Steel columns carry vertical compression down through a building frame and deliver the load to the foundations. The design work looks simple at first, because a column is a straight member, but the checks behind it cover material strength, section shape, end restraints, and stability. This article follows the procedure in Eurocode 3, EN 1993-1-1, from section classification through to buckling resistance. A column is never designed in isolation, and the wider process of beam design, column buckling, connections and composite construction is covered in the structural steel design guide on this site.
How Steel Columns Fail
Before any formula is applied, it is useful to know what the checks are protecting against. Steel columns fail in one of two ways: by crushing of the material or by member buckling. The two failures look different and are governed by different properties, so each is checked separately in the code.
| Failure Mode | Cause | Governed By |
|---|---|---|
| Crushing of material | Section reaches its compressive capacity | Cross-section area, yield strength |
| Local buckling | Slender plates in the flange or web | Width-to-thickness ratios |
| Overall buckling | Instability of the whole member | Length, end restraints, stiffness |
Crushing Failure
Crushing means the material reaches its capacity and fails because the section cannot carry the applied load. This happens when the compressive strength of the steel or the cross-sectional area is inadequate for the load. The check is a direct capacity comparison, and for stocky columns it usually governs.
Overall and Local Buckling
Buckling is a stability failure in two forms. Local buckling depends on the sectional properties, specifically the slenderness of the flange and web plates. Overall buckling depends on the column as a whole, influenced by the column length, the restraints at each end (unrestrained, partially restrained, or fully restrained), and the sectional properties such as area and shape.
Restraints at the Column Ends
End restraints change the effective length of the column and therefore its buckling load. A fully restrained end resists rotation and raises the critical load; an unrestrained end behaves like a pin and lowers it. The same column section can carry very different loads depending on how it is connected into the frame, which is why the principles of steel framing and connection design matter to the column designer.
Section Classification
The first step in the design procedure is to classify the section according to its dimensions and material properties. Classification is covered in Clause 5.5.2 of EN 1993-1-1, and it sorts sections into four classes based on slenderness limits. Classes 1, 2, and 3 are non-slender sections, while Class 4 sections are slender.
For a rolled H section, the classification limits come from Table 5.2 of the code. The limits are expressed as ratios of element width to thickness, and they are scaled by the factor epsilon, where ε = √(235/fy).
| Ratio | Class 1 | Class 2 | Class 3 |
|---|---|---|---|
| Compression flange of rolled section, cf/tf | 9ε | 10ε | 14ε |
| Web of rolled section, cw/tw | 33ε | 38ε | 42ε |
The class determines which resistance formula applies later in the design. A small change in flange thickness or steel grade can move a section from a simple plastic check to an effective-area calculation, so classification is worth repeating whenever the section changes.
What Each Class Means
The class tells the designer how the section will behave before it yields:
- Class 1 sections can form a plastic hinge with full rotation capacity
- Class 2 sections reach their plastic resistance but have limited rotation capacity
- Class 3 sections reach yield before local buckling but cannot develop a plastic hinge
- Class 4 sections buckle locally before yield and must use effective properties
The Value of Epsilon
Epsilon adjusts the limits for the grade of steel. For S235 steel, ε equals 1.0 and the limits are used directly. For S355 steel, ε = √(235/355) = 0.814, so a Class 1 flange limit of 9ε becomes 9 × 0.814 = 7.3. Higher strength steel demands tighter width-to-thickness limits because thinner plates buckle earlier relative to their yield stress.
Classification is only one step in a complete design. The column must also sit on a foundation that spreads the load, and the column footing design process covers how base reactions are transferred into the soil.
Cross-Section Resistance
The plastic resistance of the cross-section, Nc,Rd, is the first capacity value calculated. For non-slender sections in Classes 1, 2, and 3 it is Nc,Rd = A fy / γM0. For slender Class 4 sections the effective area replaces the gross area: Nc,Rd = Aeff fy / γM0. The gross area A is taken per Clause 6.2.2.1, and the effective area Aeff per Clause 6.2.2.5.
A worked example fixes the idea. Take an HEA 200 column in S355 steel. The gross area is 53.8 cm², fy is 355 N/mm², and γM0 is 1.0. The plastic resistance is 5380 × 355 / 1.0 = 1910 kN. The design action NEd must satisfy the capacity check NEd / Nc,Rd ≤ 1.0.
Effective Area for Slender Sections
Class 4 sections lose part of their plate to local buckling before the full yield stress is reached. The effective area Aeff removes the ineffective strips from the flange and web, and the calculation is iterative because the effective width depends on the stress distribution. Cold-formed sections are almost always Class 4, and the design and assembly of cold-formed steel framing follows the same effective-width logic with thin plate elements.
