Beam shear design: A $12-$inch$-$wide beam below supports two equal concentrated loads at its two third points. The two loads are factored $($combined$)$ and have magnitude of $90$ kips. Neglect the self$-$weight of the beam and use $f_{c^{\text{'}}}^{\text{'}}=5000($normal weight concrete$)$ and $f_{yt}=60,000$ for all the parts below. The effective depth of the tension reinforcement is $21\mathrm{.}5$ in$..$

$($a$)$ Draw the shear diagram of the beam under the two concentrated loads. $(10$ points$)$

$($b$)$ On the shear diagram in $($a$),$ mark up the regions of the beam where shear reinforcement is NOT required per ACI$318-19.$ Show calculations if necessary. $(10$ points$)$

$($c$)$ If No$.4$ double$-$leg stirrups are used as shear reinforcement, determine the spacing of the stirrups in the regions where shear reinforcement is required. Check your design with the requirements on minimum shear reinforcement and maximum spacing of stirrups per ACI$318-19.(15$ points$)$

Column design: A column shown below has ties as transverse reinforcement conforming to ACl $25\mathrm{.}7\mathrm{.}3.$ Assume normal$-$weight concrete with $f_c^{\text{'}}=4000$ and Grade $60$ reinforcement.

$($a$)$ Calculate the theoretical compression strength $P_o$ per ACI$318-19.(10$ points$)$

$($b$)$ Calculate the maximum design axial compression strength $P_{n,\text{m}\text{a}\text{x}}$ of the column. $(10$ points$)$

$($c$)$ Calculate the nominal compressive strength $(P_n)$ if the neutral axis is $6$ in$.$ measured from the right edge of the column. Assume bending is about the $Y$ axis. $(10$ points$)$