Flexural buckling
Determine the buckling curve, imperfection factor, and reduction factor χ about both principal axes to EN 1993-1-1 §6.3.1.
EN 1990EN 1993-1-1
Design a steel column to Eurocode 3
Describe the column height, boundary conditions, section, steel grade, axial force, and end moments. Mia checks flexural buckling about both axes and the combined compression-bending interaction, then explains the governing result.
Worked exampleDesign verified: weak-axis buckling interaction governs
HEB 200 · 4.00 m · NEd 700 kN + MEd 40 kNm
Key results
- Flexural buckling resistance Nb,z,Rd
- 1168 kN
- Bending resistance Mc,Rd
- 151.0 kNm
- Interaction, eq. 6.62
- η = 0.78
- Governing utilisation
- η = 0.78 (6.62, z-axis)
Transparent stepsStandards-basedDocument as PDF
Worked example
HEB 200 · 4.00 m · NEd 700 kN + MEd 40 kNm
- System
- Pinned–pinned column
- Section
- HEB 200 · S235
- Height
- 4.00 m
- Axial force
- NEd = 700 kN
- End moments
- M1 = M2 = 40 kNm (single curvature)
Design a braced HEB 200 steel column in S235, height 4.0 m, pinned at both ends, with NEd = 700 kN and equal end moments M1 = M2 = 40 kNm about the major axis (single curvature), the member restrained against lateral-torsional buckling, to EN 1993-1-1 (EN-recommended values). Check the cross-section resistance, flexural buckling about both axes, and the compression-bending interaction.
Calculate the example with MiaKey results
- Flexural buckling resistance Nb,z,Rd
- 1168 kN
- Bending resistance Mc,Rd
- 151.0 kNm
- Interaction, eq. 6.62
- η = 0.78
- Governing utilisation
- η = 0.78 (6.62, z-axis)
All values are deterministic for the stated inputs. EN-recommended partial factors (γM0 = γM1 = 1.00); buckling curve b about y-y and c about z-z (h/b = 1.0 ≤ 1.2); Annex B, Table B.1 interaction factors for a member not susceptible to torsional deformation.
- — χLT = 1.0: the member is confirmed restrained against lateral-torsional buckling.
- — Cross-section class 1 in both pure compression and bending; the c/t ratios are well inside the class-1 limits.
- — Equal end moments (ψ = 1, single curvature) give Cmy = 1.0.
Required inputs
- Column height and boundary conditions per axis
- Cross-section and steel grade
- Design axial force NEd
- End moments M1 and M2 (or zero for pure compression)
- Confirmation of lateral-torsional restraint and the National Annex
What you receive
- Governing check and utilisation
- Flexural buckling resistance about both principal axes
- Lateral-torsional buckling resistance when the column is not restrained
- Combined compression-bending interaction (EN 1993-1-1, 6.61/6.62)
- Assumptions and normative references
Reviewed calculation example
Prepare your calculation
Configure your column
System sketch
m
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kN
kNm
kNm
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Yes
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Inputs completeReady to calculate
What this skill checks
Lateral-torsional buckling
For an unrestrained column, compute the elastic critical moment M_cr and the reduction factor χ_LT to EN 1993-1-1 §6.3.2 and fold it into the interaction check.
Combined compression and bending
Check the N+M interaction of §6.3.3 using the Annex B interaction factors, for both a restrained and an unrestrained member.
Cross-section resistance
Classify the section and verify the compression and bending resistance before the member stability checks.
Frequently asked questions
Which inputs does Mia need for the design?
At minimum, the column height, boundary conditions, section, steel grade, axial force, and end moments (or zero for pure compression). Mia asks targeted questions when a governing input is missing.
Does the check cover lateral-torsional buckling?
Yes. When the member is not restrained, Mia computes the elastic critical moment and the reduction factor χLT to EN 1993-1-1 §6.3.2 and includes it in the compression-bending interaction. A restrained member skips this calculation (χLT = 1.0).
Which buckling curve is used?
Mia selects the curve from EN 1993-1-1 Table 6.2 based on the section's h/b ratio and flange thickness, and always states the curve it used.
Can I document the calculation?
CALC presents inputs, assumptions, checks, the governing utilisation, and normative references in a structured answer that can be exported as a PDF.
Standards & references
EN 1990EN 1993-1-1
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