## 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 (*q _{net}*)

*= 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*

_{all}*k*= 50000 [kN/m

_{s}^{3}]. A thin plain concrete of thickness 0.15 [m] is chosen under the footing and is not considered in any calculation.