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Peak footing pressure after one edge lifts
Peak contact pressure under a rigid rectangular footing loaded eccentrically along its width B once the resultant moves outside the middle third (B/6 < e < B/2) and one edge lifts off.
- Ref
- CIV-49
- Rev
- v1
- Field
- Civil
- Result
- qmax [Pa]
When the load eccentricity along B exceeds B/6, the resultant falls outside the middle third and one edge lifts off. The soil carries only compression, so the pressure becomes a triangle over a contact width 3(B/2 − e), uniform along L. Vertical equilibrium then requires a peak pressure q = 2P/[3L(B/2 − e)]. At e = B/6 this equals the full-contact value.
Peak contact pressure under a rigid rectangular footing loaded eccentrically along its width B once the resultant moves outside the middle third (B/6 < e < B/2) and one edge lifts off. The soil carries compression only, in a triangular pattern over a width 3(B/2 − e), uniform along L. At e = B/6 it matches the full-contact value.
Calculator
- Contact width, 3(B/2 − e)1.5 m
- Fraction of the base in contact0.75
- Mean pressure over the whole base, P/(BL)100,000 Pa
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Only 75 % of the base stays in contact, and the peak pressure of 266.7 kPa is 2.67 times the mean pressure.
- As e approaches B/2 the contact width goes to zero and the pressure to infinity, so the footing would overturn before that.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Pa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| eB Eccentricity along B | 0.34 to 0.99 m | 202,000 | 1.333e7 | 1.313e7 | +10% | +11.1 % |
| B Footing width | 1.05 to 2.95 m | 136,800 | 5,333,000 | 5,197,000 | +10% | −16.7 % |
| P Vertical load | 10,000 to 1e7 N | 4,444 | 4,444,000 | 4,440,000 | +10% | +10 % |
| L Footing length | 1 to 10 m | 80,000 | 800,000 | 720,000 | +10% | −9.09 % |
Sweep of Eccentricity along B
| Eccentricity along B (m) | Peak pressure (Pa) |
|---|---|
| 0.34 | 202,000 |
| 0.4213 | 230,400 |
| 0.5025 | 268,000 |
| 0.5837 | 320,300 |
| 0.665 | 398,000 |
| 0.7462 | 525,500 |
| 0.8275 | 772,900 |
| 0.9087 | 1,461,000 |
| 0.99 | 1.333e7 |
Sweep one variable
Variables and how each one contributes
Peak pressure
What the equation gives you. Everything else feeds it.
Vertical load
The vertical load, in N. Scales the peak pressure in direct proportion. Raising it by 10 % (to 660,000) moves the result by +10 %, from 266,700 to 293,300 Pa.
Footing length
The footing length, in m. A longer footing spreads the load, lowering the pressure in inverse proportion. Raising it by 10 % (to 3.3) moves the result by −9.09 %, from 266,700 to 242,400 Pa.
Footing width
The footing width, in m (the direction of the eccentricity). A wider footing has a larger B/2 − e, lowering the pressure. Raising it by 10 % (to 2.2) moves the result by −16.7 %, from 266,700 to 222,200 Pa.
Eccentricity along B
The load eccentricity along B, in m, with B/6 < e < B/2. A larger eccentricity shrinks the contact width and raises the peak pressure steeply. Raising it by 10 % (to 0.55) moves the result by +11.1 %, from 266,700 to 296,300 Pa.
Worked example with the values above
- Contact width: 3(B/2 − e) = 3 × (1 − 0.5) = 1.5 m.
- Triangular pressure over that width and the length 3 m: P = ½ q × 1.5 × 3.
- q = 2P / (3L(B/2 − e)) = 266,667 Pa.
Assumptions and limits
- A rigid or flexible footing on a homogeneous elastic half-space with a level surface.
- A full-contact plane pressure distribution unless the page says that one edge lifts off.
Common mistakes
- Using it when e is not between B/6 and B/2, where the full-contact formula applies or the footing overturns.
- Assuming soil can carry tension across the lifted edge.
- Reading the peak pressure as bearing capacity without a separate check.
Statistics and uncertainty
Elastic stress solutions idealise the soil as homogeneous, isotropic and linear. Measured stresses under real footings differ from these by 20 % to 30 % because of soil layering and non-linearity. Use them for settlement estimates, not for precise stress values.
Where it is used
- Checking footing pressures and stress increments for settlement calculations.
- Estimating stresses under tanks and silos.
Maths you need
- Middle-third rule: a footing stays in full compression if the load acts within the middle third
- Boussinesq solution: stress in an elastic half-space from a point load
- Net load: the load applied less the weight of soil removed