Combined pile punching
Supplied-reaction punching checks across circular pile subsets and free edges.
Combined pile punching assesses supplied factored compression reactions from up to eight equal circular piles. It does not solve load distribution or establish complete pile-cap adequacy.
Method and scope
The scalar concrete shear equation and circular individual, pair and corner contours follow FHWA-NHI-16-009 (2016), Figures 8-9/8-10 and equations 8-86/8-87/8-91, reproducing AASHTO LRFD 2014. This separate assessment leaves the historical AASHTO 2002 cap method unchanged.
Declare effective shear depth above the embedded pile top. The program checks that it fits within cap thickness minus embedment; you must establish that depth from reinforcement and force resultants. Normal-weight concrete is limited to 2.4–10 ksi.
Combined and boundary contours
Every nonempty pile subset is enumerated. The convex hull of its centers is offset by (pile diameter + effective shear depth) / 2. Single-edge and adjacent-edge corner candidates include hull projections to those free edges before offsetting and clipping. Resisting lengths are exact line and circular-arc lengths; free concrete edges add no shear resistance.
The multirow hull construction is a mathematical extension of the published pair and corner diagrams. Every bearing circle touched contributes its full positive reaction, including partial intersections. No beneficial downward load or cap-weight relief is deducted. An aspect-ratio upper bound, (maximum center separation + pile diameter) / pile diameter, makes resistance conservative for multirow or nonrectangular subsets.
Limits and evidence
Opposite-edge strip mechanisms, column punching, one-way shear, flexure, anchorage, strut-and-tie action and eccentric shear stress transfer are outside this scalar assessment. A passing result is a punching bound, not a whole-cap acceptance. Source-derived analytical cases verify single, pair, edge and corner geometry; they are not published multirow worked examples, field qualification or professional signoff.