Problem $1(75$ points$)$

A$.$ For the three cases shown determine the factored moment, Mu$,$ at the critical section. The $q_{u,\text{n}\text{e}\text{t}}$value is $4\mathrm{.}98$ ksf $.$ In all cases the footings have a width of $6$ feet and a total depth of $2$ feet.

B$.$ A normal weight reinforced concrete square footing $(8ft8ft$ has a total depth of $22$ in $.$ It carries a square column $(20in.x20in.).$ If $q_{u,\text{n}\text{e}\text{t}}$ value is $5\mathrm{.}24$ ksf determine if the footing can carry the shear $($Two$-$way and one$-$way$)$ without shear reinforcement. Assume $d=18in.,f_c^{\text{'}}=3,000,f_y=60,000,$ and $A_s=1i\frac{n^2}{f}t.$

C$.$ A normal weight reinforced concrete square footing $(6ft6ft)$ has a total depth of $20$ in $.$ It carries a square column $(20in.x20in.).$ If $P_u=144$kips determine the dowels needed to transfer the load between the column and the footing. Assume $d=16$ in$.,f_c^{\text{'}}=3,500$ psi and $f_y=60,000$ psi.

D$.$ For the concrete footing and concrete column in part A$,$ determine the tension steel to carry the calculated moment. Assume the footing to be square, $d=20in.,f_c^{\text{'}}=3,000$ and $f_y=60,000$ psi.