Problem $3$:

$($a$)$ Compare $M_n$ for singly reinforced rectangular beams having the following properties.

$($b$)$ Taking beam $1$ as the reference point, discuss the effects of changing $A_s,f_y,f_c^{\text{'}},d,$ and $b$ on

$M_n.($Note that each beam has the same properties as beam $1$ except for the italicized

quantity.$)$

$($c$)$ What is the most effective way of increasing $M_n?$ What is the least effective way?