Source: https://guthlabs.ai/docs/instruments/shaft-diameter-sizing-torsion-bending/

instrument / verified-with-binding-errata

# Shaft Diameter Sizing (Torsion + Bending)

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

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/shaft-diameter-sizing-torsion-bending/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/shaft-diameter-sizing-torsion-bending/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/shaft-diameter-sizing-torsion-bending/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/shaft-diameter-sizing-torsion-bending/qualification/>)

## 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

**d_mm** · vector 1

46.702

21.677

d³ off by 10× (Te 1e5 treated as 1e6); her own v2-v4 use the same formula correctly

## 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

[Motor & Drivetrain Benchshaft size](<https://guthlabs.ai/docs/instrument-workflows/motor-drive/>)

## 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`