Structural Analysis Fundamentals / module 7
Stress and strain
From force to stress, from movement to strain, and the law that links them.
What you will understand
- Explain why stress matters more than force when comparing members
- Calculate direct stress, direct strain and axial extension
- Use Hooke's law and Young's modulus correctly
- Distinguish material stiffness, member stiffness and strength
- Say where simple stress theory stops being reliable
Lessons
Stress and strain
Why engineers divide by area, and what strain actually measures.
Hooke's law, stiffness and strength
The elastic relationship, and three ideas that are constantly confused.
Shear strain and the Poisson effect
The second kind of stress, and why stretching one way shrinks the others.
Pressure vessels and shared load paths
Membrane pressure stresses and compatible axial load sharing.
Module summary
- Stress is force per unit area; strain is change in length per unit length
- Hooke's law: σ = Eε, valid while the material stays elastic
- Extension δ = PL/AE — length and material matter, not just load and area
- Stiffness and strength are different properties and are often confused
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Practice
An aluminium bar (E = 70 000 N/mm²) is 2000 mm long with an area of 500 mm² and carries 35 kN in tension. How much does it stretch?
Check yourself
Which change would halve the extension of an axially loaded bar, all else equal?
Check yourself
What does a steeper line on a stress–strain graph mean?