A worked example — a two-column spread footing
Two columns 7 m apart on one 12 m spread footing: the region between them behaves like a deep beam turned upside down, carrying the ground pressure back up to the columns. The truss has 45 elements and every one of them is either a strut or a tie.
AStrutTie 2020 Technical Book, Example 02-2.4 (two-column spread foundation).
Given
- Footing 12,000 × 5,000 × 1,500 mm; two columns 1,300 × 1,300 mm at 7,000 mm centres
- fck = 30 MPa · fy = 400 MPa
- Column 1: V = 8,500 kN · H = 120 kN · M = 5,500 kN·m
- Column 2: V = 8,000 kN · H = 130 kN · M = 6,000 kN·m
- Reinforcement: top and bottom 33-#8 · vertical shear 7-#6 @300 · horizontal 6-#6 @300
The model
24 nodes, 45 elements, 6 supports (three under each column), 4 bearing plates. Top chord 1–11, bottom chord nodes 13–24, with vertical and diagonal web members alternating between them.
Ties — the bottom chord does the work
ACI 318 §23.7Provided 33-#8 = 16,721.39 mm² — the governing tie (Tie 45, 2,535 kN) needs about half of it. Shear ties 7-#6 with weff = 1,180.0 mm, sh = 300.0 mm give φFn = 2,354.3 kN against a maximum demand of 1,741.94 kN (Tie 26).
| Tie | Fu (kN) | As,req (mm²) |
|---|---|---|
| Tie 35 | 1,356.90 | 4,523.01 |
| Tie 37 | 1,390.76 | 4,635.85 |
| Tie 42 | 1,898.72 | 6,329.05 |
| Tie 43 | 2,501.55 | 8,338.49 |
| Tie 45 | 2,535.40 | 8,451.34 |
Struts
ACI 318 §23.4S9 governs: 158.3 mm of the 200.0 mm available, a 21% margin. Every strut here is bottle-shaped without crack-control steel across it (βs = 0.40) — the conservative end of the table.
| Strut | θ | Fu (kN) | wreq (mm) | wprov (mm) |
|---|---|---|---|---|
| S9 | 0.0° | 4,844.4 | 158.3 | 200.0 |
| S3 | 0.0° | 4,050.0 | 132.4 | 200.0 |
| S19 | 47.8° | 3,995.9 | 130.6 | 208.5 |
| S10 | 0.0° | 2,559.4 | 83.6 | 200.0 |
| S21 | 47.8° | 2,029.9 | 66.3 | 297.6 |
Nodal zones
ACI 318 §23.9Node 3 is CCC (βn = 1.00): C-2 1,332.9, C-3 4,050.0, C-16 602.5, C-17 1,033.8 kN. Nodes 5, 7 and 8 are CCT (βn = 0.80) — one tie each. Concentrated nodes N2, N4, N9, N11 are CCC; N13 and N24 are CCT. All faces O.K.
Two columns, one footing, 45 elements — and the answer is legible: Tie 45 governs the steel, S9 governs the concrete, and the widest margin in the model sits where you would expect it, directly under the columns. How we verify →