GATE 2025 CE (CE1) – Question 52
Consider a reinforced concrete beam section of 300 mm width and 700 mm depth. The beam is reinforced with the tension steel of 2000 mm$^2$ area at an effective cover of 50 mm. Concrete in the tension zone is assumed to be cracked. Assume the modular ratio of 12 and Young's modulus of 200 GPa for steel. When the extreme fibre in the compression zone undergoes the strain of 0.0004 due to the applied bending moment, the stress in the steel (in MPa) is ______________ (*rounded off to the nearest integer*).
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Correct answer: 126
Explanation
The effective depth is $d = 700 - 50 = 650$ mm. For a cracked elastic section the neutral axis depth $x$ follows from $\frac{bx^2}{2} = mA_s(d - x)$, so $150x^2 = 24000(650 - x)$ and $x = 252.3$ mm. The strain varies linearly, so the steel strain is $0.0004 \times \frac{650 - 252.3}{252.3} = 0.000631$. The steel stress is $200000 \times 0.000631 = 126$ MPa.