Moment–curvature that feeds straight into the lateral run.
Axial-equilibrated fiber M–φ for steel, reinforced/prestressed concrete, and composite sections — with explicit material models and direct nonlinear-EI coupling into the p-y solver.
The section module solves axial equilibrium and integrates the material stresses over fibers to build the moment–curvature response and secant EI as a function of moment. Every curve carries its method edition, convergence residual, and governing endpoint.
In PileCalc the M–φ result plugs directly into the lateral solver — EI is updated from the local moment at every node, every iteration — the same coupling LPILE sells as its nonlinear-EI feature.
Fiber equilibrium
Steel shapes plus round/rectangular reinforced concrete, prestress, casing, steel core, and explicit rectangular core/cover regions.
Nonlinear EI coupling
EI(M) feeds the p-y run automatically for cracked/plastic-section analysis.
Full curve visible
The complete M–φ curve and derived EI, exportable — not a black box.
One consistent model
Section, soil and solver share one definition of the pile.
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.
Plane-sections fiber equilibrium, PileCalc formulation 2026.07
| Quantity | PileCalc | Reference | Agreement |
|---|---|---|---|
| Official OpenSees 15×24-in rectangular RC core/cover curve (100 points, P = 180 kip)UC Berkeley OpenSees Moment Curvature Example; independently executed refined fiber mesh | peak 4,858.32 kip·in at 5.5238×10⁻⁴ /in | peak 4,858.39 kip·in at 5.5238×10⁻⁴ /in | all frozen curve checkpoints within 1%; peak within 0.01% |
| Solid-circle plastic shape factor Mp/My (= 32/6π)Closed-form section mechanics | 1.696 | 1.698 | within 0.1% |
| Pipe yield moment My = Fy·S (12.75 × 0.5 in, Fy 50 ksi)S = π(Dₒ⁴−Dᵢ⁴)/(32Dₒ) — closed form | 2.836×10⁶ lb·in | 2.836×10⁶ lb·in | exact |
| Pipe plastic moment Mp = Fy·Z, Z = (Dₒ³−Dᵢ³)/6Closed-form plastic modulus | 3.756×10⁶ lb·in | 3.754×10⁶ lb·in | within 0.1% |
| Plain-concrete shaft M–P interaction diagram (Hognestad fiber model)Independent-code verification example (printed interaction table) | all 15 points | 15-point Mn(P) table | worst point 0.45% |
| Reinforced round shaft (12 bars) M–P interaction diagramIndependent-code verification example (printed interaction table) | all 13 points | 13-point Mn(P) table | worst point 0.07% |
| Composite M–φ, 42-in shaft with permanent steel casing: initial EI / nominal momentIndependent-code verification example (cased-shaft section) | 1.0290×10⁹ kip·in² / 47,968 in·kip | 1.0251×10⁹ kip·in² / 48,384 in·kip | within 0.38% / 0.86% |
| Composite M–φ, same cased shaft with a 12-in steel core: initial EI / nominal momentIndependent-code verification example (cased + core section) | 1.0333×10⁹ kip·in² / 52,093 in·kip | 1.0295×10⁹ kip·in² / 52,772 in·kip | within 0.37% / 1.29% |
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.
Moment–curvature: common questions
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