Question

If modular ratio is 'm', effective depth is D and stress ratio is 'r' $(r=\frac{{\sigma }_{st}}{{\sigma }_{cbc}}),$ the depth of neutral axis of a balanced section is

• A. $\left(\frac{m}{m-r}\right)\times D$
• B. $\left(\frac{m}{m+r}\right)\times D$
• C. $\left(\frac{m+r}{m}\right)\times D$
• D. $\left(\frac{m}{r}\right)\times D$

Answer 1

The correct option is B $\left(\frac{m}{m+r}\right)\times D$


From $\Delta OAB$ and $\Delta BFC$
Depth of neutral axis,
$x_u=\frac{{\sigma }_{cbc}}{{\sigma }_{cbc}+\frac{{\sigma }_{st}}{m}}D=\left(\frac{m}{m+r}\right)D$