{
  "capability_id": "mechanical.statics.plastic_moment",
  "tool_id": "plastic-moment",
  "engine": "plastic-moment",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-23T21:48:01.336Z",
  "engine_build": "2026-09-23",
  "test_count": 5,
  "passed": 5,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 2,
      "passed": 2
    },
    "boundary": {
      "total": 3,
      "passed": 3
    },
    "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/plastic-moment",
  "api": "https://www.calculatorx.com/api/v1/calc/plastic-moment",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.plastic_moment.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.plastic_moment.output.json",
  "assumptions": [],
  "limitations": [
    "One centroidal axis",
    "Mp = σ_y Z",
    "Z is an input, not rebuilt from b and h",
    "Not transverse shear"
  ],
  "boundary_conditions": [
    "missing σ_y or Z → MISSING_REQUIRED_INPUT",
    "σ_y ≤ 0 or Z ≤ 0 → VALUE_MUST_BE_POSITIVE"
  ],
  "sources": [
    {
      "title": "Hibbeler, Mechanics of Materials",
      "section": "Plastic deformation — plastic moment",
      "supports": "The fully plastic moment on a centroidal axis is the yield stress times the plastic modulus of that axis.",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:8995d9c691a960bc261d46f9dee908fde1bc2f2a8af775d2d6bdb6738d038a10",
  "tests": [
    {
      "id": "golden-rect",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "sigma_y": 250,
        "Z": 18
      },
      "expect": {
        "Mp": 4500,
        "sigma_y": 250,
        "Z": 18,
        "model": "plastic_moment"
      },
      "expectWarning": null,
      "actual": {
        "model": "plastic_moment",
        "sigma_y": 250,
        "Z": 18,
        "Mp": 4500,
        "solver": "plastic moment",
        "convention": "Mp = σ_y Z on one centroidal axis. Z comes from a plastic-modulus page. This page does not rebuild the section. Transverse shear is its own page."
      },
      "tol": 1e-12
    },
    {
      "id": "golden-circle",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "sigma_y": 250,
        "Z": 10.666666666666666
      },
      "expect": {
        "Mp": 2666.6666666666665,
        "Z": 10.666666666666666
      },
      "expectWarning": null,
      "actual": {
        "model": "plastic_moment",
        "sigma_y": 250,
        "Z": 10.666666666666666,
        "Mp": 2666.6666666666665,
        "solver": "plastic moment",
        "convention": "Mp = σ_y Z on one centroidal axis. Z comes from a plastic-modulus page. This page does not rebuild the section. Transverse shear is its own page."
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zero-yield",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "sigma_y": 0,
        "Z": 18
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Yield stress must be positive."
    },
    {
      "id": "boundary-zero-z",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "sigma_y": 250,
        "Z": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Plastic modulus Z must be positive."
    },
    {
      "id": "boundary-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "Z": 18
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "sigma_y is required."
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 5,
      "total": 5,
      "golden": 2,
      "boundary": 3,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-23T21:25:13.013Z",
  "rendered_at": "2026-09-23T21:48:01.336Z",
  "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": "f591158501975d56b9f8c74effb2346cca2e4e0ad23baa0ce07c2bd2017ffe48",
      "output_schema_sha256": "439227ed3103e58a52f2325683bf89ed74c547d57e5e7a393c305ef91f568640",
      "evidence_sha256": "3ac3d92bfd8c3323e25fdcdd274361e82fd5f6b84b9c21d26d9c0c691839b004",
      "evidence_core_sha256": "3ac3d92bfd8c3323e25fdcdd274361e82fd5f6b84b9c21d26d9c0c691839b004",
      "capability_sha256": "6da7baae21875ce3819ed52a8207e025f8e90263486e710a033261211a3460cf",
      "engine_sha256": "9c01357c59289b486db75219c319b48412c2e4bcd3a700b0d2dd8145ce528650",
      "mcp_contract_sha256": "70bebadd7ed143df4a08cee8eb28a96620802497fda67dd843f4f57c33fd45d3"
    },
    "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"
  }
}
