An axial load $P=12$kips is applied with an eccentricity $e=0\mathrm{.}375in.$ to the circular steel rod $BC$ that is free at its top $C$ and fixed at its base $B.$ Knowing that the stock of rods available for use have diameters in increments of $\frac{1}{8}in.$ from $1\mathrm{.}5$ in $.$ to $3$ in $.,$ determine the lightest rod that can be used if ${}_{\text{a}\text{l}\text{l}}=15$ksi. Use $E=29{10}^6.$

The diameter of the lightest rod that can be used is $$ in$.$