An invented section carries a bending moment of 50.0 N·m about its local y axis and −30.0 N·m about its local z axis. The section moduli about those axes are 25.0 m³ and 15.0 m³. What bending normal stress does each moment produce, and does the sign of the negative moment carry through to its stress?

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.

Each bending normal stress component is the moment about an axis divided by the section modulus about the same axis. The two axes are treated separately and the sign of each stress follows the sign of its moment.

3.Results.

The tests check that:

• The stress recovery completes without being blocked.
• The bending stress about y matches 2.0 Pa.
• The bending stress about z matches −2.0 Pa, sign included.

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 recovered stress must match the hand calculation to within an absolute difference of 1.0 × 10⁻⁹ Pa. Yes-or-no conditions, such as whether the result is blocked, are checked 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/stress/Cargo.toml recovers_bending_normal_fixture

Hand calculation: validation/hand_calcs/stress/bending_normal.md. Test record, with the recorded run of 2026-07-10: stress-bending-normal-original.md.