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The
area of each corner section is the square of 28.5 inches, or 812.25 square
inches. At 6,000 pounds per square foot, the pressure on such a section will be
33,844 pounds, and the center of gravity of this section is of course at the
center of the square, which is 14.25 X 1.414 = 20.15 inches from the corner of
the concrete column. A bar immediately under this diagonal line would have a
lever-arm of 20.15 inches. A bar parallel to it would have the same lever-arm
from the middle of the bar to the point where it passes under the concrete
column. Therefore, if we consider that this entire pressure of 33,844 pounds
has an average lever-arm of 20.15 inches, we have a moment of 681,957
inch-pounds. Using, as before, the moment equation M. = 80bd2, we may transpose
this equation to read b = 80d2. This area of steel will be furnished by five
1k-inch round bars. The diagonal reinforcement will therefore consist of five
11-inch round bars running diagonally in both directions. These bars should be spaced
about 4 inches apart. Those that are precisely under the diagonal lines of the
square should be about 9 feet 8 inches long; those parallel to them will each
be 8 inches shorter than the next bar. The total load of this concrete column
is 300,000 pounds. The shear in the concrete footing is of course a maximum
immediately under the edges of the concrete column.

The perimeter of the
concrete column is four times 28 inches, or 112 inches. The thickness of the
concrete footing is something greater than the value found above for d (14.5
inches), and we shall therefore make it, say, and 18 inches. This will mean
that the surface area which would need to be punched out if the concrete column
were to shear its way through the concrete footing would be 18 X 112 inches, or
2,016 square inches. Since the area of the concrete column is approximately
one-ninth of the area of the concrete footing, the shearing force is about
eight-ninths of the total load on a concrete column, or it is eight-ninths of
300,000 pounds, which is 266,667 pounds. Dividing this by 2,016, we have about as
the shearing force on the concrete of 130 pounds per square inch the concrete
footing, ignoring the assistance from the 26 bars in the concrete footing.
There is therefore no occasion to provide for shear in such a concrete footing.
The intensity of the shear decreases from the maximum value just given, to zero
at the edges of the concrete footing. Continuous concrete beams are sometimes
used to save the expense of underpinning an adjacent concrete foundation or concrete
wall.

These concrete footings are designed as simple concrete beams, but the
steel is placed in the top of the concrete beams. Assume that the concrete
columns on one side of a building are to be supported by a continuous concrete
footing; that the concrete columns are 22 inches square, spaced 12 feet on
center; and that they support a load of 195,000 pounds each. If the soil will
safely support 6,000 pounds per square foot, the area required for a concrete
footing will be 195,000 ± 6,000 = 32.5 square feet. Since the concrete columns
are spaced 12 feet apart, the width of concrete footing will be 32.5 ± 12 =
2.71 feet, or 2 feet 9 inches. To find the depth and amount of reinforcement
necessary for this concrete footing, it is designed as a simple inverted concrete
beam supported at both ends (the concrete columns), and loaded with an upward
pressure of 6,000 pounds per square foot on a concrete beam 2 feet 9 inches
wide. In computing the moment of this concrete beam, the continuous-concrete
beam principle may be utilized on all except the end spans, and thus reduce the
moment and therefore the required dimensions of the concrete beam. Many
engineers ignore this principle, since it merely increases the factor of safety
to do so.

**Are You in Windham ****New Hampshire****? Do You
Need Concrete Cutting?**

**We Are Your Local
Concrete Cutter**

**Call 603-622-4441**

**We Service Windham NH
and all surrounding Cities & Towns**