**Question: **In the context of elastic theory of reinforced concrete, the modular ratio is

defined as the ratio of

(A) Young’s modulus of elasticity of reinforcement material to Young’s modulus of

elasticity of concrete.

(B) Young’s modulus of elasticity of concrete to Young’s modulus of elasticity of

reinforcement material.

(C) shear modulus of reinforcement material to the shear modulus of concrete.

(D) Young’s modulus of elasticity of reinforcement material to the shear modulus of

concrete. (GATE 2022)

**Solution:**

In considering the elasticity of reinforced concrete, the modular ratio is defined as the ratio of Young's elastic modulus of the concrete to Young's elastic modulus of the reinforced material

Therefore, the correct answer is (B).

The elasticity theory of reinforced concrete is based on the assumption that under applied load both concrete and reinforcement behave elastically, in other words, the stress-strain relationship between both materials is linear until they reach their yield points.

The modular ratio is an important parameter in the elastic theory of reinforced concrete. It is defined as the ratio of the concrete Young’s elastic modulus to the Young’s elastic modulus of the reinforcing material. Mathematically, the modular ratio can be expressed as:

Modular dimension (m) = Eₛ/Eᵣ

where Eₛ is Young’s elasticity parameter for concrete and Eᵣ is Young’s elasticity parameter for reinforcing materials.

The modular ratio is used to calculate the resilience time of reinforced concrete. It is also used to determine the amount of strength required in a part to resist applied loads.

In practice, the modular ratio is usually taken as a constant value for a given type of concrete and reinforcement. However, the actual value of the modular ratio may vary depending on the material properties and design of the reinforced concrete