QUESTION $1(20$ Marks$)$

a$)$ Differentiate between the Serviceability limit state and the Ultimate limit state in the analysis of reinforced concrete structures. $[2|$

b$)$ Briefly explain why concrete's partial material safety factor is relatively higher than steel, according to SANS$10100-1,[2]$

c$)$ Figure $1$ presents the cross$-$section of a singly reinforced concrete beam at the midspan of a simply supported beam. Using the principles for ultimate limit state design according to SANS$10100-1,$ calculate the ultimate moment of resistance $(M_{\text{u}\text{l}\text{t}})$ for the section. $[16]$

Given: $f_{cu}=30$MPa

$f_y=460$MPa

$A_x=1600m{m}^2$