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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 corresponding to $0.2\%$ 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 the nearest integer ) of the neutral axis measured from the extreme compression fiber, is ________.

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