Moment of Inertia / Section Properties Calculator mechanism

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

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