Stress, Strain & Young’s Modulus
How much does a rod, cable or column stretch under load? Fill in any four of the seven quantities and the other three are calculated, with a safety check against the material’s yield strength.
What are Stress and Strain?
Stress is force per unit area: the same load is far more severe on a thin wire than on a thick bar. Strain is the relative change in length — a dimensionless ratio, often given in percent.
For most materials, below the yield strength, stress and strain are proportional (Hooke’s law). The constant of proportionality is Young’s modulus E: a measure of stiffness. Steel is about three times stiffer than aluminium.
Stress–Strain Diagram
elasticMaterial Properties
typical values| Material | E | Yield σy |
|---|---|---|
| Structural steel S235 | 210 GPa | 235 MPa |
| Aluminium 6061-T6 | 69 GPa | 276 MPa |
| Copper (annealed) | 117 GPa | 70 MPa |
| Titanium Ti-6Al-4V | 114 GPa | 880 MPa |
| Concrete (compression) | 30 GPa | ~30 MPa |
| Oak, along the grain | 11 GPa | ~50 MPa |
| Rubber | 0.01–0.1 GPa | ~15 MPa |
Key Relations
Combine the three definitions: longer and thinner members stretch more, stiffer materials stretch less.
How many times the load could increase before the material yields. Structures typically use 1.5–3; lifting equipment 5 or more.
Designing works the other way round: choose a safety factor, then size the cross-section so the stress stays low enough.
Sources & Verification
- R. C. Hibbeler, Mechanics of Materials in SI Units, 10th ed., Pearson, 2018 — Ch. 1 (Stress), Ch. 2 (Strain) and Ch. 3 (Mechanical Properties of Materials).
- W. D. Callister & D. G. Rethwisch, Materials Science and Engineering: An Introduction, 10th ed., Wiley, 2018 — Ch. 6 (Mechanical Properties of Metals).