Part VI
Verification
B. Elements and loads · Resultants at several stations
A cantilever pipe four meters long carries −2.0 N/m over its middle half, from 1.0 m to 3.0 m. Requested shear and bending stations are deliberately out of order: 0.75, 0.25, 0.5 and 1.0 of the length. Does the solver retain that order and return the correct value at each station?
This page preserves a recorded benchmark and its expected values. The dated run below is not a new run of the current product.
Independent numerical comparison. The recorded test exercises a benchmark crate. It does not exercise the desktop product route.
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 y | Iy | 1.5 m4 |
| Second moment about z | Iz | 2.0 m4 |
| Torsion constant | J | 1.0 m4 |
| Uniform load, global Y | q | −2.0 N/m |
| Loaded span start | a/L | 0.25 |
| Loaded span end | b/L | 0.75 |
| Requested stations, in order | x/L | 0.75, 0.25, 0.5, 1.0 |
| Supports | — | Node 0 fixed, node 1 free |
2.Method.
The loading and the fixed-free solution are those of the partial-span case. The fixed-end shear is 4.0 N and the fixed-end moment 8.0 N·m.
At each station only the part of the patch between the fixed end and the station counts. The shear is the end shear plus the load on that part. The moment is the end moment less the end shear times the distance, less the moment of that part of the load about the station.
3.Results.
| Order | Station x/L | x (m) | Vy (N) | Mz (N·m) |
|---|---|---|---|---|
| 0 | 0.75 | 3.0 | 0.0 | 0.0 |
| 1 | 0.25 | 1.0 | 4.0 | 4.0 |
| 2 | 0.5 | 2.0 | 2.0 | 1.0 |
| 3 | 1.0 | 4.0 | 0.0 | 0.0 |
The case record describes these checks:
- The solver returns four stations, in the order 0.75, 0.25, 0.5, 1.0.
- The shear and bending moment at each station match the hand values.
- All returned values are finite.
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. Each computed value must match the reference within an absolute difference of 1.0 × 10−9 in the case’s own units. Counts and structural outcomes must match exactly. Long values are shown here to seven significant figures; the tests compare the full values in the record.
From 0.75 of the length onward the whole patch lies behind the section and nothing lies beyond it. Shear and moment are zero there, just as they are at the free end.
4.Recorded command.
This command belongs to the archived source at 462f66975d36cd10d5b8455193ada9517d28d353. Use a checkout of that exact revision. This edition did not run the command. The recorded result does not establish current product support.
git checkout --detach 462f66975d36cd10d5b8455193ada9517d28d353 cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/mechanics/Cargo.toml tp_phys_007_station_sweep_fixture_preserves_requested_order_and_values
Hand calculation:
validation/hand_calcs/mechanics/tp_phys_007_station_sweep_resultants.md.
Test record, with the recorded run of 2026-07-10:
mech-tp-phys-007-station-sweep-resultants.md.