Thick-Wall Cylinder Stress (Lamé)

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

Tranche

tranche-6

Evidence ID

t6-044

Ledger rows

1

No ledger note is attached.

Review findings

The radial and hoop Lamé formulas are standard and pass the four checks above. Verdict is NEEDS_REVIEW because units, admissible input constraints, sign convention, Lamé assumptions, and the conditional nature of the claimed inner-wall maximum are not fully specified.

Formula and scope findings

• The Lamé formulas are correct when the stated minus sign applies only to the second B/r² term: σ_hoop=A+B/r² and σ_radial=A−B/r², with A=(p_i r_i²−p_o r_o²)/(r_o²−r_i²) and B=r_i² r_o²(p_i−p_o)/(r_o²−r_i²).
• The claim 'max at inner wall' is conditional, not universal: hoop stress decreases outward when p_i>p_o, increases outward when p_i<p_o, and is constant when p_i=p_o. The instrument should state whether 'max' means maximum algebraic value or maximum absolute stress.
• The specification omits the required geometric constraint r_o>r_i>0 and the evaluation constraint r_i≤r≤r_o.
• The honest label should state the usual Lamé assumptions: homogeneous isotropic elastic material, axisymmetric loading, static equilibrium, small strain, and no body-force contribution. Axial stress from closed ends is not computed.

Unit assumptions

• r_i, r_o, and r must use the same length unit; all squared-radius terms then use that unit squared.
• p_i and p_o must use the same pressure/stress unit, and the output stresses use that unit.
• Tensile stress is taken as positive and compressive stress as negative; positive p_i and p_o denote applied inward pressure magnitudes.
• The formulas are valid only for r_o>r_i>0 and r_i≤r≤r_o.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The supplied specification has no stated validation for r_o>r_i. Setting r_o=r_i makes the Lamé denominator zero and both stress outputs undefined; the instrument must reject this input rather than plot or return a numeric value.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "r_i": 50,
    "r_o": 100,
    "p_i": 10,
    "p_o": 0,
    "r": 50,
    "length_unit": "mm",
    "pressure_unit": "MPa"
  },
  "expected_outputs": {
    "sigma_hoop": 16.666667,
    "sigma_radial": -10,
    "max_hoop_stress_in_wall": 16.666667,
    "max_hoop_location": "r_i=50 mm",
    "stress_unit": "MPa"
  },
  "working": "D=r_o²−r_i²=100²−50²=10000−2500=7500 mm². A=(10×2500−0×10000)/7500=25000/7500=3.333333 MPa. B=(2500×10000×(10−0))/7500=250000000/7500=33333.333333 MPa·mm². At r=50 mm, B/r²=33333.333333/2500=13.333333 MPa. Therefore σ_hoop=A+B/r²=3.333333+13.333333=16.666667 MPa; σ_radial=A−B/r²=3.333333−13.333333=−10.000000 MPa. Since B>0, hoop stress decreases with r, so the algebraic maximum is at the inner wall."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json