What are the BS 8110 basic span/depth ratios?

For rectangular sections: 7 for a cantilever, 20 for a simply supported member and 26 for a continuous one. These are then multiplied by a modification factor for the tension reinforcement, and where present by a further factor for compression reinforcement, to give the allowable ratio of span to effective depth.

Why does adding a little depth help deflection so much?

Because it works on three terms at once. Extra depth increases the effective depth, which reduces the actual span/depth ratio directly. It also reduces the moment per unit of bd squared, which raises the modification factor. And it reduces the steel needed, which lowers the service stress and raises the modification factor again. Ten millimetres on a slab commonly moves the check by fifteen per cent or more.

Can you fix a deflection failure by adding more steel?

Only a little, and it is usually poor value. Adding tension steel beyond what bending requires lowers the service stress and so raises the modification factor, but the return diminishes quickly and the factor is capped at 2.0. Adding compression steel helps too, up to a factor of 1.5. Depth is nearly always the cheaper answer, because it improves three terms at once while steel improves one.

Which span is used for a two-way slab?

The shorter span. A two-way slab spans predominantly the short way, and the check is made on that span using the effective depth of the steel in that direction — which is the outer layer, and so slightly deeper than the other.

Span/depth ratios and deflection control

Ask a student what sizes a slab and they say bending. Ask an engineer and they say deflection. Both are looking at the same building.

For every ordinary floor slab and most beams in a residential building, the strength calculation is satisfied comfortably and the member is then made deeper — sometimes much deeper — to keep it stiff enough. That is why this check is worth understanding rather than just performing: it is the one that costs the concrete.

Why a ratio, and not a deflection

The real requirement is a deflection limit — commonly span/250 overall, and span/500 or 20 mm after finishes are applied, so that partitions do not crack and doors still shut. Calculating that properly means creep, shrinkage, the sequence of construction and how cracked the section is by the time the load arrives. It is possible, and it is rarely worth it.

So BS 8110 offers a deemed-to-satisfy route: keep the span-to-effective-depth ratio below a limit and the deflection limits are taken as met. Everything below is that route.

Check span / d <= basic ratio x MF(tension) x MF(compression)

Deemed-to-satisfy is not the same as satisfied. Where deflection really matters — a long span over a brittle finish, a slab supporting a masonry partition, a cantilever balcony people will notice moving — the ratio is a starting point and an actual deflection calculation is the answer.

The basic ratios

Support condition	Rectangular	Flanged, b_w/b ≤ 0.3
Cantilever	7	5.6
Simply supported	20	16.0
Continuous	26	20.8

The flanged column is the rectangular one times 0.8. Between b_w/b of 0.3 and 1.0, interpolate linearly between 0.8 and 1.0.

Two adjustments sit alongside these:

Spans over 10 m, other than cantilevers, where deflection has to be limited to avoid damaging finishes: multiply by 10/span.
Stair flights get 15% more, provided the flight occupies at least 60% of the span. See the staircase example, where that allowance is the difference between a workable waist and a silly one.

The cantilever ratio of 7 assumes the support does not rotate. A cantilever off a slender edge beam, or off a slab that is itself flexible, deflects far more than the ratio implies — the tip moves because the root turned, and no amount of depth in the cantilever fixes that. Balconies are where this shows up.

Modification factor for tension steel

This is where most of the movement is. The idea is simple: a member whose steel is working hard is more cracked and therefore less stiff. So the factor rewards low service stress and low moment intensity.

MF = 0.55 + (477 - fs) / (120 (0.9 + M/bd2)) <= 2.0

fs = 2/3 x fy x (As,required / As,provided) x 1/Bb

Two inputs, and both are worth reading:

f_s is the estimated service stress in the steel. The 2/3 converts from ultimate to service; the As,req/As,prov ratio is the reward for rounding up to the next bar arrangement. With fy = 460 and steel exactly matched to requirement, f_s = 307 N/mm².
M/bd² is the moment intensity, in N/mm², at midspan for a continuous member or at the support for a cantilever. Use the design moment after any redistribution.

Tabulated, for fy = 460

M/bd²	f_s = 150	200	250	307 fully stressed
0.50	2.00	2.00	1.90	1.56
0.75	2.00	1.95	1.70	1.41
1.00	1.98	1.77	1.55	1.30
1.50	1.69	1.51	1.34	1.14
2.00	1.49	1.35	1.20	1.04
3.00	1.25	1.14	1.04	0.91
4.00	1.11	1.02	0.94	0.84
6.00	0.95	0.89	0.82	0.76

Capped at 2.00. Values from the formula above; use it rather than the table when you are near a limit.

Read the right-hand column and the bottom row. A lightly stressed slab gets a factor of 2.0 — its allowable ratio doubles. A heavily loaded beam with fully stressed steel gets 0.76, which cuts the allowable ratio by a quarter. The factor spans a range of nearly three to one, so it is not a correction. It is the calculation.

