Source: https://guthlabs.ai/docs/instruments/thick-wall-cylinder-stress-lame/
instrument / verified-clean
# Thick-Wall Cylinder Stress (Lamé)
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## 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_ir_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`