Civil Engineering Reference
In-Depth Information
The effect of the moment is to produce a uniformly varying soil pressure, which can
be determined at any point with the expression
P
A
Mc
I
q
In this discussion the term
kern
is used. If the resultant force strikes the footing base
within the kern, the value of
Mc
/
I
at every point and the entire foot-
ing base is in compression, as shown in Figure 12.23(a). If the resultant force strikes the
footing base outside the kern, the value of
P
/
A
is larger than
P
/
A
and there will be uplift or tension. The soil cannot resist tension, and the pressure varia-
tion will be as shown in Figure 12.23(b). The location of the kern can be determined by
replacing
Mc
/
I
with
Pec
/
I
, equating it to
P
/
A
, and solving for
e
.
Should the eccentricity be larger than this value, the method described for calculating
soil pressures [(
Mc
/
I
will at some points be larger than
(
Mc
/
I
)] is not correct. To compute the pressure for such a situa-
tion it is necessary to realize that the centroid of the upward pressure must for equilibrium
coincide with the centroid of the vertical component of the downward load. In Figure
12.24 it is assumed that the distance to this point from the right edge of the footing is
a
.
Then the soil pressure will be spread over the distance 3
a
as shown. For a rectangular
footing with dimensions
P
/
A
)
b
, the total upward soil pressure is equated to the downward
load and the resulting expression solved for
q
max
as follows:
1
2
(3
ab
)(
q
max
)
P
2
P
3
ab
q
max
Example 12.8 shows that the required area of a footing subjected to a vertical load
and a lateral moment can be determined by trial and error. The procedure is to assume a
size, calculate the maximum soil pressure, compare it with the allowable pressure, assume
another size, and so on.
Once the area has been established, the remaining design will be handled as it was for
other footings. Although the shears and moments are not uniform, the theory of design is
unchanged. The factored loads are computed, the bearing pressures are determined, and
Figure 12.24
