Learn · worked example

Slab on grade design to SANS 51992-1-1

A surface bed rests on the ground everywhere, so it does not span like a suspended slab. A heavy point load (a rack leg, a forklift wheel) makes it crack in a pattern of yield lines: radial cracks under the load and a circle on top around it. The collapse load of that pattern, with the ground pushing back, is the design capacity. Uniform loads in aisles, punching under the load, and the joint layout are checked too. Every number below comes from the free STATIX slab on grade calculator with the inputs in step 1.

1. The problem

Input	Value
Design code	SANS 51992-1-1 (SA Eurocode, 2023 draft annex)
Thickness h	150 mm
Concrete fck	25 MPa
Mesh top SANS 1024 ref	193
k subgrade modulus	40000 kN/m³
Allowable bearing qa, for thickenings	100 kPa
Point load Q, e.g. a rack leg	25 kN
Contact size square side	100 mm
Where	Interior and at edges (not corners)
Uniform load Q, storage	10 kPa
Top cover	40 mm
Exposure class	XC1
Cement SANS 51992 cover	CEM I, II-A, II-B-S, SRPC
Design life	50 years

2. The slab and the ground

The ground is modelled as springs of stiffness k (modulus of subgrade reaction). The radius of relative stiffness l tells how far a load spreads: a stiffer slab or softer ground spreads it further.

h = 150 mm, k = 40,000 kN/m³, E_cm = 31,476 MPa radius of relative stiffness l = 692.9 mm flexural tensile strength f_ctd,fl = 1.736 MPa moment capacity: plain 6.51, with mesh: sagging 6.51 / hogging 8.23 kNm/m

3. Point loads: the yield-line collapse load

Under a concentrated load the slab first cracks radially on its underside, then a circular crack forms on top. The load that forms this mechanism, with the ground reaction, is the collapse load. An edge or corner load has fewer yield lines, so it carries less. The factored point load must not exceed it.

Point load, interior (yield-line collapse load): [Meyerhof (1962) yield-line theory on an elastic subgrade; SANS 51992-1-1 3.1.8(1) eq.(3.23), Table 3.1; SANS 10160-1 STR] P_Ed = STR 1,2 G + 1,6 Q (all imposed) -> 40 kN on 100 x 100 mm (a = 56.4 mm); l = 692.9 mm, a/l = 0.081; M_un = f_ctd,fl h^2/6 = 1.74 x 150^2 / 6 = 6.51 kNm/m (f_ctd,fl = 0,7 f_ctm 2.56 x (1,6 - h/1000) / 1,5); M_n (top) 8.23 (mesh ref 193: A_s f_yk / 1,15 x 0,95 d 106.5), M_p (bottom) 6.51 (plain); P_u = 135.7 kN 40.0 ≤ 135.7 kN OK Point load, edge (yield-line collapse load): [Meyerhof (1962) yield-line theory on an elastic subgrade; SANS 51992-1-1 3.1.8(1) eq.(3.23), Table 3.1; SANS 10160-1 STR] P_Ed = STR 1,2 G + 1,6 Q (all imposed) -> 40 kN on 100 x 100 mm (a = 56.4 mm) (no load transfer across the edge or joint); l = 692.9 mm, a/l = 0.081; M_un = f_ctd,fl h^2/6 = 1.74 x 150^2 / 6 = 6.51 kNm/m (f_ctd,fl = 0,7 f_ctm 2.56 x (1,6 - h/1000) / 1,5); M_n (top) 8.23 (mesh ref 193: A_s f_yk / 1,15 x 0,95 d 106.5), M_p (bottom) 6.51 (plain); P_u = 60.7 kN 40.0 ≤ 60.7 kN OK

4. Punching under the point load

A small loaded area on a thin slab can also punch through. The shear stress at the face of the loaded area and on a perimeter away from it is checked, with the ground pressure inside the perimeter helping.

Punching under the point load, interior: [SANS 51992-1-1 6.4.3, 6.4.4(1), 6.4.5(3) (SA annex 0,5 nu f_cd)] V_Ed = 40 kN; d = h - c - phi/2 = 106.5 mm; u_0 = 400 mm: v = 0.94 <= v_Rd,max 4.5 MPa; u_1 (2d) = 1738.3 mm: v = 0.22 <= v_Rd,c 0.49 MPa (rho_l 0.181 %, v_min 0.495); beta 1,0, the soil inside u_1 ignored 0.22 ≤ 0.49 MPa OK Punching under the point load, edge: [SANS 51992-1-1 6.4.3, 6.4.4(1), 6.4.5(3) (SA annex 0,5 nu f_cd)] V_Ed = 40 kN; d = h - c - phi/2 = 106.5 mm; u_0 = 300 mm: v = 1.25 <= v_Rd,max 4.5 MPa; u_1 (2d) = 969.1 mm: v = 0.39 <= v_Rd,c 0.49 MPa (rho_l 0.181 %, v_min 0.495); beta 1,0, the soil inside u_1 ignored 0.39 ≤ 0.49 MPa OK

5. Uniform load and aisles

A uniform load over the whole slab bends nothing: the ground carries it directly. The worst case is a loaded strip next to an empty aisle, which bends the slab like a beam on an elastic foundation. The worst aisle width gives the moment that the cracking moment of the slab must resist.

[Hetenyi (1946) beam on elastic foundation; SANS 51992-1-1 3.1.8(1); SANS 10160-1 STR] q_Ed = 16 kPa; w_allow = 5,95 lambda^2 M_un = 5,95 x (1.031 /m)^2 x 6.51 = 41.2 kPa; lambda = (3k / (E_cm h^3))^0,25, the plain moment (no cracking on top) 16.0 ≤ 41.2 kPa OK

6. Joints

Shrinkage makes a long slab crack anyway; sawn joints decide where. Bays are kept small (a limit on length relative to the depth) and nearly square.

[practice: sawn joints at most the smaller of 25 h and 6 m; bays not longer than 1,5 x their width] 6 x 4 bays; joint lines at x = 3.33, 6.67, 10, 13.33, 16.67 m, y = 3, 6, 9 m; aspect 1.11; the mesh is cut at sawn joints (no dowels designed here) 3,330.0 ≤ 3,750.0 mm OK

7. Other checks

Wall line loads, thickenings, cover and anything else the design adds.

Durability: nominal cover: [SANS 51992-1-1 4.4.1; SANS 51992-1-1-1 NA 6.6.1, Table 2] XC1 (CEM I, II-A, II-B-S or SRPC, 50 years), C25/30: c_min,dur 15 mm (the C20/25 cell; specify its w/c and cement content from the table); c_min,b 7 -> c_min 15 + delta c_dev 10 = c_nom 25 mm (cement not given: CEM I, II-A, II-B-S or SRPC assumed); given 40 mm 25.0 ≤ 40.0 mm OK

Yield-line capacities rely on the slab cracking in a ductile way; the mesh gives that ductility. The calc sheet shows every formula.

Run this example yourselfOpen the free STATIX slab on grade calculator and press Load the example (150 mm bed, 25 kN rack leg) under "How it is calculated". Change any value and every step updates, with a calc sheet.
Open the slab on grade calculator

A worked example for learning, not a design. Check every value against the current code and your own project, and have the design checked and signed by a registered professional engineer.

Early access

Be first to use STATIX 3D and STATIX 2D.

Leave your email and we will tell you when each part is ready for testing. One confirmation now, one message then. A short monthly update only if you tick the box.