A worked example — an abutment footing on ground
An abutment footing is the least symmetric member in this set: a wall pushes down and sideways at one end, the heel carries backfill along its length, and the ground answers with a pressure that is anything but uniform. The forces here are an order of magnitude larger than in the pier footings — the governing strut carries 35,379 kN.
AStrutTie 2020 Technical Book, Example 03-3.2 (abutment, spread foundation).
Given
- Base slab 6,900 × 11,400 × 1,600 mm; wall 1,600 mm wide; base divided 3,700 + 1,600 + 1,600 mm
- fck = 24 MPa · fy = 400 MPa · check width b = 11,400 mm
- Wall W: V = 13,460 kN · H = 3,590 kN · M = 42,700 kN·m
- Heel D: distributed w₁ = 1,300 kN/m · w₂ = 650 kN/m
- Load case LC01 = 1.00 W + 1.00 D
- Reinforcement: top and bottom 91-#9 · vertical shear 22-#6 @300 · horizontal 2-#6 @300
The model
12 nodes, 21 elements, 2 supports, 5 bearing plates. Top chord 1–6, bottom chord 7–12. Node offset from the wall face is 150 mm here (larger than the footings) with 100 mm cover top and bottom.
Member forces — where the size shows
| Element | Force (kN) | Element | Force (kN) |
|---|---|---|---|
| E3 (tie) | +17,522.3 | E13 (strut) | −35,379.0 |
| E4 (tie) | +17,522.3 | E15 (strut) | −13,300.1 |
| E12 (tie) | +29,683.8 | E11 (strut) | −10,878.0 |
| E21 (tie) | +9,660.2 | E9 (strut) | −10,227.0 |
| E20 (tie) | +8,892.7 | E14 (strut) | −9,675.3 |
Ties — and the one with almost no margin
ACI 318 §23.7Provided 91-#9 = 58,670.22 mm². Tie 3 needs 58,407.55 mm² — it passes with 0.4% to spare. That is the number worth seeing: an O.K. that is one bar away from not being one, and it is printed rather than hidden inside a summary verdict.
| Tie | Fu (kN) | As,req (mm²) |
|---|---|---|
| Tie 1 | 3,465.98 | 11,553.28 |
| Tie 2 | 10,277.36 | 34,257.87 |
| Tie 3 | 17,522.27 | 58,407.55 |
| Tie 20 | 8,892.74 | 29,642.46 |
| Tie 21 | 9,660.17 | 32,200.56 |
Struts
ACI 318 §23.4S13 carries 35,379 kN and still passes — 507.1 mm required against 1,052.0 mm provided — because the check width here is the full 11.4 m of the base slab.
| Strut | θ | Fu (kN) | wreq (mm) | wprov (mm) |
|---|---|---|---|---|
| S13 | 47.1° | 35,379.0 | 507.1 | 1,052.0 |
| S15 | 40.3° | 13,300.1 | 190.6 | 262.0 |
| S11 | 48.2° | 10,878.0 | 155.9 | 300.0 |
| S9 | 48.2° | 10,227.0 | 146.6 | 300.0 |
| S14 | 90.0° | 9,675.3 | 138.7 | 1,300.0 |
| S19 | 0.0° | 8,599.4 | 123.3 | 200.0 |
Nodal zones
ACI 318 §23.9Node 2 and Node 3 are CTT (βn = 0.60), Node 7 is TTT, Node 11 is CTT. Concentrated nodes: N1 CTT · N4 TTT · N5 CCT · N8 CTT · N9 CCT · N10 CTT · N12 CCT. All faces O.K. — the extended nodal zone geometry (W₁,prov = 269.8 mm at Node 12) is what makes the tight ones work.
Wall, heel, backfill and ground pressure on one asymmetric slab — and the design still reduces to the three checks. Tie 3 is the number to remember: O.K. by 0.4%, stated plainly. How we verify →