Newmark's Chart

Draw your foundation to scale on the chart, and the chart gives the vertical stress increase beneath its centre, at depth z. Ring i is drawn at the radius a of a uniformly loaded disc that gives σ_z/q = i/rings at depth z, from Fröhlich's σ_z/q = 1 − [1 + (a/z)²]^−n/2, and the rings are cut into equal sectors. Every cell then carries the same unit influence, 1/(rings × sectors), so Δσ_z = q × (cells covered) × (unit influence). With φ = 0 the concentration factor is n = 3 and this is Newmark's Boussinesq chart; a friction angle sets n from φ, which moves the rings.

What you are seeing

• The chart. The rings and sectors, with the r/z of each ring labelled along the diagonal. The last ring, out to infinity, is not drawn. The black bar at the bottom left is the scale: its length on the chart is the depth z.
• Your sketch. Drag on the chart to draw the loaded area, in orange. Cells whose centre lies inside it are shaded orange and counted.
• The results. The concentration factor, the unit influence of one cell, the cells covered, the influence value I, and the stress increase, with the calculation written out.

The sketch is held in r/z. Changing the rings, sectors or φ redraws it at the new scale of the chart, so it stays the same footing; changing z leaves it where it is on the chart, so it then stands for a footing scaled with z.