API: pile buckling

Solves the smallest positive generalized eigenvalue of a finite Euler–Bernoulli pile on explicitly linear Winkler support. The method and limitations are explained in Pile buckling; the same analysis runs interactively at the buckling tool.

Endpoint

The request reuses the lateral pile geometry, but the soil profile is restricted toelastic layers or a user layer declaring only a constant linear es. Declare headFixity and tipFixity as free, fixed-rotation, pinned, or fixed. Optional controls set mesh size and convergence tolerances.

Authentication, rate limits, and the error envelope are shared by every endpoint — see the API overview. Requests are unit-agnostic: any self-consistent unit system works, and results come back in the same units. The examples below use SI (m, kN, kPa, kN/m³).

Request fields

This table is generated from the same schema that validates the request, so it cannot drift. Where a field appears once per variant row, it belongs to that variant only.

Response fields

Code examples

A complete, runnable request. Replace YOUR_API_KEY (or set PILECALC_API_KEY in your environment).

curl https://api.pilecalc.com/v1/buckling \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
  "unitSystem": "si",
  "pile": {
    "kind": "uniform",
    "length": 20,
    "diameter": 0.61,
    "ei": 143000,
    "groundSurfaceDepth": 4
  },
  "soil": {
    "layers": [
      {
        "model": "elastic",
        "top": 0,
        "bottom": 16,
        "gamma": 9,
        "esTop": 0,
        "esBottom": 12000
      }
    ]
  },
  "headFixity": "fixed-rotation",
  "tipFixity": "fixed",
  "increments": 80
}'

The GET variant returns criticalLoad,method,convergence as a plain-text CSV line — made for Excel's WEBSERVICE() and Sheets' IMPORTDATA() (see Use PileCalc in Excel). Omit fields to get the full JSON response.

Interpreting results

• criticalLoad is an elastic stability limit, not allowable or factored resistance.
• The mode sign and amplitude are arbitrary; the API fixes sign deterministically and normalizes max |y| to one.
• The response is returned only after both the eigen residual and the fine/coarse mesh difference satisfy their limits.
• Nonlinear p-y curves are rejected because they require a separately declared reference state and linearization.
• The geometric-stiffness matrix assumes constant compression over the full pile length; variable axial-force distributions from shaft transfer or self-weight are outside this method.
• A zero-stiffness foundation is accepted only when the declared end restraints remove both rigid-body modes.