Problem #$2(40$ points$)$

A slab as shown in Figure $2$ is to be analyzed using the Yield Line Method. The slab is simply supported on three sides and free on the fourth. Assuming the slab is orthotropically reinforced with resistant moments $M_{px}$ and $M_{py}$ in the $x$ and $Y$ directions respectively and subjected to uniformly distributed load $q_f,$ determine the ultimate $($collapse$)$ load gfip that the slab can support.

Given:

$f_y=60,000$

$f_c=4,000$

Normal$-$weight concrete

$M_{py}=16ft-$kip$\frac{s}{f}t$

$M_{px}=20ft-$kip$\frac{s}{f}t$