Structural Analysis Fundamentals / Composite beams

Steel and concrete composite beams

Making a slab and a beam act as one member, and what it is worth.

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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.

Checks needed for project use

An independent structural reviewer must check remaining derivations, diagrams, sign conventions and the interactive models across their full input ranges.
Independent review of diagrams, idealisations and full interactive input ranges remains required.

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.

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Why this matters

A steel beam and concrete slab can act together when a designed connection transfers longitudinal shear. The full-interaction elastic model shows the resulting stiffness and stress distribution. Actual design also considers construction sequence, effective slab width, connector behaviour, cracking and time-dependent effects.

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)

If two elastic members remain in vertical contact but can slip freely along their interface, a simplified model gives each its own neutral axis. A designed shear connection transfers longitudinal force and develops composite action.

The full-interaction model assumes no slip and uses a common strain distribution. Its elastic interface demand follows q = VQ/I using transformed section properties. Connector strength, slip capacity and detailing require their own assessment; design rules may permit distributions that do not simply follow the local elastic shear diagram.

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
E_steel = 205 000 N/mm², E_concrete = 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 E_steel = 205 000 N/mm² and E_concrete = 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 = E_s/E_c
With n = E_s/E_c, divide equivalent-steel stress by n for concrete; multiply equivalent-concrete stress by n for steel
The worked example gives about 2.8 times the stiffness and a 31% reduction in bottom steel stress
Elastic interface shear demand is q = VQ/I; connector distribution must follow the chosen design method and detailing rules
The elastic analysis assumes full interaction; real slip, cracking and creep all modify it