How do you calculate the soil bearing pressures?
When the loads of the two columns are about of the same order of magnitude, generally the combined footing is designed as rectangular, so that the bearing pressures are about uniform. However there are cases where one column load is much heavier than the other, so the footing should be designed as trapezoidal in order to keep the pressures uniform. Another example of a trapezoidal footing is when the available space is limited due to the presence of other existing footings in the area.
The calculation of the bearing pressures is relatively simple for rectangular footings in full bearing, but it becomes increasingly complex for trapezoidal footings. Furthermore, the calculation is very cumbersome when a trapezoidal footing is in partial bearing, since the location of the zero pressure line is unknown.
The maximum bearing stress depends on the shape of the bearing area, which in turn depends on the location of the centroid of the bearing volume, which in turn depends on the maximum bearing stress. So, how do you solve this puzzle? One option would be multiple trial and error cycles, until finally the applied load equals the bearing volume, and the location of both the load and the volume centroid coincide. This is time-consuming.
The closed solution lies in the integral calculus field. ASDIP FOUNDATION uses an algorithm consisting of double integrals of the type P = ∫∫z dy dx where z is the bearing stress. The centroid of the bearing volume is therefore located at X = ∫∫x z dy dx / P. The resulting solution is applicable to any footing geometry, either in full or partial bearing, as shown in the picture below.