Please provide calculations for given solutions.

Consider a a HSS$140\mathrm{.}500$ A$500$ Gr B $(F_y=46$ksi$)$ section filled with normal weight concrete $f_c^{\text{'}}=4$ksi and $w_c=145pcf.$ Column length $=30ft.$ Both column ends are fixed.

$($i$)$ Determine design strength of the composite column. Answer: $P_n=881$ kip. Intermediate answers: $P_e=3122$kip,$P_{no}=1421$ kip.

$($ii$)$ A load of $500$ kip is applied to the steel section directly from beam that is $12$ inch deep.

Using $4$ in$.$ long $\frac{3}{4}$ in$.$ diameter $F_u=65$ksi shear studs determine appropriate number of the anchors for shear transfer. Answer: Provide $3$ sets of $4$ connectors for a total of $12$ connectors. Intermediate answers: $R_{n,\text{D}\text{i}\text{r}\text{e}\text{c}\text{t}\text{B}\text{o}\text{n}\text{d}}=99\mathrm{.}36$kip.$V_r^{\text{'}}=179\mathrm{.}4$ kip, for one shear stud

$Q_n=18\mathrm{.}67$ kip.