Effective area

When solving the problem of eccentrically loaded foundations the program offers two options to deal with an effective dimension of the foundation area:

• a rectangular shape of effective area is assumed
• general shape of effective area is assumed

Rectangular shape

A simplified solution is used in such cases. In case of axial eccentricity (bending moment acts in one plane only) the analysis assumes a uniform distribution of contact stress σ applied only over a portion of the foundation l₁, which is less by twice the eccentricity e compared to the total length l.

Determination of effective area in case of axial eccentricity

An effective area (b * l₁) is assumed to compute the contact stress, so that we have:

In case of a general eccentric loading (foundation is loaded by the vertical force V and by bending moments M₁ and M₂ the loading is replaced by a single force with given eccentricities:

The size of effective area follows from the condition that the force V must act eccentrically:

General shape of contact stress

In case of an eccentric loading the effective area is determined from the assumption that the resultant force V must act in the center of gravity of the compressive area. The theoretically correct solution appears in Fig.

Determination of contact stress for general eccentricity – general shape

Owing to a considerable complexity in determining the exact location of the neutral axis, which in turn is decisive when computing the effective area, the program follows the solution proposed by Highter a Anders¹⁾, where the effective areas are derived with help of graphs.

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¹⁾Highter, W.H. – Anders,J.C.: Dimensioning Footings Subjected to Eccentric Loads Journal of Geotechnical Engineering. ASCE, Vol. 111, No GT5,  pp 659 - 665