Beam Deflection & Reactions — Simply Supported, UDL 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

t6-014

Effect

Computation or source lookup only

Input and validation requirements

The deflection calculation is undefined when I=0 because its denominator 384EI vanishes; an implementation must reject zero or nonpositive E and I instead of returning an infinite or misleading numeric deflection.

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": {
    "w": 1000,
    "w_unit": "N/m",
    "L": 4,
    "L_unit": "m",
    "E": 200000000000,
    "E_unit": "Pa",
    "I": 0.000008,
    "I_unit": "m^4",
    "sample_x": [
      0,
      1,
      2,
      3,
      4
    ]
  },
  "expected_outputs": {
    "R1_N": 2000,
    "R2_N": 2000,
    "Vmax_absolute_N": 2000,
    "Mmax_Nm": 2000,
    "delta_max_m": 0.00208333333333,
    "delta_max_location_m": 2,
    "sampled_points": [
      {
        "x_m": 0,
        "V_N": 2000,
        "M_Nm": 0,
        "deflection_down_m": 0
      },
      {
        "x_m": 1,
        "V_N": 1000,
        "M_Nm": 1500,
        "deflection_down_m": 0.001484375
      },
      {
        "x_m": 2,
        "V_N": 0,
        "M_Nm": 2000,
        "deflection_down_m": 0.00208333333333
      },
      {
        "x_m": 3,
        "V_N": -1000,
        "M_Nm": 1500,
        "deflection_down_m": 0.001484375
      },
      {
        "x_m": 4,
        "V_N": -2000,
        "M_Nm": 0,
        "deflection_down_m": 0
      }
    ],
    "curve_features": {
      "shear_zero_m": 2,
      "moment_roots_m": [
        0,
        4
      ],
      "moment_max_at_m": 2,
      "deflection_max_at_m": 2,
      "deflection_asymptotes": []
    }
  },
  "working": "EI=200000000000*0.000008=1600000 N·m^2. R1=R2=wL/2=1000*4/2=2000 N. Vmax=2000 N. Mmax=wL^2/8=1000*4^2/8=16000/8=2000 N·m. delta_max=5wL^4/(384EI)=5*1000*4^4/(384*1600000)=5*1000*256/(614400000)=1280000/614400000=0.00208333333333 m. For plotting, V(x)=2000-1000x, M(x)=2000x-500x^2, and d(x)=1000x(64-8x^2+x^3)/(24*1600000)=1000x(64-8x^2+x^3)/38400000. At x=1: V=1000, M=2000-500=1500, d=1000(64-8+1)/38400000=57000/38400000=0.001484375 m. At x=2: V=0, M=4000-2000=2000, d=2000(64-32+8)/38400000=80000/38400000=0.00208333333333 m. Symmetry gives the x=3 values; at x=4, V=-2000, M=0, d=0."
}

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