Problem: A steel rod of length 2 m and diameter 30 mm is subjected to a tensile force of 80 kN. Find the stress and strain in the rod. Take E = 200 GPa.
Solution:
Given:
- Force (F) = 80 kN = 80,000 N
- Diameter (d) = 30 mm = 0.03 m
- Length (L) = 2 m
- Young’s Modulus (E) = 200 GPa = 200 × 10^9 Pa
Step 1: Calculate Cross-Sectional Area
Area (A) = π(d/2)² = π(0.03/2)² = 7.065 × 10^(-4) m²
Step 2: Calculate Stress
Stress (σ) = F / A = 80,000 / (7.065 × 10^(-4)) = 113.23 MPa
Step 3: Calculate Strain
Strain (ε) = σ / E = (113.23 × 10^6) / (200 × 10^9) = 0.000566
Results:
- Stress = 113.23 MPa
- Strain = 0.000566 or 566 microstrain