Stress: The Intuition
Imagine holding a heavy book in your palm. Your hand feels a push — a force distributed over the area where the book rests. Now imagine balancing that same book on the tip of your finger. The force is the same (the book's weight), but the area is tiny. The sensation is completely different — it hurts. That difference is stress.
Stress is not just force. It is force spread over an area. The same force concentrated on a small area produces a large stress; spread over a large area, it produces a small stress. This is why a sharp knife cuts easily (small area, large stress) while a blunt knife does not (larger area, smaller stress).
In everyday language, we say "pressure" for fluids and "stress" for solids. In physics and engineering, stress is the internal resistance a material offers when an external force tries to deform it.
The Precise Definition
Stress (σ) is defined as the internal restoring force per unit area that develops inside a body when an external deforming force is applied.
Mathematically:
σ=AF
where:
- F is the magnitude of the force applied perpendicular to the cross-section (in newtons, N)
- A is the cross-sectional area over which the force acts (in square metres, m²)
- σ is the stress (in pascals, Pa, or N/m²)
Stress is a tensor quantity (it has magnitude, direction, and orientation of the plane it acts on), but for introductory problems you treat it as a scalar magnitude. The SI unit is the pascal (Pa): 1 Pa=1 N/m2.
Types of Stress
Stress is classified by how the force is applied relative to the surface:
| Type | Force direction | Example |
|---|
| Tensile stress | Pulling, perpendicular outward | Stretching a rubber band |
| Compressive stress | Pushing, perpendicular inward | Standing on a concrete pillar |
| Shear stress | Parallel to the surface | Scissors cutting paper |
Tensile/Compressive stress: σ=AF (force perpendicular to area)
Shear stress: τ=AF (force parallel to area)
Worked Examples
Example 1: A steel wire of diameter 2 mm supports a load of 100 N. Find the tensile stress.
Area of cross-section: A=πr2=π(1×10−3)2=3.14×10−6 m2 …