Beam Deflection — Propped Cantilever

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

t2-046

Ledger rows

1

No ledger note is attached.

Review findings

The stated UDL formulas are correct in magnitude under the standard idealized propped-cantilever assumptions. The specification needs explicit fixed-reaction and Mmax formulas, a stated sign convention, the maximum-deflection location, and separate point-load formulas before the instrument can be labeled fully verified.

Formula and scope findings

• The UDL formulas R_prop=3wL/8 and |M_fixed|=wL²/8 are standard for a constant-EI propped cantilever with a full-span uniformly distributed load, but the fixed vertical reaction is not stated even though reactions are an output.
• The input specification allows P, but no point-load formulas are provided; the instrument cannot compute the claimed outputs for a point load without additional formulas and load-position data.
• Mmax is not explicitly defined. For the stated full-span UDL, the maximum absolute bending moment is |M_fixed|=wL²/8, but this relationship should be stated explicitly, including the sign convention.
• The deflection expression wL⁴/(185EI) is an approximate maximum-deflection magnitude; the location of maximum deflection is not supplied despite the wording '(approx location)'.
• The formulas require a prismatic member with constant E and I, an ideal fixed support, an ideal simple prop, and small-deflection linear-elastic behavior; these constraints are not stated.

Unit assumptions

• w is force per unit length and L is length, so wL gives force and wL² gives moment.
• E and I must use a consistent unit system: E in force/length² and I in length⁴.
• δmax has the same length unit as L.
• Examples use either N, m, Pa, and m⁴, or N, mm, N/mm², and mm⁴; mixing kN/m with mm or GPa with mm⁴ without conversion is invalid.
• R_fixed is taken as the upward vertical reaction 5wL/8 for the full-span UDL. M_fixed and Mmax are reported as positive magnitudes; the physical fixed-end moment is hogging and its algebraic sign depends on convention.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The specification has an undefined deflection result when E or I is zero and does not provide the required formulas for the advertised point-load P branch. A robust instrument should reject zero stiffness and explicitly reject or separately implement point-load inputs.

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": {
    "load_type": "full-span UDL",
    "w": 10000,
    "w_unit": "N/m",
    "L": 4,
    "L_unit": "m",
    "E": 200000000000,
    "E_unit": "Pa",
    "I": 0.000008,
    "I_unit": "m^4"
  },
  "expected_outputs": {
    "R_prop": 15000,
    "R_prop_unit": "N",
    "R_fixed": 25000,
    "R_fixed_unit": "N",
    "M_fixed": 20000,
    "M_fixed_unit": "N*m",
    "Mmax": 20000,
    "Mmax_unit": "N*m",
    "delta_max": 0.00864864865,
    "delta_max_unit": "m"
  },
  "working": "R_prop=3wL/8=3×10000×4/8=120000/8=15000 N. R_fixed=wL−R_prop=10000×4−15000=40000−15000=25000 N. |M_fixed|=wL²/8=10000×4²/8=10000×16/8=160000/8=20000 N·m. For this UDL, Mmax=|M_fixed|=20000 N·m. δmax=wL⁴/(185EI)=10000×4⁴/(185×200000000000×0.000008)=10000×256/(185×1600000)=2560000/296000000=0.00864864865 m."
}

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