Reinforced Concrete Design / module 4
Flexural behaviour and section analysis
The central calculation of reinforced concrete, built from three principles and nothing else — and an honest account of which parts a code decides.
What you will understand
- Follow a section from zero load through cracking and yield to failure
- Derive the moment of resistance from strain compatibility and equilibrium
- Distinguish what is mechanics from what the stress block assumes
- Design tension reinforcement for a rectangular section, and check the bars fit
- Explain why compression reinforcement is added for ductility, not strength
- Analyse a flanged section, and know when it stops behaving as one
Lessons
How a section behaves, from zero load to failure
Four distinct states, and the one the design calculation actually describes.
Deriving the moment of resistance
Three principles, no formula quoted — and a clear account of which step the code decides.
Designing a section, and making the bars fit
Running the derivation backwards — and the step that turns a number into a buildable beam.
Compression steel and flanged sections
What to do when the section is working too hard, and why a T-beam is usually easier than it looks.
Module summary
- Three principles: material models, strain compatibility, equilibrium
- The neutral-axis depth is solved from C = T, never assumed
- M = Tz = Cz — the moment is a couple, and z is the internal lever arm
- Plane sections remaining plane is mechanics; the stress block is a chosen model
- x/d controls ductility: too much steel and the concrete crushes before yield
- Compression steel restores ductility above Klim, and only incidentally adds strength
- A flanged section in sagging is usually a wide rectangle — but check the block depth
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
A section has As = 1200 mm² with fyd = 434.8 N/mm², b = 250 mm and η fcd = 17.0 N/mm². What is the depth of the rectangular stress block, in mm?
Check yourself
In the flexural derivation, which step is pure mechanics rather than a code choice?
Practice
A beam has h = 600 mm, cover 35 mm, 10 mm links and 20 mm bars in one layer. What is the effective depth, in mm?
Check yourself
Why does design limit the neutral-axis depth ratio x/d?
Practice
For a T-beam with a 900 mm wide flange, a tension force of 500 kN and η fcd = 17.0 N/mm², what is the stress-block depth, in mm?