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GATE 2023 CE (CE1) – Question 37

Concrete Structures · Design and detailing of beams and slabs · 2 marks · Multiple choice

Consider a doubly reinforced RCC beam with the option of using either Fe250 plain bars or Fe500 deformed bars in the compression zone. The modulus of elasticity of steel is $2 \times 10^5$ N/mm$^2$. As per IS456:2000, in which type(s) of the bars, the stress in the compression steel ($f_{sc}$) can reach the design strength ($0.87f_y$) at the limit state of collapse?

  1. Fe250 plain bars only
  2. Fe500 deformed bars only
  3. Both Fe250 plain bars and Fe500 deformed bars
  4. Neither Fe250 plain bars nor Fe500 deformed bars

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Correct answer: (A) Fe250 plain bars only

Explanation

For Fe250 the design stress-strain curve yields at a strain of $\frac{0.87 \times 250}{2 \times 10^5} = 0.0011$, which is below the limiting concrete strain of 0.0035, so $f_{sc}$ can reach $0.87f_y$. For Fe500 deformed bars the curve is non-linear and yield is taken at the strain $\frac{0.87 \times 500}{2 \times 10^5} + 0.002 = 0.0042$, above 0.0035, so the compression steel cannot reach $0.87f_y$ at the limit state.