Stress

Learn stress as the internal force per unit area that develops inside a material when an external force acts on it.

1. Concept Overview

When a force is applied on a solid body, its particles resist the deformation. This internal resistance creates a force inside the material. Stress is simply a measure of how much internal force per unit area develops due to the external load.

This helps us understand how strongly a material is being pushed, pulled, compressed, twisted, or sheared from the inside.

2. Definition

Stress: The internal restoring force developed per unit area of a material when an external force acts on it. It is given by \( \text{Stress} = \dfrac{F}{A} \), where \(F\) is the applied force and \(A\) is the cross-sectional area.

3. Key Ideas Explained

3.1. Why Stress Develops

Inside any solid, atoms are held together by intermolecular forces. When a force tries to stretch or compress the material, these particles resist movement, generating internal forces. The larger the external force, the greater the internal stress.

This is why even a thin wire can lift a heavy weight—it develops high internal stress to balance the load.

3.2. Formula for Stress

The basic formula is:

\( \sigma = \dfrac{F}{A} \)

where:

  • \( \sigma \) = stress
  • \( F \) = applied force
  • \( A \) = area on which the force acts

Stress increases when force increases or when the area becomes smaller.

3.3. Types of Stress

3.3.1. Tensile Stress

Occurs when the material is pulled or stretched. The internal forces act to resist the elongation.

Example: Pulling a rope or stretching a rubber band.

3.3.2. Compressive Stress

Occurs when the material is pushed or compressed. The internal forces act to resist shortening.

Example: Pressing a sponge or squeezing a metal rod.

3.3.3. Shear Stress

Occurs when forces act parallel to a surface, causing layers of the material to slide past each other.

Example: Cutting paper with scissors or rubbing hands together.

3.3.4. Volumetric Stress

Occurs when the material is under uniform pressure from all sides, leading to a change in volume.

Example: A deep-sea object compressed by water pressure.

3.4. Stress Depends on Area

For the same force, a thinner object experiences more stress than a thicker one. This is why a thin wire breaks more easily than a thick wire under the same load.

Reducing the area increases the intensity of internal forces.

4. Stress and Material Behaviour

4.1. Elastic Region

At low stress, the material deforms slightly and returns to its original shape once the force is removed. This is the region where Hooke’s Law applies.

4.2. Beyond Elastic Limit

If the stress becomes too large, the material undergoes permanent deformation. This zone is called plastic deformation. Going further may cause fracture or failure.

5. Examples to Build Intuition

5.1. Hanging a Weight from a Wire

When a weight is attached to a wire, the wire becomes slightly longer. This elongation occurs because the internal stress in the wire balances the weight pulling downward.

5.2. Stepping on Soft Ground

Soft ground sinks more under a sharp heel compared to a flat shoe. A sharp heel has a smaller contact area, producing larger stress on the ground.

5.3. Pushing a Stack of Cards

When you push the top card sideways, the layers beneath shift slightly. This is shear stress in action, where layers slide relative to one another.