Rigid and structural pile cap

The group-cap tool couples two named calculations: the Saul/USACE CPGA rigid-body pile-load distribution and an edition-specific reinforced-concrete cap check. It never treats a plausible pile reaction as proof that the cap itself has adequate flexure or shear resistance.

Two explicit analysis scopes

• Distribution only preserves all six cap actions (Fx, Fy, Fz, Mx, My, Mz) and returns cap displacement plus every pile-head reaction. It makes no concrete resistance claim.
• Distribution + structural accepts explicit cap, column/pedestal, pile-head footprints, normal-weight concrete, four reinforcement mats, and already-factored load combinations. It checks flexure, one-way shear, column/pedestal punching, pile punching, required reinforcement, and the governing demand/capacity ratio.

Rigid-cap distribution

Each pile contributes its vertical, lateral, and optional rotational head springs at its declared plan coordinates. The full 6×6 stiffness K = Σ B_iᵀ k_i B_i retains coupling for asymmetric layouts. Solving for u = [ux, uy, uz, rx, ry, rz] gives, for example, the compression-positive pile reaction Q_i = kz(uz + rx·y_i − ry·x_i). This is the classic Saul (1968) formulation used by USACE CPGA and discussed in EM 1110-2-2906.

Structural cap method

The current structural method is deliberately frozen to the AASHTO LRFD Bridge Design Specifications, Second Edition with 2002 interims, matching the public FHWA NHI-04-041 pile-footing worked examples. A newer AASHTO edition will be a separate method ID; the engine will not substitute revised coefficients or resistance factors silently.

Flexure is cut at each loaded-area face. One-way shear uses the edition-specific critical section and effective shear depth. Column and pile punching perimeters are offset bydv/2, clipped at cap edges, and include fractional pile-head pressure when a rectangular footprint crosses a cut. The four top/bottom X/Y mats carry physical bar area, diameter, spacing, cover, and layer order so d is auditable.

Loads and combinations

Every combination has a stable ID and contains already-factored loads. Cap self-weight is applied only through its explicit combination factor and the declared concrete unit weight; no hidden 1.0 or 1.25 default is inserted. In structural mode, loads act at the column/pedestal centroid and are transformed to the cap origin. The sign convention is right-handed with z downward: positive Fz is downward and positive pile axial reaction is compression.

Checks and governing utilization

• Combination envelope — maximum pile compression, uplift, and lateral reaction across all combinations.
• Flexure — actual moment, minimum design moment, resistance, required/provided reinforcement, tension face, and DCR at four faces.
• One-way shear — cut coordinate, demand, resistance, effective shear depth, and DCR in ±X and ±Y.
• Punching — separate column/pedestal and applicable pile checks with demand, bo, dv, resistance, and DCR.
• Governing utilization — the largest DCR with its combination and location; over 1.0 is a failed structural check.

Public benchmark and status

Automated tests reproduce FHWA NHI-04-041 Design Step 8.11: its 20-pile geometry and biaxial load formula give Pile 1 ≈ 290.45 kip; the 14 reactions outside the column punching perimeter give ≈ 2509 kip; and the published bo ≈ 625.61 in, dv ≈ 36.40 in, and factored punching resistance ≈ 4082 kip are recovered within worked-example rounding. SI and US twins execute one inch-kip-ksi calculation path and agree to conversion precision.

Primary public sources: the FHWA abutment pile-footing example, pier pile-footing example, and USACE EM 1110-2-2906.

Applicability and fail-closed limits

Structural mode currently requires all of the following:

• a perfectly rigid rectangular cap on uncoupled linear springs for vertical piles;
• rectangular column/pedestal and pile-head bearing footprints wholly inside the cap;
• normal-weight concrete (λ = 1), f′c 2.4–10 ksi, and fy 40–75 ksi;
• no transverse shear reinforcement in the resistance equations;
• factored vertical load and biaxial overturning only; and
• compression pile reactions only—pile-head anchorage/pullout is not represented.

Overlapping footprints, impossible bar layers, out-of-range materials, horizontal or torsional structural load transfer, uplift reactions, and substantial pile-punching overlap with the loaded area all fail clearly. Flexible caps, battered piles, strut-and-tie regions, shear friction, development/anchorage, durability, seismic detailing, and newer-code checks remain outside this method ID.