What size should a column be?

The capacities, the estimate, and the four things that override both

Everybody asks this question about storeys — what size for a two-storey, what size for a three-storey — and the honest answer is that storeys are only one of five things that decide it, and rarely the one that governs.

This page gives the arithmetic for the axial part, so you can size a trial section in a minute, and then spends the rest of its length on the four things that make the trial section wrong.

Estimating the load in one line

A load takedown is how you get the real number. For a first section, this is close enough:

N = 12 x (tributary area, m²) x (floor levels carried) kN, ultimate

4 x 4 m bays tributary = 16 m²
3 floors N = 12 x 16 x 3 = 576 kN

That 12 kN/m² per floor is not a guess. It is what the worked takedown on this site arrives at from first principles — 196 kN per storey on a 16 m² tributary, giving 589 kN over three storeys — for a 160 mm slab with ordinary finishes, partitions and residential imposed load. Heavier finishes, thicker slabs or a public building push it up.

Tributary area is half the span each way, not the bay. An interior column on 4 m bays takes 2 m in every direction: 4 × 4 = 16 m². An edge column takes half of that, and a corner column a quarter — which is exactly why corner columns are not sized by their load.

What each section can carry

For a short braced column with no significant moment, BS 8110 gives two one-line capacities. Equation 38 is for nominal eccentricity only; equation 39 is the lower figure, for a column supporting an approximately symmetrical arrangement of beams, because that case admits a little unbalanced moment.

eq 38 N = 0.4 fcu Ac + 0.75 Asc fy
eq 39 N = 0.35 fcu Ac + 0.67 Asc fy
SectionBarsSteel eq 38eq 39
225 × 2254T120.89% 658 kN578 kN
225 × 2254T161.59% 776 kN684 kN
230 × 2304T161.52% 798 kN704 kN
225 × 3004T161.19% 944 kN831 kN
225 × 4506T161.19% 1417 kN1247 kN
300 × 3004T201.40% 1321 kN1164 kN
300 × 4506T201.40% 1981 kN1746 kN

Ultimate axial capacity, fcu 25, fy 460, all within the 0.4% to 6% steel limits. Every one of these numbers assumes the column is short, braced, and carries no real moment. None of them is a design.

Concrete does most of the work. Going from 4T12 to 4T16 in a 225 square buys 118 kN; going from 225 square to 225 × 300 with the same bars buys 168 kN and costs nothing in steel — and under equation 39 the widening wins by more still, 147 kN against 106. If a column is short of capacity, widening it is usually cheaper and always less congested than adding bars.

Storey by storey, for the standard case

Interior column, 4 × 4 m bays, braced frame, grade 25, gravity load only:

Floor levels carriedN, ultimateSection that works
2394 kN225 × 225, 4T12
3590 kN225 × 225, 4T16
4787 kN225 × 300, 4T16
5984 kN300 × 300, 4T20

Taking the takedown's 196 kN per storey rather than the rounded 12 kN/m², so the three-storey row matches its 589 kN. Every section listed carries its load under both equation 38 and the more conservative equation 39.

Read the fourth and fifth rows with suspicion. Once a building has four or more suspended floors, wind is no longer something you can leave out, and a column sized on gravity alone is answering a question nobody asked. Those rows are the axial arithmetic, not a recommendation — see wind loads and stability and what this engine will not do.

Override 1 — moment, which is why corners are different

Equations 38 and 39 both assume the column carries no real bending. That assumption holds for an interior column of a regular braced frame and for almost nothing else:

When any of these apply, the one-line equations are gone and the section is designed from a moment–axial interaction. The practical consequence on a small building is blunt: corner columns commonly end up the same size as interior columns carrying three times the load, and shrinking them to match their axial load is one of the more reliable ways to crack a building.

Override 2 — slenderness

A column is short if it fails by crushing and slender if it fails by buckling. The test is the effective height over the section depth, and the limit depends on whether something else resists the horizontal load.

le = β lo β = 0.75 braced, 1.2 to 1.6 unbraced

Braced short if le/h < 15
Unbraced short if le/h < 10
Section depthBraced: short up toUnbraced: short up to
225 mm4.5 m clear1.7 m clear
300 mm6.0 m clear2.3 m clear
450 mm9.0 m clear3.5 m clear

Clear storey height, taking β = 0.75 braced and 1.3 unbraced.

Every unbraced column in an ordinary building is slender. There is no realistic storey height at which a 225 or even a 300 deep column in a sway frame is short. That is not a disaster — slender columns are designed all the time, with an additional moment Madd from the deflection — but it does mean the one-line capacity table above never applies to them, and a building with no shear walls, no core and no stiff staircase is an unbraced building whatever the drawing says.

Override 3 — fire

Fire resistance sets a minimum dimension, quite separately from anything structural. For a fully exposed column, BS 8110's tabulated minima are:

Fire resistanceMinimum column dimension
1 hour200 mm
1½ hours250 mm
2 hours300 mm
3 hours400 mm
4 hours450 mm

So a 225 square column is a one-hour column, and no amount of reinforcement changes that. If the occupancy needs an hour and a half, the minimum is 250 mm before the first load is counted. Columns with fewer exposed faces have lower minima, and the cover to the steel has to keep pace — see cover, grades and mixes.

What fire resistance a building actually needs comes from its occupancy and its regulations, not from a structural calculation. That is why Structura reports the fire section on every sheet and marks it to be confirmed: the engine knows the dimensions, and it does not know what the building is for.

Override 4 — whether the bars fit and the concrete gets in

A section that passes every check on paper still has to be built. Two dimensions decide that, and both are worst at the lap, not at mid-height, because every bar is doubled there:

225 square, 8T20, cover 25, T8 links
Centre to centre across the face = 225 - 2(25 + 8 + 10) = 139 mm
Between adjacent bars = 139 / 2 = 69.5 mm
Clear gap at mid-height = 69.5 - 20 = 49.5 mm
Clear gap through the lap = 69.5 - 40 = 29.5 mm no poker fits

The code's minimum clear spacing is the largest aggregate plus 5 mm, which 29.5 mm satisfies. The vibrator does not care about the code. Concrete that cannot be compacted around the steel is honeycombed concrete at the most heavily stressed section of the column, which is why heavily reinforced small columns are a worse idea than their arithmetic suggests.

Two more geometric rules worth applying before anything else:

So is a 225 square column enough?

For a bungalow, comfortably. For a two-storey house on ordinary bays, yes with margin. For a three-storey, the axial arithmetic passes with 4T16 — and every one of the following is a way for that answer to be wrong:

The reason "9 inches" persists is that it is right for the building most people are putting up, and the reason it is dangerous is that it stays in the drawing when the building changes. A section is an answer to a load, a height, a position in the frame and a fire requirement. Change any of the four and the answer changes with it.

Size it properly, in about a minute

Structura runs the whole thing: effective height and the short/slender test, equations 38 and 39 where they are valid, a moment–axial interaction where they are not, biaxial bending on corner columns, steel limits, link sizing and spacing, and the fire and robustness-tie sections that do not fall out of the structural arithmetic. Every line comes with its clause and a PASS or FAIL.

Single columns are free to run, as many as you like. The whole-building takedown and the per-column grid — which work out the tributary areas for you, column by column, from the plan — are the paid part.

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