When a column is located on the edge of a base designed to be centrally loaded, the ground pressure is substantially increased: the increase is shown in mathematical expressions. The base rotates as the soil under the edge is compressed creating a large moment on the column which can fail as shown in the pictures above. While engineers know that the load of the column should be supported by a beam extending from it to a penultimate column thereby loading the edge base in its centre this is sometimes ignored with fatal consequences.
Structures fail in various ways for a number of reasons; one of the cause is failures in structures is the incorrect design and/or construction of foundations.
The design of foundations is dependent on the geotechnical properties of the soil beneath the structure (subgrade), the magnitude of column loads to be carried and their position vis-à-vis the center of gravity of the foundation.
Often times in Kenya, engineers get the geotechnical properties of the sub-grade and the loads to be carried correct but fail to consider the eccentricity caused by the position of loads hence end up with induced momentswhich are not considered in their designs hence causing the structure to collapse.
This paper will highlight the various load positions, their effect on the foundation and also the pressure magnitudes that results from various eccentricity values.
Note that eccentricity is the distance from the position of the load to the center ofareaof the foundation base and that the foundation has two components; the base and the sub grade.
In considering the influence of eccentric loading on rectangular bases three cases are considered; in the following expressions eccentricity it is shown as the variable “e”. In the first two cases the column is assumed for simplicity to have no bending strength and in the third the bending strength of the column is taken into account when locating the eccentricity.
No eccentricity; e = 0
Eccentricity is located within the middle third of bases
Eccentricity is located outside the middle third.
Case1: eccentricity e=0
In this case, there is no eccentricity hence the pressure on the ground uniform and is equal to:
Where: Pb=pressure at the base
L&B=Length and breadth respectively
Case2: eccentricity e ≤ L/6
The eccentricity e causes a moment which creates a non-uniform pressure on the ground so that equilibrium is maintained by the centers of action of the pressure and the load being coincident. This results in a maximum and minimum pressure at the heel and the toe of the base respectively.
These pressures are given by:
Where: Z = Section modulus
M = Bending moment
Case3: eccentricity (e>L/6)