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Queensferry

Module 4 · Lesson 4.4

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.

Why this matters

Two situations depart from the plain singly reinforced rectangle, and both are common. A section forced to carry more than Klim needs compression reinforcement — added for ductility rather than strength, which surprises people. And almost every beam cast with a slab is really a T-beam, which is nearly always easier to design, not harder.

By the end of this lesson you should be able to

  • Explain why compression steel is added above Klim
  • Split a doubly reinforced section into two contributions
  • Recognise why the concrete displaced by compression bars must be deducted
  • Analyse a flanged section and check where the stress block ends

What you should already know

  • Designing a singly reinforced section (this module)
  • The derivation of MRd (this module)

When K exceeds Klim, the section cannot carry the moment with tension steel alone without pushing the neutral axis past its ductility limit. There are three responses, and only one of them is usually available:

  1. 1.Make the section deeper. Almost always the best answer — depth is powerful and cheap. Often ruled out by floor-to-floor height.
  2. 2.Use stronger concrete. Raises Klim a little. Rarely decisive on its own.
  3. 3.Add compression reinforcement. Steel in the compression zone takes part of the compression, so the concrete block does not have to be as deep, so the neutral axis stays up where ductility requires.

The calculation splits into two parts that superpose:

  • The concrete carries its limiting moment, Mlim = Klim b d² fck, with the neutral axis exactly at its limit.
  • The excess MEd − Mlim is carried by a couple between the compression steel and an equal additional tension steel.

There is one trap in the second part, and it is easy to miss. The compression bars sit inside concrete the stress block has already counted. Only their stress in excess of the concrete's is a net gain:

net compression from the bars = Asc (σsc − η fcd)

Omit that deduction and you overstate the compression, so the section ends up with x/d slightly above the limit it was designed to respect — a quiet failure of the very ductility check that motivated the compression steel.

Predict first

Why is compression reinforcement usually added to a beam?

Worked example

A section that needs compression reinforcement

Given

  • Design moment MEd = 560 kNm — the section cannot be made deeper
  • Section 300 mm wide, effective depth 540 mm, C30/37, fyk = 500 N/mm²
  • Compression bars at 50 mm from the compression face

Find

The tension and compression reinforcement required.

    Flanged sections are the other common departure, and they are good news.

    A beam cast monolithically with a slab acts with part of that slab as a compression flange. In sagging, the compression zone is at the top, which is exactly where the flange is. So the compression zone is very wide, which means:

    • the stress block is very shallow;
    • the neutral axis is high, so x/d is small;
    • the lever arm is close to d;
    • the section is comfortably ductile and usually needs no compression steel.

    The design procedure is almost the same as for a rectangle, with one check:

    1. 1.Analyse as a rectangle of the flange width, bf.
    2. 2.Check whether the resulting stress-block depth s exceeds the flange thickness hf.
    3. 3.If s ≤ hf, the compression zone is entirely within the flange, and the wide rectangle answer is exact. This is the usual outcome.
    4. 4.If s > hf, the block extends into the narrower web, and the compression must be split into a flange part and a web part.

    In hogging — over a support of a continuous beam — the compression zone is at the bottom, in the narrow web, and the flange is in tension where it is cracked and useless. So a T-beam over a support is designed as a rectangle of the web width, and that is where continuous beams are usually most heavily reinforced.

    Worked example

    A T-beam in sagging

    Given

    • T-beam: flange 1200 mm wide × 150 mm thick, web 250 mm wide
    • Effective depth 440 mm, C30/37, tension steel 1470 mm² of fyk = 500 N/mm²

    Find

    The moment of resistance, and whether the flange really is doing the work.

      Practice

      A T-beam has a 1200 mm wide flange and carries a tension force of 639 kN. With η fcd = 17.0 N/mm², what stress-block depth is required, in mm?

      Practice

      For that T-beam with d = 440 mm and s = 31.3 mm, what is the moment of resistance, in kNm?

      Practice

      Compression bars sit at 50 mm from the face, with the neutral axis at 243 mm and an ultimate concrete strain of 0.0035. What is the strain in the compression bars?

      Summary

      • Above Klim the choices are: deeper section, stronger concrete, or compression steel
      • Compression steel is added for ductility; the strength gain is a by-product
      • Split the analysis: concrete carries Mlim, a steel couple carries the excess
      • Deduct the concrete displaced by the compression bars, or x/d breaches its limit
      • Always check that the compression bars have actually yielded
      • A T-beam in sagging is usually a wide rectangle — but check s against hf
      • In hogging the flange is in tension: design as a rectangle of the web width
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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