Column slenderness & regime API

Computes the slenderness ratio λ, the transition slenderness Cc=√(2π²E/Sy), classifies the column as Euler (long) or Johnson (intermediate), and returns the governing critical stress. Answers 'Does my column buckle elastically or yield first?', 'What critical stress applies?'.

Price$0.06per request

MethodPOST

Route/v1/engineering/column-slenderness

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

columnslendernessjohnsoneulerbucklingcritical-stressradius-of-gyrationmachine-design

API URLhttps://x402.hexl.dev/v1/engineering/column-slenderness

Integration docs

Example request

{
  "effectiveLengthM": 3,
  "radiusOfGyrationM": 0.025,
  "youngsModulusGpa": 200,
  "yieldStrengthMpa": 250
}

Example response

{
  "slendernessRatio": 120,
  "transitionSlendernessCc": 125.6637,
  "regime": "intermediate-short (Johnson / inelastic)",
  "criticalStressMpa": 136.0137,
  "formula": "σcr = Sy·[1 − Sy·λ²/(4π²E)]  (Johnson)",
  "interpretation": "Above Cc the column buckles elastically (Euler); below it, yielding interacts — Johnson governs."
}

Input schema

{
  "type": "object",
  "required": [
    "radiusOfGyrationM",
    "youngsModulusGpa",
    "yieldStrengthMpa"
  ],
  "properties": {
    "effectiveLengthM": {
      "type": "number",
      "examples": [
        3
      ]
    },
    "radiusOfGyrationM": {
      "type": "number",
      "examples": [
        0.025
      ]
    },
    "youngsModulusGpa": {
      "type": "number",
      "examples": [
        200
      ]
    },
    "yieldStrengthMpa": {
      "type": "number",
      "examples": [
        250
      ]
    },
    "endConditionK": {
      "type": "number",
      "examples": [
        1
      ]
    },
    "unbracedLengthM": {
      "type": "number",
      "examples": [
        3
      ]
    }
  }
}

Output schema

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