Foundations · Rafts & slabs on ground
Slab on ground (Westergaard) calculator
Flexural stress for interior, edge and corner wheel or post loads on a slab on grade.
Standard: Westergaard (1926) · AS 3600 f'ct,f · AS 2870 context
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 |
|---|---|---|
| Point / wheel load | 40 | kN |
| Contact radius a | 150 | mm |
| Slab thickness h | 180 | mm |
| f'c | 32 | MPa |
| Concrete E | 30100 | MPa |
| Poisson's ratio | 0.15 | |
| Subgrade modulus k | 40 | MPa/m |
| Factor of safety on f'ct,f | 2 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Radius of relative stiffness ℓ | 782 | mm |
| Equivalent radius b | 140 | mm |
| Interior stress | 1.58 | MPa |
| Edge stress | 2.36 | MPa |
| Corner stress | 2.01 | MPa |
| f'ct,f = 0.6√f'c | 3.39 | MPa |
| Allowable | 1.70 | MPa |
- ✓ Interior
- ✗ Edge
- ✗ Corner
Method, formulas and assumptions
- ℓ = [E h³ / (12(1 − ν²) k)]^¼
- b = √(1.6a² + h²) − 0.675h when a < 1.724h, else b = a
- Interior σ = 0.316 P/h² [4 log(ℓ/b) + 1.069]
- Edge σ = 0.572 P/h² [4 log(ℓ/b) + 0.359]
- Corner σ = 3P/h² [1 − (a√2/ℓ)^0.6]
- Residential slabs on reactive sites are designed to AS 2870 (site classification, stiffened rafts); this checks concentrated loads.
Related foundations calculators
- Raft foundation — Corner pressures with two-way eccentricity, kern check, elastic and consolidation settlement.
- Slab on elastic subgrade (Winkler plate, grillage) — Rectangular slab or raft on a Winkler subgrade (GEO5 Slab), analysed as a grillage of crossing slab strips…
- Pad footing — Square pad: bearing, flexural steel, one-way shear and punching shear.
- Bearing capacity — Ultimate and allowable bearing pressure for strip or rectangular footings with shape and depth factors.
- Spread footing from CPT: bearing and settlement — Pad or strip footing designed directly from a CPT, as in GEO5 Spread Footing CPT. The equivalent cone…
- Strip footing with eccentric load — Strip footing under a wall with moment: eccentricity, effective width B′, trapezoidal pressure and ultimate…
For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.