Composite Section Builder mechanism

Model scope

The supplied centroid and parallel-axis formulas are conditionally standard, but the instrument's advertised outputs are underdefined. Before release, specify coordinate conventions, target inertia axis, x-bar support, void and overlap semantics, rotated-shape handling, and explicit section-modulus definition(s). The empty honest_label is a concern because the current claim implies general combined centroid, I, and S computation despite those missing definitions.

• The centroid formula is standard for the y-coordinate only; a claim of combined centroid normally requires both x-bar and y-bar, but no x-coordinate formula is provided.
• The inertia formula is standard only for a specified common axis and parallel centroidal component inertias: I=Σ(I_ci+A_i d_i²). The target axis, orientation, and whether I means I_x, I_y, or another property are unspecified.
• Section modulus S is listed as an output but no formula is provided. Under a simple bending interpretation, S=I/c, with separate values for the nearest extreme fiber above and below the neutral axis when they differ.
• The specification does not state how rotated shapes, holes, negative areas, or component products of inertia are handled.
• The specification does not state whether shape positions are bottom-edge coordinates, centroid coordinates, or global reference coordinates; the meaning of y_i and d_i is therefore ambiguous.

Units and conventions

• All dimensions and coordinates in a vector use one consistent length unit.
• Area uses length², centroid coordinates use length, second moment of area I uses length⁴, and section modulus S uses length³.
• The test vectors interpret y as the vertical coordinate, I as the second moment about the horizontal centroidal x-axis, and d_i=y_i-y-bar.
• For rectangles, I_ci=b h³/12 about the rectangle's own horizontal centroidal axis.
• For section modulus, S=I/c where c is the larger distance from the combined centroidal axis to the relevant outer extreme fiber; this convention must be made explicit in the product.
• Negative-area components are interpreted as voids, with both their area and inertia contribution signed negatively.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "units": "mm",
    "axis": "horizontal centroidal x-axis",
    "shapes": [
      {
        "type": "rectangle",
        "width": 20,
        "height": 180,
        "y_bottom": 0,
        "area_sign": 1
      },
      {
        "type": "rectangle",
        "width": 100,
        "height": 20,
        "y_bottom": 180,
        "area_sign": 1
      }
    ]
  },
  "expected_outputs": {
    "A_mm2": 5600,
    "y_bar_mm": 125.7142857143,
    "I_x_mm4": 24643809.5238,
    "S_mm3": 196030.3030303
  },
  "working": "Web: A1=20×180=3600 mm²; y1=0+180/2=90 mm; Ic1=20×180³/12=9,720,000 mm⁴. Flange: A2=100×20=2000 mm²; y2=180+20/2=190 mm; Ic2=100×20³/12=66,666.6667 mm⁴. Total area: A=3600+2000=5600 mm². Centroid: y-bar=(3600×90+2000×190)/5600=(324,000+380,000)/5600=125.7142857 mm. Offsets: d1=90−125.7142857=−35.7142857 mm; d2=190−125.7142857=64.2857143 mm. Inertia: I=[9,720,000+3600×(35.7142857)²]+[66,666.6667+2000×(64.2857143)²]=[9,720,000+4,591,836.7347]+[66,666.6667+8,265,306.1224]=24,643,809.5238 mm⁴. Extreme distances: bottom c_bottom=125.7142857 mm; top c_top=200−125.7142857=74.2857143 mm; use c=max=125.7142857 mm. S=24,643,809.5238/125.7142857=196,030.3030 mm³."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

An all-zero assembled section creates ΣA=0 and produces an undefined centroid and section modulus; the builder must reject it. Degenerate zero-dimension shapes also require an explicit acceptance or rejection policy. In addition, the single S output is convention-sensitive unless the instrument clearly defines the reference extreme fiber and the positive-y direction.

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