Lateral Torsional Buckling | Factors influencing LTB

Lateral Torsional Buckling occurs in unrestrained beams. A beam is unrestrained when its compression flange is free to displace laterally and rotate. When I sections are used as beams or beam columns the compression flange is under compressive stress and has a tendency to buckle but it is attached to the tension flange which resists the buckling giving rise to torsion within the beam section. This torsion twists and warps the unrestrained part of beam leading to lateral torsional buckling.

lateral torsional buckling

lateral torsional buckling

The best analogy for lateral torsional buckling is a person on a tight rope. As the rope gets longer, it will become more difficult for the person to remain balanced as the twist of the rope will become greater. Without Lateral torsion buckling, a beam would have the same flexural strength whether it stretched 5 feet, or 10 feet or even 100 feet.

the lateral displacement and twisting experienced by a beam when lateral torsional buckling occurs.

the lateral displacement and twisting experienced by a beam when lateral torsional buckling occurs.

Lateral torsional buckling is prevented by:

  • Bracing the member laterally at small intervals.
  • Using a larger section size, which will increase the radius of gyration.

Causes of lateral deflection

The applied vertical load results in compression and tension in the flanges of the section. This leads in the deflection of the compression flange, laterally away from the original position where as the tension flange attempts to keep the member straight. This lateral bending of section creates restoring forces that oppose the movement because the section wants to remain straight. These created lateral forces are not adequate to stop the section from deflecting laterally. The lateral component of the tensile forces and the restoring forces together determine the buckling resistance of the member.

lateral deflection

lateral deflection

Torsional effect:

The forces in the flanges cause the section to twist about its longitudinal axis along with the lateral movement of the section. This twisting is opposed by the torsional stiffness of the section which is then dominated by the flange thickness. Hence the section with thicker flanges, has a larger bending strength when compared with same depth section of thinner flange.

torsional effect

torsional effect

Following are the factors that influence the lateral torsional bending:

  • Distance between lateral supports to the compression flange.
  • End support conditions.
  • Type and position of the loads.
  • Moment gradient along the length.
  • Type of cross-section.
  • Non-prismatic nature of the member.
  • Material properties.
  • Magnitude and distribution of residual stresses.
  • Initial imperfections of geometry and loading.

 Remarks:

  • Lateral torsional buckling effect should not be neglected.
  • The finite element method can be used to determine the lateral torsional buckling moment.