Two-column pier coping · ACI 318-25

A worked example — a two-column pier-coping D-region

A two-column pier coping spans between two columns and carries the girder bearing reactions down to them. Like the single-column case it is a D-region, designed with a strut-and-tie model — here is the same workflow in AStrutTie on the two-column geometry.

Based on the AStrutTie 2020 Technical Book, Example 01 §1.2 (two-column pier), run under ACI 318-25.

Given

f_ck = 24 MPa (concrete)
f_y = 400 MPa (steel)
φ = 0.75 (strength-reduction factor)
Coping dimensions, bearing plates & service loads — entered in the template (see the drawing below)

①

The problem

A two-column pier coping carries the girder bearing reactions across to two supporting columns. Its geometry, bearings and loads define the design — typed straight onto the drawing.

Two-column pier-coping geometry and dimensions — External geometry, bearings and loads of the two-column coping.

②

Build the model — template → strut-and-tie

The pier-coping template builds a strut-and-tie model automatically: struts (compression, dashed), ties (tension, solid), and nodal zones typed CCC / CCT / CTT. It is then refined to follow the load path between the two columns.

Strut-and-tie model of the two-column coping — The strut-and-tie model on the AStrutTie canvas.

③

Analyze & check — every member, every combination

This coping is statically indeterminate (degree 2), so it is solved by ACore stiffness analysis; every member is then checked against the code — here 36 / 0.

Two-column coping analysis results — Analysis · Check — indeterminate model solved by stiffness analysis, 36 / 0.

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 two-column coping 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.

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

Strut strength verification of the two-column coping — 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	20.4
CCT	0.8	16.3
CTT	0.6	12.2

Nodal-zone strength verification of the two-column coping — 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 at the node: 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 two-column coping — Anchorage check — available ℓanc vs required development ℓd.

These are the same checks AStrutTie runs — and Technical Book Example 01 is one of the cases our verification gate holds the engine to, unsafe-side zero. How we verify →