Torsional shear stress — SWBPIPE verification

Part VI · VerificationVI–C6

Part VI

Verification

C. Stress recovery · Torsional shear stress

An invented section with torsion constant 80.0 m⁴ carries torque of 40.0 N·m. What shear stress occurs at radius 2.0 m? Torque, radius and torsion constant are direct inputs. The case tests only recovery.

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.

Fig. VI–C6.—Torsional shear 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
Torsional moment	T	40.0 N·m
Torsion radius	r	2.0 m
Torsion constant	J	80.0 m⁴

2.Method.

In elastic torsion of a circular or annular section the shear stress grows in proportion to the radius. At radius r it is the torque times r divided by the torsion constant.

τ = T r / J = 40.0 × 2.0 / 80.0 = 1.0 Pa(1)

3.Results.

Expected torsional shear stress
Quantity	Expected
Torsional shear stress, τ	1.0 Pa

The case record describes these checks:

The stress recovery completes without being blocked.
The recovered torsional shear stress matches 1.0 Pa.

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. The 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 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 recovers_torsional_shear_fixture

Hand calculation: validation/hand_calcs/stress/torsional_shear.md. Test record, with the recorded run of 2026-07-10: stress-torsional-shear-original.md.