Question$3$: $(8$ points$)$ A bar AB of modulus of elasticity $50$ GPa and square cross section $(bb)$ has a pinned supports at the base and top. The horizontal beam supporting a load $F=100kN.$

A$.(2-$points$)$ Assume that the desired factor of safety with respeet to Euter$-$Buekling is $3\mathrm{.}0,$ what is the required cross sectional area of the bar if $a=0\mathrm{.}8m.$

B$.(2-$points$)$ What is the required distance $"a"$ if the bar is about to buckle and $b=80mm?$

C$.(2-$points$)$ Find the normal stress in the bar $($For the case in Question $3$: Part B$).$

D$.(2-$points$)$ Assume now that yield stress of the bar is ${}_p=4=25$MPa, what should be done to prevent the plastic deformation of the bar? Support your suggestion with a logical solution $($that is$,$ give number that support your idea$)!$