The Chartership Forum

Structural Analysis Fundamentals / module 9

Bending of beams

Why bending stretches one face and squashes the other, and what makes a good section.

What you will understand

  • Explain why bending produces tension on one face and compression on the other
  • Locate the neutral axis and say what happens there
  • Use the flexure formula to find bending stress
  • Explain what second moment of area and section modulus really mean
  • Say why an I-section is efficient and where simple bending theory stops

Lessons

  1. Why bending causes stress

    Curvature, the neutral axis, and the linear stress distribution.

  2. Deriving the bending formula

    Building σ = My/I from geometry, Hooke's law and equilibrium — not quoting it.

  3. Second moment of area and section modulus

    The flexure formula, and what makes one section better than another.

  4. Combined bending and axial load

    Adding two stress distributions, and the point where tension disappears.

  5. Plastic bending and the plastic hinge

    What a ductile section can still do after its extreme fibre has yielded.

  6. Unsymmetrical bending and principal axes

    Resolving bending about centroidal principal axes and locating the neutral axis.

Module summary
  • Bending stress varies linearly from zero at the neutral axis to a maximum at the extreme fibres
  • σ = My/I, or σmax = M/Z at the extreme fibre
  • I rewards material placed far from the neutral axis — depth matters enormously
  • Z = I/c packages the geometry into one number for checking stress
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 notes

Check your understanding

Practice

A beam section has Z = 5.0 × 10⁵ mm³ and carries a bending moment of 40 kN·m. What is the maximum bending stress?

Check yourself

A rectangular beam's depth is doubled, keeping the width the same. What happens to I?

Check yourself

Why does an I-section carry bending efficiently?