Part VI
Verification
E. Algorithm and software checks · Portal frame sway
Two columns four metres tall stand six metres apart and are joined across the top by a beam. Both column bases are fixed. A lateral force of 3.0 N acts at the top of the right-hand column. How far does the frame sway?
The reference does not work the sway by hand. The expected value is the solver’s own answer, stored when the case was made. The case is therefore a repeatability check on multi-element assembly and solution, not a comparison with an independent result.
A slope-deflection solution would give the sway in closed form; until it is added, this case shows only that the solve repeats.
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 |
|---|---|---|
| Node 0 (left base) | — | (0.0, 0.0, 0.0) m |
| Node 1 (left top) | — | (0.0, 4.0, 0.0) m |
| Node 2 (right top) | — | (6.0, 4.0, 0.0) m |
| Node 3 (right base) | — | (6.0, 0.0, 0.0) m |
| Elastic modulus | E | 1800.0 Pa |
| Shear modulus | G | 700.0 Pa |
| Area | A | 2.5 m2 |
| Second moment about y | Iy | 2.0 m4 |
| Second moment about z | Iz | 2.0 m4 |
| Torsion constant | J | 1.0 m4 |
| Lateral force at node 2, global X | F | 3.0 N |
2.Method.
No hand calculation of the sway is given. The reference records the frame, its supports and its load. The expected top-right sway is taken from the solver’s frame assembly and dense solution of the restrained system.
3.Results.
| Quantity | Expected |
|---|---|
| Top-right sway in X | The solver’s stored result; no hand value |
The tests check that:
- The solver assembles the three members and solves the restrained system.
- The solved sway equals the stored value, which the solver itself produced.
- The solved sway is a finite number.
What it shows. Checks that the solved value repeats a stored value. It is not an independent check.
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 solved sway must repeat the stored value within an absolute difference of 1.0 × 10−9 m. This shows repeatability only, not agreement with an independent answer. Long values are shown here to seven significant figures; the tests compare the full values in the record.
4.Run it yourself.
cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/mechanics/Cargo.toml portal_frame_fixture_solves_repeatably
Hand calculation:
validation/hand_calcs/mechanics/portal_frame_sway.md.
Test record, with the recorded run of 2026-07-10:
mech-portal-sway-original.md.