Beam Deflection & Reactions — Simply Supported, Point Load 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-clean

Evidence ID

t6-002

Effect

Computation or source lookup only

Input and validation requirements

A zero-span input makes reaction and moment formulas divide by zero and makes the deflection model physically invalid. The instrument must validate L>0 and reject this case rather than returning a misleading zero or NaN result.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

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

{
  "inputs": {
    "P": 1000,
    "L": 4,
    "a": 2,
    "E": 200000000000,
    "I": 0.000008,
    "units": "N,m,Pa,m^4",
    "curve_x": [
      0,
      1,
      2,
      3,
      4
    ]
  },
  "expected_outputs": {
    "R1_N": 500,
    "R2_N": 500,
    "Vmax_N": 500,
    "Mmax_Nm": 1000,
    "delta_max_m": 0.0008333333333333334,
    "deflection_curve_m": {
      "x=0": 0,
      "x=1": 0.0005729166666666667,
      "x=2": 0.0008333333333333334,
      "x=3": 0.0005729166666666667,
      "x=4": 0
    },
    "curve_features": {
      "roots_x_m": [
        0,
        4
      ],
      "maximum_at_x_m": 2,
      "maximum_deflection_m": 0.0008333333333333334,
      "asymptotes": []
    }
  },
  "working": "b = L-a = 4-2 = 2 m. EI = 200000000000*0.000008 = 1600000 N*m^2. R1 = P*b/L = 1000*2/4 = 500 N. R2 = P*a/L = 1000*2/4 = 500 N. Vmax = max(500,500) = 500 N. Mmax = P*a*b/L = 1000*2*2/4 = 1000 N*m. Since the load is centered, delta_max = P*L^3/(48*E*I) = 1000*4^3/(48*1600000) = 64000/76800000 = 0.0008333333333333334 m. For 0 <= x <= 2, y = P*b*x*(L^2-b^2-x^2)/(6*L*E*I) = x*(12-x^2)/19200 m, giving y(0)=0, y(1)=11/19200=0.0005729166666666667, and y(2)=16/19200=0.0008333333333333334. Symmetry gives y(3)=0.0005729166666666667 and y(4)=0. The first derivative vanishes at x=2, so the maximum is at midspan."
}

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