Source: https://guthlabs.ai/docs/instruments/moment-of-inertia-section-properties-calculator/mechanism/

instrument mechanism / verified-clean

# Moment of Inertia / Section Properties Calculator mechanism

The inspectable method record for Moment of Inertia / Section Properties Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The listed equations are standard under explicit axis and unit conventions, but the specification does not define those conventions, the component formulas, or validation rules. The honest_label field is empty; it should disclose that results are axis-specific and that composite sections require fully defined geometry and parallel-axis treatment.

- The rectangle formula I=bh³/12 is correct only for the centroidal axis parallel to the width b, with h measured perpendicular to that axis; the axis is not specified.

- The circle formula I=πd⁴/64 is correct for a centroidal diameter axis of a solid circular section, but the section type, axis, and whether d is an outside diameter are not specified.

- A and centroid formulas are not explicitly provided, although A and centroid are listed as outputs.

- Composite subtraction is incomplete without the parallel-axis theorem for components whose centroids do not coincide; signed component areas and centroid locations must be defined.

- The section modulus formula S=I/c is correct only for the selected bending axis and the relevant extreme-fiber distance. For an unsymmetric section, separate top and bottom section moduli may be required.

- The radius of gyration r=√(I/A) is axis-specific, but the axis is not specified.

## Units and conventions

- All dimensions in a calculation must use one consistent length unit.

- A has units of length², centroid and c have units of length, I has units of length⁴, S has units of length³, and r has units of length.

- The test vectors use a horizontal centroidal x-axis for I, with y measured upward from the stated reference.

- For the circle vector, the origin is at the circle center, so ȳ=0 and c=d/2.

- For the hollow rectangle, the inner and outer rectangles are concentric, so no parallel-axis offset is needed.

- For mixed-unit inputs, dimensions must be converted before arithmetic; the fourth vector converts 300 mm to 0.3 m.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "section_type": "solid_rectangle",
    "b": 200,
    "h": 300,
    "length_unit": "mm",
    "axis": "centroidal horizontal x-axis",
    "y_reference": "bottom edge"
  },
  "expected_outputs": {
    "A": 60000,
    "y_bar": 150,
    "I": 450000000,
    "S": 3000000,
    "r": 86.6025
  },
  "working": "A=b×h=200×300=60,000 mm². ȳ=h/2=300/2=150 mm. I=bh³/12=200×300³/12=200×27,000,000/12=5,400,000,000/12=450,000,000 mm⁴. c=h/2=150 mm. S=I/c=450,000,000/150=3,000,000 mm³. r=√(I/A)=√(450,000,000/60,000)=√7,500=86.6025 mm."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

Zero dimensions create invalid zero-area sections and undefined radius of gyration or section modulus, while the specification does not state required positive-dimension validation. Axis selection and unspecified units can also produce materially different outputs if conventions are not made explicit.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/moment-of-inertia-section-properties-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/moment-of-inertia-section-properties-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/moment-of-inertia-section-properties-calculator/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche3/tranche3-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`