{
  "family": "bending_stress",
  "generator_id": "bending-stress-mpmath-o3",
  "generator_version": "1.0.0",
  "seed": "20260927.bending-stress-o3",
  "mpmath_dps": 80,
  "precision_bits": 265,
  "library": "mpmath 1.4.1",
  "notes": "\u03c3 = M/S. S may be Ix/c. Not plastic modulus, not rectangle b\u00b7h.",
  "vectors": [
    {
      "id": "o3-MS",
      "kind": "S",
      "inputs": {
        "M": "12",
        "S": "4"
      },
      "sigma_f64": 3.0,
      "sigma_decimal": "3.000000000000000000000000000000000000000",
      "M_f64": 12.0,
      "M_decimal": "12.00000000000000000000000000000000000000",
      "S_f64": 4.0,
      "S_decimal": "4.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-Ix",
      "kind": "Ix",
      "inputs": {
        "M": "100",
        "Ix": "50",
        "c": "2"
      },
      "sigma_f64": 4.0,
      "sigma_decimal": "4.000000000000000000000000000000000000000",
      "M_f64": 100.0,
      "M_decimal": "100.0000000000000000000000000000000000000",
      "S_f64": 25.0,
      "S_decimal": "25.00000000000000000000000000000000000000",
      "Ix_f64": 50.0,
      "c_f64": 2.0
    },
    {
      "id": "o3-alias",
      "kind": "alias",
      "inputs": {
        "moment": "24",
        "section_modulus": "8"
      },
      "sigma_f64": 3.0,
      "sigma_decimal": "3.000000000000000000000000000000000000000",
      "M_f64": 24.0,
      "M_decimal": "24.00000000000000000000000000000000000000",
      "S_f64": 8.0,
      "S_decimal": "8.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-awkward",
      "kind": "awkward",
      "inputs": {
        "M": "12.5",
        "S": "3.7"
      },
      "sigma_f64": 3.3783783783783785,
      "sigma_decimal": "3.378378378378378378378378378378378378378",
      "M_f64": 12.5,
      "M_decimal": "12.50000000000000000000000000000000000000",
      "S_f64": 3.7,
      "S_decimal": "3.700000000000000000000000000000000000000"
    },
    {
      "id": "o3-I-alias",
      "kind": "I",
      "inputs": {
        "M": "40",
        "I": "20",
        "cy": "2"
      },
      "sigma_f64": 4.0,
      "sigma_decimal": "4.000000000000000000000000000000000000000",
      "M_f64": 40.0,
      "M_decimal": "40.00000000000000000000000000000000000000",
      "S_f64": 10.0,
      "S_decimal": "10.00000000000000000000000000000000000000",
      "Ix_f64": 20.0,
      "c_f64": 2.0
    },
    {
      "id": "o3-neg-M",
      "kind": "signed",
      "inputs": {
        "M": "-18",
        "S": "6"
      },
      "sigma_f64": -3.0,
      "sigma_decimal": "-3.000000000000000000000000000000000000000",
      "M_f64": -18.0,
      "M_decimal": "-18.00000000000000000000000000000000000000",
      "S_f64": 6.0,
      "S_decimal": "6.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-small",
      "kind": "small",
      "inputs": {
        "M": "0.08",
        "S": "0.02"
      },
      "sigma_f64": 4.0,
      "sigma_decimal": "4.000000000000000000000000000000000000000",
      "M_f64": 0.08,
      "M_decimal": "0.08000000000000000000000000000000000000000",
      "S_f64": 0.02,
      "S_decimal": "0.02000000000000000000000000000000000000000"
    },
    {
      "id": "o3-large",
      "kind": "large",
      "inputs": {
        "M": "1e6",
        "S": "2500"
      },
      "sigma_f64": 400.0,
      "sigma_decimal": "400.0000000000000000000000000000000000000",
      "M_f64": 1000000.0,
      "M_decimal": "1000000.000000000000000000000000000000000",
      "S_f64": 2500.0,
      "S_decimal": "2500.000000000000000000000000000000000000"
    }
  ]
}