Foundations · Rafts & slabs on ground
Slab on elastic subgrade (Winkler plate, grillage) calculator
Rectangular slab or raft on a Winkler subgrade (GEO5 Slab), analysed as a grillage of crossing slab strips with bending and torsional stiffness on spring supports at every node. Uniform load plus any number of point loads (rack legs, columns, forklift wheels). Springs that would go into tension can be released and the model re-solved. Reports deflections, contact pressures and the sagging and hogging moments per metre in each direction, with the reinforcement and a Westergaard check for the largest point load.
Standard: Plate on Winkler springs modelled as a grillage of slab strips (bending EI and torsion GJ = Gbh³/6) · no-tension iteration · AS 3600 flexure · Westergaard interior check
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 |
|---|---|---|
| Slab length Lx | 8 | m |
| Slab width Ly | 6 | m |
| Thickness | 200 | mm |
| Concrete E | 30000 | MPa |
| Poisson's ratio | 0.2 | |
| Subgrade modulus k | 30 | kPa/mm |
| Uniform load | 5 | kPa |
| Point loads: x (m), y (m), P (kN) | 2, 2, 60 6, 2, 60 2, 4, 60 6, 4, 60 4, 3, 40 | |
| Grid nodes per side | 11 | |
| Release springs in tension | Yes | |
| f′c | 32 | MPa |
| fsy | 500 | MPa |
| Cover | 40 | mm |
| Flexural strength f′cf | 4 | MPa |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Flexural rigidity D | 20,833 | kNm |
| Radius of relative stiffness ℓ | 913 | mm |
| Maximum deflection | 0.57 | mm |
| Minimum deflection (uplift if negative) | 0.05 | mm |
| Maximum contact pressure | 17.1 | kPa |
| Sagging moment Mx / My | 8.0 / 8.3 | kNm/m |
| Hogging moment Mx / My | -2.4 / -1.9 | kNm/m |
| Bottom steel for sagging | 128 | mm²/m |
| Top steel for hogging | 36 | mm²/m |
| Westergaard interior stress, largest point load | 2.14 | MPa |
| Nodes released (tension) | 0 |
- ✓ Flexural stress M/Z ≤ f′cf/1.5 (unreinforced design) — 1.24 MPa
- ✓ Westergaard interior stress ≤ f′cf/1.5 — 2.14 MPa
- ✓ Section adequate for the moments
Method, formulas and assumptions
- Grillage: strips of width equal to the node spacing carry bending EI = Ebh³/12 and torsion GJ = Gbh³/6 (plate equivalence); springs k × tributary area at each node; loads lumped to the nearest node.
- Moments per metre from the deflected shape: Mx = −D(∂²w/∂x² + ν∂²w/∂y²) at interior nodes (free edges carry no moment).
- No-tension iteration removes springs where the slab lifts and re-solves (up to 8 passes).
- Westergaard interior: σ = 3(1 + ν)P/(2πh²)[ln(ℓ/b) + 0.6159] with a 150 mm contact radius.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.