Question

The cross-section of the reinforced concrete beam having an effective depth of 500 mm is shown in the figure (not drawn to the scale). The grades of concrete and steel used are M35 and Fe550, respectively. The area of tension reinforcement is 400 mm${}^2$. It is given that the corresponding to 0.2% proof stress, the material safety factor is 0.2% proof stress, the material safety factor is 1.15 and the yield strain of Fe550 steel is 0.0044.



As per IS 456:2000 the limiting depth (in mm, round off to nearest integer) of the neutral axis measured from the extreme compression fiber, is _______.

• A. 222

Answer 1

The correct option is A 222
Yield strain of Fe550 steel = 0.0044


In strain diagram (similar triangulation)

$\frac{x_{ulimit}}{0.0035}=\frac{d-x_{ulimit}}{0.0044}$

$\Rightarrow \frac{x_{ulimit}}{d-x_{ulimit}}=0.79545$

$\Rightarrow x_{ulimit}=0.44304d$

$\Rightarrow x_{ulimit}=0.44304\times 500$

$=221.52\approx 222$ mm