The Partial Factor γM0
γM0 is the partial factor for cross-section resistance, normally 1.0 under the UK National Annex. Some national annexes adopt different values, so the designer must check the annex applicable to the project before the resistance values are finalised.
Buckling Resistance
Most columns are governed by buckling rather than crushing, so the second major check is the buckling resistance Nb,Rd. For non-slender sections: Nb,Rd = χ A fy / γM1. For Class 4 sections: Nb,Rd = χ Aeff fy / γM1.
The symbol χ is the reduction factor for buckling, and it is read from the buckling curves or calculated from the non-dimensional slenderness λ̄ = √(A fy / Ncr), where Ncr is the elastic critical load of the column, usually the Euler load π²EI/L² for flexural buckling.
| Buckling curve | a0 | a | b | c | d |
|---|---|---|---|---|---|
| Imperfection factor α | 0.13 | 0.21 | 0.34 | 0.49 | 0.76 |
The Reduction Factor χ
The reduction factor is calculated from χ = 1 / (Φ + √(Φ² − λ̄²)), where Φ = 0.5 [1 + α(λ̄ − 0.2) + λ̄²]. The imperfection factor α comes from Table 6.1 of the code, and the buckling curve is selected from the section type, the axis of buckling, and the flange thickness. Rolled I-sections with h/b ≤ 1.2 and tf ≤ 100 mm use curve b about the major axis and curve c about the minor axis.
Non-Dimensional Slenderness
Slenderness λ̄ relates the squash load of the column to its elastic critical load. A short, stocky column has λ̄ below 0.2 and hardly buckles, so χ approaches 1.0. A long, slender column has high λ̄ and a χ well below 1.0, and the buckling check governs the design.
The restraints available at each level depend on how the column is tied into the floor and facade, and the architectural design and building envelope process sets the geometry and grid that the structural engineer works within.
Worked Design Sequence
The full procedure for an axially loaded column runs in a fixed order:
- Determine the design action NEd from the load combinations
- Select a trial section
- Classify the section using the Table 5.2 limits
- Calculate Nc,Rd and check NEd / Nc,Rd ≤ 1.0
- Determine the effective length from the end restraints
- Calculate Ncr and the non-dimensional slenderness λ̄
- Select the buckling curve and the imperfection factor α from Table 6.1
- Calculate the reduction factor χ
- Calculate Nb,Rd and check NEd / Nb,Rd ≤ 1.0
- Repeat with a larger or smaller section until the utilisation is acceptable
Numbers for a Typical Column
A 3.5 m HEA 200 column in S355 with pinned ends shows the magnitude of the numbers. With Iy = 3692 cm⁴ and E = 210,000 N/mm², the Euler load is π²EI/L² = 6246 kN. The non-dimensional slenderness is λ̄ = √(5380 × 355 / 6,246,000) = 0.55. From curve b, α = 0.34, which gives Φ = 0.713 and χ = 0.86. The buckling resistance is 0.86 × 5380 × 355 / 1.0 = 1643 kN, about 14 percent below the squash load of 1910 kN.
Both utilisation ratios stay below 1.0, so the column accepts a design action up to about 1643 kN. Beyond that, the options are a deeper section, a higher steel grade, or intermediate restraints that shorten the effective length.
What the Numbers Show
The worked numbers demonstrate the two checks. The section carries 1910 kN in pure compression, but once stability is considered the allowable load drops to 1643 kN. For comparison, reinforced concrete columns follow a different slenderness treatment, and the guide to reinforced concrete design covers flexural analysis, shear, torsion, column design and slenderness effects for concrete members.
Final Checks and Practical Notes
The axial checks are the core of column design, but real columns also carry bending from connecting elements. Beam reactions, eccentric loads, and moments from rigid connections all add bending stress, and the code requires an interaction check for combined axial load and bending in Clause 6.3.3. The full treatment of compression members, flexural design, connections and tension members for building frames is in the steel structure design guide, which carries the same logic through every element of the frame.
Combined Axial Load and Bending
When moments are present, the section is checked for the interaction of NEd, MEd, and the member buckling resistances. The utilisation from the axial check and the bending checks are combined with factors that account for the shape of the moment diagram and the amplification from second-order effects. Columns in unbraced frames are almost always governed by this combined check.
Detailing and Site Considerations
A few practical points close out the design:
- Holes for fasteners at the column ends are ignored when A and Aeff are determined
- Base plates and holding-down bolts must transfer the design force into the foundation
- Fire protection and corrosion protection are specified separately from strength
- Erection sequence and temporary restraints are checked before the frame is made stable
Fastener Holes at Column Ends
The code is explicit that holes for fasteners at the column ends need not be taken into account when determining the area A or the effective area Aeff. The allowance is small, and the rule keeps the design simple for the typical case of a column bolted to a base plate or spliced at a floor.