Example $29\mathrm{.}1$

As an example the problem of a load on an L$-$shaped region is considered, see Figure $29\mathrm{.}4.$ On the short leg the load is $15$kPa, on the larger leg the load is

$5$kPa. The problem is to determine the vertical normal stress at a depth of $8m$ below the point A$.$ The first step in the solution is to draw the loaded area

on such a scale that the reference length $z$ in Newmark's diagram corresponds to $8m,$ see Figure $29\mathrm{.}5,$ and such that the point A is located in the origin of

the circles. The short leg of the loaded area now covers about $7$ rectangles, and the long leg covers about $34$ rectangles. This means that the stress is

${}_{zz}=70\mathrm{.}00115$kPa$+340\mathrm{.}0015$kPa$=0\mathrm{.}275$kPa.

In order to determine the stress at a greater depth, say at a depth of $16m,$ the loaded area should be drawn half as large. This then covers a smaller

number of rectangles, so that the stress will be smaller.

Problem $29\mathrm{.}1$ In the example considered above, determine the vertical stress ${}_{zz}$ at a depth of $8m$ below the corner point in the upper right corner in

the plan.

Problem $29\mathrm{.}2$ Determine the stress in that corner point at the surface $($for $z=0).$ Also determine the stress in the point $A$ at the surface. And finally,

also calculate the stress at a depth of $8000m.$

Problem $29\mathrm{.}3$ A square region of dimensions $4m$ times $4m$ is loaded by a uniform load $10$kPa. Determine the vertical normal stress at a depth of $4m$

in a number of characteristic points : the center, one of the corners, and a point in the center of one of the sides.