the same mesh (FV9).
FV1: FE corner bending against App 13 at FE dimensions, with mesh refinement (psi)
| Reference, Sb at Q | 23538.8 |
| Mesh factor 3 (786 elements) | 23379.8 (−0.68 %) |
| Mesh factor 2 (1374) | 23447.6 (−0.39 %) |
| Mesh factor 1.4 (2704) | 23491.9 (−0.20 %) |
| Mesh factor 1 (5122) | 23513.6 (−0.11 %) |
| Mesh factor 0.7 (10458) | 23526.5 (−0.05 %) |
Values from the validation note, measured 2026-10-12. The percentages are computed here. Membranes agree to 0.00 %. The corner converges from below, monotonic toward the closed-form value. FV9 (CalculiX S4, same mesh): displacement at M −0.9 %, midspan transverse stress at A.N and B.M 0.00 %.
Where they do not agree
- FV2 (Lv about 3.9 times the span): midspan bending of pair A is +3.19 % on the coarser mesh, over the 3 % target. About 2.4 % is end-plate restraint; the target is met on the finer mesh.
- FV3 (short box, Lv/h 1.5): recorded only. Pair A midspan bending in the FE is about twice the App 13 basic value, and the J2 of the code does not describe it. This is a small difference of large moments.
- FV7 (inside-offset): corners and M within 4.3 %, but midspan N of pair A is −42 %, outside the 5 % target. Open for an engineer's decision.
- FV5, FV6 (stays): corners and N within 1.2 % on the mid-surface mesh. The stay junction is −12 % for sketch (7) and +3 % and −37 % on the two sides of an (8) stay. The cause is that 13-9 takes the plates inextensible and the stays pin-jointed; a beam frame on the same node lines agrees with the FE within about 2 %.
Not covered
- FV8, sketch (4) members as shell webs and flanges: the mesher refuses members in this version. Sketch (4) has the closed-form check against PTB-4 but no FE comparison.
- Nozzles and openings, local piping loads, thermal gradients and fatigue: none of these is in the box model or in the engine.
- Not run in a signed-in browser at the time of the validation note; the page behaviour was tested in unit tests and static renders.
- Sketches (5), (6), obround shells, external pressure and the other App 13 paragraphs listed in article 2.
[UNVERIFIED] The FE agreement figures quoted here come from the validation note of 2026-10-12 and were not re-run for this article. The span-effect example and the refinement percentages were recomputed from the formulas and the quoted values.