The Chartership Forum

Reinforced Concrete Design / Reinforced-concrete slabs

One-way and two-way action

Why a slab chooses a direction, and why the choice is decided by the fourth power of the span ratio.

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.

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.
  • Verify plate-action, corner-restraint and maximum-moment spacing provisions. Crossing strips are a teaching approximation, not a certified conservative slab analysis.

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

Everyone learns that a slab is one-way if it is more than about twice as long as it is wide. Almost nobody is told where the rule comes from — and it comes from one line of algebra that also tells you exactly how wrong the idealisation is at any other ratio. Once you have that line, the rule stops being arbitrary and becomes something you can reason with.

By the end of this lesson you should be able to

  • Derive the load-share relation from compatible deflections
  • Explain the fourth-power dependence
  • Justify the 2:1 rule quantitatively
  • Say why secondary reinforcement is required even in a one-way slab

What you should already know

  • Deflection of a uniformly loaded beam (Structural Analysis Fundamentals, Module 13)
  • Flexural design (Module 4)

From first principles

How a two-way slab divides its load

We want to show: To find what fraction of a uniformly distributed load a slab sends in each direction, using only compatibility and a standard deflection formula.

Imagine cutting two strips out of the slab: one running the short way, one the long way, crossing at the centre. The slab is one piece of concrete, so at the point where the strips cross they must deflect by the same amount. They cannot separate. Each strip carries whatever share of the load it needs to reach that common deflection. A short strip is stiff, so it takes a large share; a long strip is flexible, so it takes little. The whole result follows from making those two deflections equal.

Worked example

A two-way floor slab

Given

  • Panel 5.0 m × 7.0 m, simply supported on all four edges
  • 200 mm thick, C30/37, 25 mm cover, H12 bars
  • Finishes 1.5 kN/m², imposed load 3.0 kN/m²

Find

The moments in each direction and the reinforcement.

Assumptions

  • Simply supported, corner restraint neglected — conservative for the span moments
  • Partial factors 1.35 and 1.5 — nationally determined, requiring verification

    Practice

    A slab panel is 4.0 m × 6.0 m. What fraction of a uniform load is carried by the SHORT span? Give the answer as a decimal fraction.

    Practice

    For a panel with a span ratio of exactly 2.0, what fraction goes the short way? Give the decimal fraction.

    Check yourself

    Why does load share depend on the FOURTH power of the span ratio rather than the square?

    Summary

    • Equal deflection at the crossing point gives ws Ls⁴ = wl Ll⁴
    • So the share is r⁴/(1 + r⁴), and it moves very fast with r
    • 1:1 → 50%, 1.5:1 → 83.5%, 2:1 → 94.1%
    • The crossing-strip approximation helps explain the 2:1 convention; actual slab behaviour depends on supports and plate action
    • The model neglects plate torsion and transverse distribution; establish its suitability before using its moments for design
    • Corner reinforcement exists precisely because of the torsion this model ignores
    • Secondary reinforcement supports distribution and crack control; check transverse strength where required by the load and support arrangement