Last Updated on February 20, 2026 by Maged kamel
Lateral-Torsional Buckling For Beams.
A new subject: Lateral-torsional buckling of beams. Torsion will occur in a beam accompanied by lateral movement; refer to the definition in Schaum’s book, Structural Steel Design. Topics included in the content
Introduction to lateral-torsional buckling for steel beams.
We talked earlier about lateral buckling for both the flange and the web of a beam, and that lateral buckling depends on the lambda coefficients. Lambda value λ is affected by the width and thickness of the flange, the height of the web, and the thickness of the web; this is a new subject.
Suppose we have a beam braced at both ends. Due to the load, bending moments will cause horizontal movement and rotation, as shown.
I quote from Prof. Salmon’s Chapter 9. Consider the compression zone of the laterally unsupported beam of Fig. 9.1.1, which can buckle laterally. The beam is held at the two ends.
Point A and Point B are equally stressed. Imperfection in the beam and accidental eccentricity in loading results in different stresses at A and B, furthermore, residual stresses as discussed in Chapter 6 contribute to unequal stresses across the flange width at any distance from the neutral axis.
Due to residual stresses from the variation in cooling and heating during the fabrication process, the compression flange moves, causing resistance from the tension bottom flange, which is why we have rotation.
Another definition from Schaum’s book, I quote, is that, as the name implies, lateral-torsional buckling is the overall instability condition of a beam involving the simultaneous twisting of the member and lateral buckling of the compression flange.
Due to torsion, the compression flange of the I beam moved laterally. However, the lower flange moved a smaller lateral distance, lateral buckling occurred, and the line passing by the web has an angle φ with the original web line.
To prevent Lateral-torsional buckling, a beam must be braced at certain intervals against either the cross-section’s twisting or the compression flange’s lateral displacement.
The interaction of the compression and tension flanges forces an unrestrained beam to twist. The resistance to this twist depends on the beam section’s torsional resistance.
From the IDEA Statica link, beams with large flange thicknesses, for example, have greater torsional resistance than those with lesser flange thicknesses for any given depth. Other sections also offer excellent resistance (RHS/SHS), which are often used when large spans are needed to carry vertical loads (e.g., openings involving bi-fold doors), which are prone to out-of-plane force effects.
This is why an adequate number of bracings with proper spacing is required, unlike the bracing of the column, which requires member framing into the column.
The moment will have components: Mo, Mo cos φ. Referring to the top view, a curvature occurs, taking a section at A-A that shows the moment in the x’ and y’ directions. Due to lateral-torsional buckling, the moment will have components in both lateral and torsional directions. Mo, Mo cos φ. Referring to the top view, a curvature occurs, taking section A-A that shows the moment at x’ and y’ direction.
Secondary beams can help minimize lateral-torsional buckling in beams, as shown in the next slide.
The effect of bracing on steel beams will be discussed. In post 17, a new factor, the Cb factor, which is the coefficient of bending for beams, will be presented.
The PDF for the data of this post and the next one can be reviewed or downloaded.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 14th ed.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 15th ed.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 16th ed.
The next post will be the Regions for Lateral-torsional buckling for beams.