Example Footing Width Calculation with Truss Roof

Outline

1. Problem Statement
2. Load Combinations
3. Footing Width
4. Live Load Reduction
5. Footing Thickness
6. Footing Reinforcement
7. Conclusion
8. References

1. Problem Statement

Let's continue with our previous example but change a few things. Let's say that the long, higher grade rafters became too much of an issue and with the Owner we decided to go with truss construction (trusses bearing on the exterior walls), and that we also decided to go with a slab on grade for the main floor. We will look at the calculated footing width using and not using the reduction allowed for combined loads. Let's drop the eave width to 12 in.

2. Load Combinations

So far we have been using Allowable Stress Design (ASD) for this `footing size thing'. And it is appropriate, since allowable bearing pressures of soils are generally given in terms of `allowable stress'. The International Building Code (IBC), Section 1605.3.1 says that we will add the effects of D, L, and S, which we have done, previously, but it also allows a load reduction, Sec. 1603.1.1, whereby the combined effects of variable loads may be multiplied by 0.75 and added to the Dead load. But, in no case may this reduced combined load be less than the effect of dead plus any one of the variable loads. Expressed in equations, we need to ...

Use the larger of ...

D + S

D + L

D + 0.75 (S + L)

3. Footing Width

So, let's proceed with our example, and calculate the minimum footing width.

Our Loads ...

Roof Snow load ... (½ of 40 ft + 1 ft) x 40 psf ... 840 plf ... (trusses span ext wall to ext wall + eave)

Roof Dead load ... (½ of 40 + 1) ft x 12 psf = 252 plf

Upper wall ... 9 x 10 = 90 plf

Upper floor Live ... ½ of ½ of 40 x 40 psf = 400 plf ( ... interior bearing wall down middle)

Upper floor Dead ... 10 x 10 = 100 plf

Main wall ... 90 plf

Main floor Live ... n/a

Main floor Dead ... n/a

Total Superstructure Loads ...

Dead ... 240 + 12 + 90 + 100 + 90 = 532 plf

Snow ... 800 + 80 = 840 plf

Live ... 400 plf

Foundation ...

Let's use a stem wall of 8 x 30 ... (8/12 x 30/12 x 150) = 250 plf Dead ...

And try 8 x 16 footing ... (8/12 x 16/12 x 150) = 133 plf Dead ...

TOTAL LOAD ...

Dead ... 532 (super) + 250 (stem) + 133 (footing) = 915 plf

Snow ... 840 plf

Live ... 400 plf

Now let's look at the load combos ...

D + S = 1755 plf

D + L = 1315 plf

D + S + L = 2155 plf

... and ...

D + 0.75 (L + S) = 915 + 0.75 (840 + 400) = 1845 plf

So, with just adding the loads without reduction we get 2155 plf ... and taking into account the reduction ... 1845 plf.

Looking at soil pressures, 16 in. wide footing ...

Un-reduced total ... fp = 2155 plf /(16/12 ft) = 1616 psf ... NOT good (allowable is 1500) ...

Reduced total ... fp = 1845 / (16/12) = 1384 psf ... GOOD!

So, taking into account the reduced load allowed when variable loads (in this case Snow and Live) occur simultaneously ... a 16 in. wide footing works!

In fact, a 15-in. wide footing would work, but generally we stick with even number footing widths.

4. Live Load Reduction

The IBC also allows a reduction in the Live load itself. For beams, columns, and two-way slabs see 1607.9.1 and for an alternate reduction that includes reductions for walls and foundations, see 1607.9.2. In my area of practice I generally don't take the reduction for a number of reasons. First, the calculation involves the length also, of the foundation element, which often varies. Second, where I practice often the Snow loads are considerable and either govern, or overshadow, relatively small reductions in Live loads. Third, I have left some stuff out ... for example, I have not included the weight of the soil and slab on grade `over' the footing (though these contributions would be small), nor have I included Occupancy and soil surcharge loads over the footing (also probably small). And, finally, I like to have some reserve capacity in the foundation, if the Owner should decide on changes in dimensions or materials. (And, note, in this example I have used pretty `lean' Dead loads.) For structures with large areas where Live load is more significant, or duplications of smaller structures, reduced Live loads may well be worth consideration.

5. Footing Thickness

We have assumed a thickness of 8 in. Generally 6 in. would be `bare-bones' minimum, with many jurisdictions expecting to see 8 in. or more. The projection of the footing past the stem wall is ... (16 - 8 ) / 2 = 4 in. Since the thickness (8 in.) is (way) greater than the projection, we don't expect the footing to shear. Further, the 8 in. thickness will allow 5 in. of stem wall vertical steel (V.S.) embedment and still meet the 3 in. minimum cover between these pieces and the bottom of the footing.

6. Footing Reinforcement

Since the footing thickness is (way) greater than the projection we likewise don't expect to need transverse reinforcement. Hence, the only reinforcement in the footing (besides the V.S ends) will be longitudinal steel. Let's use 2 # 4 and check to make sure we meet the temperature-shrinkage minimum ratio of A_s/A_g = 0.0018 (for Gr. 60). A single # 4 bar has a cross sectional area of 0.20 in.² ... so,

A_s/A_g = 2 (0.20) / (8 x 16) = 0.0031 ... GOOD!

7. Conclusion

We have now seen how we can use a reduced combined load when determining the minimum footing width. If we had not taken the reduction our footing would probably have had to be a couple inches wider. And there is some `hair-splitting' we have not done. (For example: while we are required to consider ice damming on the eave at 2 x the Snow load, we are not required to combine it with the Snow load over the main span; thus the above loads are robust. In fact, to design the roof framing itself, we are required NOT to use the Snow load on the main span as we double the load over the eave.) In the design of footings I prefer to have at least a little excess capacity. Concrete is a relatively less expensive construction material, and often in the foundation we have the room (space) for a few spare inches. In the superstructure where spaces are limited and materials may be more expensive, taking all the `reductions' possible may indeed be prudent. Also, with a slightly robust foundation there is now some allowance for material changes (heavier materials) as the construction proceeds. If we have designed a `bare-bones' foundation from the onset - the structure is pretty `locked in' - during the construction process, and for the future. Making a foundation change (after the concrete has been poured and cured) is a much more serious matter than changing out a superstructure beam or moving a stick framed wall.

Endnote: I ran the live load reduction using a 40-ft long section of footing (calcs not shown). We still get a 16 in. wide footing (15 in. if we don't want only even number increments).

8. References

International Building Code, International Code Council, 4051 West Flossmoor Road, Country Club Hills, IL 60478.