Problem $1)$ Consider the column shown in the figure. $f^{\text{'}}c=6,500$ psi and $fy=80,000,$

$A_S=8$#$9$ bars. Calculate the nominal strength $Pn,M_n$ and design strength $Pn,Mn$

for the following points in the interaction diagram.

In each case indicate the value of the $$ factor according to the ACI $318$ Building Code.

a$.$ axial compression

b$.$ axial tension

c$.$ pure bending

d$.$ balanced failure condition

e$.$ tension controlled limit$.$

f$.$ neutral axis depth $c=16$ in$.$

g$.$ sketch the axial load$-$moment

interaction diagram. Indicate

whether the section has adequate

capacity to carry axial load $P_u=$

$800$ kips and a moment $M_u=250$

ft$-$kips.