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-loadParameters
| 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]