Question $4(30$ Points$)$:

a$)$ The rectangular RC beam in the figure is subjected to pure bending. Calculate the

moment capacities and corresponding curvature values for;

i$)$ Yielding of the tension reinforcement $($Assume concrete stress distribution

is linear$),$

ii$)$ ultimate state,

and draw the moment$-$curvature graph by using the calculated values. Determine

the section ductility of this section.

b$)$ For the same section, describe the expected variation in ductility by explaining the

reasons without any calculations if;

i$)$ the area of tension reinforcement is increased

ii$)$ Concrete grade is changed to $C40$

iii$)$ Steel grade is changed to S$220$

iv$)$ compression reinforcement is added to the cross$-$section without

changing the amount of tension reinforcement.

Materials: C$30/$ S$420,$ Concrete Cover $(d^{\text{'}})50mm$