Civil Engineering Reference
In-Depth Information
e
eccentricity of the load
Q,
that is, the lateral distance from
Q
to the center
of gravity of footing, m or ft.
B
width of footing, m or ft.
A usual requirement is that the load
Q
be located within the middle one-third of the foot-
ing, and the above equations are valid only for this condition. The value of
q
must not
exceed the allowable bearing pressure
q
all
.
Figure 8.9 presents another approach for footings subjected to moments. As indicated
in Fig. 8.9
a,
the moment
M
is converted to a load
Q
that is offset from the center of grav-
ity of the footing by an eccentricity
e.
This approach is identical to the procedure outlined
for Eq. (8.7).
The next step is to calculate a reduced area of the footing. As indicated in Fig. 8.9
b,
the
new footing dimensions are calculated as
L
L
2
e
1
and
B
B
2
e
2
. A reduction in
footing dimensions in both directions would be applicable only for the case where the foot-
ing is subjected to two moments, one moment in the long direction of the footing (hence
e
1
)
and the other moment across the footing (hence
e
2
). If the footing is subjected to only one
moment in either the long or short direction of the footing, then the footing is reduced in
only one direction. Similar to Eq. (8.7), this method should be utilized only if the load
Q
is
located within the middle one-third of the footing.
Once the new dimensions
L
and
B
of the footing have been calculated, the procedure
outlined in Sec. 8.2.3 is used by substituting
L
for
L
and
B
for
B.
Sloping Ground Conditions.
Although methods have been developed to determine the
allowable bearing capacity of foundations at the top of slopes (e.g., NAVFAC DM-7.2,
1982, page 7.2-135), these methods should be used with caution when dealing with earth-
quake analyses of soil that will liquefy during the design earthquake. This is because, as
shown in Sec. 3.4, the site could be impacted by liquefaction-induced lateral spreading and
flow slides. Even if the general vicinity of the site is relatively level, the effect of liquefac-
tion on adjacent slopes or retaining walls must be included in the analysis. For example,
Fig. 8.10 shows an example of a warehouse that experienced 2 m of settlement due to lat-
eral movement of a quay wall caused by the liquefaction of a sand layer. If the site consists
of sloping ground or if there is a retaining wall adjacent to the site, then in addition to a
bearing capacity analysis, a slope stability analysis (Chap. 9) or a retaining wall analysis
(Chap. 10) should also be performed.
Inclined Base of Footing.
Charts have been developed to determine the bearing capac-
ity factors for footings having inclined bottoms. However, it has been stated that inclined
bases should never be constructed for footings (AASHTO 1996). During the earthquake,
the inclined footing could translate laterally along the sloping soil or rock contact. If a slop-
ing contact of underlying hard material will be encountered during the excavation of the
footing, then the hard material should be excavated in order to construct a level footing that
is entirely founded within the hard material.
8.2.6 Example Problem
This example problem for cohesive surface layer illustrates the use of Eq. (8.7) and Fig. 8.9.
Use the data from the example problem in Sec. 8.2.2. Assume that in addition to the verti-
cal loads, the strip footing and spread footing will experience an earthquake-induced
moment equal to 5 kN
m, respectively. Furthermore, assume that these
moments act in a single direction (i.e., in the
B
direction).
m/m and 150 kN
