Free Tool · EN 1993-1-1 §6.3.2

Lateral-Torsional Buckling Calculator

Calculate the LTB resistance Mb,Rd per EN 1993-1-1 §6.3.2. Computes Mcr (critical moment), λ̄LT (slenderness), χLT (reduction factor), and Mb,Rd for simply-supported, fixed, or cantilever beams. IPE, HEA, HEB, HEM, UB, UC.

Compression Tension LTB mode
Beam Parameters
Enter to compute utilisation η = MEd / Mb,Rd
LTB Results
73.07
Mb,Rd (kNm)
Mcr93.95 kNm
λ̄LT1.5404
φLT1.9144
χLT0.3278
Buckling curve B (α = 0.34)
Mc,Rd (no LTB)222.94 kNm
Mb,Rd73.07 kNm
Wy (Class 1)628,000 mm³
1. Section: IPE 300 | S355 (fy = 355 N/mm²)
Iz = 6,038,000 mm⁴ | It = 201,000 mm⁴ | Iw = 6.26e+10 mm⁶
h/b = 2 → Buckling curve B (αLT = 0.34)

2. M_cr (EN 1993-1-1 Annex F, Eq F.2)
C1 = 1.13 | C2 = 0.45 | k = 1 | zg = 0 mm
Mcr = 93.95 kNm

3. λ̄LT (Eq 6.56)
λ̄LT = √(Wy · fy / Mcr) = √(628,000 × 355 / 93950000) = 1.5404
λ̄LT,0 = 0.2

4. χLT (§6.3.2.2 (general))
φLT = 0.5 × [1 + αLT(λ̄LT − λ̄LT,0) + β·λ̄LT²] = 1.9144
χLT = 1 / (φLT + √(φLT² − β·λ̄LT²)) = 0.3278

5. Mb,Rd (Eq 6.55)
Mb,Rd = χLT · Wy · fy / γM1 = 0.3278 × 628,000 × 355 / 1 = 73.07 kNm
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Related tools
Beam moment capacity (§6.2.5) Column buckling (§6.3.1) Section classification (Table 5.2) Deflection check (§7.2) LTB Cheatsheet PDF

FAQ

What is lateral-torsional buckling (LTB)?
LTB occurs in unrestrained beams when the compression flange buckles laterally while the tension flange remains in place, causing the beam to twist and deflect out-of-plane. It is analogous to column buckling but for beams. The slender a beam is (long unrestrained length relative to minor-axis stiffness), the lower the LTB resistance.
What is Mcr and how is it calculated?
Mcr is the elastic critical moment — the theoretical moment at which an idealised perfect beam would buckle. It depends on the torsional stiffness (GIt), warping stiffness (EIw), minor-axis stiffness (EIz), moment diagram shape (C1), and effective length (kL). Per EN 1993-1-1 Annex F: Mcr = C1·(π²EIz/(kL)²)·√[(Iw/Iz) + (kL²·G·It)/(π²·E·Iz) + (C2·zg)²] − C2·zg.
What is the difference between method §6.3.2.2 and §6.3.2.3?
§6.3.2.2 is the general method applicable to all steel sections (rolled and welded). It uses λLT,0 = 0.2. §6.3.2.3 is an improved method for rolled or equivalent welded sections that accounts for the actual moment distribution via the f-factor correction (Eq 6.58, Table 6.6). It uses λLT,0 = 0.4 and β = 0.75, giving higher resistance for common loading conditions. The National Annex can specify which method is used.
How are the buckling curves selected for LTB?
Per Table 6.4: for rolled I/H sections with h/b ≤ 2, use curve b (αLT=0.34); for h/b > 2, use curve c (αLT=0.49). Welded I sections use curve c (h/b ≤ 2) or curve d (αLT=0.76, h/b > 2). The curves are the same imperfection amplitudes as column buckling but specifically calibrated for LTB.
What does γM1 = 1.0 mean and is it the same in DE?
γM1 is the partial factor for member buckling resistance. The EN default is 1.0. NL and BE follow EN with γM1 = 1.0. The German National Annex (DIN EN 1993-1-1/NA) specifies γM1 = 1.1, which reduces Mb,Rd by about 9% compared to other annexes.