Sometimes, the design parameters not have to change, all are fixed but there is constrains of space or considering aesthetic, we have to design doubly reinforcement.
If grade of concrete, grade of steel, size of section are fixed MoR,lim=Qbd2 is also fixed for singly reinforced section. If singly reinforcement is design for BM>MoR,lim then Ast, provided would make over-reinforced section. Hence this additional BM can be resisted by providing r/f on the compression side of the section, it is termed as doubly r/f section. Doubly reinforcement section also provide to reduce deflection due to creep & shrinkage or when section is subjected to dynamic loading (Stress-reversed). To avoid the buckling of reinforcement of compression side, it must be enclosed within stirrups.
For doubly reinforcement section d’/d = 0.05-0.20
From Similar Triangle,
