Reinforced Concrete Design / Reinforced-concrete beams

Sizing, and the order of the checks

Why the first guess matters, and why the design is circular until you break the circle deliberately.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Corrections checked in this pass

Recalculated the beam with a 650 mm depth, provided-bar neutral axis, shear links, span/depth and crack checks.

Checks needed for project use

A concrete-design reviewer must check the stated first-generation clauses, National Annex choices, detailing rules and factor sets. Numerical agreement alone does not establish code compliance.
Actual support geometry, anchorage availability, top reinforcement, exposure and fire requirements need project-specific checking.

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

Why this matters

Every design equation so far has needed the effective depth d. But d depends on the bar diameter, which depends on the steel area, which comes from the bending calculation, which needs d. Start with a trial size and bar arrangement, then revise the calculation until the chosen reinforcement, effective depth and checks are consistent.

By the end of this lesson you should be able to

Make a defensible first estimate of beam size
State the order in which the checks are carried out, and why
Explain the circular dependency and how it is broken
Recognise when the first guess was wrong enough to need redoing

What you should already know

Flexural design (Module 4)
Shear design (Module 5)
Span/depth ratios (Module 6)

The first guess

Before any calculation, choose a depth. The span/depth ratio is the tool, and the numbers to carry in your head are:

Simply supported beam: span/depth ≈ 15
End span of a continuous beam: ≈ 18 to 20
Interior span: ≈ 20 to 22
Cantilever: ≈ 6

These are overall depth, not effective depth, and they are deliberately crude. A 7.5 m simply supported beam therefore wants about 500 mm — round up to 600 mm if the loading is heavy, which for a beam carrying a floor it usually is.

Width is chosen separately, and rarely by calculation. It is set by the columns it frames into, by the wall it sits in, or by the need to fit the bars in one layer. A useful default is between one third and one half of the depth.

The first guess is not a calculation, and it does not need defending as one. It needs to be close enough that the design does not have to start again.

The sequence, and why it is that order

1.Size the member. Span/depth, as above.
2.Establish the actions. Now the self-weight is known, because the size is.
3.Analyse. Moments and shears, with the load patterns from Module 3.
4.Bending design. K, then K_lim, then the lever arm, then A_s.
5.Choose bars. And check they fit — this is where d becomes real.
6.Revise d after selecting bars. Repeat the affected checks until the design and detail agree.
7.Shear design. Links, then spacing against both limits.
8.Curtailment and anchorage. Where bars stop, and how far past that they run.
9.Serviceability. Span/depth and crack control.
10.Detail. Draw it, and check it can be built.

Step 6 is the one people skip. Steps 1 to 5 assumed a bar diameter; step 5 chose one. If the assumption was H20 and the answer is H32, d has fallen by 6 mm and the whole bending calculation shifts slightly. Usually that is negligible. Occasionally — a shallow member, two layers of bars — it is not.

Check yourself

A 9 m simply supported beam is sized at 600 mm deep from the span/depth rule of thumb. What is the most likely outcome?

Summary

First guess from span/depth: 15 simply supported, 18–22 continuous, 6 cantilever
Width is usually set by the columns or the bars, not by calculation
Start with a trial arrangement and repeat the affected checks until the detail and calculation agree
Check span/depth at step 1 as well as step 9, so deflection holds no surprises
On spans over about 7 m, serviceability commonly governs