EngiMetric
Civil & Structural Design guide Understand a concept

Why a column fails long before the steel reaches its yield strength

Euler and Johnson behaviour, the slenderness ratio, and recognising the member that will buckle rather than crush.

The engineering question

A column is carrying far less than its material strength suggests. What is it actually failing by, and how do you check which mode governs?

Worked example

The figures below were produced by running the Column Buckling Calculator with the same inputs — during the build, from its authoritative engine.

Results
Critical load 1733 kN
Slenderness ratio 30.8571 –
Radius of gyration 129.6299 mm
Euler critical load 10573 kN
Johnson critical load 1733 kN
Governing formula Johnson short-column
Assessment Effective length 4 m, slenderness 30.9 — Johnson short-column; critical load 1733 kN. Apply the code safety factor (typically 1.67–2.0).
  1. Radius of gyration is √(I/A); slenderness is the effective length divided by it.
  2. Euler applies to long columns, Johnson to short ones, and the crossover slenderness is √(2π²E/Fy).
  3. The lower of the two predictions is the one to report.

Sanity check

A stocky column fails by crushing near its yield load; a slender one fails by buckling far below it. If both give the same answer, check the slenderness.

Tools for this problem

These are the EngiMetric calculators that compute the numbers in this topic. Each one shows its formula, its units and its limits rather than returning a bare result.

Engineering review required

This topic supports professional engineering work; it does not replace a sealed design. The result depends on site data, the governing standard and engineering judgement, and should be confirmed by a competent engineer before it is built.

References & standards

  • EN 1993-1-1 — buckling resistance of compression members
  • AISC 360 — column buckling and effective length

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