Problem $2$

The beam section is under positive bending. $f_c^{\text{'}}=4500$ psi and $f_y=60$ksi.

$(1)$ Determine the cracking moment $(M_{cr})$ and corresponding curvature $({}_{cr})$ using beam

gross section $($i$.$e$.,$ no need to consider transformed section$)$

$(2)$ Determine $M_n,M_n,$ and ultimate curvature, $$ult