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Column Buckling Calculator

§ Code basis: EN 1993-1-1 (Europe / Commonwealth) — The design equations differ, so the values are not interchangeable - recalculate with your own code.

Half the effective length means four times the Euler load — but the design resistance differs by less, and how much depends on slenderness.

Also known as buckling load · euler buckling · slenderness ratio

Quick answer

With the default inputs: Section area A 7810 mm² · Minor axis second moment I 56960000 mm⁴ · Yield strength fy 235 MPa etc.Buckling resistance 1548.4 kN

Use your own dimensions ↓

Inputs

mm²
mm⁴
MPa

Result

Buckling resistance
1548.4kN
Effective length Lcr4000mm
Radius of gyration r85.4mm
Slenderness λ46.8
Reference slenderness λ193.9
Relative slenderness λ̄0.499
Reduction factor χ0.844
Euler critical load Pcr7379kN
Squash load Npl1835kN
Buckling resistance Nb,Rd1548kN
Strength used84%
How this is worked out

A column rarely fails by crushing; it fails by buckling, and almost every steel compression member is stability-governed. Slenderness Lcr/r is the dividing line: below 40 the member is stocky and reaches 95% of yield on curve a, 88% on curve c; above 120 it is slender with a reduction factor around 0.4 on curve c, so only four tenths of the strength is available. The easy thing to under-estimate is effective length — pinned at both ends K = 1.0 against fixed-fixed K = 0.5 is a factor of four in the Euler load, since it enters squared. The design resistance Nb,Rd is not four times anything: at a slenderness of 46.8 here, changing K from 1.0 to 0.5 lifts chi from 0.844 to 0.975, only 16% more capacity. Only genuinely slender columns approach the factor of four, because there Nb falls roughly as 1/lambda_bar squared — so "fixed ends halve the steel" is a long-column statement. Real fixity is hard to achieve (bolted connections slip, base plates rotate), which is why codes rarely let you use 0.5 and 0.7 to 0.8 is normal. The Euler load is theoretical: no initial imperfection, no residual stress, no load eccentricity, so it is always higher than reality — here 7379 kN against a resistance of 1548 kN, a factor of 4.8. Treat Euler as the ceiling of elastic stability, never as capacity.

Next up: Steel Beam Span Calculator · Section Properties Calculator

Formula

Effective lengthLcr = K·L
Slendernessλ = Lcr/r, r = √(I/A)
Reference slendernessλ1 = 93.9·√(235/fy)
Reduction factorΦ = 0.5[1+α(λ̄−0.2)+λ̄²], χ = 1/(Φ+√(Φ²−λ̄²)) ≤ 1
ResistanceNb,Rd = χ·A·fy/γM1
Euler loadPcr = π²EI/Lcr²
HEB200 (A 7810 mm², I 5696 cm⁴) in S235, 4000 mm long, pinned-pinned, curve c: radius of gyration 85.4 mm, slenderness 46.8, relative slenderness 0.499, reduction factor 0.844, Euler load 7379 kN and 1548 kN buckling resistance.

Basis

The codes below are listed for comparison. This calculator returns EN 1993-1-1 values only.

FAQ

What is the difference between buckling and yielding?
Yielding is the material reaching its strength — stress hits fy and the member can still carry load as it goes plastic. Buckling is geometric instability: the member bows sideways and capacity drops off a cliff. Stocky columns (slenderness under 40) yield first, with warning; slender ones (over 120) buckle and collapse suddenly at well below the yield load. That is why compression members need a stability check and tension members do not.
What value of K should I use?
Theory gives 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned and 2.0 cantilever. In practice be conservative: true fixity needs a stiff base plate, a stiff foundation and no slip in the connection, so codes rarely allow 0.5 and 0.7 to 0.8 is normal for nominally fixed ends. Frame columns also depend on whether the frame is braced: 0.5 to 0.85 when braced, 1.2 to 2.0 when sway is unrestrained.
Why can't the Euler load be used as capacity?
Because Euler assumes a perfectly straight member with no initial bow, no residual stress and a perfectly centred load. Real members have all three, so capacity is much lower — 7379 kN against 1548 kN here. The EN reduction factor folds those imperfections in: curves a to c represent increasing severity, hot-rolled I sections on curve a and welded sections on b or c. Using Euler directly is unsafe; its only real job is judging whether slenderness is excessive.
What slenderness is too high?
Compression members are usually held below 150 and primary members below 120 in some codes; tension members to 250-350. Excessive slenderness is not really a strength problem — the member is too flexible: it distorts in handling, vibrates in service and has no reserve against accidental lateral load. In order of value for money: reduce the effective length with bracing, then increase the second moment by choosing a deeper section rather than a thicker wall.

What to calculate next

These jobs are done back to back on site — follow the steps to work through the whole sequence.

Steel: span to connectionStep 3 of 4

  1. 1Steel Beam Span Calculator
  2. 2Section Properties Calculator
  3. 3Column Buckling Calculator
  4. 4Fillet Weld Strength Calculator

Cite this page

Use this format in reports, method statements or coursework. The link is permanent.

Building Calculator. Column Buckling Calculator. 2026-10-25. https://jianzhujisuan.com/en/column-buckling

Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.