Part VI
Verification
C. Stress recovery · Oriented pipe, midspan stress
A 4.0 m cantilever runs from (0.0, 0.0, 0.0) to (0.0, 4.0, 0.0), along global Y. Reference vector (1.0, 0.0, 0.0) fixes local y. The pipe carries local load of −2.0 N/m and a midspan point force of −4.0 N. Free-end movement is given in global coordinates. Does recovery give the same midspan moment and bending stress as the pipe along X?
This page preserves a recorded benchmark and its expected values. The dated run below is not a new run of the current product.
These calculations recover separate stress components, not code stress. The current ordinary preview reports supported straight circular normal-stress extrema. Torsional shear remains separate, and arc maxima are withheld. Component recovery in this benchmark does not establish the current maximum or its coverage.
1.Inputs.
Illustrative values, taken from no standard and chosen so the arithmetic can be followed by hand. Most do not describe a real pipe; read them in any consistent set of units.
| Quantity | Symbol | Value |
|---|---|---|
| Length | L | 4.0 m |
| Elastic modulus | E | 1000.0 Pa |
| Shear modulus | G | 400.0 Pa |
| Area | A | 3.0 m2 |
| Second moment about local y | Iy | 1.5 m4 |
| Second moment about local z | Iz | 2.0 m4 |
| Torsion constant | J | 1.0 m4 |
| Uniform local y load | q | −2.0 N/m |
| Point local y force | P | −4.0 N |
| Point force station | a/L | 0.5 |
| Node 1 global displacement | UX | −0.04533333 m |
| Node 1 global rotation | RZ | 0.01466667 rad |
| Section modulus about y | Zy | 2.5 m3 |
| Section modulus about z | Zz | 2.0 m3 |
| Torsion radius | r | 0.5 m |
2.Method.
With the reference vector, local x follows global +Y, and local y follows global +X. Local z follows global −Z. Before force recovery, the solver transforms global displacements into local coordinates. Local deflection and rotation then equal those of the pipe along global X.
Recovery along the pipe is unchanged. Fixed-end shear is Vy,i = 12.0, and moment is Mz,i = 24.0. Recovery includes the point force at the station. Bending stress equals moment divided by section modulus.
3.Results.
| Quantity | Expected |
|---|---|
| Midspan bending moment, Mz | 4.0 N·m |
| Bending stress about z | 2.0 Pa |
| Axial normal stress | 0.0 Pa |
The case record describes these checks:
- The midspan stress recovery completes without being blocked and is labeled as this case’s midspan station.
- The midspan bending moment matches 4.0 N·m.
- The bending stress about z matches 2.0 Pa.
- The axial normal stress is exactly zero.
- The result carries the review flags the program attaches to every result.
What it shows. Compared with an independent hand calculation.
Path exercised. The benchmark calls the solver’s components directly: elements, loads, frame solver and stress recovery. It does not go through the program’s own model-to-solve path.
Agreement. The moment and stresses must match the hand calculation to within an absolute difference of 1.0 × 10−9 in their own units. The zero axial stress, station label and review flag are checked exactly. Long values are shown here to seven significant figures; the tests compare the full values in the record.
Global rotation about Z is positive, while local rotation about z is negative. The local z axis follows global −Z, so one physical rotation has opposite signs in these frames. Force recovery in the wrong frame can produce sign errors.
4.Recorded command.
This command belongs to the linked case record and its recorded execution path. This website update did not rerun it. A historical command or result does not establish current product support.
cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/stress/Cargo.toml oriented_load_to_stress_fixture_recovers_midspan_bending_from_global_model
Hand calculation:
validation/hand_calcs/stress/tp_phys_005_oriented_load_to_stress.md.
Test record, with the recorded run of 2026-07-10:
stress-tp-phys-005-oriented-load-to-stress.md.