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)

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

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

The χ_LT reduction factor formula governs (0.360 < 1/λ_LT² = 0.40, so the upper-bound cap does not control). The LTB resistance is 80.3 kN·m compared to M_pl,Rd = 223.1 kN·m (64% reduction).

Effect of Lateral Restraint

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.

Related Pages

• 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.

Design Resources

Calculator tools

• Column Capacity Calculator
• Steel Buckling Calculator
• Steel Column Base Design Calculator
• Torsion Analysis Calculator

Design guides

• Column Capacity Worked Example
• Column Buckling Guide
• Column Buckling Calculator Guide
• EN 1993-1-1 Column Buckling Worked Example

Reference pages

• EU Torsion