Euler column buckling load API

Computes the critical elastic buckling load Pcr=π²EI/(KL)² with the effective-length factor for the end condition, plus slenderness ratio, critical stress, and buckling factor of safety. Answers 'What is the critical buckling load of a column?', 'What is the slenderness ratio?'.

Price$0.06per request

MethodPOST

Route/v1/engineering/euler-buckling

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringmechanicsbucklingeulercolumncritical-loadslendernessstabilitystructural

API URLhttps://x402.hexl.dev/v1/engineering/euler-buckling

Integration docs

Example request

{
  "elasticModulusPa": 200000000000,
  "momentOfInertiaM4": 4.909e-7,
  "lengthM": 3,
  "endCondition": "pinned-pinned",
  "areaM2": 0.00785,
  "appliedLoadN": 50000
}

Example response

{
  "elasticModulusPa": 200000000000,
  "momentOfInertiaM4": 4.909e-7,
  "lengthM": 3,
  "effectiveLengthFactor": 1,
  "effectiveLengthM": 3,
  "criticalLoadN": 107666.4178,
  "criticalLoadKN": 107.666418,
  "formula": "Pcr = π²*E*I / (K*L)²",
  "interpretation": "Above Pcr the column buckles elastically; thinner/longer columns fail sooner.",
  "areaM2": 0.00785,
  "radiusOfGyrationM": 0.007907909,
  "slendernessRatio": 379.367,
  "criticalStressPa": 13715467.2342,
  "criticalStressMPa": 13.715467,
  "appliedLoadN": 50000,
  "bucklingFactorOfSafety": 2.1533
}

Input schema

{
  "type": "object",
  "required": [
    "elasticModulusPa",
    "momentOfInertiaM4",
    "lengthM"
  ],
  "properties": {
    "elasticModulusPa": {
      "type": "number",
      "description": "Young's modulus E (Pa)",
      "examples": [
        200000000000
      ]
    },
    "momentOfInertiaM4": {
      "type": "number",
      "description": "least second moment of area I (m^4)"
    },
    "lengthM": {
      "type": "number",
      "description": "unbraced column length (m)"
    },
    "endCondition": {
      "type": "string",
      "enum": [
        "pinned-pinned",
        "fixed-free",
        "fixed-fixed",
        "fixed-pinned"
      ],
      "examples": [
        "pinned-pinned"
      ]
    },
    "effectiveLengthFactor": {
      "type": "number",
      "description": "override K directly"
    },
    "areaM2": {
      "type": "number",
      "description": "cross-section area (m^2) for slenderness & critical stress"
    },
    "appliedLoadN": {
      "type": "number",
      "description": "applied axial load (N) for FoS"
    }
  }
}

Output schema

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