A hollow steel pipe $($E $=30$ x $106$

psi and

u $=0\mathrm{.}3)$ of length $4$ ft with outside diameter of $6$ in$.$

& inside diameter of $4\mathrm{.}5$ in is uniformly compressed by an axial force of $140$ kips. Determine

$($a$)$ the shortening of the pipe under the axial load, $($b$)$ lateral strain, $($c$)$ change in inside and

outside diameters, $($d$)$ change in wall thickness, and $($e$)$ change in volume of the pipe.