Stress-Strain and Young's Modulus
Calculate stress, strain, and Young's modulus for materials under load.
Includes tensile and compressive stress examples.
The Formulas
Stress (σ) = Force / Area = F / A
Strain (ε) = Change in Length / Original Length = ΔL / L₀
Young's Modulus (E) = Stress / Strain = σ / ε
Strain (ε) = Change in Length / Original Length = ΔL / L₀
Young's Modulus (E) = Stress / Strain = σ / ε
Stress measures the internal force per unit area in a material. Strain measures how much the material deforms relative to its original size. Young's modulus describes how stiff a material is.
Variables
| Symbol | Meaning | Units |
|---|---|---|
| σ | Stress | Pascals (Pa) or N/m² |
| F | Applied force | Newtons (N) |
| A | Cross-sectional area | Square meters (m²) |
| ε | Strain (dimensionless) | No units (ratio) |
| ΔL | Change in length | Meters (m) |
| L₀ | Original length | Meters (m) |
| E | Young's modulus | Pascals (Pa) or GPa |
Common Young's Modulus Values
| Material | Young's Modulus (GPa) |
|---|---|
| Steel | 200 |
| Aluminum | 69 |
| Copper | 117 |
| Concrete | 30 |
| Wood (along grain) | 11 |
| Rubber | 0.01–0.1 |
Example 1
A steel rod with cross-section 0.0001 m² is pulled with 20,000 N. What is the stress?
σ = F / A = 20,000 / 0.0001
σ = 200,000,000 Pa = 200 MPa
Example 2
A 2 m aluminum rod stretches by 0.58 mm under a stress of 20 MPa. Verify the Young's modulus.
ε = ΔL / L₀ = 0.00058 / 2 = 0.00029
E = σ / ε = 20,000,000 / 0.00029
E ≈ 69 GPa (matches the known value for aluminum)
When to Use It
Use stress-strain formulas in structural and materials engineering:
- Designing beams, columns, and structural elements
- Selecting appropriate materials for a given load
- Predicting how much a part will stretch or compress under force
- Ensuring components stay within safe stress limits