Area moment of inertia & section modulus API

Returns the centroidal second moment of area I, section modulus S=I/c, cross-sectional area, and radius of gyration for rectangle, solid/hollow circle, or symmetric I-beam sections. Answers 'What is the moment of inertia of an I-beam?', 'What is the section modulus of a rectangular beam?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/section-inertia

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringmechanicsmoment-of-inertiasection-modulussecond-moment-of-areabeami-beamradius-of-gyrationstructural

API URLhttps://x402.hexl.dev/v1/engineering/section-inertia

Integration docs

Example request

{
  "shape": "i-beam",
  "flangeWidthM": 0.1,
  "totalHeightM": 0.2,
  "flangeThicknessM": 0.012,
  "webThicknessM": 0.008
}

Example response

{
  "shape": "i-beam",
  "areaM2": 0.003808,
  "momentOfInertiaM4": 0.000024869717,
  "neutralAxisToExtremeFiberM": 0.1,
  "sectionModulusM3": 0.000248697173,
  "radiusOfGyrationM": 0.080814065,
  "formula": "I = [B*H^3 - (B-tw)*hw^3]/12, hw = H - 2*tf, c = H/2",
  "interpretation": "Larger I/S resists bending; radius of gyration drives buckling slenderness."
}

Input schema

{
  "type": "object",
  "required": [
    "shape"
  ],
  "properties": {
    "shape": {
      "type": "string",
      "enum": [
        "rectangle",
        "circle",
        "hollow-circle",
        "i-beam"
      ],
      "examples": [
        "i-beam"
      ]
    },
    "widthM": {
      "type": "number",
      "description": "rectangle width (m)"
    },
    "heightM": {
      "type": "number",
      "description": "rectangle height (m)"
    },
    "diameterM": {
      "type": "number",
      "description": "solid circle diameter (m)"
    },
    "outerDiameterM": {
      "type": "number",
      "description": "hollow circle outer diameter (m)"
    },
    "innerDiameterM": {
      "type": "number",
      "description": "hollow circle inner diameter (m)"
    },
    "flangeWidthM": {
      "type": "number",
      "description": "I-beam flange width B (m)"
    },
    "totalHeightM": {
      "type": "number",
      "description": "I-beam total height H (m)"
    },
    "flangeThicknessM": {
      "type": "number",
      "description": "I-beam flange thickness tf (m)"
    },
    "webThicknessM": {
      "type": "number",
      "description": "I-beam web thickness tw (m)"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}