Lateral Torsional Buckling (LTB) Check: A Practical Guide to Eurocode 3

Lateral Torsional Buckling (LTB) is a failure mode for steel beams subjected to bending. It occurs when a beam, without adequate lateral bracing, deflects sideways and twists simultaneously under load. This guide provides guidance for the LTB calculation tool.

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A diagram showing a steel H-beam undergoing lateral torsional buckling, where it deflects sideways and twists.
Lateral-torsional buckling in a steel H-beam.
Source: ResearchGate (Carvalho et al.), CC BY 4.0.

Basis of the LTB check

The basic principle of the LTB design check is to ensure that the design bending moment acting on the beam (\(M_{Ed}\)) does not exceed the beam's design buckling resistance moment (\(M_{b,Rd}\)).

\[ \frac{M_{Ed}}{M_{b,Rd}} \le 1.0 \]

The main goal of the following paragraphs is to clear up the required input for this calculation.

Load application point

The point where the load is applied relative to the beam its shear center significantly impacts stability. The load is always applied through the center of the beam, but the applied height can differ.

  • Top Flange: This is a destabilizing position. As the beam starts to buckle, the load moves with it, exacerbating the twisting effect. This is the most conservative and common assumption.
  • Shear Center (Middle): This is a neutral position. The load does not add any extra torsional effect during buckling.
  • Bottom Flange: This is a stabilizing position. As the beam twists, the load its center of gravity is raised, creating a restoring moment that resists buckling.
Diagram showing load application on the top flange and in line with the shear center.
Diagram showing load application on the top flange.

Free standing load

The formal name for free standing load is: destabilizing load. This condition applies to loads that have no inherent lateral stability and can move with the beam as it buckles. A classic example is a freestanding brick wall sitting on the top flange of a beam with no connection to a stabilizing floor system. Activating this option adjusts the calculation to reflect this more severe condition, as per EN 1993-1-1. If the load is part of a system that provides lateral restraint (like a floor), it is not a destabilizing load.

Lateral restrains

Lateral restraints are arguably the most important part you control as a designer to prevent LTB. They define how easy the beam can buckle. Better and more lateral restraints results in a significantly higher buckling resistance.

End support conditions:

  • Fully restrained: This is the ideal condition. The support prevents the beam from moving sideways and from twisting. This is representative if the support:
    • Is fixed to a column or wall
    • Is build into a masonry wall
    • Its bottom flange is fixed and there are stiffeners welded from flange to flange at the end supports.
  • Bottom flange fixed: This assumes the bottom flange is prevented from moving sideways (e.g., the bottom flange is fixed with bolts or anchors), but the top compression flange has less no restraint.
  • Compression only: This represents a minimal support condition that is generally considered the worst-case scenario for resisting LTB.

Intermediate lateral restraints (bracing):

  • No Restraint: The beam is only supported at its ends. The buckling length is the full span of the beam.
  • Fully Restrained: This option models a full brace against both lateral movement and twisting at one or more specific points. Practical Examples: A concrete slab connected with shear studs; Profiled metal decking that is properly welded to the top flange, creating a rigid diaphragm.
  • Enter Position: This allows you to define the exact locations of full restraints along the beam.
  • Enter Buckling Length: This is an advanced option for users who want to bypass the calculator's internal logic. You can manually enter the effective buckling length directly.

C1 and C2 factors

The \(C_1\) factor accounts for the shape of the bending moment diagram between points of lateral restraint. A uniform bending moment is the most severe case (\(C_1 = 1.0\)), which is also the default value. It is possible to add your custom \(C_1\) factor.

The \(C_2\) factor accounts for the load application height.