Two-way slabs

How a slab panel supported on four sides is designed to EN 1992-1-1 on the Eurocode 2 route of the STATIX slab design calculator: the plate method and twisting moments, corners, the two layers of steel, the minimum steel and bar spacing, span over depth and shear.

1. Learning outcomes

After this lesson you can:

explain how a two-way slab carries load, and how the edge conditions change it;
read the plate method’s moments, including the twisting moments at corners;
design both layers of bottom steel and the top steel at continuous edges;
apply the minimum steel and the spacing limits of 9.3.1.1;
check span over depth and shear for a slab.

2. Before you start

Lesson 1 (bending) and lesson 4 (span over depth).
The slab design calculator, set to Eurocode 2 (EN 1992-1-1).
A pocket calculator and about 50 minutes.
The same lesson on the SA code: RC Design 1, lesson 6 (SANS 10100-1).

What the slab page’s Eurocode 2 route uses: the elastic plate method (ν = 0.2) with the Wood–Armer design moments, corners held down; EN 1990 6.10 (1.35 and 1.5); the bending rules of lesson 1 (K′ 0.167, z with 1.134, α_cc 0.85, z ≤ 0.95d); A_s,min of 9.3.1.1(1) on the d of each layer; main-bar spacing ≤ min(2h, 250 mm) for every layer (9.3.1.1(3), the area of the largest moment); shear by 6.2.2 with v_min. On its Eurocode 2 route the span over depth check is EN 1992-1-1 7.4.2 (eq 7.16a/b, with K from the ends of the span checked); the SANS and BS routes keep the basic ratios 20, 24 and 28 with a steel-stress factor.

3. How a slab panel works

A two-way slab. A panel supported on all four sides carries its load in both directions. The short span works harder, so it gets more steel and the outer (lower) layer, with the larger effective depth.

Edge conditions. A continuous edge, over a beam or wall with a slab beyond, is restrained against rotation: it hogs and needs top steel. A simply supported edge only holds the slab up.

The plate method. EN 1992-1-1 has no moment coefficient tables; it allows any analysis that respects equilibrium (5.1). The calculator solves the elastic plate equation on a grid (checked against the classic Timoshenko results), so it gives the bending and twisting moments over the whole panel, for any edge conditions and loads.

Twisting moments. A plate twists as well as bends, especially near its corners. Bars run only in x and y, so the calculator folds the twisting moment into the design moments of the two layers by the Wood–Armer rules.

Corners. A simply supported slab tries to lift at its corners. The plate method assumes the corners are held down, which gives smaller mid-span moments; then the corners need top and bottom steel to carry the twisting moment (9.3.1.3). The calculator reports that corner steel.

4. Steel, spacing, deflection and shear

Effective depths. The two layers of bottom bars cannot both be at the bottom. The short-span bars go below, where the lever arm is largest; the long-span bars sit on them, one bar diameter higher.

Bending steel. Each layer is designed like a beam one metre wide. In a lightly loaded slab the minimum steel often governs, as it does in both examples of this lesson.

Bar spacing. The Eurocode limits the spacing of slab bars, more tightly in the areas of the largest moment (mid-span and over continuous edges). On its Eurocode route the calculator checks the main bars of every layer against the tighter rule, min(2h, 250).

Deflection by span/d. The Eurocode check is the one of lesson 4, with K for the slab’s support conditions and ρ = A_s,req/(b d) of the spanning steel. On its Eurocode 2 route the slab page checks span/d the same way, by eq 7.16a/b with K for the span’s ends; its ρ includes the minimum steel, so its limit can be a little lower than one worked on A_s,req alone.

Shear. A slab is wide and the shear per metre is small, so the concrete alone carries it. The calculator takes the edge shear as 0.5nl_x, or the plate’s own edge shear at a continuous edge if larger, and checks it against v_Rd,c with v_min.

Top steel at continuous edges. The hogging moment is largest at the edge and dies away into the panel. The calculator lays top strips along each continuous edge, extending about 0.3 of the span into the panel, with the bottom mats over the whole panel.