Problem $1$ and $2$: There are two steel columns$-$C$1(10\text{'}$ long$)$ and C$2(20\text{'}$ long$).$ Both columns are made of W$1640($A$36$ steel$)$ and bave the same cross$-$section.

If both columns have the same connection methods, which column can support more load before buckling? Explain why?

How much more load can one column support than the other before buckling?

There is an A $36$ steel column. Its $P_{\text{c}\text{r}\text{i}\text{t}\text{i}\text{c}\text{a}\text{l}}$ was found to be $300$ k while its $P_{\text{a}\text{l}\text{l}\text{o}\text{w}\text{r}\text{a}\text{b}\text{l}\text{e}}$ was equal to $200$ k $.$ Determine the safety factor of the column design.

There is a $20-$long column, of which the critical buckling load about the weak axis is determined to be $20$ kips $.$ If you add a lateral bracing along the same axis at $15$ ft from the bottom of the column, then determine the theoretical maximum critical buckling load about the axis.

Determine the appropriateness of the column design described below.

Loading $=$ axial Load $120$ kips, Material W$10$