Parallel Axis Theorem Calculator mechanism

Model scope

Formula is mathematically standard but the instrument specification is ambiguous about area moment of inertia versus mass moment of inertia, the required parallel-axis condition, and whether inputs describe one component or a complete composite section. The honest label should explicitly say 'Area Moment of Inertia (Second Moment of Area) about a Parallel Shifted Axis' and should document the composite summation rule.

• I=I_c+Ad² is correct for the second moment of area of one component about an axis parallel to its centroidal axis, with d measured perpendicular to the axes.
• For a composite section, the formula must be applied and summed component-by-component: I=Σ(I_ci+A_i d_i²). Holes require signed component areas and centroidal inertias.
• The term 'moment of inertia' is ambiguous: this formula computes area moment of inertia (second moment of area), not mass moment of inertia.
• The spec does not state that I_c is the centroidal second moment of area or that the shifted axis is parallel to the centroidal axis.

Units and conventions

• I_c and the output I use units of length⁴.
• A uses units of length² and d uses units of length; all three inputs must use mutually consistent length units.
• d is the perpendicular distance between parallel axes and is treated as a nonnegative distance; squaring makes the sign irrelevant mathematically.
• If SI units are used, A in m², d in m, and I_c/I in m⁴ are required.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "I_c": 200000,
    "A": 6000,
    "d": 50,
    "units": "mm⁴, mm², mm"
  },
  "expected_outputs": {
    "I": 15200000,
    "units": "mm⁴"
  },
  "working": "d² = 50² = 2,500 mm². Ad² = 6,000 × 2,500 = 15,000,000 mm⁴. I = I_c + Ad² = 200,000 + 15,000,000 = 15,200,000 mm⁴."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

An extreme but representable-looking input causes the plain JavaScript arithmetic to overflow A d² to Infinity. The calculator should reject or flag non-finite inputs and outputs. The specification has no denominator trap and no genuine formula regime switch.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json