# Foundation stresses below a triangularly distributed load

### Tom Bowling

The square reinforced concrete footing of a wind turbine generator is subjected to a large overturning moment due to wind loading on the tower, nacelle and rotor blades. As a result, and for analysis purposes, the footing can be considered to exert a triangularly distributed contact pressure onto the immediate foundation. For extreme overturning this pressure distribution does not extend over the full area of the footing as some lift off of the footing occurs. A maximum contact pressure occurs along an edge of the footing when the overturning moment vector is parallel to a footing side, called “square overturning” in the following. However the greatest contact pressure occurs under a corner of the square footing when the vector of the overturning moment is parallel to a diagonal of the square footing, called “diagonal overturning” in the following.

In assessing the competence of the foundation material to resist the above described footing loading, it is of interest to determine the distributions of vertical stress in the foundation material at various depths below the footing. This can be done by computer methods such as a three dimensional finite element analysis. However a simple solution for vertical stresses beneath the axis of symmetry of the loaded area, which includes the maximum stress for a particular depth, is presented in the following. The solution is based on the integration of Boussinesq’s equation for a point load over the extent of the loaded (elastic) foundation.