Course · lesson 7 of 7

Slabs on grade

How a ground-bearing slab is designed with the STATIX slab on grade calculator: the subgrade, racking and vehicle loads, the slab as a plate on springs with yield-line collapse loads, punching under a post, uniform storage, and joints. SANS 10100-1 has no ground-slab method, so the page works to SANS 51992-1-1 or EN 1992-1-1.

1. Learning outcomes

After this lesson you can:

describe the subgrade by its modulus k and find the radius of relative stiffness;
check rack legs, wheels and posts at the interior, an edge and a corner;
check punching under a post and uniform storage with aisles;
choose plain or mesh, and set out sawn joints;
say what the page leaves to the designer.

2. Before you start

Foundations 1 (soils and bearing) and lesson 1 (punching).
The slab on grade calculator.
A pocket calculator and about 50 minutes.

3. The slab and the ground

A slab on grade. A warehouse or factory floor sits on a compacted sub-base over the natural subgrade and carries racking, stored goods and vehicles directly to the ground. SANS 10100-1 has no method for it, so the calculator takes its materials and resistances from SANS 51992-1-1 (the SA Eurocode, 2023 draft annex) or EN 1992-1-1, with published theory for the slab on the soil.

The subgrade as springs. The ground is modelled as a bed of independent springs (Winkler), stiffness k per unit area per unit settlement. A good sub-base raises the k the slab sees; the page takes one k, so the sub-base is in it, not modelled separately.

The radius of relative stiffness. How far a load spreads depends on the slab’s stiffness against the ground’s: l. A thicker slab or softer ground gives a larger l, and the load is shared by a wider area of slab.

4. Loads and capacities

Point loads by yield lines. Under a heavy point load the slab cracks radially underneath and then in a ring on top before it fails. The page uses Meyerhof’s (1962) yield-line collapse loads for an interior, edge and corner load, with the moment capacities M_p (bottom) and M_n (top); it does not use Westergaard’s elastic stresses.

Where the load stands. A load at an edge or at a sawn joint has only half a slab around it; at a corner, where two joints cross, less still. The page treats every joint as a free edge, which is conservative: keep heavy legs off joint crossings, or design dowels.

Uniform loads. Bulk storage with aisles between can crack the top of the slab in the unloaded aisle, because the loaded areas either side bend it upwards there. The page takes the worst aisle width by beam-on-springs theory (Hetenyi) with the plain-concrete moment.

Loads. Racking legs and posts are point loads on their base plates; a forklift or truck wheel is a point load on its contact area; bulk storage is a uniform load; a wall built on the slab is a line load, with a thickened strip under it if needed. The page factors point loads as imposed loads.

Punching under a post. A concentrated load can also punch through. The page checks the face of the base plate and a perimeter at 2d (SANS 51992-1-1 6.4); without top mesh there is no tension steel, so v_Rd,c falls back to v_min.

5. Materials and joints

Plain, mesh or fibre. The page designs plain slabs and slabs with a SANS 1024 mesh near the top, the bottom or both; the mesh adds moment capacity once the slab has cracked and helps punching. Steel-fibre concrete is not offered: its design needs the fibre supplier’s residual strengths.

Joints, shrinkage and curling. Concrete shrinks as it dries and the top dries first, so a slab both shortens and curls up at its edges. Sawn contraction joints decide where it cracks: the page sets them at the smaller of 25h and 6 m (practice), lays out the bays and counts the mesh sheets. Curling and dowels are not calculated.

What the page covers. This lesson uses the SANS 51992-1-1 route (SANS 10160-1 load factors). Settlement of the ground, flatness for very narrow aisles and dowelled joints are the designer’s to add.