Bridges · Substructure & abutments
Bridge abutment: stability and stem design calculator
Cantilever abutment carrying the deck reactions on its bearing shelf, with earth pressure from the approach fill and a traffic surcharge. ULS load factors per AS 5100.2 are applied to sliding (with 0.9 on stabilising weight), overturning and the stem moment at the base (earth pressure, surcharge and braking at bearing level); bearing pressure and eccentricity are checked at serviceability.
Standard: AS 5100.2 (traffic surcharge, braking, load factors 1.2G / 1.8 traffic / 1.5 earth pressure) · AS 5100.3 foundation checks · AS 5100.5 stem flexure
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Height, base underside to top of the ballast wall | 7 | m |
| Bearing shelf height above the base | 5.5 | m |
| Stem thickness | 1 | m |
| Base thickness | 1 | m |
| Toe | 1.5 | m |
| Heel | 3.5 | m |
| Deck dead reaction per metre | 180 | kN/m |
| Deck traffic reaction per metre | 90 | kN/m |
| Braking force per metre (at bearings) | 12 | kN/m |
| Bearing eccentricity toward the river from stem centre | 0.15 | m |
| Earth pressure coefficient | Active (wall can yield) | |
| Fill γ | 20 | kN/m³ |
| Traffic surcharge on the approach | 12 | kPa |
| Base friction | 0.55 | |
| Allowable bearing (service) | 350 | kPa |
| f′c | 40 | MPa |
| fsy | 500 | MPa |
| Cover | 65 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Permanent vertical load (incl. deck) | 900 | kN/m |
| Earth pressure / surcharge thrust | 162 / 28 | kN/m |
| ULS horizontal force | 314 | kN/m |
| Sliding FS (0.9G, ULS actions) | 1.42 | |
| Overturning FS (0.9G) | 3.00 | |
| Service eccentricity (B/6 = 1.00) | 0.481 | m |
| Service bearing qmax | 244 | kPa |
| Stem M* at the base | 582 | kNm/m |
| Stem back-face steel | 1,509 mm²/m |
- ✓ Sliding FS ≥ 1.0 (factored) — 1.42
- ✓ Overturning FS ≥ 1.0 (factored) — 3.00
- ✓ Resultant in the middle third (service)
- ✓ Bearing ≤ allowable — 244 kPa
- ✓ Stem section adequate
Method, formulas and assumptions
- ULS (AS 5100.2): earth pressure × 1.5, traffic surcharge and braking × 1.8, stabilising permanent loads × 0.9; sliding μ·0.9G ≥ H*, overturning 0.9ΣM_R ≥ ΣM_O (factored FS ≥ 1).
- Service: G + Q with unfactored earth pressure; Meyerhof pressure distribution for the bearing.
- Stem moment at the base from earth pressure on the stem height, surcharge and braking at bearing level; As from the AS 3600 stress block (φ = 0.85). Add wing walls, approach slab and seismic (AS 5100.2 Sec 15) separately.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.