A reinforced concrete rectangular beam section is subjected to bending. The section has the following properties:

Width $($b$)$: $300$ mm

Effective depth $($d$)$: $500$ mm

Characteristic strength of concrete $($fck$)$: $30\frac{N}{m}{m}^2$

Yield strength of steel $($fyk$)$: $500\frac{N}{m}{m}^2$

Area of tensile reinforcement $($As$)$: $2000m{m}^2$

a$)$ Calculate the depth of the neutral axis $($x$)$ for the given section.

$(3$ Marks$)$

b$)$ Determine whether the section is under$-$reinforced, balanced, or over$-$reinforced.

$(2$ Marks$)$

c$)$ Calculate the moment of resistance $($MR$)$ of the section.

$(5$ Marks$)$

d$)$ Calculate the Moment of Resistance $($MR$)$ if the area of tensile reinforcement $($As$)$ is increased to $2500m{m}^2$

$(6$ Marks$)$

e$)$ Evaluate if the New Section is Under$-$reinforced, Balanced, or Over$-$reinforced

$(4$ Marks$)$

$($CLO$2-$PLO$3$:C$5)$