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GATE 2022 CE (CE1) – Question 14

Concrete Structures · Working stress and limit state design concepts · 1 mark · Multiple choice

In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio of

  1. Young’s modulus of elasticity of reinforcement material to Young’s modulus of elasticity of concrete.
  2. Young’s modulus of elasticity of concrete to Young’s modulus of elasticity of reinforcement material.
  3. shear modulus of reinforcement material to the shear modulus of concrete.
  4. Young’s modulus of elasticity of reinforcement material to the shear modulus of concrete.

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Show answer and explanation

Correct answer: (A) Young’s modulus of elasticity of reinforcement material to Young’s modulus of elasticity of concrete.

Explanation

The modular ratio transforms steel area into equivalent concrete area by preserving strain compatibility and axial force. Equal strain gives $\sigma_s/\sigma_c=E_s/E_c$.

Hence $m=\mathbf{E_s/E_c}$, reinforcement Young’s modulus divided by concrete Young’s modulus, **A**. Neither shear modulus enters this definition.