An invented pipe has outside diameter 2.0 m and wall thickness 0.25 m. Midspan shear is 4.0 N, and bending moment is 4.0 N·m. Axial force and torque are zero. What area, section modulus and torsion constant does the section have? What stresses do the midspan resultants produce?

The case also tests transfer of section properties. A separate section calculation supplies properties with its own source record. The properties are not typed directly into the stress benchmark.

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 mechanics stress components. Component recovery does not establish a combined stress maximum or code stress.

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.

2.Method.

Inside diameter equals outside diameter minus twice the wall thickness. Annulus formulas give area, second moment and torsion constant. Symmetry gives equal section moduli about y and z. Each section modulus equals second moment divided by outer radius.

Midspan resultants from the upstream mechanics case enter recovery directly. This test does not solve the model again. A separate machine-readable section calculation evaluates the same formulas independently of the solver. Its results are compared with exported section values.

3.Results.

The case record describes these checks:

• The section properties carry their source record, with an outside diameter of 2.0 m and a wall of 0.25 m.
• The section moduli about y and z are equal.
• The midspan stress recovery completes without being blocked and is labeled as this case’s midspan station.
• The midspan shear matches 4.0 N and the bending moment matches 4.0 N·m.
• The axial stress, bending stress about y and torsional shear stress match 0.0 Pa. The bending stress about z matches 7.450270250336039 Pa.
• No pressure stress is reported, and the result carries the standard review flags.

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 checked value must match the hand calculation to within an absolute difference of 1.0 × 10⁻⁹ in its own units. Labels, flags and the source record are checked exactly. Long values are shown here to seven significant figures; the tests compare the full values in the record.

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/stress/Cargo.toml canonical_analytical_payload_resultants_feed_station_stress_recovery

Hand calculation: validation/hand_calcs/stress/tp_phys_015_canonical_resultant_stress.md (with validation/hand_calcs/stress/generated/tp_phys_015_section_property_stress_witness.md). Test record, with the recorded run of 2026-07-10: stress-tp-phys-015-canonical-resultant-stress-recovery.md.