Here are the steps for analysing and designing singly reinforced section.

A) ANALYSIS.

1) Steps for determining Moment of Resistance.

i. First calculate the depth of critical neutral axis `(x_c)`using the following formula.

`sigma_(cbc)/(sigma_(st)/m)=x_c/(d-x_c)`

ii. Find the depth of actual neutral axis `x` using this formula.

`b×x×x/2=mA_(st)×(d-x)`

iii. Compare `x` and `x_c`.

If `x` < `x_c` ( under reinforced section )

`MOR = sigma_(st) ×A_(st)×(d-x/3)`

If `x ` > `x_c` (over reinforced section)

`MOR = sigma_(cbc)/2×b×x×(d-x/3)`

i) First calculate depth of actual neutral axis using following formula.

`b×x×x/2=mA_(st)×(d-x)`

ii) Calculate `sigma_(st)` using following formula.

`MOR = sigma_(st) ×A_(st)×(d-x/3)`

iii) Find ` sigma_(cbc)` using following formula.

`sigma_(cbc)/(sigma_(st)/m)=x_c/(d-x_c)`

i) Assume balanced section. Assume `d/b=1.5` to ` 2`

i) First calculate position of neutral axis in terms of `d` using this formula.

`sigma_(cbc)/(sigma_(st)/m)=x_c/(d-x_c)`

ii) Find MOR in terms of `b` using following formula.

`MOR = sigma_(cbc)/2×b×x×(d-x/3)`

iii) Equate BM and MOR and find `b` and `d`.

iv) Find `A_(st)` using the following formula.

`MOR = sigma_(st) ×A_(st)×(d-x/3)`

v) Find number of bars required assuming a suitable dia of bar using following formula.

`n= A_(st)/(pi×phi^2/4)`