Question $3(20$ Marks$)$

For the wide flange built$-$up section shown below, as well as its equivalent $13"82"$ solid rectangular section, derive the equations and calculate the values for:

$($i$)$ The elastic section modulus $(S_x)$

$($ii$)$ The plastic section modulus $(Z_x)$

$($iii$)$ The $\frac{Z_x}{S_x}$ ratio

Compare the $\frac{Z_x}{S_x}$ ratio for the two sections and discuss any conclusions drawn.