Pile-cap footing · ACI 318-25

A worked example — a pile-cap footing D-region

A pile cap turns a single column's load a sharp corner and spreads it onto a group of piles. That abrupt change is what makes it a D-region — beam theory no longer applies, so it is designed with a strut-and-tie model. Here is the workflow in AStrutTie on a one-column pile cap.

Based on the AStrutTie 2020 Technical Book, Example 2.1 (one-column pile foundation), run under ACI 318-25.

Given

f_ck = 35 MPa (concrete)
f_y = 400 MPa (steel)
φ = 0.75 (strength-reduction factor)
Footing dimensions, pile layout & column load — entered in the template (see the drawing below)

①

The problem

A pile cap carries a column's load down to a group of piles. Its footing dimensions, pile layout and column load define the design — typed straight onto the drawing.

One-column pile-cap footing geometry and dimensions — External geometry, piles and column load of the pile cap.

②

Build the model — template → strut-and-tie

The pier-footing template builds a strut-and-tie model automatically: compression struts (dashed) fan from the column down to each pile, tension ties (solid) span between the pile heads, and nodal zones are typed CCC / CCT / CTT.

Strut-and-tie model of the one-column pile cap — The strut-and-tie model on the AStrutTie canvas.

③

Analyze & check — every member, every combination

AStrutTie resolves the member forces and checks every member against the code — ties, struts, nodal zones and anchorage — in one pass.

Pile-cap analysis results — Analysis · Check — member forces and per-member verdicts.

④

Tie check — required reinforcement

ACI 318-25

Required steel A_s,req is compared with the provided bars (size × count). φ = 0.75, f_y = 400 MPa.

As,req = Fu / (φ · fy)

Required reinforcement table for the pile-cap ties — Tie checks — required vs provided A_s per member.

⑤

Strut check — effective strength & width

ACI 318-25

Effective strength depends on strut type — Boundary (f_ce = 0.85 f_ck = 29.8 MPa) or Interior, reinforced (0.637 f_ck = 22.3 MPa). The required width must fit the available width.

fce = 0.85 · βs · βc · fck
wreq = Fu / (φ · fce · b) ≤ wprov

Strut strength verification of the pile cap — Strut checks — f_ce, required width and safety factor per member.

⑥

Nodal-zone check — by node type

ACI 318-25

fce = 0.85 · βn · βc · fck
wreq = Fu / (φ · fce · b) ≤ wprov

Node	β_n	f_ce (MPa)
CCC	1.0	29.8
CCT	0.8	23.8
CTT	0.6	17.9

Nodal-zone strength verification of the pile cap — Nodal-zone checks — each face against its node type.

⑦

Anchorage check — development at the node

ACI 318-25 §23.8.2 · §25.4

The tie must be anchored where it meets the pile nodes: the available anchorage ℓanc (§23.8.2, extended nodal zone) must reach the required development length ℓd (§25.4). Available = straight length along the tie plus a code hook-tail credit where a hook fits.

Tie anchorage verification of the pile cap — Anchorage check — available ℓanc vs required development ℓd.

These are the same checks AStrutTie runs — the pile-cap load path, from column down to the piles, verified member by member. How we verify →