$(1)$ The $W831$ column is the notes is strengthened with cover plates $(\frac{3}{8^{\text{'}\text{'}}}{8}^{\text{'}\text{'}}).$ What is the colomn capacity $P_n$ for both configurations shown?

$L={24}^{\text{'}}$

$F_y=50ks$

$(2)$ Using the typical ${27}^{\text{'}}45$ bay, what would the columns be in a six story building with all story heights equal to ${16}^{\text{'}}-0^{\text{'}\text{'}}.$ Assume columns are $2$ stories in height $($spliced above $3^{rd}$ and $5^{th}$ floors$).$ Use W$12$ columns. Live Loads: Roof $20$ psf Floors $50$ psf office

$(3)$ The typical beams in a ${27}^{\text{'}}{40}^i$ bay A supported on the top of the typical girders, $W2468,$ making the unsupported length $L_b=9$ feet. $($Girder is supported at the ends and at $\frac{1}{3}$ points$).$ Is the girder adequate if $=622ft-$kips. Use tables $3-10$ and appropriate $C_b.$ If the beam is not adequate, choose a larger W$24$ that works. $($Note $L_b$ does not change$).$

The beam$-$column shown in Figure $6\mathrm{.}2$ is pinned at both ends and is subjected to the factored loads shown. Bending is about the strong axis. Determine whether this member satisfies the appropriate AISC Specification interaction equation.

Use Tables $3-10$ and $4\mathrm{.}1.$

FIGURE $6\mathrm{.}2$