Thick-wall Lame stress API

Solves Lame's equations for radial and hoop stress through a thick-walled cylinder under internal/external pressure, reporting bore, outer-surface and probe-radius stresses with max hoop at the bore. Answers 'What are the true stresses in a thick pressure cylinder?', 'How wrong is thin-wall theory here?'.

Price$0.08per request

MethodPOST

Route/v1/engineering/thick-wall-lame

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

pressure-vessellamethick-wallhoop-stressradial-stresscylinderboremachine-design

API URLhttps://x402.hexl.dev/v1/engineering/thick-wall-lame

Integration docs

Example request

{
  "innerRadiusM": 0.05,
  "outerRadiusM": 0.1,
  "internalPressureMpa": 100
}

Example response

{
  "bore": {
    "radialMpa": -100,
    "hoopMpa": 166.6667
  },
  "outerSurface": {
    "radialMpa": 0,
    "hoopMpa": 66.6667
  },
  "maxHoopStressMpa": 166.6667,
  "lameConstants": {
    "A": 33.333333,
    "B": 0.33333333
  },
  "formula": "σr = A − B/r², σθ = A + B/r²",
  "interpretation": "Hoop stress is highest at the bore and always tensile under internal pressure; thin-wall undersizes it."
}

Input schema

{
  "type": "object",
  "required": [
    "innerRadiusM",
    "outerRadiusM",
    "internalPressureMpa"
  ],
  "properties": {
    "innerRadiusM": {
      "type": "number",
      "examples": [
        0.05
      ]
    },
    "outerRadiusM": {
      "type": "number",
      "examples": [
        0.1
      ]
    },
    "internalPressureMpa": {
      "type": "number",
      "examples": [
        100
      ]
    },
    "externalPressureMpa": {
      "type": "number",
      "examples": [
        0
      ]
    },
    "probeRadiusM": {
      "type": "number",
      "examples": [
        0.075
      ]
    }
  }
}

Output schema

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