Stress is the internal force per unit area that resists deformation.
Mathematically: \$\sigma = \frac{F}{A}\$
where \$\sigma\$ is stress, \$F\$ is the applied load, and \$A\$ is the cross‑sectional area.
Think of a rubber band being pulled: the tighter you pull, the higher the stress inside the band.
Strain measures how much a material deforms relative to its original length.
Mathematically: \$\varepsilon = \frac{ΔL}{L_0}\$
where \$ΔL\$ is the change in length and \$L_0\$ is the original length.
Imagine a spring that stretches when you hang a weight from it – the longer it gets, the greater the strain.
For many elastic materials, stress and strain are linearly related up to a certain point:
\$\sigma = E\,\varepsilon\$
where \$E\$ is the Young’s modulus.
The limit of proportionality is the maximum stress where this linear relationship holds. Beyond this, the material may yield or break.
Analogy: A rubber band stretches linearly until it reaches its maximum stretch; after that it snaps.
| Quantity | Symbol | SI Unit |
|---|---|---|
| Stress | σ | Pa (N m⁻²) |
| Strain | ε | dimensionless (ratio) |
| Young’s Modulus | E | Pa |
1️⃣ Identify the type of deformation: Is the object being stretched (extension) or squashed (compression)?
2️⃣ Use the correct formula: Stress = Force ÷ Area; Strain = ΔLength ÷ Original Length.
3️⃣ Check units: Force in N, area in m², length in m → stress in Pa.
4️⃣ Remember Hooke’s law only applies up to the limit of proportionality.
5️⃣ Sketch a free‑body diagram: Show all forces and the direction of stress.
Good luck! 🎓