Foster-Ahlvin diagrams

Foster and Ahlvin (1954), using Boussinesq s theory, developed diagrams from which not only the stresses but also the elastic deflections caused by a circular, uniformly applied load can be calculated much easier, at any depth from the surface and distance from the axis of the loading area. 

The relevant stress, o, or is calculated from the ratio stress/applied pressure value obtained from the x-axis, since the applied pressure pg is known. 

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It should be mentioned that values of deflection obtained by the above equation and Foster and Ahlvin s nomograph are valid only when Poisson s ratio p is equal to 0.5. A supplementary work by Ahivin and Ulery (1962) allowed stresses and deflections to be calculated for any value of Poisson s ratio. The results of this work were presented in tabular form instead of diagrams. The relevant tables as well as the equations developed can be found in Ahivin and Ulery (1962) and Yoder and Witczak (1975). 

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