{
  "capability_id": "mechanical.statics.triangular_load_deflection",
  "tool_id": "triangular-load-deflection",
  "engine": "triangular-load-deflection",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-25T01:47:46.270Z",
  "engine_build": "2026-09-24",
  "test_count": 3,
  "passed": 3,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 2,
      "passed": 2
    },
    "boundary": {
      "total": 1,
      "passed": 1
    },
    "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/triangular-load-deflection",
  "api": "https://www.calculatorx.com/api/v1/calc/triangular-load-deflection",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.triangular_load_deflection.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.triangular_load_deflection.output.json",
  "assumptions": [],
  "limitations": [
    "Simply supported span",
    "Midspan value, not the maximum",
    "I is an input"
  ],
  "boundary_conditions": [
    "missing w0, 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 triangular load",
      "supports": "Midspan δ = 5 w0 L⁴ / (768 E I) when the intensity is zero at one end and w0 at the other.",
      "kind": "reference"
    },
    {
      "title": "Gere and Goodno, Mechanics of Materials",
      "section": "Deflection of beams — triangular load",
      "supports": "Supports the page formula. The same midspan number is a uniform load of intensity w0/2.",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:3d1de450eb412bc00ad456973cc3c048618fb74f76a3e1518b6205d6f9fccae3",
  "tests": [
    {
      "id": "golden-mid",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "w0": 24,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": 2.5,
        "model": "triangular_load_deflection"
      },
      "expectWarning": null,
      "actual": {
        "model": "triangular_load_deflection",
        "w0": 24,
        "L": 2,
        "E": 1,
        "I": 1,
        "delta": 2.5,
        "solver": "simply supported triangular load midspan",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. Midspan δ = 5 w0 L⁴/(768 E I). That equals a uniform load of intensity w0/2. Positive w0 is the positive deflection direction. I is an input. The largest deflection is not at midspan."
      },
      "tol": 1e-12
    },
    {
      "id": "golden-sign",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "w0": -24,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": -2.5
      },
      "expectWarning": null,
      "actual": {
        "model": "triangular_load_deflection",
        "w0": -24,
        "L": 2,
        "E": 1,
        "I": 1,
        "delta": -2.5,
        "solver": "simply supported triangular load midspan",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. Midspan δ = 5 w0 L⁴/(768 E I). That equals a uniform load of intensity w0/2. Positive w0 is the positive deflection direction. I is an input. The largest deflection is not at midspan."
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zero-span",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "w0": 24,
        "L": 0,
        "E": 1,
        "I": 1
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Span L must be positive."
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 3,
      "total": 3,
      "golden": 2,
      "boundary": 1,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-24T20:42:59.007Z",
  "rendered_at": "2026-09-25T01:47:46.270Z",
  "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": "66d8203fa74a018766585a5421aaaacd867e0f2fc3cc9e39e82c7b5298cefbb6",
      "output_schema_sha256": "675fde7e88d601e729838ee508a58321750ffadd82453b6912fbf86130fa8dc6",
      "evidence_sha256": "8b064310ee67c7b1a6ecfddd0ee8054a9718ddab9bb1485efbb89a135b6e597d",
      "evidence_core_sha256": "8b064310ee67c7b1a6ecfddd0ee8054a9718ddab9bb1485efbb89a135b6e597d",
      "capability_sha256": "9b6bf4e726015c4db7725825f37122ca521374c2742cb711aa828e54220fade4",
      "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"
  }
}