EN 1993 Lateral-Torsional Buckling — LTB per Eurocode 3 Clause 6.3.2

Q: When is lateral-torsional buckling not required per EN 1993-1-1?

LTB is not required when the compression flange is continuously restrained (e.g., by a concrete slab), when λ_LT ≤ λ_LT,0 = 0.4 (very stocky beams), or for CHS/RHS sections where LTB is not critical. Clause 6.3.2.4 also provides simplified rules for specific rolled sections.

Q: What buckling curve should I use for IPE sections in LTB?

IPE sections have h/b > 2 for all standard sizes (e.g., IPE 300 h/b = 300/150 = 2.0, IPE 400 h/b = 2.35). Per EN 1993-1-1 Table 6.5, rolled I-sections with h/b > 2 use buckling curve c with α_LT = 0.49.

Complete guide to lateral-torsional buckling (LTB) design per EN 1993-1-1:2005 Clause 6.3.2. Elastic critical moment M_cr, reduction factor χ_LT, buckling curves, and general method for non-standard cases. Worked example with IPE 300 beam including moment gradient C_1 factors.

Quick access: EN 1993 Beam Design → | Compact Section Limits → | European Beam Sizes →

LTB Design Procedure — Clause 6.3.2.1

The design buckling resistance moment is:

M_b,Rd = χ_LT × W_y × f_y / γ_M1

Where:

χ_LT = reduction factor for LTB (≤ 1.0)
W_y = W_pl,y for Class 1/2, W_el,y for Class 3, Weff for Class 4
γ_M1 = 1.00

The non-dimensional slenderness:

λ_LT = √(W_y × f_y / M_cr)

Where M_cr is the elastic critical moment for LTB.

Elastic Critical Moment M_cr

For a doubly symmetric section under uniform moment (worst case), the elastic critical moment is:

M_cr = (π² × E × I_z / L²) × √(I_w / I_z + L² × G × I_t / (π² × E × I_z))

For practical design, factor the M_cr by C_1 to account for moment gradient:

M_cr = C_1 × (π² × E × I_z / L²) × √(I_w / I_z + L² × G × I_t / (π² × E × I_z))

Where:

I_z = minor axis second moment of area
I_t = torsional constant
I_w = warping constant
L = beam length between lateral restraints
C_1 = moment modification factor (see C_1 factor guide)

Typical M_cr Values for IPE Sections (5 m, uniform moment)

Section	I_z (cm⁴)	I_t (cm⁴)	I_w (cm⁶)	M_cr (kN·m)
IPE 200	142	6.98	4980	23.5
IPE 300	604	20.2	33400	89.4
IPE 400	1320	48.8	220000	241.0
IPE 500	2140	89.3	791000	414.0

Reduction Factor χ_LT — Clause 6.3.2.2

For rolled sections or equivalent welded sections:

χ_LT = 1 / (Φ_LT + √(Φ_LT² - β × λ_LT²)) but χ_LT ≤ 1.0

Where: Φ_LT = 0.5 × [1 + α_LT × (λ_LT - λ_LT,0) + β × λ_LT²]

Parameters per EN 1993-1-1 Table 6.3 and 6.4:

λ_LT,0 = 0.4 (plateau length)
β = 0.75 (for rolled sections)

Buckling Curves

Cross-section	Buckling Curve	α_LT
Rolled I-sections (h/b ≤ 2)	b	0.34
Rolled I-sections (h/b > 2)	c	0.49
Welded I-sections (general)	c	0.49
Welded I-sections (thin flange)	d	0.76

For IPE sections, h/b > 2 for all sizes, so use buckling curve c (α_LT = 0.49).

Worked Example — IPE 300, 5 m Span, S355

Parameter	Value
Section	IPE 300
Steel	S355 (fy = 355 MPa)
L	5.0 m
Restraint	Simply supported, no intermediate
W_pl,y	628.4 cm³
M_cr	89.4 kN·m
λ_LT	√(628.4×10³ × 355 / 89.4×10⁶) = 1.58
Curve	c, α_LT = 0.49
Φ_LT	0.5 × [1 + 0.49×(1.58-0.4) + 0.75×1.58²] = 1.226
χ_LT	1 / (1.226 + √(1.226² - 0.75×1.58²)) = 0.53
But χ_LT ≤ 1.0 and χ_LT ≤ 1/λ_LT² = 0.40	χ_LT = 0.40
M_b,Rd	0.40 × 628.4×10³ × 355 / 1.00 = 89.2 kN·m

The χ_LT reduction from the upper bound 1/λ_LT² governs. The LTB resistance is 89.2 kN·m compared to M_pl,Rd = 223.1 kN·m (60% reduction).

Effect of Lateral Restraint

Restraint Spacing	Reduced χ_LT	M_b,Rd (kN·m)	Gain
No intermediate	0.40	89.2	—
L/2 (2.5 m)	0.60	134.0	+50%
L/3 (1.67 m)	0.76	169.6	+90%
L/4 (1.25 m)	0.87	194.1	+118%

Moment Gradient Effects — C_1 Factor

EN 1993 uses the C_1 factor to modify M_cr for non-uniform moment diagrams. See the C_1 factor guide for detailed values. For sagging moment with end restraints, C_1 = 1.77 (triangular moment) compared to C_1 = 1.0 (uniform moment), increasing M_cr by 77%.

Simplified Assessment — Clause 6.3.2.4

For rolled I and H sections, a simplified method is permitted where:

λ_LT ≤ λ_LT,0 = 0.4 — No LTB check required

This means beams with very short spans or high M_cr need not check LTB. For IPE 300, λ_LT < 0.4 requires L ≤ 1.2 m between restraints.

Frequently Asked Questions

When is lateral-torsional buckling not required per EN 1993-1-1?

LTB is not required when the compression flange is continuously restrained (e.g., by a concrete slab), when λ_LT ≤ λ_LT,0 = 0.4 (very stocky beams), or for CHS/RHS sections where LTB is not critical. Clause 6.3.2.4 also provides simplified rules for specific rolled sections.

What buckling curve should I use for IPE sections in LTB?

IPE sections have h/b > 2 for all standard sizes (e.g., IPE 300 h/b = 300/150 = 2.0, IPE 400 h/b = 2.35). Per EN 1993-1-1 Table 6.5, rolled I-sections with h/b > 2 use buckling curve c with α_LT = 0.49.

EN 1993 Beam Design — Full flexural design guide
C_1 Factor Guide — Moment modification factors
Compact Section Limits — Class 1-4 per Table 5.2
Column Design Guide — Compression per EN 1993-1-1
All European References

Educational reference only. Design per EN 1993-1-1:2005 + A1:2014 Clause 6.3.2. LTB curves per Table 6.5. Verify buckling curve selection for actual section geometry. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification.

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