A straight pipe 4.0 m long carries an axial effect of 120.0 N. Known I-end shear is 4.0 N, and I-end bending moment is 8.0 N·m. A uniform load of −2.0 N/m acts along the full length. What axial force and bending moment occur at midspan? What axial and bending stresses follow? No pressure is supplied.

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.

The axial effect is recovered as in the thermal axial case: with no displacement, the I-end axial force is N_i = 120.0. That force is combined with the given I-end shear and moment.

At midspan, x = 2.0 m, the load acting on the I-side free body runs from 0.0 m to 2.0 m. The axial force is unchanged along the pipe. The two stresses follow from force over area and moment over section modulus.

3.Results.

The case record describes these checks:

• The midspan stress recovery completes without being blocked and is labeled as this case’s midspan station.
• The midspan axial force matches 120.0 N and the bending moment matches 4.0 N·m.
• The axial stress matches 20.0 Pa and the bending stress about z matches 2.0 Pa.
• No hoop or longitudinal pressure stress is reported.
• The result carries the review flags the program attaches to every result.

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 force, moment and stress must match the hand calculation to within an absolute difference of 1.0 × 10⁻⁹ in its own units. Labels, flags and the absence of pressure stresses 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 combined_axial_effect_and_bending_resultants_feed_station_stress_recovery

Hand calculation: validation/hand_calcs/stress/tp_phys_009_combined_axial_bending_to_stress.md. Test record, with the recorded run of 2026-07-10: stress-tp-phys-009-combined-axial-bending-to-stress.md.