## Lateral-Torsional Buckling For Beams.

### Brief content of the video.

Lateral torsional buckling of beams will cause a torsion that will occur for a beam accompanied by a lateral movement.

The second subject is how to make a design analysis for beams. And how to get Lp plastic distance and Lr distance Lr is the unbraced length, the boundary between elastic and in-elastic torsional buckling and limiting value L specified by the AISC code, was a part of the **video** that has a subtitle and a closed caption in English.

You can click on any picture to enlarge, then press the small arrow at the right to review all the other images as a slide show.

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 have 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 compression flange*

, which is moving, accompanied by resistance from the tension bottom flange, that is why we have a rotation.

The shape of lateral-torsional buckling can be viewed, as per the sketch of the beam after deformation. Another definition from Schaum’s book, I quote, 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.

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.

This is the reason why adequate number bracings with proper spacing are required. Unlike the bracing of the column, which requires member framing into the column.

Due to lateral-torsional buckling, the moment will have components. 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.

The use of secondary beams can help to minimize the effect of lateral-torsional buckling.

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

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