Source: https://guthlabs.ai/docs/instruments/weld-group-line-property-calculator/mechanism/

instrument mechanism / verified-clean

# Weld Group (Line) Property Calculator mechanism

The inspectable method record for Weld Group (Line) Property Calculator, kept separate from implementation and qualification.

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

## Model scope

NEEDS_REVIEW because the supplied formula is incomplete and Ju, axis conventions, units, centroid handling, and segment rules are ambiguous. The four vectors use an explicit standard interpretation: uniform zero-width weld lines, centroidal geometric properties, u-axis along global x, Iu=∫(y-yc)²ds, and Ju=∫[(x-xc)²+(y-yc)²]ds. The honest label should state that these are idealized line-group geometric properties, not weld capacity or stress results, and should identify the output units as length³.

- The stated formula "Iu=bd²/2+..." is incomplete: variables, axis definition, segment-orientation terms, centroidal shift terms, and summation rules are undefined.

- "Ju similar for torsion" is not a formula. For a line weld group, the standard centroidal polar line property is Ju=Iu+Iv, with Ju=∫[(x-xc)²+(y-yc)²]ds.

- The specification does not define whether Iu and Ju are geometric line properties with units of length³, normalized properties, or properties including weld throat thickness.

- AISC weld-as-line tables use specific axis and geometry conventions; the cited shorthand cannot verify arbitrary line-segment geometry without an explicit general formula.

- The centroid formula and handling of disconnected, intersecting, overlapping, or zero-length segments are not specified.

## Units and conventions

- The test vectors interpret each weld as a zero-width line with uniform unit line density, so Iu, Iv, and Ju have units of length³.

- The u-axis is the global x-axis; therefore Iu=∫(y-yc)²ds.

- The perpendicular line property is Iv=∫(x-xc)²ds, and Ju=Iu+Iv.

- For a segment of length L, its own contribution about a parallel centroidal axis is L³/12; parallel-axis offsets use Ld².

- Centroid coordinates are length-weighted: xc=Σ(Li x̄i)/ΣLi and yc=Σ(Li ȳi)/ΣLi.

- Input coordinates and output properties use the declared input length unit; no automatic inch-to-millimetre conversion is assumed.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "units": "mm",
    "u_axis": "x",
    "segments": [
      {
        "start": [
          0,
          0
        ],
        "end": [
          100,
          0
        ]
      }
    ]
  },
  "expected_outputs": {
    "centroid": [
      50,
      0
    ],
    "Iu_mm3": 0,
    "Ju_mm3": 83333.333333
  },
  "working": "Segment length L=100 mm. Centroid=(0+100)/2,(0+0)/2=(50,0) mm. Iu=∫y² ds=100×0²=0 mm³. Ju=∫(x-50)²dx=100³/12=1000000/12=83333.333333 mm³."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

An empty weld pattern has total line length zero, so centroid, Iu, and Ju about that centroid are undefined. The calculator must reject the input rather than return numeric values or propagate NaN silently.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/weld-group-line-property-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/weld-group-line-property-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/weld-group-line-property-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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`