Module 12 · Lesson 12.3
Steel and concrete composite beams
Making a slab and a beam act as one member, and what it is worth.
Why this matters
A concrete slab usually sits directly on a steel beam. Left alone the two slide over each other and each carries its own share of the load. Connect them so they cannot slide, and they act as a single deep section — with the concrete doing what concrete is good at, and the steel doing what steel is good at. The gain is large enough that composite construction is the default for steel-framed floors.
By the end of this lesson you should be able to
- Explain what shear connectors do and why they are essential
- Build the transformed section of a composite beam
- Locate the elastic neutral axis and calculate stresses in both materials
- Quantify what composite action is worth compared with the bare steel beam
What you should already know
- Strain compatibility and the transformed section (this module)
- Modular ratio (this module)
- Shear flow q = VQ/I (Module 10)
Put a slab on a beam with nothing joining them and load it. Both bend to the same curvature, but each has its own neutral axis. The bottom of the slab stretches while the top of the beam shortens, so the two surfaces slide relative to one another. Each member carries its own share of the moment, in proportion to its own EI.
Now weld shear connectors — headed studs, typically — to the top flange and cast them into the slab. They prevent that sliding. The two parts now have a single neutral axis through the combined section, and the whole depth from the top of the slab to the bottom of the beam is working as one.
The lever arm has increased dramatically, and so has the second moment of area. Typically a composite beam is two to three times stiffer than the bare steel section, and the stress in the steel drops by a third or more.
The connectors carry the horizontal shear flow at the interface, q = VQ/I, where Q is the first moment of the transformed slab about the composite neutral axis. That flow is what they exist to resist, and it is greatest near the supports where V is greatest — which is why studs are spaced more closely there.
Predict first
What is the primary job of the shear connectors in a composite beam?
Worked example
A composite floor beam
Given
- Steel beam: area 9500 mm², depth 450 mm, I = 3.30 × 10⁸ mm⁴
- Concrete slab: 1500 mm effective width × 120 mm thick, sitting directly on the top flange
- Esteel = 205 000 N/mm², Econcrete = 30 000 N/mm²
- Applied moment M = 600 kNm
Find
The transformed section, the neutral axis, the stresses, and the benefit over the bare beam.
Practice
A composite beam has Esteel = 205 000 N/mm² and Econcrete = 30 000 N/mm². A slab 1500 mm wide is transformed into equivalent steel. What is the transformed width, in mm?
Practice
The transformed composite section has I = 9.29 × 10⁸ mm⁴ with the neutral axis 434 mm above the bottom of the steel. Under a moment of 600 kNm, what is the steel stress at the bottom fibre, in N/mm²?
Practice
The bare steel beam alone has I = 3.30 × 10⁸ mm⁴ and a depth of 450 mm. Under the same 600 kNm, what stress would it carry on its own, in N/mm²?
Summary
- Without shear connection, slab and beam each have their own neutral axis and slide at the interface
- Connectors prevent the slip, giving one neutral axis through the whole depth
- Transform the concrete into equivalent steel by dividing its width by n = Es/Ec
- Divide the resulting stress by n in whichever material was transformed
- Composite action typically triples the stiffness and cuts the steel stress by about a third
- Connectors carry the interface shear flow q = VQ/I, so they are closest together near the supports
- The elastic analysis assumes full interaction; real slip, cracking and creep all modify it
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