## Lateral-Torsional Buckling For Beams.

A new subject, which is about the *Lateral-torsional buckling* of beams, a torsion will occur for a beam accompanied by a lateral movement, refer to the definition from Schaum’s book, Structural Steel Design. Topics included in the content

### Introduction to lateral-torsional buckling for steel beams.

We talked earlier about the lateral buckling for both flange and web for a beam and that lateral buckling depends on 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, that is braced at the two ends, and due to the load, the bending moment will create a horizontal movement, with rotation as you can see.

I quote, from Prof. Salmon’s* chapter 9*, consider the compression zone of the laterally unsupported beam of Fig. 9.1.1, which can have buckling laterally, and 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 between cooling and heating during the fabrication process, this causes *torsional and rotation for the *compression flange, which is moving, accompanied by resistance from the tension bottom flange, which is why we have a rotation.

Another definition from Schaum’s book, I quote, as the name implies, is 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.

The I beam due to torsion, its compression flange has moved laterally. but the lower flange has moved a smaller lateral distance lateral buckling has 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 twisting of the cross-section or Lateral displacement of the compression flange.

The interaction of the compression and tension flanges forces an unrestrained beam to twist. The resistance to this twist is dependent on the torsional resistance of the beam section.

From the IDEA statiCA link, beams with large flange thicknesses, for example, have greater torsional resistance than those of lesser flange thicknesses for any given depth. Other sections also offer greater resistance (RHS/SHS) and these are often used in situations where there is a need for large(ish) spans to carry the vertical load (e.g. openings involving bi-fold doors) which are prone to out-of-plane force effects.

This is the reason 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 section at A-A that shows the moment in x’ and y’ direction.

The use of secondary beams can help to minimize the effect of lateral-torsional buckling for beams can be shown in the next slide picture. There will be a discussion about the effect of bracing on steel beams, a new factor Cb factor which is the coefficient of bending for beams will be presented in post 17.

For a useful external source, **Chapter 8 – Bending Members**.

The next post will be the Regions for Lateral-torsional buckling for beams.