Module 8 · Lesson 8.1

Sizing, and the order of the checks

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

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. The circle is real, and the way out of it is a deliberate first guess followed by one revision — not iteration to convergence, and not pretending the circle is not there.

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 if the guess was poor. One revision, not a loop.
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
The design is circular; break it with a guess and one revision, not a loop
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

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This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint