$5\mathrm{.}1$ Given: A ${16}^{\text{'}}$ long column with carrying an axial load of Dead $=125$ kips and Live $=$

$250$ kips.

Find: Most economical shape with the following end conditions $($interpolate$.$ axial

capacities$)$:

a$)$ Pinned ends $($W$-$shape, A$992)$

shape:

${}_c{P}_n$ :

b$)$ Fixed bottom, pinned top $($W$-$shape$)$

shape:

${}_c{P}_n$:

c$)$ Fixed ends $($HSS square$)$

shape:

${}_{}{P}_n$ :