Modification factor for compression steel

Steel in the compression face resists creep, so it earns a second factor — but a much smaller one:

MF = 1 + (100 As'prov / bd) / (3 + 100 As'prov / bd) <= 1.5

100 A_s'/bd	0.25	0.50	1.00	1.50	2.00	3.00
Factor	1.08	1.14	1.25	1.33	1.40	1.50

Note it uses the steel provided, not required — so the hanger bars a beam has anyway to carry its links count, as long as they are properly enclosed by those links.

Worked: the slab that fails at 150 and passes at 160

A one-way slab, continuous, 4.2 m span, grade 25, 25 mm cover, T12 bars.

Try 150 mm

d = 150 - 25 - 6 = 119 mm
n = 12.2 kN/m2 (includes 3.60 self weight)
M = nL2/10 = 12.2 x 4.2^2 / 10 = 21.5 kNm/m
As = 446 mm2/m -> T12 @ 250 = 452 mm2/m

M/bd2 = 21.5e6 / (1000 x 119^2) = 1.52
fs = 2/3 x 460 x 446/452 = 303 N/mm2
MF = 0.55 + (477-303)/(120 x 2.42) = 1.15

Allowable 26 x 1.15 = 29.9
Actual 4200 / 119 = 35.3
Check 35.3 > 29.9 FAIL by 18%

Try 160 mm

d = 160 - 25 - 6 = 129 mm
n = 12.5 kN/m2 (self weight up to 3.84)
M = 12.5 x 4.2^2 / 10 = 22.1 kNm/m
As = 417 mm2/m -> T12 @ 250 = 452 mm2/m

M/bd2 = 22.1e6 / (1000 x 129^2) = 1.33
fs = 2/3 x 460 x 417/452 = 283 N/mm2
MF = 0.55 + (477-283)/(120 x 2.23) = 1.28

Allowable 26 x 1.28 = 33.2
Actual 4200 / 129 = 32.6
Check 32.6 <= 33.2 PASS

Ten millimetres — under 7% more concrete — closed a gap of 18%. That is the compounding this page exists to explain, and it works on three terms at once:

d rose 8.4%, so the actual ratio fell;
M/bd² fell from 1.52 to 1.33, raising the factor;
less steel was needed against the same bars provided, so f_s fell from 303 to 283, raising it again.

Meanwhile the load only rose 2%, because the self weight of 10 mm of concrete is small. Depth is very nearly free in this trade, and that is the whole reason it is always the answer.

Worth noticing: the same T12 @ 250 serves both slabs. The 150 mm one did not fail for want of steel — it had plenty. It failed for want of stiffness, and those are different problems with different fixes.

When it fails, in order of what to try

More depth. Improves three terms and costs almost no load. Round to a buildable figure — slabs in 25 mm steps, beams in 50.
Continuity. Going from simply supported to continuous raises the basic ratio from 20 to 26 — a 30% gain for a detailing decision. It is usually free if the member is genuinely continuous and you are willing to detail the top steel over the supports.
A shorter span. An extra beam line halves the slab span and the check improves faster than linearly. Often cheaper than it looks, and it is the answer nobody considers because the grid is treated as fixed.
More tension steel than bending needs. Lowers f_s. Real, but diminishing and capped at 2.0 — you are paying for steel to buy stiffness, which is a poor exchange rate. Reasonable for closing a 2% gap, not a 20% one.
Compression steel. Up to 1.5, and it may already be there in a beam.

What not to do: raise the concrete grade. It does not appear anywhere in this check. Stiffness goes with the elastic modulus and the section, and E rises only weakly with strength — so grade 30 instead of 25 buys strength you did not need and essentially no stiffness.

Details that catch people

Use the effective span, not the clear span — clear span plus effective depth, or centre to centre of supports, whichever is less.
Two-way slabs use the shorter span, with the effective depth of the steel spanning that way. That is the outer layer, so it is the deeper one — use it, it is worth 12 mm.
Take M/bd² at midspan for simply supported and continuous members, and at the support for a cantilever.
b for a flanged beam is the effective flange width in the ratio b_w/b, but M/bd² uses the web width b_w. Mixing them up is a large error.
Cover eats depth. Going from 25 to 40 mm cover for exposure costs 15 mm of d — more than the 10 mm that rescued the slab above. Settle cover before checking deflection, not after. See cover, grades and mixes.
Deflection is checked once, on the final section. If you change depth, the load changes, the moment changes, the steel changes and f_s changes. Iterate the whole thing rather than patching one term.

Run it yourself

Every Structura member that needs a deflection check does it this way, and shows the modification factor with the numbers that produced it — so when a slab fails you can see whether it was f_s, M/bd² or the basic ratio that did it, and therefore what to change. Single members are free to run, as many as you like.

Open Structura in your browser

On Android, get it on Google Play; on iPhone and iPad, get it on the App Store — same account as the browser.