Learning Objective #$7$: Stress and Strain

Given: A steel pad supporting heavy machinery rests on four short, hollow, cast iron piers. The ultimate strength $({}_u)$ of the cast iron in compression is $65$ ksi and Young's modulus $($ E $)$ is $10\mathrm{.}0{10}^3$ksi. The outer diameter of each pier is $d=6\mathrm{.}0in.$ and the wall thickness is $t=0\mathrm{.}40in.$ Assume the weight of the machinery is evenly split over the four piers.

Find: $($a$)$ What is the longitudinal strain in each pier if the machinery weighs $450$ kips $(1$kip$=1000$ pounds$)?$ Provide the answer to thousandths of an inch: $0\mathrm{.}0001.$

$($b$)$ Using a factor of safety of $1\mathrm{.}3$ with respect to ultimate strength and the same load in part $($a$),$ what is the smallest wall thickness of the pier $(t)$ that is possible with the same outer diameter d $?$ Provide you answer to hundredths of an inch: $0\mathrm{.}01.$