Archive · 12 October 2026 · Reduced wall to section stress

Part VI · VerificationVI–C14

Part VI

Verification

C. Stress recovery · Reduced wall to section stress

A pipe has outside diameter 0.2 m and nominal wall thickness 0.01 m. The user removes 0.002 m for corrosion and 0.00125 m for mill tolerance, both entered as thicknesses. The pipe carries axial force, two moments, torque and internal pressure. What properties and stresses follow from the thinner wall? Does the additional reduction decrease section modulus?

Mill tolerance is a user-entered absolute thickness, not a fraction. The solver supplies no value. If the input is absent, the calculation makes no mill-tolerance reduction. The numbers are invented.

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 stress components, not code stress. The current ordinary preview reports supported straight circular normal-stress extrema. Torsional shear remains separate, and arc maxima are withheld. Component recovery in this benchmark does not establish the current maximum or its coverage.

This benchmark supplies pressure inputs directly to the historical membrane-stress helper. The current ordinary preview refuses nonzero legacy pressure. The exact_straight_pressure_v2 route admits homogeneous isotropic straight circular members. It requires selected E/nu, explicit collinear equal-bore pressure regions, terminal ownership and declared closure-transfer paths. Pressure is uniform internal differential pressure with zero external pressure. This recorded calculation does not establish that route.

Read with

This case uses the reduced wall for stress. The program also uses the reduced wall for stiffness and weight. Flexibility analysis normally distinguishes those wall bases (Status).

Fig. VI–C14.—Reduced wall to section 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
Outside diameter	D_o	0.2 m
Nominal wall thickness	t_nom	0.01 m
Corrosion allowance	c	0.002 m
Mill tolerance	m	0.00125 m
Axial force	F	5000.0 N
Bending moment about local y	M_y	1000.0 N·m
Bending moment about local z	M_z	−400.0 N·m
Torsional moment	T	250.0 N·m
Internal pressure	p	2000.0 Pa

2.Method.

Effective wall equals nominal wall minus corrosion allowance and mill tolerance. Outside diameter stays constant, and the bore increases. Annulus formulas give area and second moment. Section modulus equals second moment divided by outer radius. Torsion constant equals twice the second moment.

Stress formulas use force divided by area, moment divided by section modulus, and torque times outer radius divided by torsion constant. Hoop stress uses mean radius and effective wall. Longitudinal pressure stress is half the hoop stress. A section with corrosion allowance alone provides the comparison.

The benchmark calculates effective-wall section properties and passes them to stress recovery. The source note also records independent decimal arithmetic for the reference values.

t_eff = 0.01 − 0.002 − 0.00125 = 0.00675 m(1)

D_i = D_o − 2t_eff = 0.2 − 0.0135 = 0.1865 m(2)

A = (π/4)(D_o² − D_i²) = (π/4)(0.04 − 0.03478225) = 4.098011267067042 × 10⁻³ m²(3)

I = (π/64)(D_o⁴ − D_i⁴) = 1.9153656442289003 × 10⁻⁵ m⁴(4)

Z = I / (D_o/2) = 1.9153656442289 × 10⁻⁴ m³, J = 2I = 3.8307312884578006 × 10⁻⁵ m⁴(5)

r_torsion = D_o/2 = 0.1 m, r_m = (D_o − t_eff)/2 = 0.096625 m(6)

σ_hoop = p r_m / t_eff = 2000.0 × 0.096625 / 0.00675 = 2.862962962962963 × 10⁴ Pa(7)

Corrosion only: t_eff,c = 0.01 − 0.002 = 0.008 m, D_i,c = 0.184 m, Z_c = 2.2274444834258686 × 10⁻⁴ m³(8)

3.Results.

Expected section properties and stresses
Quantity	Expected
Effective wall, t_eff	0.00675 m
Area, A	4.098011 × 10⁻³ m²
Section modulus, Z	1.915366 × 10⁻⁴ m³
Section modulus, corrosion only, Z_c	2.227444 × 10⁻⁴ m³
Axial normal stress	1.220104 × 10⁶ Pa
Bending stress about y	5.220935 × 10⁶ Pa
Bending stress about z	−2.088374 × 10⁶ Pa
Torsional shear stress	6.526169 × 10⁵ Pa
Hoop pressure stress	2.862963 × 10⁴ Pa
Longitudinal pressure stress	1.431481 × 10⁴ Pa

The case record describes these checks:

The stress recovery on the effective-wall section completes without being blocked.
The axial, both bending, torsional shear, hoop and longitudinal stresses each match the table.
The section modulus with the mill tolerance taken off is smaller than with the corrosion allowance alone.
The section area with the mill tolerance taken off is also smaller.
The two section comparisons are made on the benchmark’s own section arithmetic, not on a solver section-property routine.

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 stress must match the hand calculation to within an absolute difference of 1.0 × 10⁻⁹ Pa. The two section comparisons are strict inequalities, checked exactly. Long values are shown here to seven significant figures; the tests compare the full values in the record.

For the student

The bore increases while outside diameter stays constant, so outer-fiber distance is unchanged. Bending stress rises because second moment and section modulus decrease. Hoop stress rises because the wall is thinner and mean radius is larger.

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/stress/Cargo.toml recovers_milltol_effective_wall_fixture
cargo test --manifest-path validation/benchmarks/stress/Cargo.toml milltol_reduction_strictly_reduces_section_modulus

Hand calculation: validation/hand_calcs/stress/tp_pmm_p3_milltol_effective_wall_stress.md. Test record, with the recorded run of 2026-07-10: stress-tp-pmm-p3-milltol-effective-wall-stress.md.