Math & Numbers

Fatigue Limit Calculator (Goodman / Gerber / Soderberg)

Mean-stress fatigue correction under cyclic loading. Given stress amplitude σ_a, mean stress σ_m, and material σ_uts / σ_-1 (endurance limit) / σ_y, compute safety factors from three classical criteria: Modified Goodman (linear, conservative), Gerber (parabolic, better for ductile metals), and Soderberg (uses σ_y, most conservative). Reports the governing (smallest) value and whether the operating point lies inside the Goodman line.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/fatigue-limit-calculator' \
  -H 'Content-Type: application/json' \
  -d '{"stressAmplitude":100,"meanStress":200,"uts":800,"enduranceLimit":300,"yield":500,"decimalPlaces":4}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/fatigue-limit-calculator

Parameters

Name	Type	Required	Description
stressAmplitude	number	Yes	Alternating stress amplitude σ_a = (σ_max − σ_min)/2 in MPa. Must be > 0 (zero amplitude means no cycling).
meanStress	number	No	Mean stress σ_m = (σ_max + σ_min)/2 in MPa. Tensile (>0) reduces fatigue life; compressive (<0) is beneficial but unusual in textbook problems.
uts	number	No	Ultimate tensile strength of the material in MPa. Required by Goodman and Gerber.
enduranceLimit	number	No	Fully reversed fatigue (endurance) limit σ_-1 in MPa, typically for 10⁶ cycles or more. Must not exceed σ_uts.

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-fatigue-limit-calculator": {
      "name": "fatigue-limit-calculator",
      "description": "Mean-stress fatigue correction under cyclic loading. Given stress amplitude σ_a, mean stress σ_m, and material σ_uts / σ_-1 (endurance limit) / σ_y, compute safety factors from three classical criteria: Modified Goodman (linear, conservative), Gerber (parabolic, better for ductile metals), and Soderberg (uses σ_y, most conservative). Reports the governing (smallest) value and whether the operating point lies inside the Goodman line.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=fatigue-limit-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "fatigue-limit-calculator",
    "arguments": {
  "stressAmplitude": 100,
  "meanStress": 200,
  "uts": 800,
  "enduranceLimit": 300,
  "yield": 500,
  "decimalPlaces": 4
}
  }
}

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