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Murat Güven

Why steel beams twist

Load a steel beam and watch it swing sideways and twist: lateral-torsional buckling in 3D, with the critical moment and the Eurocode resistance.

Try the steps, or set the beam below.

6.0 m
Load height

Your browser can’t show the 3D view; the numbers and the cross-section still work.

Section at 3.0 m
McrM_{\mathrm{cr}} = 102 kNm. The beam sways and twists in one half-wave.

Press Load it to see the buckled shape.

McrM_{\mathrm{cr}}
102 kNm
Equivalent McrM_{\mathrm{cr}} ratio
1.13
λˉLT\bar\lambda_{\mathrm{LT}}
1.48
Curve
b
χLT\chi_{\mathrm{LT}}
0.44
Mb,RdM_{\mathrm{b,Rd}}
97.5 kNm
Mpl,RdM_{\mathrm{pl,Rd}}
223 kNm
Section class
1

What twisting costs you: Mb,RdM_{\mathrm{b,Rd}} is 44 % of Mpl,RdM_{\mathrm{pl,Rd}}.

Section at 3.0 m
01200.51
Curve b, rolled sections

Method

The beam is divided into 40 finite elements. Each node carries the sideways displacement and the twist of the shear center, and their slopes (cubic Hermite functions). The elastic critical moment McrM_{\mathrm{cr}} is the lowest eigenvalue of the stability problem, including the height of the load above or below the shear center (after Trahair 1993). Fork supports and restraints are exact constraints.

Section properties come from the nominal dimensions (EN 10365), root fillets included, and agree with the ArcelorMittal catalog within its rounding.

The design resistance follows EN 1993-1-1:2005, 6.3.2.3, for rolled sections with the recommended values: λˉLT,0=0.4\bar\lambda_{\mathrm{LT,0}}=0.4, β=0.75\beta=0.75, curve b for h/b≤2h/b\le 2 and c above, γM1=1.0\gamma_{\mathrm{M1}}=1.0.

Checked against the closed form under uniform moment, the C1C_{1} factors of NCCI SN003 in their limit κ=0\kappa=0 (1.127 and 1.348), an independent Ritz sine series, and a hand calculation of the resistance.

ReferencesCode

Assumptions and limits

Doubly symmetric rolled sections on fork supports (free warping), elastic, with prebuckling deflections ignored. No local or distortional buckling, no web openings, no post-buckling.

Restraints are discrete and rigid. “Top flange” holds the top flange sideways; “Full” holds the sideways movement and the twist. Loads act downwards, so the top flange is in compression.

The drawn shape is the buckling mode, enlarged: an eigenvalue analysis gives its shape, not its size. McrM_{\mathrm{cr}} is a stability threshold, not a resistance.

Recommended values of the 2005 edition, not a National Annex; the factor f of 6.3.2.3(2) is not used, which is conservative. The second-generation Eurocodes replace this edition nationally by 2028. For design, check with software such as LTBeam (CTICM).

Cite

@software{guven_beam_twist,
  author = {Güven, Murat},
  title  = {Why steel beams twist},
  year   = {2026},
  url    = {https://likemaestro.github.io/tools/beam-twist}
}

References

  1. Access Steel (2006). NCCI: Elastic critical moment for lateral torsional buckling (SN003a-EN-EU). eurocodes.jrc.ec.europa.eu/sites/default/files/2022-06/SN003a-EN-EU.pdf
  2. CEN (2005). EN 1993-1-1: Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings. European Committee for Standardization.
  3. CEN (2017). EN 10365: Hot rolled steel channels, I and H sections – Dimensions and masses. European Committee for Standardization.
  4. Trahair, N. S. (1993). Flexural-Torsional Buckling of Structures. CRC Press. doi:10.1201/9781482271218