Foundation Engineering / Eccentric and inclined loading
The effective area method
Shrink the footing until the load is in the middle.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Corrections checked in this pass
- Distinguished the compression kern, physical contact area and effective area used in bearing calculations.
Checks needed for project use
- A geotechnical reviewer must confirm drainage and stress basis, bearing-factor formulation, correlations and settlement influence factors. Partial factors and project-specific ground conditions are outside these teaching checks.
- Unilateral contact and biaxial moments require a compatible contact model; effective-area method is a resistance approximation.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
Columns, retaining walls and machine bases can apply moments as well as vertical loads. The effective-area method represents eccentric loading by reducing the area used in the bearing-resistance calculation. Its assumptions and permitted use depend on the chosen design method.
By the end of this lesson you should be able to
- Compute the effective area of an eccentrically loaded footing
- Apply the middle-third rule and explain its physical meaning
- Say why the method is conservative
Meyerhof's idea: if the load acts at an eccentricity e from the centre, imagine trimming the footing down until the load is central on what is left. To move the centroid by e you must remove 2e from the width — e from the far side twice over, in effect — so the effective width is
B′ = B − 2e
Then calculate the bearing capacity for a footing of width B′, and check it against the load spread over the effective area only. The trimmed-off strip is assumed to contribute nothing.
This is an approximate representation of eccentric bearing resistance. The discarded strip is not a literal prediction of the contact area, and discarding it alone does not prove conservatism for every loading and soil condition.
What it calculates: The reduced footing area used for an eccentric load
- B′
- Effective width (m)
- e
- Eccentricity of the resultant from the centroid (m)
- A′
- Effective area, used for both capacity and applied pressure (m²)
This assumes
- The resultant acts within the footing — beyond that there is no effective area at all
- Eccentricity in each direction is treated independently
In plain terms: Eccentricity costs twice its own value in width. A 0.4 m eccentricity on a 3 m footing removes 0.8 m — over a quarter of it.
Worked example
A pad with a column moment
Given
- Square pad, B = L = 3.0 m, founded at 1.5 m
- Vertical load V = 900 kN
- Column moment M = 360 kNm about one axis
Find
The effective area, and whether contact is lost at an edge
The middle-third rule falls out of elastic stress distribution. Under combined axial load and moment the edge pressures are
q = V/A ± M·c/I
and the minimum goes to zero exactly when e = B/6. Beyond that the arithmetic gives a negative pressure at one edge — tension between the footing and the soil.
Soil cannot pull. So beyond the middle third the footing lifts off over part of its base, the contact area shrinks, and the pressure on the remaining contact rises faster than the eccentricity does.
Check yourself
A footing's resultant load falls outside the middle third. What physically happens?