The Chartership Forum

Foundation Engineering / Eccentric and inclined loading

Combined V, H and M

What the factors are approximating.

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 notes

Why this matters

A real foundation carries vertical load, horizontal load and moment together. Handling each with its own multiplier — a shape factor here, an inclination factor there, an effective area somewhere else — works, but it obscures what is actually going on. An interaction envelope shows how these actions combine and helps explain the limits of separate correction factors.

Instead of a single capacity, think of a failure envelope: a surface in V–H–M space enclosing every combination the foundation can carry. Inside the surface, the idealised bearing-resistance limit is not exceeded. The surface represents limiting combinations for that model. Settlement, sliding, structural resistance and other checks remain separate.

The shape of that surface is informative. Capacity in H is greatest at moderate V, not at low V — a footing with almost no vertical load has little friction available and slides easily. Similarly the moment capacity peaks somewhere near half the vertical capacity and falls away towards both ends.

The factor method approximates this surface by starting from the pure-vertical capacity and multiplying it down. That is why the factors are all less than or equal to 1, and why they combine multiplicatively even though the real surface is not a product of independent effects.

One practical consequence is worth stating: eccentricity and inclination are different problems with different remedies.

Eccentricity is a geometry problem. It is often cured by moving the footing — casting it off-centre under the column so that the resultant comes back to the middle — which costs nothing but coordination.

Inclination is a load problem. It cannot be designed away by moving anything; it is reduced by taking the horizontal load somewhere else, with a tie, a shear key or a propped slab.

Check yourself

A pad footing under an edge column is found to have an eccentricity of B/4. Which remedy addresses the cause?

Try it

Effective area and the middle third

A 3 m square pad. Move the resultant and compare the bearing-resistance effective area with the middle-third contact criterion.

0.40 m
900 kN

Reading it

  • Effective width is B − 2e: eccentricity costs twice its own value.
  • The shaded band is the middle third. Outside it, contact is lost at one edge.
  • Applied pressure must be V/A′ — the same reduced area the capacity used.
Vcentroidmiddle third = ±0.50 m
Equivalent moment M
360 kNm
Middle-third limit B/6
0.50 m
Effective width B′
2.20 m
Effective area A′
6.60 m²
Effective area retained
73 %
Pressure on A′
136 kPa

Inside the middle third: the linear pressure model retains full contact. The bearing-resistance effective area is 27% smaller than the plan area; this reduction is not a physical contact loss.

Summary

  • Effective width B′ = B − 2e, and both capacity and applied pressure use the reduced area
  • Beyond e = B/6 the footing lifts at one edge, because soil cannot take tension
  • The true picture is a V–H–M failure envelope; the factors approximate it by multiplication
  • Eccentricity is cured by moving the footing; inclination is cured by taking the load elsewhere