Abutment pile-cap footing · ACI 318-25

A worked example — an abutment pile-cap footing

An abutment pile cap carries an eccentric bridge-seat wall down to its piles, under both vertical load and horizontal earth pressure. The offset, two-way load path makes the cap a D-region — designed with a strut-and-tie model in AStrutTie. (Pile cap and pile footing are the same member; the codes use both names.)

Based on the AStrutTie 2020 Technical Book, Example 3.1 (abutment on pile foundation), run under ACI 318-25.

Given

f_ck = 24 MPa (concrete)
f_y = 400 MPa (steel)
φ = 0.75 (strength-reduction factor)
Footing dimensions, pile layout & wall loads (vertical + horizontal) — the Technical Book's values, from AStrutTie's built-in Example 3.1 file (see the drawing below)

①

The problem

An abutment footing carries an eccentric wall down to a pile group, under vertical load and horizontal earth pressure. Its geometry, pile layout and wall loads define the design — typed straight onto the drawing.

Abutment pile-cap footing geometry and dimensions — External geometry, piles and wall loads of the abutment footing.

②

Build the model — the Technical Book's strut-and-tie model

The model is the Technical Book's own final strut-and-tie model, carried into AStrutTie's built-in Example 3.1 file: struts carry the eccentric wall load down to the piles, ties resist the spread and the horizontal thrust, and nodal zones are typed CCC / CCT / CTT.

Strut-and-tie model of the abutment footing — 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.

Abutment footing 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.

A_s,req = F_u / (φ · f_y)

Required reinforcement table for the abutment footing 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 = 20.4 MPa) or Interior, reinforced (0.637 f_ck = 15.3 MPa). The required width must fit the available width.

f_ce = 0.85 · β_s · β_c · f_ck

w_req = F_u / (φ · f_ce · b) ≤ w_prov

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

⑥

Nodal-zone check — by node type

ACI 318-25

f_ce = 0.85 · β_n · β_c · f_ck

w_req = F_u / (φ · f_ce · b) ≤ w_prov

Node	β_n	f_ce (MPa)
CCC	1.0	20.4
CCT	0.8	16.3
CTT	0.6	12.2

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

⑦

Development length check — anchorage at the node

ACI 318-25 §23.8.2 · §25.4

The tie must be anchored at 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 — no hook-tail credit: ℓdh is measured to the outside of the hook, so the hook's contribution is already in the required length.

Tie anchorage verification of the abutment footing — Development length check — available ℓanc vs required development ℓd.

These are the same checks AStrutTie runs — the eccentric abutment load path, vertical and horizontal, verified member by member. How we verify →

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