Unit Weight / Self-Weight Load Calculator (Structural Members) mechanism

Model scope

NEEDS_REVIEW because the exact ambiguity is whether the input is mass density ρ or weight density γ, and because g is unspecified for the ρ formulation. The honest label should explicitly state accepted units, the selected formulation, the gravity constant, the assumption of uniform member properties, and that the output is a downward distributed load.

• The formula w=ρ·A·g is correct only when ρ is mass density, such as kg/m³, A is in m², and g is in m/s²; the formula w=γ·A is correct only when γ is weight density, such as N/m³ or kN/m³.
• The input description 'material density/unit weight' is ambiguous because mass density ρ and weight density γ are different quantities and require different formulas.
• The specification does not state that the member is prismatic or that density and cross-sectional area are uniform along its length; otherwise w may vary with position.

Units and conventions

• For the density formulation, ρ is mass density in kg/m³, A is cross-sectional area in m², g is gravitational acceleration in m/s², and the result is w in N/m.
• For the weight-density formulation, γ is force per volume in N/m³ or kN/m³, A is in m², and w has corresponding units of N/m or kN/m.
• Test vectors use g=9.80665 m/s² unless another value is explicitly provided.
• The resulting self-weight load acts downward in the direction of gravity.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "density_rho": 7850,
    "density_unit": "kg/m³",
    "area_A": 0.01,
    "area_unit": "m²",
    "g": 9.80665,
    "g_unit": "m/s²"
  },
  "expected_outputs": {
    "w": 769.822025,
    "w_unit": "N/m",
    "w_kN_per_m": 0.769822025
  },
  "working": "w=ρ·A·g\n=7850 kg/m³ × 0.01 m² × 9.80665 m/s²\n=78.5 kg/m × 9.80665 m/s²\n=769.822025 N/m\n=0.769822025 kN/m"
}

Failure boundary

• Reject or clearly handle negative, non-finite, or missing density, weight density, area, and gravitational acceleration values.
• A zero area produces zero self-weight and should be accepted or explicitly defined as an invalid geometry boundary; negative area must be rejected.
• Do not apply g to γ because γ already includes gravitational acceleration.
• Unit mismatches, especially mm² versus m² and N/m³ versus kN/m³, can cause errors by factors of 10⁶ or 1000.
• The calculator should identify the load direction as downward and should not imply that the scalar magnitude alone fully defines a structural load.
• No division-by-zero operation is present in the stated formulas, but any later conversion or derived calculation must guard against zero denominators.

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-tranche5/tranche5-results.json