A circular rod of 20 mm diameter and 400 mm length is subjected to a tensile force of 50 kN. What is the volumetric strain, if Poisson’s ratio = 0·25 and Young’s modulus E = 2 × 10⁵ N/mm² ?
- A79·57 × 10⁻⁵
- B39·75 × 10⁻⁵Correct
- C79·57 × 10⁻³
- D39·75 × 10⁻³
Solution
Concept
Volumetric strain under uniaxial stress
Formula
εv = ε (1 − 2ν), ε = σ / E
Step-by-step solution
1. σ = 50 000 / (π × 20² / 4) = 159.15 N/mm². 2. ε = 159.15 / 2×10⁵ = 7.958 × 10⁻⁴. 3. εv = 7.958×10⁻⁴ × (1 − 0.5) = 3.98 × 10⁻⁴ ≈ 39.75 × 10⁻⁵.
Explanation
The volumetric strain is the sum of the three direct strains: ε − 2νε = ε(1 − 2ν).
Why the other options are wrong
79.57 × 10⁻⁵ is the longitudinal strain ε (or 2εv). The ×10⁻³ options are 100 times too large.
Shortcut
εv = (σ/E)(1 − 2ν).
Common mistake
Reporting the linear strain.
Correct answer: B) 39·75 × 10⁻⁵