Source: https://guthlabs.ai/docs/instruments/bolt-group-eccentric-fastener-pattern-solver/mechanism/

instrument mechanism / verified-with-binding-errata

# Bolt Group / Eccentric Fastener Pattern Solver mechanism

The inspectable method record for Bolt Group / Eccentric Fastener Pattern Solver, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The stated method is standard for elastic planar bolt-group analysis when coordinates are centroid-relative, the group is rigid, bolts have equal stiffness, and the eccentric load is converted to a signed out-of-plane moment. The specification is NEEDS_REVIEW because it does not define the torsional vector direction/sign, centroid reference, signed eccentricity convention, or planar/unit constraints. Vector 3 is a unit-consistent inch example; its arithmetic uses J=8 in² because each of four corner bolts has r²=2 in².

- The direct-shear formula F'=P/n is valid only when the applied shear force is shared equally and is represented as a vector; the force direction is not specified.

- The torsional formula F''=Pe·r_i/Σr_i² gives only magnitude. The solver must specify the tangential direction at each bolt, including its sign, for vector summation.

- Eccentricity must be converted to a signed moment M=r_load×P, or defined as a signed perpendicular distance. A scalar Pe is ambiguous when the load and eccentricity are not perpendicular.

- Bolt coordinates must be measured from the bolt-group centroid; this required constraint is not stated.

- The method assumes a planar bolt group, identical bolt stiffness, rigid connected material, and elastic no-slip load sharing. These assumptions should be explicit in the computation model.

## Units and conventions

- All coordinates, eccentricities, and distances in a given vector use one consistent length unit.

- Force and moment units must be consistent: N with mm gives N·mm; lbf with in gives lbf·in.

- For the test vectors, the applied force is P=(0,-P), the eccentricity is e=(e,0), and the signed applied moment is M=e_xP_y=-Pe.

- Coordinates are relative to the bolt-group centroid.

- Using J=Σr_i²=Σ(x_i²+y_i²), the resisting tangential force used in the vectors is F_t,i=(M y_i/J,-M x_i/J).

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "units": "N, mm",
    "bolt_coordinates_mm": [
      [
        50,
        50
      ],
      [
        50,
        -50
      ],
      [
        -50,
        50
      ],
      [
        -50,
        -50
      ]
    ],
    "applied_force_N": [
      0,
      -4000
    ],
    "eccentricity_mm": [
      100,
      0
    ]
  },
  "expected_outputs": {
    "J_mm2": 20000,
    "moment_Nmm": -400000,
    "direct_shear_per_bolt_N": [
      0,
      -1000
    ],
    "per_bolt_resultants_N": [
      [
        -1000,
        0
      ],
      [
        1000,
        0
      ],
      [
        -1000,
        -2000
      ],
      [
        1000,
        -2000
      ]
    ],
    "per_bolt_magnitudes_N": [
      1000,
      1000,
      2236.067977,
      2236.067977
    ],
    "critical_bolts": [
      3,
      4
    ],
    "critical_force_N": 2236.067977
  },
  "working": "n=4, so F_d=P/n=(0,-4000)/4=(0,-1000) N. J=4(50²+50²)=4(5000)=20000 mm². M=e_xP_y=100(-4000)=-400000 N·mm. For each bolt F_t=(M y/J,-M x/J)=(-20y,20x) N. Bolt 1 (50,50): F_t=(-1000,1000), total=(-1000,1000)+(0,-1000)=(-1000,0), magnitude=√(1000²)=1000 N. Bolt 2 (50,-50): F_t=(1000,1000), total=(1000,0), magnitude=1000 N. Bolt 3 (-50,50): F_t=(-1000,-1000), total=(-1000,-2000), magnitude=√(1000²+2000²)=√5000000=2236.067977 N. Bolt 4 (-50,-50): F_t=(1000,-1000), total=(1000,-2000), magnitude=2236.067977 N."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The solver has an undefined-result failure for coincident bolt coordinates because the polar sum J becomes zero. It also has a convention-sensitive result: reversing the eccentricity sign or interpreting units differently reverses or rescales the torsional distribution and can change the critical bolt.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/bolt-group-eccentric-fastener-pattern-solver/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/bolt-group-eccentric-fastener-pattern-solver/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/bolt-group-eccentric-fastener-pattern-solver/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-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`