Bolt Group / Eccentric Fastener Pattern Solver

Inspectable records

Ledger state

The current ledger marks this instrument verified with errata that must be applied at binding time.

Area

Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

Tranche

tranche-6

Evidence ID

t6-099

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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).

Boundary hardening

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.

Errata and corrections

Tranche errata

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json