# Combined Footing Design: An Important Structural Element

June 10, 2020

ASDIP FOUNDATION includes the design of concrete combined footings based on the latest ACI 318 provisions. This article discusses the steps to design a combined footing when subject to a combination of vertical loads, horizontal loads, and bending moments.

## When is a combined footing required?

If a property line exists at or near the edge of an exterior column, a normal isolated footing would be placed eccentrically under this column and it would tend to tilt. This problem may be prevented by supporting this column together with an interior column on a common footing. The use of a combined footing may be justifiable under conditions where the distance between columns is short and the stability of the exterior footing is compromised.

Another common case of a combined footing is when the two columns are so close to each other that two spread footings would overlap. In industrial plants it's common to design pipe racks which typically consist on a series of moment steel frames at a certain spacing, and braced in the longitudinal direction. In those cases the two columns are usually supported on a combined footing.

## How do you calculate the soil bearing pressures?

For design and construction simplicity, generally the combined footings are designed as rectangular when the loads of the two columns are about of the same order of magnitude. However there are cases where one column load is much higher than the other, and therefore this desired simplification is not economically feasible. In those cases the footing should be designed as trapezoidal, so that the resulting bearing pressures are about uniform to minimize the probability of differential settlements. Another example of a trapezoidal footing is when the available space is limited due to the presence of existing footings or underground pipes in the area.

The calculation of the bearing pressures is relatively simple for a rectangular footing design in full bearing, but it becomes increasingly complex for trapezoidal footings. Furthermore, the calculation is very cumbersome when the footing is in partial bearing. ASDIP FOUNDATION uses an algorithm consisting of double integrals of the type P = ∫∫z dy dx where z is the bearing stress. The centroid of the bearing area is therefore = ∫∫x z dy dx / P. Evidently, this complexity arises due to the variable nature of the trapezoidal footing geometry and the uncertainty of the location of the zero pressure line.

ASDIP FOUNDATION accurately calculates the soil bearing pressure distribution for a rectangular or trapezoidal combined footing in either full or partial bearing, as shown in the picture below.

## Longitudinal moments in a combined footing design

If we consider that the transverse steel will distribute the column loads in the transverse direction, a combined footing may be designed as a beam in the longitudinal direction, being the columns the supports and the bearing pressure the applied load. A kind of upside down beam. The shear and moment diagrams help to visualize the variation of the internal forces along the footing, and therefore the required strengths.

The picture below shows the shear and moment diagrams in the longitudinal direction generated by ASDIP FOUNDATION. Note that the moment is typically negative between the columns, and therefore the main longitudinal steel should be placed at the top of the combined footing.

## How do you calculate the shears and transverse bending?

A combined footing should be designed in such a way that the shear stresses are resisted by the concrete alone, otherwise a special and expensive shear reinforcement would be necessary. Two separate checks are required by the ACI 318: one recognizes that the footing may fail in shear as a wide beam along a critical section at a distance d from each column face in each direction. The second check considers that the columns may penetrate, or punch, the footing at a distance d/2 all around the columns.

On the other hand, the upward bearing pressure will produce a transverse bending moment on the footing, being the critical section the face of the columns, similar to the bending design of a spread footing. Once the bending moments are found, the reinforcing steel may be designed per the concrete design theory. It should be noted that the bearing pressures are calculated using the service loads, but both shear forces and bending moments must be calculated by applying the factored loads. The picture below shows the typical reinforcement of a combined footing design.

## Takeaway

Combined footings are structural elements used in multiples cases. The design of combined footings may be cumbersome and time-consuming, particularly for trapezoidal footings in partial bearing conditions. ASDIP FOUNDATION includes the design of combined footings, with multiple options to optimize the design in less time.

For a combined footing design example, please see the blog post Eccentric Combined Footing Example Using ASDIP FOUNDATION. For our collection of blog posts about foundation design please visit Structural Footing Design.

Best regards,

Javier Encinas, PE

ASDIP Structural Software

• Jake C. Martinez says:

sir good day!! may i ask if i would input the loading in designing combined ftg should i consider there negative signs? hopefully you can help me sir. Thank you!!

• Javier Encinas, PE says:

The orientation of positive loads are as shown in the image at the Loads tab of the software. If any of your loads go in the opposite direction, just enter the negative value of that load.

• kasiita muhtasim says:

very interesting

• Bambang says:

Dear Sir,

Is it possible to modify and add rebar dimensions for reinforcements input?

• Javier Encinas, PE says:

Yes, you can edit the reinforcement as you need, add or remove rebars, change spacing, cover, etc.

• Hein Htet Aung says:

Hi Sir,
Have a good day !

May I know how to modify for 3 column on footing in Combined Footing or Raft Footing.