Two columns on a mechanical test system must support a large axial load.

a$.$ Using Euler's curve, specify the column diameter if each column has to carry a maximum load of $10$ kN $.$ Use a design factor $n_d=4,$ and consider the column ends as fixed$-$free $(C=0\mathrm{.}25).$ The steel column has a yield strength of $200$ MPa $,$ a modulus of elasticity of $120$ GPa $,$ and a radius of gyration $k=\frac{d}{4}.[7$ pts$]$

b$.$ Should you have used the Johnson formula instead of Euler's formula to calculate the column diameter $($circle below$)?$ Support your conclusion using calculations $($show your work$).[4$ pts$]$ Yes $($use Johnson$)$ No $($use Euler$)$