Beam Deflection — Cantilever, UDL mechanism

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

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