Beam Deflection — Fixed-Fixed, Point/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

t2-034

Ledger rows

1

No ledger note is attached.

Review findings

The instrument cannot pass as specified because its UDL maximum-deflection formula is wrong and its claimed reaction outputs lack formulas. The honest label should identify the model as Euler-Bernoulli, linear-elastic theory for an ideal fixed-fixed prismatic beam, with a full-span UDL or a centered point load.

Formula and scope findings

• The UDL maximum-deflection formula is incorrect: for a fixed-fixed beam under a full-span uniform load, the standard formula is δmax=5wL⁴/(384EI), not wL⁴/(384EI).
• The listed formulas do not provide the reactions required by the claimed outputs. For symmetric full-span UDL, each reaction is wL/2; for a centered point load, each reaction is P/2.
• The point-load formulas are valid only for a point load located at midspan. The point-load position is not represented in the inputs, so the scope must be explicitly restricted to midspan.
• The stated UDL end and midspan moments are correct for a full-span UDL with ideal fixed ends: Mend=wL²/12 in magnitude and Mmid=wL²/24 in magnitude.

Unit assumptions

• Use a consistent SI system: P in N, w in N/m, L in m, E in Pa (N/m²), and I in m⁴.
• Moments are returned in N·m; reactions are returned in N; deflection is returned in m.
• Mend denotes the magnitude of the hogging moment at either fixed support; the signed value depends on the adopted bending-moment convention.
• The beam is prismatic, Euler-Bernoulli, linear-elastic, and has ideal fixed restraints.
• The UDL acts uniformly over the full span, and the point load acts exactly at midspan.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

An input with E = 0 produces a zero denominator in the deflection formula, so the instrument must reject it or report an undefined result. The specification also leaves reaction sign conventions and signed-versus-magnitude reporting ambiguous.

Errata and corrections

Stress-test correction

{
  "vector_inputs": {
    "load_type": "central_point",
    "P": 7500,
    "L": 2.7,
    "E": 70000000000,
    "I": 0.0000135
  },
  "wrong_outputs": {
    "left_end_moment": -253.125,
    "right_end_moment": -253.125,
    "midspan_moment": 253.125
  },
  "corrected_outputs": {
    "left_end_moment": -2531.25,
    "right_end_moment": -2531.25,
    "midspan_moment": 2531.25
  },
  "method": "PL/8 = 7500*2.7/8 = 2531.25 N·m; her own working shows the division \"20,250/8=253.125\" — a 10x slip. The deflection field (0.0008136 m) used a separate correct calculation and was unaffected."
}

Inspectable example

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

{
  "inputs": {
    "load_type": "UDL",
    "w_N_per_m": 10000,
    "L_m": 6,
    "E_Pa": 200000000000,
    "I_m4": 0.000008
  },
  "expected_outputs": {
    "reaction_left_N": 30000,
    "reaction_right_N": 30000,
    "Mend_Nm": 30000,
    "Mmid_Nm": 15000,
    "delta_max_standard_m": 0.10546875,
    "delta_max_as_written_m": 0.02109375
  },
  "working": "Reactions: wL/2 = 10000×6/2 = 30000 N each. End moment: wL²/12 = 10000×6²/12 = 10000×36/12 = 30000 N·m. Midspan moment: wL²/24 = 10000×36/24 = 15000 N·m. EI = 200000000000×0.000008 = 1600000 N·m². Correct deflection: 5wL⁴/(384EI) = 5×10000×6⁴/(384×1600000) = 5×10000×1296/614400000 = 64800000/614400000 = 0.10546875 m. Specified deflection: wL⁴/(384EI) = 10000×1296/614400000 = 0.02109375 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_WITH_ERRATA
• evidence-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json
• STRESS_TEST_CORRECTIONS_APPLIED.json