One-way and two-way slab design

Which way it spans, and why deflection usually decides the thickness

One-way or two-way?

Take the panel's longer side ly and its shorter side lx, and look at the ratio:

ly / lx <= 2 the panel spans two ways
ly / lx > 2 the panel spans one way, across the short span

The reason is physical, not arbitrary. A long thin panel is so much stiffer across its short direction that almost all the load goes that way, and the long-span steel becomes nominal. Once the sides are within a factor of two, both directions carry a real share and ignoring one wastes steel in the other.

A one-way slab is designed as a 1 m wide strip of beam. A two-way slab uses the moment coefficients in BS 8110 Table 3.14, chosen for the panel's edge conditions — how many sides are continuous, and how many are simply supported or free.

Worked example: one-way slab, 3.5 m span

Simply supported, residential, carrying the loads worked out in the load takedown. Concrete fcu 25, steel fy 460, cover 20 mm, T12 bars.

First try: 150 mm slab

Gk = 0.15 x 24 + 1.2 + 1.0 = 5.80 kN/m²
n = 1.4(5.80) + 1.6(1.5) = 10.52 kN/m²
M = nL²/8 = 10.52 x 3.5² / 8 = 16.11 kNm/m
d = 150 - 20 cover - 12/2 = 124 mm

K = M / (b d² fcu) = 16.11 x 10&sup6; / (1000 x 124² x 25) = 0.042
z = d[0.5 + sqrt(0.25 - K/0.9)] = 117.8 mm
As = M / (0.87 fy z) = 342 mm²/m -> T12 @ 300 (377 mm²/m)

Deflection span/d = 3500 / 124 = 28.2
allowable = 20 x 1.40 = 28.0
28.2 > 28.0 FAIL

Look at what failed. The bending was never in doubt — K = 0.042 against a limit of 0.156, so the section has three times the moment capacity it needs. What it does not have is stiffness.

Second try: 160 mm slab

Gk = 0.16 x 24 + 1.2 + 1.0 = 6.04 kN/m²
n = 1.4(6.04) + 1.6(1.5) = 10.86 kN/m²
M = 10.86 x 3.5² / 8 = 16.62 kNm/m
d = 160 - 20 - 6 = 134 mm

K = 16.62 x 10&sup6; / (1000 x 134² x 25) = 0.037
z = 0.95d = 127.3 mm (the formula gives more, so the cap applies)
As = 16.62 x 10&sup6; / (0.87 x 460 x 127.3) = 326 mm²/m
Provide T12 @ 300 c/c = 377 mm²/m
As,min = 0.13% bh = 0.0013 x 1000 x 160 = 208 mm²/m  OK

Deflection span/d = 3500 / 134 = 26.1
allowable = 20 x 1.52 = 30.3
26.1 <= 30.3 PASS

Ten millimetres of extra thickness bought 4.2 on the span/depth ratio: the depth helped twice, once by raising d and again by lowering the steel stress that sets the modification factor.

Why the deflection check is the one that bites

BS 8110 controls deflection indirectly, through a limit on span/depth rather than by calculating a deflection. You start from a basic ratio — 7 for a cantilever, 20 simply supported, 26 continuous — and multiply it by a modification factor that rewards you for providing more steel than you strictly need:

fs = (2/3) fy x As,req / As,prov
MF = 0.55 + (477 - fs) / [120 (0.9 + M/bd²)]   <= 2.0

That is why slabs are almost never governed by bending. Spans are long relative to the depth, so stiffness runs out long before strength does. If you are ever tempted to trim a slab to the steel it needs, this is the check that stops you.

The rest of the checks

Run it, and check the sheet

Structura designs one-way and two-way solid slabs, with the Table 3.14 coefficients picked from the edge conditions you describe. It shows the same lines you see above, including the modification factor and both deflection numbers — so when it fails, you can see it was stiffness rather than strength.

Slabs are free to run, as many as you like.

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