Combined Footings: How to Calculate the Bearing Pressures

ASDIP FOUNDATION includes the design of concrete combined footings based on the latest ACI 318 provisions. This post explains the calculation of the soil bearing pressures in a typical combined footing, and the different factors that may affect the size and shape of the footing.

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A combined footing usually supports two columns. The use of a combined footing may be justifiable under conditions where the distance between columns is short, so a large excavation is not required. When the distance between columns is longer than about 15 feet, it may be more convenient to design a strap footing instead. There are two common scenarios in practice:

• A property line exists at or near the edge of an exterior column, so a normal isolated footing would be eccentric and it would tend to tilt. This problem may be prevented by supporting this column together with an interior column on a common footing.
• Two columns are so close to each other that two spread footings would overlap. In this case it’s easier to design a common footing for both columns.

What factors affect the footing geometry?

When the loads of the two columns are about of the same order of magnitude, generally the combined footing is designed as rectangular, so that the bearing pressures are about uniform. However there are cases where one column load is much heavier than the other, so the footing can be designed as trapezoidal in order to keep the pressures uniform and prevent differential settlements.

Usually the combined footings are rectangular for simplicity during construction. However, when the available space is limited due to the presence of other existing footings or underground piping in the area, a trapezoidal footing may be the only option. In any case, the calculation of the soil bearing pressures will be effected accordingly.

How do you calculate the soil bearing pressures?

The calculation of the bearing pressures is relatively simple for rectangular footings in full bearing, but it becomes increasingly complex for trapezoidal footings. Furthermore, the calculation is very cumbersome when a trapezoidal footing is in partial bearing, since the soil cannot resist tension and the location of the zero-pressure line is unknown.

This is the problem: The maximum bearing stress depends on the shape of the bearing area, which in turn depends on the location of the centroid of the bearing volume, which in turn depends on the maximum bearing stress. It's like the dog that keeps trying to bite his own tail. So, how do you solve this puzzle? One option would be multiple trial-and-error cycles, until finally the applied load equals the bearing volume, and the location of both the load and the volume centroid coincide. This procedure is obviously unpractical and time-consuming.

The closed solution to this problem lies in the integral calculus field. ASDIP FOUNDATION uses an algorithm consisting of double integrals of the type P = ∫∫z dy dx, where z is the bearing stress and P is the applied load. The centroid of the bearing volume is therefore located at X = ∫∫x z dy dx / P. The resulting solution is applicable to any footing geometry, either in full or partial bearing, as shown in the picture below.

Takeaway

The calculation of the bearing pressures for a combined footing may become complex and time-consuming. ASDIP FOUNDATION accurately calculates the bearing pressures for any geometry and loads. This is particularly useful when you have trapezoidal combined footings, either in partial or full bearing.

Best regards,

Javier Encinas, PE

ASDIP Structural Software