Bolt Group / Eccentric Fastener Pattern Solver mechanism

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

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