Saul/USACE CPGA · AASHTO LRFD 2nd edition through 2002 interims

Distribute the piles. Check the cap.

Apply explicit factored load combinations, recover every pile-head demand with the Saul/CPGA rigid-cap method, then check the concrete cap for flexure, one-way shear, loaded-area punching, pile punching, and reinforcement adequacy.

Given a cap under combined loads, the question is how much each pile carries. The classical answer is the rigid-cap stiffness method — Saul (1968), implemented by the US Army Corps as CPGA (EM 1110-2-2906): assemble each pile's stiffness at its coordinates, sum into a 6×6 cap stiffness, solve for the cap's rigid-body displacement, and recover every pile's demands from its own displacement.

The structural mode carries those pile reactions into explicit cap geometry, column or pedestal dimensions, concrete and reinforcing-steel properties, and four physical reinforcement mats. It evaluates the sectional checks of the AASHTO LRFD 2nd edition through the 2002 interims, benchmarked against the public FHWA NHI-04-041 pile-footing examples — the code edition is stamped on every result, so a newer edition or local amendments are never silently implied.

Explicit load combinations

Named, already-factored combinations are evaluated independently, including optional cap self-weight factors; no hidden load factors are applied.

Arbitrary layouts

Piles at any coordinates; the rigid-cap stiffness matrix is assembled from the layout you define, not from a template grid.

Structural cap checks

Flexure and required/provided reinforcement, one-way shear, column or pedestal punching, pile punching, and the governing utilization are reported by combination.

Explicit applicability

Unsupported tension, horizontal structural loading, overlapping footprints, impossible bar layouts, and out-of-domain materials are rejected instead of silently extrapolated.

Traceable reports

Reports stamp the method and edition, retain each load combination, and show pile reactions and sectional checks — every number traceable to its input.

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.

Saul/USACE CPGA distribution + AASHTO LRFD 2nd edition with 2002 interims structural checks

QuantityPileCalcReferenceAgreement
Pure moment on a 2×2 group: axialᵢ = M·kz·xᵢ / Σ(kz·x²)Saul (1968) / USACE CPGA closed form (My = 500 kN·m, kz = 100 MN/m)±125 kN±125 kNexact
3×1 line group under Fx + My: axial −150/0/+150 kN, lateral 100 kN eachElastic-center hand calculation−150/0/+150; 100 kN−150/0/+150; 100 kNexact
Global 6-DOF equilibrium, asymmetric 5-pile layout with mixed stiffnessesStiffness-method identity, all six load componentsΣ reactions ≡ applied loadsexact equilibriumwithin 1e-9 (relative)
FHWA NHI-04-041 Pier Step 8.11 — Pile 1 under Pu + biaxial momentFHWA NHI-04-041, Design Step 8.11, published 20-pile geometry and pile-load equation290.44 kip290.45 kipwithin 0.01% (published rounding)
FHWA column punching demand — 14 pile reactions outside the dᵥ/2 perimeterFHWA NHI-04-041, Design Step 8.11 (alternate equal-load check: 2508 kip)2508.1 kip2509 kipwithin 0.04% (published rounded inputs)
FHWA column punching resistance (b₀ ≈ 625.61 in, dᵥ ≈ 36.40 in)FHWA NHI-04-041, AASHTO LRFD 5.13.3.6.3 worked calculation4081.94 kip4082 kipwithin 0.01%
See the full per-tool validation report

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.

Free-head pile (EI 1.43×10⁶, D 1 m, L 24.4 m)Liang et al. (2014) exact solution / RSPile
Max moment
792.2 kN·m
792.1 kN·m (exact)
within 0.1%
Fixed-head pile (EI 1.43×10⁶, D 1 m, L 24.4 m)Liang et al. (2014) exact solution / RSPile
Head moment
−581.1 kN·m
−581.0 kN·m (exact)
within 0.1%
Cantilever pile (EI 320, D 0.1 m, L 5.25 m)Liang et al. (2014) exact solution / RSPile
Head deflection
8.75 mm
8.750 mm (exact)
within 0.1%
Cantilever pile (EI 320, D 0.1 m, L 5.25 m)Liang et al. (2014) exact solution / RSPile
Max moment
2.335 kN·m
2.334 kN·m (exact)
within 0.1%
Circular pile, API sand (D 0.5 m, L 10 m, H 100 kN)RSPile verification manual
Deflection & moment profile
RSPile 2018 problems #1/#2/#8/#15
chart-reading tolerance
within 1–3%
Steel pile, multi-layer slope stabilization (17 m)RSPile / TZPile / LPile
Lateral resistance
607 kN
582 kN
within ~4%
Read how we validate — and why against two independent codes

Rigid and structural pile cap: common questions

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