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Two-way slab to SANS 10100-1

A 4,5 × 6,0 m panel simply supported on four edges: the plate moments and a hand check, bottom steel in both directions, the minimum steel, torsion steel at the corners, shear and deflection. The numbers come from the free STATIX two-way slab calculator.

1. The problem

Input	Value
Panel	4,5 × 6,0 m, simply supported on all four edges, corners held down
Thickness	200 mm, cover 25 mm
Loads	g_k = 6,5 kPa (self-weight 4,8 + finishes and services), q_k = 3,0 kPa
Materials	f_cu = 30 MPa, f_y = 450 MPa

n = 1,2 × 6,5 + 1,6 × 3,0 = 12,6 kN/m²

2. The moments: plate analysis

The calculator solves the panel as an elastic plate (Poisson's ratio 0,2) on a 29 × 22 grid, so it can also take openings, point loads and free edges. For this simple panel the classic Navier series gives the same answer and is a good hand check:

short span (4,5 m): m = 0,0683 n l_x² = 0,0683 × 12,6 × 4,5² = 17,4 kNm/m
long span (6,0 m): 11,3 kNm/m · twisting moment at the corners: 11,7 kNm/m

The long-span design moment includes the twisting moment where it adds (Wood–Armer): 12,4 kNm/m. The SANS 10100-1 coefficient table for a panel whose corners are not held down gives a higher short-span moment, because the corners are then free to lift.

3. Bottom steel (4.3.3.4.1)

The short-span bars go in the outer layer: d = 200 − 25 − 6 = 169 mm.

K = 17,4 × 10⁶ / (30 × 1 000 × 169²) = 0,020 ≤ 0,156
z = 169 (0,5 + √(0,25 − 0,020/0,9)) = 165 > 0,95 d ⇒ z = 160,6 mm
A_s = 17,4 × 10⁶ / (0,87 × 450 × 160,6) = 277 mm²/m → Y12 @ 400 = 283 mm²/m

Long span, inner layer, d = 158 mm: A_s,req = 211 mm²/m, less than the minimum 0,13 % × 1 000 × 200 = 260 mm²/m (table 23), so the minimum governs: Y10 @ 300 = 262 mm²/m.

4. Torsion steel at the corners (4.4.4.2.2)

Where the corners are held down and both edges are simply supported, top and bottom mats of 3/4 of the short-span steel are needed over l_x/5 = 0,9 m in each direction:

0,75 × 277 = 207 mm²/m → top Y10 @ 375 = 209 mm²/m both ways in each corner (the bottom mat is already there)

5. Shear and deflection

Shear: V = 12,6 × 4,5 / 2 = 28,4 kN/m; v = 28,4 / (1 000 × 158) = 0,18 MPa ≤ v_c = 0,40 MPa (44 %).
Deflection (4.4.6): L/d = 4 500 / 169 = 26,6 ≤ 20 × 1,56 = 31,3 on the short span (85 %).
Crack control (4.11.8.2.2): clear spacing 388 mm ≤ 507 mm allowed (77 %).

6. Result

Item	Value
Short span (outer layer)	M = 17,4 kNm/m, A_s 277 → Y12 @ 400 (283)
Long span (inner layer)	M = 12,4 kNm/m, minimum 260 → Y10 @ 300 (262)
Corners	top Y10 @ 375 both ways over 0,9 × 0,9 m
Shear	0,18 ≤ 0,40 MPa
Deflection	26,6 ≤ 31,3 (85 %)

Run this example yourselfThe free STATIX two-way slab calculator checks to SANS 10100-1 by default. Enter the inputs from step 1 and every number above appears, with each clause and a printable calc sheet.
Open the free two-way slab 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.

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