$1.$ A new building will be constructed on a mat foundation near an existing building that is on spread footings. The bottom of all foundations are $5$ feet below the ground surface. The bearing pressure from the mat on the soil is shown in the figure. The soil profile consists of $40$ feet of sand, over $20$ feet of clay, over sand. Calculate the change in the vertical stress at the midpoint of the clay layer below the corner of the existing building $($point A $)$ using the elastic solutions for the vertical stress below the corner of a rectangular loaded area.

$2.$ Repeat Problem $1$ using the elastic solutions presented in Newmark's chart.

Holtz and Kovacs $(1981)$

The answer to both problems is $0\mathrm{.}5$ ksf$.$ Please show all steps to get to the answer $0\mathrm{.}5$ ksf for a thumbs up$.$