Question

According to IS 456-2000, which one of the following statements about the depth of neutral axis $x_{u,bal}$ for a balanced reinforced concrete section is correct?

• A. $x_{u,bal}$ depends on the grade of concrete only
• B. $x_{u,bal}$ depends on the grade of steel only
• C. $x_{u,bal}$ depends on both the grade of concrete and grade of steel
• D. $x_{u,bal}$ does not depend on the grade of concrete and grade of steel

Answer 1

The correct option is B $x_{u,bal}$ depends on the grade of steel only

For limiting or balanced depth of neutral axis.


For the recommendation that,
${\epsilon }_{st}\ge \frac{0.87f_y}{E_s}+0.002$
and strain in concrete at collapse, should be max of 0.0035
$\frac{0.0035(d-x_u)}{x_u}\ge \frac{0.87f_y}{E_s}+0.002$
$(\frac{d}{x_u}-1)\ge \frac{\frac{0.87f_y}{E_s}+0.002}{0.0035}$
$\frac{d}{x_u}\ge \frac{\frac{0.87f_y}{E_s}+0.0055}{0.0035}$
$\frac{x_u}{d}\le \frac{0.0035}{\frac{0.87f_y}{E_s}+0.0055}$
Thus limiting value of neutral axis depth is given by.

${\left(\frac{x_u}{d}\right)}_{lim}=\frac{0.0035}{0.0055+\frac{0.87f_y}{E_s}}$

Hence, balanced or limiting depth of neutral axis is dependent on grade of steel only.