Problem $1$:

The A$-36$ steel column is encased in high$-$strength concrete, as shown in the figure below.

The original length of the composite column is $8$ ft $,$ and it is subjected to an axial force of

$60$ kips $.$ Use $E_{st}=29(10{)}^3$Ksi and $E_c=4\mathrm{.}2(10{)}^3$Ksi.

a$)$ Determine the required total area of the steel I$-$beam so that the force is shared

equally between the steel and concrete.

b$)$ How far does the column shorten?