Shaft Diameter Sizing (Torsion + Bending)

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-4

Evidence ID

t4-082

Ledger rows

1

No ledger note is attached.

Review findings

NEEDS_REVIEW because the exact input-unit convention is unspecified, the shaft geometry/applicability is unspecified, and the allowable-stress and ASME factor-selection basis is unspecified. The stated honest label appropriately limits the result to preliminary sizing, but the instrument should require or display these assumptions before presenting a final diameter.

Formula and scope findings

• The formula is the standard ASME equivalent-twisting-moment equation for a solid, round shaft: d = [16/(π·τallow)·√((Kb·Mb)^2 + (Kt·Tt)^2)]^(1/3). Its applicability is not stated for non-solid, non-circular, keyed, grooved, or otherwise stress-concentrated shafts.
• The required ASME factor-selection method and allowable-stress basis are not defined; Kb, Kt, and τallow cannot be treated as arbitrary independent inputs.

Unit assumptions

• Mb and Tt must use the same torque units, and τallow must use force per area units consistent with those lengths; for example, N·mm with MPa (N/mm²) produces d in mm.
• Kb and Kt are dimensionless shock/fatigue factors and should normally be nonnegative.
• The test vectors assume a solid circular shaft and use the supplied allowable shear stress directly.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The formula returns an undefined result when tauallow=0 and returns a nonphysical zero diameter when both bending moment and torque are zero. The specified equation has no actual conditional formula branch; sign crossing does not change the result.

Errata and corrections

Tranche errata

Inspectable example

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

{
  "inputs": {
    "Mb": 0,
    "Tt": 100000,
    "tauallow": 50,
    "Kb": 1.5,
    "Kt": 1,
    "units": "Mb,Tt in N·mm; tauallow in MPa"
  },
  "expected_outputs": {
    "d_mm": 46.702
  },
  "working": "d = [16/(π·50)·√((1.5·0)^2 + (1.0·100000)^2)]^(1/3)\n= [16/(50π)·√(0 + 10000000000)]^(1/3)\n= [16/(50π)·100000]^(1/3)\n= [101859.16]^(1/3)\n= 46.702 mm"
}

Related workflows

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json