Problem $4(25\%)$

For each section below, assuming material properties $f_c=3,000$ and $E_s=29,000$ksi, compute the following:

$($a$)$ The cracking moment using the gross moment of inertia of the section.

$($b$)$ The allowable moment using the transformed area method. Assume an allowable stress $f_s=36,000$ and $f_c^{\text{'}}=1,200$ psi for steel and concrete respectively.

$($A$)$

$($B$)$

$()$