Source: https://guthlabs.ai/docs/instruments/beam-deflection-cantilever-udl/mechanism/

instrument mechanism / verified-with-binding-errata

# Beam Deflection — Cantilever, UDL mechanism

The inspectable method record for Beam Deflection — Cantilever, UDL, kept separate from implementation and qualification.

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

## Model scope

The δ and Mmax formulas are standard for a cantilever with a full-span UDL. The catalog claim is incomplete because Vmax is an advertised output without a corresponding formula. The honest label 'linear-elastic theory' is directionally correct but should also state the Euler-Bernoulli, small-deflection, constant-E/constant-I, full-span-UDL assumptions.

- The listed outputs include Vmax, but no formula is provided for it; for a full-span uniform distributed load on a cantilever, Vmax = wL at the fixed end.

- The formulas are valid only for a prismatic Euler-Bernoulli cantilever with constant E and I, small deflection, linear elastic behavior, and a UDL applied over the entire span.

- δ is given as a magnitude; the sign convention for downward versus upward deflection is not specified.

## Units and conventions

- Use a consistent unit system.

- w is force per unit length, such as N/m or kN/m.

- L is length, such as m or mm.

- E is elastic modulus, such as Pa or N/mm².

- I is the second moment of area about the bending axis, such as m⁴ or mm⁴.

- With SI units, δ is in m, Mmax is in N·m, and Vmax is in N.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "w": "2 kN/m",
    "L": "3 m",
    "E": "200 GPa",
    "I": "8e-6 m^4"
  },
  "expected_outputs": {
    "delta": "0.01265625 m",
    "Mmax": "9000 N·m",
    "Vmax": "6000 N"
  },
  "working": "Convert w = 2 kN/m = 2000 N/m and E = 200 GPa = 200,000,000,000 N/m². L⁴ = 3⁴ = 81 m⁴. δ = (2000 × 81) / (8 × 200,000,000,000 × 8e-6) = 162000 / 12,800,000 = 0.01265625 m. Mmax = wL²/2 = 2000 × 3² / 2 = 2000 × 9 / 2 = 9000 N·m. Vmax = wL = 2000 × 3 = 6000 N."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification permits an E=0 input that makes the deflection denominator vanish, producing an undefined or infinite result unless rejected. It also specifies no actual formula branches, so a branch-switch test has no genuine alternate regime to evaluate.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/beam-deflection-cantilever-udl/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/beam-deflection-cantilever-udl/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/beam-deflection-cantilever-udl/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche2/tranche2-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`