Question

A composite bar consisting of two different materials having same length and same cross- sectional area will have the same

• A. Stress
• B. Strain
• C. Load sharing
• D. Poisson's ratio

Hint:

For composite structures, remember the key compatibility condition for each arrangement:
- Parallel bars (loaded axially): Strain is the same.
- Series bars (loaded axially): Stress (and Load) is the same.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question describes a composite bar made of two materials, perfectly bonded together, with the same length and area. It asks which quantity will be the same for both materials when the bar is subjected to an axial load.

Step 2: Detailed Explanation:
This describes a "parallel composite" system. When an axial load is applied to the composite bar, the two materials must deform together.

• Since the bars are rigidly fixed together and have the same initial length ($L$), their change in length ($\delta L$) must be identical to maintain compatibility.

• Strain ($\epsilon$) is defined as the change in length divided by the original length ($\epsilon = \delta L / L$). Since both $\delta L$ and $L$ are the same for both materials, the strain must be the same in both.

• Stress ($\sigma$) is related to strain by Hooke's Law: $\sigma = E \epsilon$. Since the two materials are different, their moduli of elasticity ($E_1$ and $E_2$) will be different. Because the strain ($\epsilon$) is the same for both, but the moduli are different, the stresses in the two materials will be different ($\sigma_1 \neq \sigma_2$).

• Load sharing: The total load ($P$) is shared between the two materials ($P = P_1 + P_2$). Since the stresses are different and the areas are the same, the loads carried by each material ($P_1 = \sigma_1 A$ and $P_2 = \sigma_2 A$) will be different.

• Poisson's ratio is an intrinsic material property and will be different for the two different materials.



Step 3: Final Answer:
The strain will be the same for both materials in the composite bar.