Question $1$: $(35$ points$)$

a$.$ Explain the difference between elastic and inelastic buckling.

b$.$ Discuss how are initial imperfections considered in the design of axially loaded columns according to the AISC standards? Which is more sensitive to initial imperfections: elastic or inelastic buckling strength.

c$.$ True or False? And why?

a$.$ The elastic buckling stress of a steel column depends on the yield strength.

b$.$ The buckling strength of an axially loaded column depends only on the slenderness ratio.

c$.$ For Fy $\backslash (=50\backslash )$ ksi, a column with slenderness ratio $\backslash (=80\backslash )$ will buckle inelastically.

d$.$ The limiting width to thickness ratio of a stiffened element is higher than that of unstiffened element, assuming that both have the same yield strength.

d$.$ A column has an LRFD critical buckling stress $\backslash (\backslash$phi F$\_\{$c$\}=37\mathrm{.}5\backslash$mathrm$\{$ksi$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$Fy$\}=50\backslash )$ ksi. Compute its slenderness ratio and determine if the buckling is elastic or inelastic.