Beam Deflection — Cantilever, Point Load at Free End

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mechanical, Civil & Structural Engineering

Tranche

tranche-2

Evidence ID

t2-010

Ledger rows

2

• name corrected to match catalog exactly (was abbreviated in calibration-1 bookkeeping)

Review findings

The deflection, slope, and maximum-moment formulas are correct in magnitude for the stated idealized load case. The specification is incomplete because Vmax is listed but not defined, and it is ambiguous about units and signs. The honest label should additionally state small-deflection Euler-Bernoulli beam assumptions, constant EI, and negligible shear deformation.

Formula and scope findings

• The stated formulas for δ=PL³/(3EI), θ=PL²/(2EI), and the magnitude Mmax=PL are standard for a prismatic Euler-Bernoulli cantilever with a transverse point load at the free end, assuming constant E and I and small linear-elastic deflection.
• The output list includes Vmax, but no formula is provided; for this loading case the maximum internal shear magnitude is Vmax=|P| and is constant along the beam.
• Mmax=PL is a magnitude only. The signed fixed-end reaction moment depends on the selected load and sign convention and is typically -PL relative to the applied-load moment.
• The formulas require E and I to be nonzero, with L>=0; a negative or zero flexural rigidity EI is invalid, and L should be positive for a physical beam.
• The formulas do not state the required Euler-Bernoulli assumptions: prismatic beam, constant EI, small deflection, linear elastic material, and negligible shear deformation.

Unit assumptions

• All quantities must use a dimensionally consistent unit system.
• The test vectors use SI units unless explicitly noted: P in N, L in m, E in Pa=N/m², I in m⁴; outputs are δ in m, θ in radians, Mmax in N·m, and Vmax in N.
• Radians are dimensionless, but θ should be labeled as radians for user clarity.
• If mixed units are accepted, the implementation must explicitly convert them; for example, 1 mm⁴=10^-12 m⁴ and 1 GPa=10^9 Pa.
• P and Mmax may be signed or unsigned only if the interface clearly defines the sign convention; the vectors use positive magnitudes.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The zero-modulus input makes deflection and slope undefined, and the specification provides no stated validation or unit/sign convention, creating additional boundary and interpretation hazards.

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": {
    "P": 1000,
    "L": 2,
    "E": 200000000000,
    "I": 0.000008,
    "units": "N, m, Pa, m^4"
  },
  "expected_outputs": {
    "delta_m": 0.001666666667,
    "theta_rad": 0.00125,
    "Mmax_Nm": 2000,
    "Vmax_N": 1000
  },
  "working": "L³=2³=8. δ=(1000×8)/(3×200000000000×0.000008)=8000/4800000=0.001666666667 m. L²=2²=4. θ=(1000×4)/(2×200000000000×0.000008)=4000/3200000=0.00125 rad. Mmax=P×L=1000×2=2000 N·m. Vmax=|P|=1000 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_CLEAN
• evidence-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json