Clause 9.4 deals with beams that are not continuously laterally supported — i.e., the compression flange can buckle laterally (lateral-torsional buckling or LTB). The bending capacity is reduced from the full plastic moment by a factor χLT that depends on the non-dimensional slenderness λLT and the elastic critical moment Mcr.
Key Requirements
•Md = βb × Zp × fbd for Class 1/2 sections
•fbd = χLT × fy / γm0
•χLT = 1 / [φLT + √(φLT² − λLT²)] ≤ 1.0
•φLT = 0.5 × [1 + αLT(λLT − 0.2) + λLT²]
•λLT = √(βb × Zp × fy / Mcr)
Reference Tables
LTB Imperfection Factor αLT (Clause 9.4)
Section Type
αLT
Rolled I-section
0.21
Welded I-section
0.49
αLT = 0.21 corresponds to buckling curve 'a' for rolled sections; αLT = 0.49 corresponds to curve 'c' for welded sections.
Elastic critical moment for lateral-torsional buckling (simplified for uniform moment)
Mcr = Elastic critical moment (N·mm)E = Modulus of elasticity = 2 × 10⁵ MPaIy = Moment of inertia about minor axis (mm⁴)LLT = Effective laterally unsupported length (mm)Iw = Warping constant (mm⁶)G = Shear modulus = 0.769 × 10⁵ MPaIt = St. Venant's torsion constant (mm⁴)
λLT = √(βb × Zp × fy / Mcr)
Non-dimensional slenderness for lateral-torsional buckling
λLT = Non-dimensional LTB slendernessβb = 1.0 for Class 1/2; Ze/Zp for Class 3Zp = Plastic section modulus about major axis (mm³)fy = Yield stress (MPa)Mcr = Elastic critical moment (N·mm)
fbd = χLT × fy / γm0
Design bending compressive stress accounting for LTB
✓LTB is critical for deep narrow beams with long unsupported spans — e.g., ISLB 400 used as a purlin over 6 m with no intermediate bracing. Such beams may lose 40–60% of their full moment capacity.
✓For beams supporting a concrete slab connected to the top flange, LTB typically does not govern for positive moment regions. However, at supports of continuous beams (negative moment), the bottom flange is in compression and may be unsupported.
✓As a rule of thumb, if L/ry < 40 for rolled I-sections in E250, LTB reduction is usually less than 10%. Above L/ry = 80, the reduction becomes very significant.
Common Mistakes
⚠Ignoring LTB for beams without lateral support — this is the most dangerous oversight in steel beam design. An unsupported ISMB 400 over 8 m may have only 50% of its full Md.
⚠Using the wrong Mcr formula — the simplified formula assumes uniform moment. For non-uniform moment distributions (point loads, UDL), use the moment modification factor from Table 14.
⚠Not checking LTB at negative moment regions of continuous beams — the bottom flange is in compression near supports and is usually not laterally restrained.