Straight pipe weight and axial recovery

Part VI · VerificationVI–B6

Part VI

Verification

B. Elements and loads · Straight pipe weight and axial recovery

A straight pipe two meters long has a mass of 2.5 kg per meter. Entered gravitational acceleration is 9.0 m/s², an invented value that keeps the arithmetic simple. What weight per meter should the element produce? If the far end moves 0.01 m axially, what force does the element report there?

This page preserves a recorded benchmark and its expected values. The dated run below is not a new run of the current product.

Fig. VI–B6.—Straight pipe weight and axial recovery

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
Length	L	2.0 m
Elastic modulus	E	1200.0 Pa
Area	A	3.0 m²
Mass per length	m	2.5 kg/m
Gravitational acceleration	g	9.0 m/s²
Axial displacement at end j	u_j	0.01 m

2.Method.

Weight per meter is mass per meter times gravity. The axial end force is the axial stiffness EA/L times the end displacement.

w = mg = 2.5 × 9.0 = 22.5 N/m(1)

F_j = EAu_j / L = 1200.0 × 3.0 × 0.01 / 2.0 = 18.0 N(2)

3.Results.

Weight and recovered force
Quantity	Expected
Weight per length	22.5 N/m
Local axial end force at j	18.0 N

The case record describes these checks:

The pipe element forms its local and global stiffness matrices.
Its length is 2.0 m.
Its weight per length matches the hand value.
The axial end force recovered from the given displacement matches the hand value.

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 computed value must match the reference within an absolute difference of 1.0 × 10⁻⁹ in the case’s own units. Counts and structural outcomes must match 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/mechanics/Cargo.toml straight_pipe_fixture_exercises_weight_and_recovery_path

Hand calculation: validation/hand_calcs/mechanics/straight_pipe_weight_recovery.md. Test record, with the recorded run of 2026-07-10: mech-straight-pipe-weight-recovery.md.