Key & Keyway Shear/Bearing Stress Calculator mechanism

Model scope

The two supplied stress formulas are conditionally standard, but the instrument cannot be released as specified because SF is an advertised output with no input or formula, and the meaning of h is not explicitly defined. Specify the torque unit policy, effective bearing height convention, allowable-stress basis, and safety-factor definition before release.

• The shear formula τ=2T/(d·w·L) is standard for nominal key shear stress when the transmitted tangential force is 2T/d and T, d, w, and L use compatible units.
• The bearing formula σ_bearing=4T/(d·h·L) is standard only when h is the effective key height bearing against the hub or shaft, typically h/2 for a conventional sunk key. If h means the full key height without this convention, the formula is ambiguous.
• SF is listed as an output, but no allowable shear stress, allowable bearing stress, material strength, yield criterion, or safety-factor formula is provided. SF cannot be computed from the specified inputs.
• The specification does not define whether stresses should use signed torque or torque magnitude; stress results should normally use |T|.

Units and conventions

• Use T in N·mm and d, w, h, and L in mm to obtain τ and σ_bearing in N/mm², numerically equal to MPa.
• If torque is supplied in N·m while dimensions are in mm, convert T to N·mm by multiplying by 1000 before applying the formulas.
• The dimensions d, w, h, and L must all be positive and use the same length unit.
• The bearing formula assumes h is the effective bearing height, conventionally half the total key height for a sunk key unless otherwise specified.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "T": 100000,
    "T_unit": "N·mm",
    "d": 50,
    "w": 10,
    "h": 6,
    "L": 40,
    "length_unit": "mm"
  },
  "expected_outputs": {
    "tau_MPa": 10,
    "sigma_bearing_MPa": 33.3333333333,
    "SF": "undefined: no allowable-stress input or safety-factor formula"
  },
  "working": "τ = 2T/(d·w·L) = 2(100000)/(50·10·40) = 200000/20000 = 10 N/mm² = 10 MPa. σ_bearing = 4T/(d·h·L) = 4(100000)/(50·6·40) = 400000/12000 = 33.3333333333 N/mm² = 33.3333333333 MPa. SF cannot be calculated because no allowable stress or SF definition is supplied."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification provides no safety-factor formula or allowable-strength input, so SF cannot be computed honestly. It also requires rejection of zero geometric dimensions; otherwise the stress formulas produce undefined division-by-zero results. Torque-sign handling is unspecified and can reverse both reported stresses.

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-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json