Stress and Strain

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand that deformation is caused by tensile or compressive forces (forces and deformations will be assumed to be in one dimension only)
  2. Understand and use the terms load, extension, compression and limit of proportionality
  3. Recall and use Hooke's law
  4. Recall and use the formula for the spring constant k = F/x
  5. Define and use the terms stress, strain and the Young modulus
  6. Describe an experiment to determine the Young modulus of a metal in the form of a wire

1. Deformation and Forces

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What is Deformation?

Deformation means changing the shape or size of an object. When you apply a force to an object, you can make it longer, shorter, or change its shape in other ways.

In this course, we only look at one-dimensional deformation – this means we only consider forces and changes in length along one straight line (either stretching or squashing).

Types of Forces that Cause Deformation

There are two main types of forces that cause deformation:

1. Tensile Forces (Tension)

  • These are forces that pull on an object
  • They act in opposite directions, pulling away from the object
  • They make the object longer (stretch it)
  • Example: Hanging a weight from a spring pulls it downward, while the support pulls it upward

2. Compressive Forces (Compression)

  • These are forces that push on an object
  • They act in opposite directions, pushing toward the object
  • They make the object shorter (squash it)
  • Example: Placing a heavy book on top of a foam block pushes it down, while the table pushes it up

Important: In both cases, you need two forces acting in opposite directions to cause deformation. A single force would just make the object move, not change its shape.

2. Load, Extension, Compression, and Limit of Proportionality

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Load

Load is simply another word for the force applied to an object. When we hang weights on a spring, the weight is the load. Load is measured in newtons (N).

Extension

Extension is how much longer an object becomes when a tensile force is applied.

Formula:

Extension=Final length−Original length\text{Extension} = \text{Final length} - \text{Original length}

x=lf−lix = l_f - l_i

Where:

  • x = extension (measured in metres, m)
  • l_f = final length (m)
  • l_i = original (initial) length (m)

Example: A spring has an original length of 10 cm. When you hang a weight on it, it stretches to 14 cm.

  • Extension = 14 cm - 10 cm = 4 cm = 0.04 m

Compression

Compression is how much shorter an object becomes when a compressive force is applied.

Formula:

Compression=Original length−Final length\text{Compression} = \text{Original length} - \text{Final length}

This is just the opposite of extension. If an object gets shorter, we can treat compression as a negative extension.

Limit of Proportionality

When you gradually increase the force on a spring or wire, at first the extension increases steadily. But if you keep adding more and more force, eventually something changes – the extension starts increasing more rapidly for each added bit of force.

The limit of proportionality is the point where this change happens. It's the maximum force you can apply while the force and extension remain directly proportional (meaning they increase at the same rate).

Key Point: Below the limit of proportionality, if you double the force, you double the extension. Above it, this simple relationship no longer works.

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