Steel column with axial load and bending to SANS 10162-1
A 203 × 203 × 46 H-section in S355, 4 m long, carrying 600 kN and 40 kNm: the compression resistance, the bending resistance with lateral-torsional buckling, the amplification factor U1 and the three interaction checks. The numbers come from the free STATIX steel member calculator.
1. The problem
| Input | Value |
|---|---|
| Member | 203 × 203 × 46 H-section column, S355 (fy = 355 MPa), 4,0 m, braced, K = 1,0 both axes |
| Section | A = 5 870 mm², Ix = 45,7 × 106 mm4, ry = 51,4 mm, Sx = 450 × 103 mm³; class 3 |
| Actions (factored) | Cu = 600 kN, Mux = 40 kNm about the strong axis, Vu = 120 kN; no lateral restraint between the ends |
2. Compression resistance (13.3.1)
Fe = π² E / (KL/r)² = π² × 200 000 / 77,9² = 325 MPa · λ = √(355 / 325) = 1,045
Cr = φ A fy (1 + λ2n)−1/n = 0,9 × 5 870 × 355 × (1 + 1,0452,68)−1/1,34 = 1 069 kN
3. Bending resistance with lateral-torsional buckling (13.6)
Class 3, so the yield moment: My = Sx fy = 450 × 103 × 355 = 159,8 kNm. The elastic critical moment over 4,0 m is Mcr = 252 kNm, more than 0,67 My, so
≤ φ My = 143,8 kNm
4. The amplification factor U1 (13.8.4)
U1x = ω1 / (1 − Cu/Cex) = 1,0 / (1 − 600 / 5 636) = 1,119
ω1 = 1,0 is the safe value for a moment that is not linear along the member; with end moments only it can be lower.
5. The interaction checks (13.8.3, class 3)
b) overall member: 600 / 1 069 + 1,119 × 40 / 143,8 = 0,561 + 0,311 = 0,873
c) lateral-torsional buckling: 600 / 1 069 + 1,119 × 40 / 136,0 = 0,561 + 0,329 = 0,890 ← governs
Shear is separate: Vr = 309 kN, so 120 kN works at 39 %.
6. Result
| Check | Result |
|---|---|
| Compression alone | 600 ≤ 1 069 kN (56 %) |
| Bending alone, with LTB | 40 ≤ 136 kNm (29 %) |
| Interaction, LTB (13.8.3 c) | 0,890, governs |
| Shear | 120 ≤ 309 kN (39 %) |
| Slenderness | 77,9 ≤ 200 |
The column passes at 89 %. Each action on its own looks light; together, with the moment amplified by the axial load, they use most of the section. That is why a column is always checked for both at once.
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