Math & Numbers

Column Buckling Load Calculator (Euler)

Calculate the Euler critical buckling load of an axially loaded column: P_cr = π²·E·I/(K·L)². Supports pinned-pinned (K=1), fixed-free (K=2), fixed-pinned (K=0.7), fixed-fixed (K=0.5). Returns effective length, radius of gyration, slenderness ratio λ, and critical stress σ_cr.

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/column-buckling-load' \
  -H 'Content-Type: application/json' \
  -d '{"endCondition":"pinned-pinned","E":200,"I":1000000,"A":1000,"L":3,"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/column-buckling-load

Parameters

Name	Type	Required	Description
endCondition	select	No	—
E	number	Yes	Elastic modulus (200 for steel, 70 for aluminum, 25–35 for concrete).
I	number	Yes	Second moment of area about the buckling axis.
A	number	Yes	—
L	number	Yes	—

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-column-buckling-load": {
      "name": "column-buckling-load",
      "description": "Calculate the Euler critical buckling load of an axially loaded column: P_cr = π²·E·I/(K·L)². Supports pinned-pinned (K=1), fixed-free (K=2), fixed-pinned (K=0.7), fixed-fixed (K=0.5). Returns effective length, radius of gyration, slenderness ratio λ, and critical stress σ_cr.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=column-buckling-load",
      "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": "column-buckling-load",
    "arguments": {
  "endCondition": "pinned-pinned",
  "E": 200,
  "I": 1000000,
  "A": 1000,
  "L": 3,
  "decimalPlaces": 4
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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