A worked example — a single-column spread footing
A spread footing has no piles to gather the reaction into neat points: the ground pushes back over the whole base, and the column drives its load, with a large moment, into the middle of it. This is Example 2.3 of the AStrutTie 2020 Technical Book, opened as a built-in example in the current AStrutTie and checked under ACI 318-25: every check value the book prints comes out the same, and the model the template builds is set beside the book's final one.
Problem data and check values are from the AStrutTie 2020 Technical Book, Example 02-2.3 (one-column spread foundation, ACI 318-19). The example ships with the app; the model and every check below were run in the current AStrutTie under ACI 318-25.
Given
- f′c = 24 MPa, the value the Technical Book's check tables use (its text gives 35 MPa) · fy = 400 MPa · φ = 0.75
- Footing 8,000 × 7,000 mm, 2,000 mm thick · one column 2,500 × 2,500 mm
- Load case ST1O05: V = 9,625 kN · H = 125 kN · M = 14,670 kN·m
- Ground springs, vertical modulus 30,000 kN/m² · bars top and bottom 69-#8 · shear bars #6, 18 legs @ 400 mm vertical and 18 bars @ 600 mm horizontal
The problem
One column brings 9,625 kN with 125 kN of shear and a moment of 14,670 kN·m. The ground answers through springs, so the pressure under the footing is far from uniform: it grows toward the side the moment pushes down. The Technical Book example opens in AStrutTie with its dimensions, load, material and bars already entered in the spread-footing template.
Build the model — the template's truss
The template puts the top chord 100 mm below the top and the bottom chord 100 mm above the bottom, with two nodes under the column and a vertical at every node: 8 nodes and 13 members, statically determinate. As in the Technical Book, the column is the support and the ground pressure comes in as loads along the bottom chord, from 177 kN at one end to 4,156 kN at the other. The book's final model has 10 nodes and 17 elements, with three nodes under the column, so the forces differ a little: the largest bottom-chord tension is 4,821.0 kN here against the book's 4,736.8 kN (+1.8%), and the largest compression 6,386.6 kN in diagonal m13 against 6,275.7 kN in the book's diagonal E12 (+1.8%).
Analyze & check — every member, every node
15 of 15 strength checks pass. The minimum safety factor is 1.77, on the diagonal strut m13 from the column to the heavily loaded end of the footing. Anchorage is reported separately from the strength verdict, and the two ends of the bottom tie fail it as straight bars; step ⑦ explains why.
Tie check — required reinforcement
ACI 318-25The bottom chord carries up to 4,821.0 kN in m3 and needs 16,070 mm²; 69-#8 give 34,963 mm² (2.18). The vertical tie m8 under the column is the shear reinforcement: 1,751.5 kN against 99 legs of #6, 28,217 mm² (4.83). The tie checks the book prints, such as T17 at 4,736.76 kN needing 15,789.21 mm², come out the same in the app's comparison.
Strut check — effective strength & width
ACI 318-25 §23.4 · §23.5The shear bars, #6 at 400 mm vertically and 600 mm horizontally, give ρ ≈ 0.0018 and 0.0012, below the 0.0025 per direction that §23.5 asks for βs = 0.75. Every strut is therefore taken as βs = 0.40, as in the Technical Book: fce = 8.16 MPa. The most loaded strut, m13, carries 6,386.6 kN and needs 149 mm of the 263 mm available (1.77); m12, the other diagonal from the column, carries 5,739.7 kN (1.90).
Nodal-zone check — by node type
ACI 318-25The tightest node is t3, the more heavily loaded of the two column supports: its bearing face needs 104.6 of 200 mm (1.91). The CTT nodes along the bottom chord, b2 and b3, have 2.68 and 2.67. The book's check of node N3, face T-9 with 3,308.2 kN needing 38.6 mm, is reproduced exactly in the app's comparison.
| Node | βn | fce (MPa) |
|---|---|---|
| CCC | 1.0 | 20.4 |
| CCT | 0.8 | 16.3 |
| CTT | 0.6 | 12.2 |
Development length check — straight bars at the edge
ACI 318-25 §23.8.2 · §25.4The bottom bars end at nodes b1 and b4, 750 mm from the ends of the footing. Straight, a #8 bar needs ℓd = 1,220 mm, and the extended nodal zone leaves 912 mm, a safety factor of 0.75. A 90° hook would bring the requirement down to 753 mm and pass (1.21); the built-in example keeps the bars straight, and the NG is shown as the app reports it. The Technical Book's check tables for this example do not cover anchorage.
What changes from the Technical Book
ACI 318-19 → ACI 318-25Same footing, same load, same bars. The strength equations and φ are the same in both editions, so every value the book's check tables print comes out the same. What differs is the model — the template's truss against the book's optimized one — and two checks: the struts keep the book's βs = 0.40 because the footing lacks §23.5 reinforcement, and the app checks the anchorage of every tie end.
| Check | Technical Book (2020 · ACI 318-19) | This example — ACI 318-25 | Why |
|---|---|---|---|
| Values that must match (8) | T17 4,736.76 kN → 15,789.21 mm² · S12 6,275.7 kN → 146.5 mm · N3 T-9 3,308.2 kN → 38.6 mm … | 8 of 8 the same | Same strength equations and φ |
| Model | Final model after optimized analysis — 10 nodes · 17 elements | Template model — 8 nodes · 13 members · statically determinate | The app starts from its template; the book refined its model |
| Largest bottom-chord tension | E17 4,736.8 kN | m3 4,821.0 kN (+1.8%) | Different model |
| Largest compression | E12 6,275.7 kN (diagonal) | m13 6,386.6 kN (diagonal, +1.8%) | Different model |
| Bottom bars, 69-#8 | 34,962.90 mm² | 34,963 mm² · 2.18 at m3 | Same bars |
| Shear reinforcement | 18-#6 · weff 1,150.0 mm · φFn 4,425.0 kN ≥ 3,308.25 kN | m8 1,751.5 kN · 28,217 mm² (4.83) | Vertical ties at the template's positions |
| βs of the struts | 0.40 | 0.40 (template default 0.75) | #6 gives ρ ≈ 0.0018 / 0.0012 < 0.0025 (§23.5) |
| f′c | 35 MPa in the text · 24 MPa in the check tables | 24 MPa | The app follows the tables (the book is inconsistent) |
| Anchorage of the end bars | Not in the check tables | 912 mm available < 1,220 mm required (0.75) — NG · a 90° hook needs 753 mm | The app checks every tie end |
These are the checks AStrutTie runs on every model — here on an example from the AStrutTie 2020 Technical Book, opened in the current app, with every check value the book prints reproduced and every difference traced to the model, a reinforcement detail or the book itself. How we verify →
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