# Column Buckling Calculator

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

- Page: https://jianzhujisuan.com/en/column-buckling
- Category: Steel Design (https://jianzhujisuan.com/en/c/steel-design)
- Chinese version: https://jianzhujisuan.com/zh/column-buckling.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Section area A 7810 mm², Minor axis second moment I 56960000 mm⁴, Yield strength fy 235 MPa, Column length L 4000 mm, End restraint Pinned-pinned K=1.0, Buckling curve Curve c (α=0.49, welded I)): **Buckling resistance 1548.4 kN**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Section area A | number | 7810 | mm² |  |
| Minor axis second moment I | number | 56960000 | mm⁴ |  |
| Yield strength fy | number | 235 | MPa |  |
| Column length L | number | 4000 | mm |  |
| End restraint | select | Pinned-pinned K=1.0 | — |  |
| Buckling curve | select | Curve c (α=0.49, welded I) | — |  |

## Formula

- **Effective length**: Lcr = K·L
- **Slenderness**: λ = Lcr/r, r = √(I/A)
- **Reference slenderness**: λ1 = 93.9·√(235/fy)
- **Reduction factor**: Φ = 0.5[1+α(λ̄−0.2)+λ̄²], χ = 1/(Φ+√(Φ²−λ̄²)) ≤ 1
- **Resistance**: Nb,Rd = χ·A·fy/γM1
- **Euler load**: Pcr = π²EI/Lcr²

## Worked example

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.

## Questions

### 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.

## Related tools

- [Steel Beam Span Calculator](https://jianzhujisuan.com/en/steel-beam-span): The depth is not looked up in a table — it falls out of the deflection limit.
- [Section Properties Calculator](https://jianzhujisuan.com/en/section-modulus): Inertia governs deflection, section modulus governs strength — they are not interchangeable.
- [Fillet Weld Strength Calculator](https://jianzhujisuan.com/en/fillet-weld): A 6 mm leg is not a 6 mm throat — capacity follows the 4.2 mm throat.
- [Base Plate Design Calculator](https://jianzhujisuan.com/en/base-plate): Thicker is not the answer — check the bearing area first, then the cantilever.

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