A column carries load two ways at once — straight down as axial force, and sideways as bending, from the beams framing into it and from any sway. Which of those you have to worry about depends almost entirely on one number: how slender the column is.
Step 1 — Effective height, and the slenderness test
The effective height le is the clear height times a factor β that describes how well the ends are held. A column held in position and direction at both ends bends into a shorter wave than one free to sway, so it behaves as if it were shorter.
le/h = 2250 / 225 = 10.0
Braced: short if le/h < 15
Unbraced: short if le/h < 10
10.0 < 15 -> this column is short
Braced means something else — a lift core, shear walls, a stiff staircase — resists the horizontal load, so the column only has to stand up. Unbraced means the columns and beams are the lateral system, and sway is theirs to carry. Get this wrong and every number after it is wrong.
Step 2 — Choose the equation
A short column with no significant moment can be designed from one line. BS 8110 gives two, and the difference is what the beams around it are doing:
nominal eccentricity only
eq 39 N = 0.35 fcu Ac + 0.67 Asc fy
approximately symmetrical beams, spans within 15%
Equation 39 is the more conservative of the two because it admits a little unbalanced moment from the beams. Neither applies once a column carries real moment — from wind, from a badly unbalanced span, or from being on the edge of the frame. Both equations assume there is none.
Choosing between them is not a matter of taste, and it is worth twice the steel. Equation 39 applies when beams frame in from both sides, are designed for uniformly distributed load, and their spans differ by no more than 15%. That describes the interior column of any regular grid — which is to say, most of the columns in most buildings. Equation 38 is for a column that is genuinely only carrying load down: a column under a single centred beam, or one taking a wall or a slab reaction with no unbalanced beam either side.
Step 3 — Worked example
The ground-floor interior column from the load takedown: N = 589 kN, say 590 kN. Section 225 × 225, fcu 25, fy 460, storey height 3.0 m, braced. The grid there is 4 m square with beams both ways, so the spans are equal and equation 39 governs.
Concrete alone 0.35 x 25 x 50 625 = 443 kN < 590 kN, so steel is needed
Asc = (590 000 - 442 969) / (0.67 x 460 - 0.35 x 25)
= 147 031 / 299.45 = 491 mm²
Asc,min = 0.4% x 50 625 = 203 mm²
Provide 4T16 = 804 mm² (1.59%, within 0.4% to 6%)
Check N = 0.35(25)(50 625 - 804) + 0.67(804)(460)
= 436 + 248 = 684 kN >= 590 kN PASS
Under equation 38 the same column would need only 243 mm² and 4T12 would do. That is the size of the difference the load case makes, and it is why the equation is chosen from the frame around the column rather than from whichever gives the friendlier answer.
6T12 (679 mm²) also clears 491, and is what a tool minimising steel area will offer — about 4 kg lighter per storey. A square column is conventionally detailed with four bars or eight, one in each corner and one at each mid-face, so 4T16 is the answer most steel fixers would expect to see.
Links
Links hold the main bars against buckling outwards, so their spacing is tied to the bar they restrain, not to the shear: 12 × the smallest longitudinal bar. Here 12 × 16 = 192 mm, so T8 links at 175 c/c. Their diameter must be at least a quarter of the main bar, and never less than 6 mm.
When the column is slender
A slender column deflects sideways under its own axial load, and that deflection multiplied by the load is an extra moment the section has to carry. BS 8110 handles it by adding a Madd to the applied moment, worked out from the slenderness ratio and the section depth, and then designing for the total.
Being slender is not a failure — it is a different route through the design. What it does mean is that equations 38 and 39 are off the table: you need the section's moment–axial interaction, whether from a design chart or from strain compatibility.
The corner column trap
A corner column is the end column of a frame in both directions, so it can be bent about both axes at once. BS 8110 cl 3.8.4.5 handles that by folding the smaller moment into the larger through a factor β, and designing for an enhanced uniaxial moment.
The trap is which plane to enhance. It is the one with the larger M/d — enhance the other and you understate the demand, because β is never greater than 1. And the fold-in has to happen before the steel is sized, not after, or the section is chosen for the un-enhanced moment.
Run a column, or the whole grid
Structura routes short columns through equations 38 and 39, and slender ones through Madd with the section's capacity solved by strain compatibility rather than read off a chart. It states the classification as a line on the sheet, never as a check — being slender is a decision about method, not a failure.
Single columns are free. A whole column grid — every column grouped by the tributary it actually carries, which on a regular grid is the familiar corner, edge and interior families — is a project.
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