understand that deformation is caused by tensile or compressive forces (forces and deformations will be assumed to be in one dimension only)

What is Stress?

Stress is the internal force per unit area that resists deformation. Think of it as the pressure inside a material when you squeeze or pull it.

Mathematically: \$\sigma = \dfrac{F}{A}\$

🔧 Tensile stress pulls the material apart. 🧱 Compressive stress pushes it together.

What is Strain?

Strain measures how much a material stretches or compresses relative to its original length.

Mathematically: \$\epsilon = \dfrac{\Delta L}{L_0}\$

Example: Stretch a rubber band. If it gets 2 cm longer from an original 10 cm, strain = 0.2 (20 %).

Hooke’s Law (Elastic Behaviour)

For many materials, stress and strain are proportional while they are still elastic.

Mathematically: \$\sigma = E\,\epsilon\$

Here, E is the Young’s modulus – a material constant that tells how stiff it is.

1. Apply a force → calculate stress.
2. Use Hooke’s Law to find strain.
3. Determine new length: \$L = L_0(1+\epsilon)\$

Deformation in Everyday Life

• 🪢 Rubber bands – tensile stress.
• 🏗️ Bridges – compressive stress in the lower parts.
• 🧱 Concrete columns – compressive stress.
• 🪜 Steel ladders – tensile stress when you climb.

Exam Tips

When solving problems:

1. Identify the type of force (tensile or compressive).
2. Write down the known quantities and the formula you’ll use.
3. Check units – stress in Pa (N/m²), strain is dimensionless.
4. Remember that strain is always positive for both stretching and compression in the formula.
5. Use the relationship \$\sigma = E\,\epsilon\$ only if the material is elastic.