Example 6: Design of trapezoidal footing
Description of the problem
In the primary design of footings or rafts, it is generally
assumed that the contact pressure distribution is planar, whatever the type of model used in
the analysis of the footing. Therefore, to achieve a desirable uniform contact stress distribution
beneath the footing it is necessary to arrange the center of area of the footing directly beneath
the center of gravity of the external loads. This may lead to irregular-shaped footing. If equal
column loads are symmetrically disposed about the center of the footing, the contact
pressure distribution will be uniform. In order to achieve a theoretically uniform contact pressure
distribution, the footing can be extended so that the center of area of the footing coincides
with the center of gravity of the external loads. This is easy to be done by rectangular
footing.
A special case of footings is the trapezoidal footing, which
may be used to carry two columns of unequal loads when distance outside the
column of the heaviest load is limited. In such case using a rectangular footing may lead to the resultant of
loads dos not fall at the middle length of the footing. To overcome this difficulty, a trapezoidal
footing is used in such a way that the center of gravity of the footing lies under the resultant of
the loads. Correspondingly, the distribution of contact pressure will be uniform.
As a design example for trapezoidal footing, consider the
trapezoidal combined footing of 0.60 [m] thickness shown in Figure (80). The footing is support
to two columns *C1 *
and *
C2 *spaced at 4.80 [m] apart. Due to the site conditions, the
projections of the footing beyond the centers of columns *C1 *
and
*C2 *
are limited to 0.90 [m] and 1.30 [m],
respectively. Column *C1 *
is 0.50 [m] * 0.50 [m], reinforced by 8Φ16 [mm] and carries a load of
1200 [kN]. Column *C2 *
is 0.60 [m] * 0.60 [m], reinforced by 12Φ19 [mm] and carries a load of
2000 [kN]. The allowable net soil pressure is (*qnet*)*all
*= 240 [kN/m ]. The subsoil model used
in the analysis of the footing is represented by isolated springs, which have a modulus of
subgrade reaction of *ks
*= 50 000 [kN/m^{3}].
A thin plain concrete of thickness 0.15 [m] is chosen under the footing and
is not considered in any calculation. |