{
  "capability_id": "mechanical.statics.beam_moment_max_deflection",
  "tool_id": "beam-moment-maximum",
  "engine": "beam-moment-maximum",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-25T01:47:46.268Z",
  "engine_build": "2026-09-24",
  "test_count": 4,
  "passed": 4,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 2,
      "passed": 2
    },
    "boundary": {
      "total": 2,
      "passed": 2
    },
    "property": {
      "total": 0,
      "passed": 0
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/physics/beam-moment-maximum",
  "api": "https://www.calculatorx.com/api/v1/calc/beam-moment-maximum",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.beam_moment_max_deflection.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.beam_moment_max_deflection.output.json",
  "assumptions": [],
  "limitations": [
    "Simply supported span",
    "One concentrated moment at one end",
    "Largest deflection, not the midspan value",
    "x is measured from the end without the moment",
    "I is an input"
  ],
  "boundary_conditions": [
    "missing M, L, E, or I → MISSING_REQUIRED_INPUT",
    "L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE"
  ],
  "sources": [
    {
      "title": "Hibbeler, Mechanics of Materials",
      "section": "Deflection of beams — simply supported beam with a concentrated moment at one end",
      "supports": "The largest deflection is M L² / (9 √3 E I) at x = L/√3 from the end opposite the moment.",
      "kind": "reference"
    },
    {
      "title": "Gere and Goodno, Mechanics of Materials",
      "section": "Deflection of beams — simply supported beam with a concentrated moment at one end",
      "supports": "Supports the page formulas: δ = M L² / (9 √3 E I) and x = L / √3",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:fc426f8b4093ed6ff5568583e5c5262f15dfe2eba8a1ca95ffdb7e972fd39d35",
  "tests": [
    {
      "id": "golden-max",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "M": 16,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": 4.105601914237339,
        "x": 1.1547005383792517,
        "model": "beam_moment_max_deflection"
      },
      "expectWarning": null,
      "actual": {
        "model": "beam_moment_max_deflection",
        "M": 16,
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1.1547005383792517,
        "delta": 4.105601914237339,
        "solver": "simply supported end moment maximum",
        "convention": "Simply supported span with one concentrated moment at one end. The largest deflection is δ = M L²/(9√3 E I) at x = L/√3 from the end that does not carry the moment. Positive M is the positive deflection direction. I is an input. Midspan deflection is its own page."
      },
      "tol": 1e-12
    },
    {
      "id": "golden-sign",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "M": -16,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": -4.105601914237339,
        "x": 1.1547005383792517
      },
      "expectWarning": null,
      "actual": {
        "model": "beam_moment_max_deflection",
        "M": -16,
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1.1547005383792517,
        "delta": -4.105601914237339,
        "solver": "simply supported end moment maximum",
        "convention": "Simply supported span with one concentrated moment at one end. The largest deflection is δ = M L²/(9√3 E I) at x = L/√3 from the end that does not carry the moment. Positive M is the positive deflection direction. I is an input. Midspan deflection is its own page."
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zero-span",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "M": 16,
        "L": 0,
        "E": 1,
        "I": 1
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Span L must be positive."
    },
    {
      "id": "boundary-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "M": 16,
        "L": 2,
        "E": 1
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "I is required."
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 4,
      "total": 4,
      "golden": 2,
      "boundary": 2,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-24T12:51:54.697Z",
  "rendered_at": "2026-09-25T01:47:46.268Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
      "engine": "1.0.0",
      "page": "1.0.0",
      "capability": "1.0.0",
      "evidence": "1.0.0",
      "input_schema": "1.0.0",
      "output_schema": "1.0.0",
      "mcp_contract": "1.0.0"
    },
    "digests": {
      "input_schema_sha256": "e6d7a6a16c2e6b3e99eae96c1994a2a9f9ebb4290e91b37d4adbc066f5763429",
      "output_schema_sha256": "f292cd7d3037f2f21b9b06c04f85350d6bb570054d971405730fce03071aee11",
      "evidence_sha256": "5494a7e495dbfad38bdb6af3d29a0f9ca8bd9f80438c1bfc922a4208d578ce7a",
      "evidence_core_sha256": "5494a7e495dbfad38bdb6af3d29a0f9ca8bd9f80438c1bfc922a4208d578ce7a",
      "capability_sha256": "3541356ec11b02ac9886213023a824168f7c71f7ead62545a0c327c5c6b79b7a",
      "engine_sha256": "08114baefe55904e75ed849baa2ac95371b8b8133c19b39348ee1070175d5f3e",
      "mcp_contract_sha256": "9cf7d41527923e8ab8bfc3047f2db08da2aa448cbb98c0359c1d2dfd503a1c40"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}