Column Problem. $[$value $=2]$

a$.$ Using Euler's curve, specify the column diameter if each column has to carry a maximum load of $10kN.$ Use a design factor $n_d=2,$ and consider the column ends as fixed$-$rounded $(C=2).$ The steel column has a yield strength of $500$MPa, and a modulus of elasticity of $200$GPa.

b$.$ If the slenderness ratio for the column you designed in part $($a$)$ was less then the slenderness ratio at point $T$ on the Euler curve, $(\frac{l}{k}{)}_1,$ clearly describe "what" you would need to do regarding the column you designed in part $($a$),$ and "why" this is necessary.