# 3.4 Lateral torsional buckling

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#### Introduction to lateral torsional buckling

The second limit state for beams is Lateral Torsional Buckling, LTB for short. LTB occurs when the compressionportion of a cross section is restrained by the tension portion and the deflection due to flexural buckling isaccompanied by torsion or twisting. The way to prevent LTB is to have adequate lateral bracing at adequate intervalsalong the beam. The limit state is the interval of the bracing.

For each cross section, it is possible to compute limits for LTB. The laterally unbraced length, ${L}_{b}$ , is compared to two limit states, ${L}_{p}$ and ${L}_{r}$ . Depending on which limit state ${L}_{b}$ sits at, the maximum moment for the beam can be calculated.

#### Equations to determine ltb

• When,
${L}_{b}< {L}_{p}$
there is no LTB because
${M}_{n}={M}_{p}$
${M}_{p}={F}_{y}Z\le 1.5{M}_{y}$
from the yielding limit state.
• When
${L}_{p}< {L}_{b}< {L}_{r}$
the graph is linear, and therefore a linear interpolation between ${M}_{p}$ and ${M}_{y}$ is used for the maximum moment:
${M}_{n}={C}_{b}({M}_{p}-({M}_{p}-{M}_{r})\frac{{L}_{b}-{L}_{p}}{{L}_{r}-{L}_{p}})\le {M}_{p}$
• And finally, when
${L}_{b}> {L}_{r}$
the graph is non-linear, and there is an equation to find the maximum moment in Chapter F of the Specificationsection of the Manual (page 16.1-34):
${M}_{n}={M}_{cr}\le {M}_{p}$

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