# How do you calculate Mcr (critical buckling moment)

When designing a steel beam, the resistance to buckling is related to Mcr; the elastic critical moment for lateral-torsional buckling.

However the Eurocodes give no advice about how to calculate this parameter.

How would you calculate it?

In case Eurocodes do not provide enough information, some sources exist. In the case of elastic critical moment for lateral-torsional buckling, an NCCI (Non-contradictory, complementary information) document exists.

The document code is SN 003, and one version (maybe not the latest) can be accessed here. Hopefully, this will cover your current needs. In addition, the French technical centre for steel construction has developped a couple pieces of software that can run the calculation for you:

• LTbeam: for beams under bending sollicitations
• LTbeamN: for beams under bending and compression sollicitations

I know it's tagged Eurocodes, but another answer for the Americans: specification section F of the AISC manual (pg. 16.1-44 of the 13th edition) delineates the equations applicable to lateral-torsional buckling. For the usual case of doubly symmetric I shapes bent about the major axis (and normal, "compact" flanges), it's section F2 (pg. 16.1-47).

However, unless you're creating a program to do your designs automatically (like in Mathcad or Excel or something), it is so much easier to just use the design tables (see section 3-5).

There are three options:

1) Using paragraph 6.3.2.4 "Simplified assessment methods form beams with restraints in buildings" Which gives a conservative way to design a beam resistant to lateral torsion buckling.

2) Looking in the Apendices and Supplementary informations of the National Annex for the country in question. In the Belgian annex, for example, there is a lengthy method for calculating Mcr by hand.

3) Using a FE-program, capable of doing a stability analysis.

The answer by Frédéric Bourgeon is great. You may also find useful this free online calculation tool for elastic critical moment in eurocodeapplied.com. It is based on the aforementioned NCCI but it is much simpler to apply as compared to LTBeam, at least for the typical cases encountered in design practice.

It covers typical I- or H- profiles (IPE, HEA, HEB, HEM), three end support conditions (both ends simply supported, both ends fixed, one end simply supported and one end fixed), and three loading arrangements (linear bending moment, parabolic bending moment, triangular bending moment).

Hope this helps.