A cantilever pipe four metres long carries −2.0 N/m over its middle half, from 1.0 m to 3.0 m. Shear and bending moment are asked for at four stations, deliberately out of order: 0.75, 0.25, 0.5 and 1.0 of the length. Does the solver return the answers in the order asked, with the right value at each station?

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.

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.

The tests check that:

• 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.

4.Run it yourself.

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.