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GATE 2023 CE (CE1) – Question 14

Concrete Structures · Design and detailing of beams and slabs · 1 mark · Multiple choice

A singly reinforced concrete beam of balanced section is made of M20 grade concrete and Fe415 grade steel bars. The magnitudes of the maximum compressive strain in concrete and the tensile strain in the bars at ultimate state under flexure, as per IS 456: 2000 are _____, respectively. (round off to four decimal places)

  1. 0.0035 and 0.0038
  2. 0.0020 and 0.0018
  3. 0.0035 and 0.0041
  4. 0.0020 and 0.0031

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Correct answer: (A) 0.0035 and 0.0038

Explanation

In a balanced section the concrete reaches its ultimate strain of 0.0035 at the same time as the steel reaches its yield. For Fe415 the design yield strain is $\frac{0.87 \times 415}{2 \times 10^5} + 0.002 = 0.001805 + 0.002 = 0.0038$.