A worked example — the ACI SP-273 hammerhead bent cap, rerun under ACI 318-25
ACI SP-273 Example 1 designs a single-column hammerhead bent cap with a simple strut-and-tie model under ACI 318-08 Appendix A. Here is the same cap and the same truss in AStrutTie, checked under ACI 318-25 — every number can be compared with a source you can open yourself, and the places where the newer code changes the answer are listed at the end.
Problem data (geometry, bearings, factored loads, materials) and the Model 1 truss are from ACI SP-273, Example 1: Bridge Pier – Hammerhead Bent Cap (R. G. Tuchscherer, M. D. Brown, O. Bayrak; American Concrete Institute, 2010), pp. 1–16. Figures and text are not reproduced; the model and every check below were run in AStrutTie under ACI 318-25.
Given
- f′c = 5,000 psi (34.5 MPa) · fy = 60,000 psi (414 MPa) · φ = 0.75
- Cap 29′-0″ long × 4′-6″ wide; 4′-0″ deep at the tips, 6′-3″ at the column; column 9′-0″ wide
- Bearings 30 × 36 in at 30, 174 and 318 in from the left tip
- Factored loads 700 · 400 · 100 kip — live load on one side only (the unbalanced case)
The problem
A single-column hammerhead cap carries three girder reactions out to the column. With 700 kip on the left and 100 kip on the right, both cantilevers are deep D-regions and an unbalanced moment goes into the column. Geometry and bearings are typed onto the drawing in kip and inch, as in the source.
Build the model — the SP-273 Model 1 truss
The pier-coping template gives a starting model, which was then edited node by node to the source's Model 1: tie ABCD 6.5 in below the top, struts from each bearing straight down to the column, and support nodes E and F set 9 in and 4 in inside the column faces. The analysis reproduces every member force in the source to the kip — AB 1,083 · BC 802 · CD 147 · AE −1,289 · BE −489 · CE −789 · DF −178 · CF 441 · EF −147. The underlay is the plane-stress flow of the same cap, for comparison.
Analyze & check — every member, every node
15 of 15 strength checks pass, minimum safety factor 1.12 (governing: vertical tie CF), and both hooked anchorages pass. The column reactions match the source as well: 1,541 kip compression at E and 341 kip tension at F.
Tie check — required reinforcement
ACI 318-25Tie ABCD carries 1,082.8 kip and needs 24.06 in²; 18-#11 in two layers give 28.11 in² (safety factor 1.17) — the same bars and the same 24.1 in² as the source, because φ = 0.75 and the tie equation are unchanged. CF (441 kip) is the column's longitudinal steel running up into the cap. The source leaves it to the column design; here 7-#11 (10.93 in², safety factor 1.12) are assumed so the truss is complete.
Strut check — effective strength & width
ACI 318-25Strut AE governs: 1,289 kip needs 9.99 in of width at fce = 3.19 ksi (interior strut, βs = 0.75), and 17.33 in is available at node E (safety factor 1.74). EF is a boundary strut (βs = 1.0). An interior strut keeps βs = 0.75 only with the distributed reinforcement of §23.5 — see step ⑧.
Nodal-zone check — by node type
ACI 318-25A and D anchor one tie, B and C anchor two, E is all-compression. The lowest margin is the tie face at node B (safety factor 1.24); the 1,541 kip support face at E has 2.01.
| Node | βn | fce (ksi) |
|---|---|---|
| CCC (E) | 1.0 | 4.25 |
| CCT (A, D, F) | 0.8 | 3.40 |
| CTT (B, C) | 0.6 | 2.55 |
Anchorage check — hooked bars at the cap tips
ACI 318-25 §23.8.2 · §25.4The 18-#11 end in standard 90° hooks. Under ACI 318-25 a #11 hook needs ℓdh = 48 in with no confining-reinforcement credit (ψr = 1.6, ψo = 1.25); the extended nodal zone gives ℓanc = 53.1 in at A (safety factor 1.11) and 52.5 in at D (1.09). The source, under ACI 318-08, needed only 23.9 in — the largest single change in this example.
What changes from the source
ACI 318-08 → ACI 318-25Same cap, same truss, same forces — the answer changes in three ways. Hooked anchorage roughly doubles. The source's crack-control grid (ratio 0.0021 each way) no longer meets §23.5, which asks for 0.0025 in each direction of an orthogonal grid: the cap is not laterally restrained, since 9 in of concrete beside a 36 in bearing is less than half the strut width. And two width assumptions differ — the source is the more conservative of the two in both.
| Check | SP-273 (ACI 318-08) | This example — ACI 318-25 | Why |
|---|---|---|---|
| Member forces (9) | AB 1,083 · AE −1,289 kip … | Identical | Same truss |
| Tie ABCD, 18-#11 | 24.1 in² required | 24.06 in² required | Same φ and tie equation |
| Hooked anchorage, #11 | ℓdh 23.9 in of 48.5 in | ℓdh 48 in of 53.1 in | Hook development reworked in ACI 318-19 |
| Distributed reinforcement | #5 4-leg @ 11 in + 7-#6 each face | #5 4-leg @ 9 in + #6 each face @ 6 in | §23.5: 0.0025 in each direction |
| Node A, tie face | 0.91 of capacity | 0.61 of capacity | Out-of-plane width: 36 in bearing (source) vs 54 in cap |
| Strut AE at node E | 0.83 of capacity | 0.58 of capacity | Face width: node E split, 12.1 in (source) vs full 18 in support, 17.3 in |
| Column bars CF | Left to the column design | 7-#11 assumed; anchorage in the cap left to the column / joint design | As in the source |
These are the checks AStrutTie runs on every model — here against a published example anyone can open, with the forces matching to the kip and every difference traced to a clause or an assumption. How we verify →
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