If the permissible stress in steel in tension is 140 N / mm2, then the depth of neutral axis for a single reinforced rectangular balanced section will be 

Concept :

A balanced section is one in which the area of tension steel is such that the failure of both concrete and steel occurs simultaneously.

For WSM method:

The critical depth of the neutral axis is given by –

From stress distribution diagram,

\(\frac{{\frac{{{σ _{st}}}}{m}}}{{d - {X_c}}} = \frac{{{σ _{cbc}}}}{{{X_c}}}\)

⇒ \(\frac{{{σ _{st}}}}{{m\; \times\; {σ _{cbc}}}} = \frac{{d - {X_c}}}{{{X_c}}}\)

Where, Xc = kd (k = Neutral axis depth factor for balanced section)

⇒ \(\frac{{{σ _{st}}}}{{m\; \times\; {σ _{cbc}}}} = \frac{{d - kd}}{{kd}}\)

⇒ \(\frac{{{σ _{st}}}}{{m\; \times \;{σ _{cbc}}}} = \frac{{1 - k}}{k}\)

\(k = \frac{{m \times {σ _{cbc}}}}{{{σ _{st}} + m \times {σ _{cbc}}}}\)

Put the value of modular ratio, \(m = \frac{{280}}{{3{σ _{cbc}}}}\)

\(k = \frac{{280}}{{3{σ _{st}} \;+\; 280}}\)

Thus the neutral axis factor for the balanced section depends only on σst and is independent of σcbc.

Calculation:

σ_st = 140 N / mm2

Neutral axis depth factor for balanced section

\(k = \frac{{280}}{{3{σ _{st}} \;+\; 280}}= \frac{{280}}{{3{\times140} \;+\; 280}}\)= 0.40

Hence, the depth of neutral axis for a single reinforced rectangular balanced section is 0.40d.