Bending normal stress — SWBPIPE verification

Part VI · VerificationVI–C2

Part VI

Verification

C. Stress recovery · Bending normal stress

An invented section carries moments of 50.0 N·m about local y and −30.0 N·m about local z. The corresponding section moduli are 25.0 m³ and 15.0 m³. What bending normal stress does each moment produce? Does the negative moment give a negative stress component?

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 stress components, not code stress. The current ordinary preview reports supported straight circular normal-stress extrema. Torsional shear remains separate, and arc maxima are withheld. Component recovery in this benchmark does not establish the current maximum or its coverage.

Fig. VI–C2.—Bending normal 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.

Quantity	Symbol	Value
Bending moment about local y	M_y	50.0 N·m
Section modulus about local y	Z_y	25.0 m³
Bending moment about local z	M_z	−30.0 N·m
Section modulus about local z	Z_z	15.0 m³

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.

σ_b,y = M_y / Z_y = 50.0 / 25.0 = 2.0 Pa(1)

σ_b,z = M_z / Z_z = −30.0 / 15.0 = −2.0 Pa(2)

3.Results.

Expected bending stresses
Quantity	Expected
Bending normal stress about y, σ_b,y	2.0 Pa
Bending normal stress about z, σ_b,z	−2.0 Pa

The case record describes these checks:

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.Recorded command.

This command belongs to the linked case record and its recorded execution path. This website update did not rerun it. A historical command or result does not establish current product support.

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.