The Chartership Forum

Structural Steel Design / module 8

Beams and lateral-torsional buckling

A beam loaded downwards can fail sideways. Understanding why turns a mysterious code check into something you can reason about — and shows that where you put the load matters as much as how big it is.

What you will understand

  • Explain LTB physically, in terms of the two flanges behaving differently
  • Read the two terms in Mcr and say which dominates at a given span
  • Explain why uniform moment is the worst case
  • Quantify the effect of applying load above or below the shear centre
  • Calculate what a lateral restraint buys, and when further restraint stops helping
  • Say what a restraint must actually do to count as one

Lessons

  1. Why a beam fails sideways

    Load it downwards and it moves sideways and twists. The reason is that the two flanges are doing opposite things.

  2. Restraint, moment shape, and where the load sits

    Three things change the answer. One is free, one is decided by the structure, and one is a detailing choice most people never think about.

Module summary
  • The compression flange is destabilising and the tension flange stabilising
  • They move by different amounts, so the section TWISTS — hence lateral-TORSIONAL
  • Mcr's root term has two pieces: warping (length-independent) and St Venant (goes with L²)
  • Uniform moment is the WORST case, and is the C₁ = 1 reference
  • Top-flange loading is destabilising and cost 26% here; bottom-flange loading is stabilising
  • One restraint at midspan MORE THAN DOUBLED the resistance of an 8 m beam
  • Restraint gains saturate once χLT reaches 1 — beyond that nothing is available
  • A restraint must reach the COMPRESSION flange and be held by something that cannot move
Teaching basis and review status

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Check your understanding

Practice

A beam has Mc,Rd = 826 kNm and Mcr = 450 kNm. What is λ̄LT?

Practice

A beam has λ̄LT = 1.20. What is the elastic cap on χLT?

Practice

A beam has χLT = 0.727 and Mc,Rd = 826 kNm. What percentage of the cross-section resistance is lost to LTB?

Practice

A 12 m beam has two intermediate lateral restraints, equally spaced. What length governs the LTB check, in m?

Practice

The warping term Iw/Iz is 66 950 and the St Venant term is 73 530. What percentage of the resistance to twist comes from warping?

Practice

For double curvature C₁ = 2.60. If Mcr under uniform moment is 290 kNm, what is it in double curvature?