GGU-FOOTING: Theoretical principles for circle/annulus
The bearing capacity of a circular footing is calculated using the equations given in DIN 4017.
An equivalent area A' must be determined for eccentric loading. For a rectangle, for example, the equivalent area is given by:
A' = (a - ex) · (b - ey)
where: ex , ey = eccentricities
The equivalent area of the circle is calculated according to the following figure (Leibnitz University, Hanover):
The 1st and 2nd core dimensions are also required. For a circle:
Core dimensions for circle:
1st core dimension = D / 8
2nd core dimension = 3 · π · D / 32
There are no bearing capacity equations for an annulus comparable to those for a circle. The annulus is therefore converted to an equivalent circle. The conversion can be performed using either an equal area circle or a circle with the same moment of inertia.
Core dimensions for annulus:
1st core dimension = [1 + (Di / Da)2] · Da / 8
2nd core dimension = 3 · π · Da / 32 · [1 - (Di / Da)4] / [1 - (Di / Da)3]
where: Di = diameter (inner)
Da = diameter (outer)
Settlement analyses are performed using triangular load areas, allowing the loads on a circle or an annulus to be exactly modelled [Dr.-Ing. Johann Buß, Setzungen und Spannungen unter "Dreiecksfundamenten" (Settlements and Stresses below Triangular Footings), Geotechnik 22 (1999) No. 1].
The position of the characteristic point is required for settlement analyses. For a circle:
Characteristic point for circle = 0.845 · R
The characteristic point cannot be derived for the annular footing. Conservative calculations assume that the characteristic point is in the same location as for a circle:
Characteristic point for annulus ⇒ assumption = circle = 0.845 · Ra
where: Ra = outer radius