Beam Deflection — Overhanging Beam implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-with-binding-errata

Evidence ID

t6-024

Effect

Computation or source lookup only

Input and validation requirements

The instrument must reject I=0 because deflection formulas divide by E*I=0. It also risks incorrect signed results unless load direction, reaction signs, and deflection-positive direction are explicitly defined.

Required corrections

[
  {
    "vector": "1,3",
    "field": "delta at overhang tip",
    "wrong": "+0.0777778 / +0.0669643",
    "correct": "-0.0666667 / -0.0595238 (0.0667/0.0595 downward)",
    "cause": "Macaulay integration omits the R2*<x-L>^3/6 term when evaluating beyond the right support; confirmed by numeric double integration and the standard P*a^2(L+a)/(3EI) formula"
  }
]

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "model": "simple supports at x=0 and x=L; free overhang to x=L+a",
    "L_m": 6,
    "a_m": 2,
    "point_loads": [
      {
        "P_N": 10000,
        "z_m": 8
      }
    ],
    "E_Pa": 200000000000,
    "I_m4": 0.000008,
    "sample_x_m": [
      0,
      3,
      6,
      8
    ]
  },
  "expected_outputs": {
    "R1_N": -3333.333333,
    "R2_N": 13333.333333,
    "V_N": {
      "0<x<8": -3333.333333,
      "8<x<8": "0 after the tip load; no beam interval beyond x=8"
    },
    "M_Nm": {
      "x=0": 0,
      "x=3": -10000,
      "x=6": -20000,
      "x=8": 0
    },
    "delta_downward_m": {
      "x=0": 0,
      "x=3": -0.028125,
      "x=6": 0,
      "x=8": 0.0777777778
    },
    "curve_features": {
      "moment_roots_m": [
        0,
        8
      ],
      "moment_extremum": {
        "type": "minimum",
        "x_m": 6,
        "M_Nm": -20000
      },
      "deflection_support_roots_m": [
        0,
        6
      ],
      "asymptotes": []
    }
  },
  "working": "Equilibrium: R2=(10000*8)/6=13333.333333 N; R1=10000-13333.333333=-3333.333333 N. EI=200000000000*0.000008=1600000 N·m^2. For x<=6, M=R1*x, so M(3)=(-3333.333333)(3)=-10000 N·m and M(6)=(-3333.333333)(6)=-20000 N·m. For x=8, M=R1*8-10000*(8-8)=-26666.666664+26666.666664=0. The deflection constant is C=(-R1*6^3/6)/6=20000. At x=3, the bracket is R1*3^3/6+C*3=(-3333.333333*27/6)+60000=-15000+60000=45000; δ=-45000/1600000=-0.028125 m. At x=6, the bracket is (-3333.333333*216/6)+20000*6=-120000+120000=0; δ=0. At x=8, the bracket is (-3333.333333*512/6)+20000*8=-284444.4444+160000=-124444.4444; δ=124444.4444/1600000=0.0777777778 m. The shear is -3333.333333 N before the tip load and jumps by -10000 N at x=8."
}

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-tranche6/tranche6-results.json
• tranche errata record