$1.(10$ pts$)$ Consider a compression member with a solid round cross$-$section $1\mathrm{.}0[$in$]$ in diameter. This member is made from carbon steel with a yield strength of $112,000[$PSI$]$ and carries a concentric load of $20,000[$lbf$].$ Both ends of the compression member are fixed. What is the greatest length this compression member can have and still qualify as an intermediate length column with central loading? C $=1\mathrm{.}2$