Straight-pipe end forces to stress — SWBPIPE verification

Part VI · VerificationVI–C3

Part VI

Verification

C. Stress recovery · Straight-pipe end forces to stress

A straight pipe 5.0 m long runs along the global x axis from node 0 to node 1. Node 1 is moved 0.01 m along the pipe and twisted 0.02 rad about its axis. What axial force and twisting moment act at that end of the element, and what axial stress and torsional shear stress do they produce in the section?

The case checks the hand-off from the element’s end forces to stress recovery. Only the axial and torsional terms are active.

Fig. VI–C3.—Straight-pipe end forces to 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
Elastic modulus	E	2000.0 Pa
Shear modulus	G	800.0 Pa
Area	A	4.0 m²
Torsion constant	J	2.0 m⁴
Torsion radius	r	0.5 m
Length	L	5.0 m
Node 1 axial displacement	u_x	0.01 m
Node 1 torsional rotation	θ_x	0.02 rad

2.Method.

The axial stiffness of the element is EA/L and its torsional stiffness is GJ/L. Each stiffness times the imposed stretch or twist gives the force or moment at end j. The end values are taken directly, with no change of sign.

The axial stress is the end force divided by the area. The torsional shear stress is the end moment times the torsion radius divided by the torsion constant.

k_x = EA / L = 2000.0 × 4.0 / 5.0 = 1600.0(1)

F_x,j = k_x u_x = 1600.0 × 0.01 = 16.0 N(2)

k_t = GJ / L = 800.0 × 2.0 / 5.0 = 320.0(3)

M_x,j = k_t θ_x = 320.0 × 0.02 = 6.4 N·m(4)

σ_axial = F_x,j / A = 16.0 / 4.0 = 4.0 Pa(5)

τ = M_x,j r / J = 6.4 × 0.5 / 2.0 = 1.6 Pa(6)

3.Results.

Expected end forces and stresses at end j
Quantity	Expected
End-j axial force, F_x,j	16.0 N
End-j torsional moment, M_x,j	6.4 N·m
Axial normal stress, σ_axial	4.0 Pa
Torsional shear stress, τ	1.6 Pa

The tests check that:

The end forces are reported for end j of the element.
The end axial force matches 16.0 N and the end torsional moment matches 6.4 N·m.
The axial normal stress matches 4.0 Pa and the torsional shear stress matches 1.6 Pa.
The stress recovery completes without being blocked.
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 checked force, moment and stress must match the hand calculation to within an absolute difference of 1.0 × 10⁻⁹ in its own units. Yes-or-no conditions, such as the end label and the review flag, are checked 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/stress/Cargo.toml integrated_straight_pipe_resultants_feed_stress_recovery_fixture

Hand calculation: validation/hand_calcs/stress/integrated_straight_pipe_resultants.md. Test record, with the recorded run of 2026-07-10: stress-integrated-straight-pipe-original.md.