Analysis & loading · Numerical geotechnics
Beam on elastic foundation (Winkler) calculator
Deflection, bending moment and contact pressure under a point load on a long beam or strip footing resting on Winkler springs.
Standard: Hetényi infinite beam, point load · modulus of subgrade reaction
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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 load P | 400 | kN |
| Modulus of subgrade reaction ks | 25000 | kN/m³ |
| Beam / footing width b | 1.2 | m |
| Elastic modulus E | 30000 | MPa |
| Section width | 1200 | mm |
| Section depth | 600 | mm |
| Actual beam length | 12 | m |
| Allowable bearing | 200 | kPa |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| EI | 648,000 | kN·m² |
| λ = (kb/4EI)^¼ | 0.3280 | 1/m |
| Characteristic length π/λ | 9.58 | m |
| Max deflection y0 = Pλ/(2kb) | 2.19 | mm |
| Max moment M0 = P/(4λ) | 304.9 | kN·m |
| Max contact pressure k·y0 | 54.7 | kPa |
| Zero moment at x = π/(4λ) | 2.39 | m |
- ✓ Contact pressure ≤ allowable — 55 kPa
- ✓ Beam long enough (λL ≥ π) for the infinite-beam solution — λL = 3.94
Method, formulas and assumptions
- y(x) = Pλ/(2kb)·e^(−λx)(cos λx + sin λx)
- M(x) = P/(4λ)·e^(−λx)(cos λx − sin λx)
- ks depends on footing size, so scale plate-test values before use
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.