Beam Deflection — Cantilever, UDL

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

Tranche

tranche-2

Evidence ID

t2-022

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

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

{
  "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."
}

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-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json