The design of highly unfavorable core loading according to DIN EN 1997-1[1] A 6.6.5 checks if a gaping joint occurs beyond the centroid of the foundation base due to permanent actions and the most unfavorable load combination. It is ensured that the eccentricity of the soil pressure resultant does not exceed the allowable limit values.
Mark 1: The limitation of the 1st core width is represented by a rhombus.
Mark 2: The limitation of the second core width is represented by an ellipse.
Mark 3: The resultant's point of application is the point at which the entire resulting load acts on the foundation base.
Permanent Actions
In the case of foundations on non-cohesive and cohesive soils, no gaping joint may arise in the foundation base as a result of characteristic permanent actions. This is ensured by placing the soil pressure resultant within the 1. Core Width. However, the first Core width limits the allowable biaxial eccentricity within a rhombic surface.
The condition to be checked is the following:
Derivation of condition
The condition is derived from the following inequality resulting from a degree equation:
The absolute values are necessary for this inequality to apply to all quadrants and for the diamond-shaped boundary to be completely covered.
The individual steps of the derivation are shown in the following figure:
Most unfavorable combination of permanent and variable actions
The eccentricity of the soil pressure resultants under permanent and variable characteristic actions may at most be so large that the foundation base continues to be subjected to compression up to its centroid. This means that the 2. core width must be observed. It is limited by an ellipse.
The condition to be checked is the following:
Derivation of condition
The condition is derived from the following inequality:
This is the elliptical equation with the center (0|0) and the diameters 2 ⋅ wy/3 and
2 ⋅ wx/3rd
The individual steps of the derivation are shown in the following figure:
