Module 6 · Lesson 6.2
Combined V, H and M
What the factors are approximating.
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. The modern picture is cleaner and worth having even if you never use it directly.
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, safe. On it, failure. Outside, impossible.
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. Slide the resultant off centre and watch the working area shrink.
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.
- 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
- Area retained
- 73 %
- Pressure on A′
- 136 kPa
Inside the middle third: full contact is maintained, and the pad has given up 27% of its area.
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
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint