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 metres long has a mass of 2.5 kg per metre. The gravitational acceleration is entered as 9.0 m/s², an invented value that keeps the arithmetic simple. What weight per metre should the pipe element produce? And if its far end is moved 0.01 m along its axis, what axial force does the element report at that end?

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 metre is mass per metre 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 tests check that:

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.Run it yourself.

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.