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Lateral-Torsional Buckling Calculator

EN 1993-1-1 §6.3.2 LTB resistance check. Enter section, span and loading — get Mcr, λ̄LT, χLT and Mb,Rd with clause references, buckling curve diagram and capacity vs. unrestrained-length chart.

Beam Parameters
Enter to compute utilisation η = M_Ed / M_b,Rd
M_cr formula — EN 1993-1-1 Annex F (Eq F.2)
M_cr = C1 · (π²EIz/(kL)²) · √[ Iw/Iz
       + (kL)²·G·It/(π²·E·Iz)
       + (C2·zg)² ] − C2·zg

C1  — moment diagram factor (load case)
C2  — load application height factor
k   — effective length factor (rotation BC)
k_w — effective length factor (warping BC)
zg  — load height above shear centre (mm)
    → top flange: +h/2 (destabilising)
    → shear centre: 0
    → bottom flange: −h/2 (stabilising)

E = 210,000 N/mm²   G = 81,000 N/mm²
Table 6.4 — LTB Buckling Curve Selection
Section type h/b Curve α_LT
Rolled I/H≤ 2b0.34
Rolled I/H> 2c0.49
Welded I≤ 2c0.49
Welded I> 2d0.76
§6.3.2.3 (rolled — modified, β=0.75, λLT,0=0.4)
M_cr
259.25kNm
λ̄_LT
1.3393
χ_LT
0.462
M_b,Rd
214.87kNm
Critical Moment M_cr
C1 (moment diagram factor)1.13
C2 (load height factor)0.45
k (rotation BC factor)1
k_w (warping BC factor)1
z_g (mm)0 mm
M_cr (kNm)259.25 kNm
LTB Check
λ̄_LT1.3393
λ̄_LT,0 (plateau)0.4
Buckling curvec
α_LT (imperfection)0.49
φ_LT1.4028
χ_LT0.462
f-factor (§6.3.2.3)0.9875
M_c,Rd (no LTB, kNm)465.05 kNm
M_b,Rd (LTB, kNm)214.87 kNm
Section class1
γ_M11
χ_LT reduction factor — Buckling curves a/b/c/d
a — αLT=0.21
b — αLT=0.34
c — αLT=0.49
d — αLT=0.76
Current λ̄_LT / χ_LT
Capacity vs. Unrestrained Length
M_b,Rd (kNm) vs. unrestrained length. Current L marked.
Related Tools
→ Beam moment capacity (§6.2.5)
→ Column buckling (§6.3.1)
→ Section classification (Table 5.2)
→ Fillet weld sizing (§4.5.3)
Run LTB on every beam in a drawing set
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Frequently Asked Questions

What is lateral-torsional buckling?
LTB occurs in unrestrained steel beams when the compression flange buckles laterally while the tension flange remains in place, causing combined lateral bending and twisting. The slenderness ratio λ̄_LT = √(Wy·fy/Mcr) governs the reduction factor χ_LT, which reduces the full plastic moment M_c,Rd to the LTB resistance M_b,Rd.
How is M_cr calculated?
Per EN 1993-1-1 Annex F (Eq F.2): M_cr = C1·(π²EIz/(kL)²)·√[(Iw/Iz)+(kL)²·G·It/(π²·E·Iz)+(C2·zg)²] − C2·zg. C1 accounts for moment diagram shape; C2 for load height; kL is the effective buckling length; zg is load application height above shear centre (positive = top flange = destabilising).
What is the difference between §6.3.2.2 and §6.3.2.3?
§6.3.2.2 (general) uses λ̄_LT,0 = 0.2 and β = 1.0 for all sections. §6.3.2.3 (rolled/equivalent welded) uses λ̄_LT,0 = 0.4, β = 0.75, and an f-factor correction (Eq 6.58, Table 6.6) that accounts for the actual moment distribution — giving higher resistance for typical spans. Most National Annexes recommend §6.3.2.3 for rolled I/H sections.
How are LTB buckling curves selected?
Per Table 6.4: rolled I/H with h/b ≤ 2 → curve b (αLT = 0.34); h/b > 2 → curve c (αLT = 0.49). Welded I with h/b ≤ 2 → curve c; h/b > 2 → curve d (αLT = 0.76). Curve a (αLT = 0.21) is not used for LTB — it is reserved for column buckling.
What does γM1 = 1.1 mean in the German NA?
The German National Annex (DIN EN 1993-1-1/NA) specifies γM1 = 1.1 for member stability checks, versus the EN default of 1.0. This reduces M_b,Rd by approximately 9% compared to EN/NL/BE. Always verify the current NA for the relevant project country.