Buckling of piles, with the soil actually in the model.
The first elastic buckling eigenvalue of a finite beam on explicit linear Winkler support — with partial embedment, variable EI, selectable head/tip restraint, and convergence evidence on every run.
Slender piles through weak or missing support can buckle under axial load — micropiles, piles affected by scour, and piles extended above grade are the usual suspects. Davisson's classical treatments idealize the support with constant or linearly increasing Winkler modulus; this tool makes that linearization explicit rather than silently converting nonlinear p-y curves.
PileCalc assembles the elastic bending, Winkler, and geometric-stiffness matrices and solves their smallest positive generalized eigenvalue. It supports finite length, unsupported stick-up, sectioned or tapered EI through the API, and four explicit restraint states at either end. The response includes a signed eigenmode, eigen residual, and an independent half-resolution mesh comparison.
True generalized eigenvalue
Solves (Kb + Ks)φ = Pcr·Kgφ directly, with no perturbation or amplification cutoff.
Explicit end restraints
Free, rotation-fixed, pinned, and fully fixed conditions are independently selectable at head and tip.
Finite partial embedment
Unsupported stick-up and every section, ground, and soil interface are represented directly in the mesh.
Convergence reported
Every accepted result includes eigen residual and fine-versus-coarse mesh agreement.
Validated against published benchmarks
Every figure below is produced by the engine on the cited published problem — closed-form solutions, design-manual tables, or independent codes — and reproduced by the test suite on every release.
Hermite-beam generalized eigenvalue on a linear Winkler foundation
| Quantity | PileCalc | Reference | Agreement |
|---|---|---|---|
| Free-end critical load Pcr = √(k·EI), long strut on uniform foundationDavisson constant-modulus formulation; independently evaluated closed form | 1.000002·√(k·EI) | √(k·EI) | 0.00018% |
| Partially embedded pile: EI=8.38×10⁹ lb·in², 20-ft stick-up, T=84 inDavisson & Robinson (1965), application example, p. 246; republished method basis in NCHRP Report 343 §4.1.1.2 | 540,285 lb | 540,000 lb | 0.053% |
The numbers, published
PileCalc's engine is checked term-by-term against the reference codes. A representative sample of the benchmarks — every intermediate value is visible in the app so you can reproduce them yourself.
Pile buckling: common questions
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