Question

A high strength steel rod with Young's modulus \(E = 200 \, \text{GPa}\) and Poisson's ratio \(\nu = 0.31\), having a diameter of 5 cm, is subjected to a compressive load of 10 kN and experiences a stress of 5 MPa. Compute the axial strain and the lateral strain.

• A. Axial strain = 25 μ strain, Lateral strain = 8 μ strain
• B. Axial strain = 25 μ strain, Lateral strain = 78 μ strain
• C. Axial strain = 78 μ strain, Lateral strain = 25 μ strain
• D. Axial strain = 8 μ strain, Lateral strain = 25 μ strain

Hint:

For axial and lateral strains, use the relationship with Young's modulus and Poisson's ratio to solve for the deformations.

Answer 1

The Correct Option is A

- The axial strain is given by: \[ \text{Axial strain} = \frac{\text{Stress}}{E} = \frac{5 \times 10^6 \, \text{Pa}}{200 \times 10^9 \, \text{Pa}} = 25 \, \mu \text{strain} \] - The lateral strain is calculated using Poisson's ratio \(\nu\), which relates the lateral strain to the axial strain: \[ \text{Lateral strain} = -\nu \times \text{Axial strain} = -0.31 \times 25 \, \mu \text{strain} = 8 \, \mu \text{strain} \] Conclusion: The axial strain is 25 μ strain, and the lateral strain is 8 μ strain, so option (a) is correct.