University Of Illinois Bulletin Vol. 40, November 10, 1942, No. 12: Influence Charts For Computation Of Stresses In Elastic Foundations (Engineering Experiment Station Bulletin Series No. 338)

"1. Scope of Investigation and Summary---This bulletin describes a simple graphical procedure for computing stresses in the interior of an elastic, homogeneous, isotropic solid bounded by a plane horizontal surface and loaded by distributed vertical loads at the surface. The stresses are computed from charts given herein merely by counting on a chart the number of elements of area, or blocks, covered by a plan of the loaded area drawn to proper scale and laid upon the chart. Influence charts of a size convenient for practical use are given in Plates 1, 2, and 3 for computing, respectively, vertical stress on horizontal planes, the sum of the principal stresses, and horizontal stress on vertical planes, the latter two charts being constructed for a value of Poisson's ratio of 0.5. Influence charts are also given to a smaller scale for computing the components of shearing stress on horizontal and vertical planes, and for computing the corrections to the various stresses when Poisson's ratio is different from 0.5. Numerical data and instructions are given in the Appendix which permit drawing any of the charts to whatever scale is desired in particular applications. For all the charts, the influence value of the individual blocks is 0.001..." [from introduction]