A W$1253$ column $($Boxed in Orange$)$ with floor$-$to$-$floor height of ${18}^{\text{'}}-0^{\text{'}\text{'}}$ was selected by the structural engineer to carry $5$ floors of the following loading $($ignore the roof$).$ Loading: blue $=$ Corridor above first floor LL$,$ green $=$ research similar to operating room lab LL$,$ yellow $=$ office with partition added LL$.$ DL in all three areas consists of s$.$w$.=62$ psf$,$ MEPFP allowance, suspended ceiling with acoustical fiberboard tiles, and a flooring of $\frac{1}{4}"$ Linoleum tiles. Calculate:

$P_n,$ given the column sits on a pier that has weak rotational resistance both directions.

$P_n,$ given the column sits on a pier where the baseplate in the $y-$direction behaves like a moment connection but in the x $-$direction is it shear only.

$P_n,$ given the column sits on a pier where the baseplate behaves like a moment connection in both directions.

Note: column fixity at the top in both directions will al