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Lateral Torsional Buckling

Module by: Michael Terk. E-mail the author

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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 compression portion of a cross section is restrained by the tension portion and the deflection due to flexural buckling is accompanied by torsion or twisting. The way to prevent LTB is to have adequate lateral bracing at adequate intervals along 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 L b , is compared to two limit states, L p L p and L r L r . Depending on which limit state L b L b sits at, the maximum moment for the beam can be calculated.

Equations to determine LTB

Figure 1: This graph illustrates the LTB options
Figure 1 (graphltb.bmp)
  • When,
    L b < L p L b L p (1)
    there is no LTB because
    M n = M p M n M p (2)
    M p = F y Z≤1.5 M y M p F y Z 1.5 M y (3)
    from the yielding limit state.

  • When
    L p < L b < L r L p L b L r (4)
    the graph is linear, and therefore a linear interpolation between M p M p and M y M y is used for the maximum moment:
    M n = C b M p − M p − M r L b − L p L r − L p ≤ M p M n C b M p M p M r L b L p L r L p M p (5)

  • And finally, when
    L b > L r L b L r (6)
    the graph is non-linear, and there is an equation to find the maximum moment in Chapter F of the Specification section of the Manual (page 16.1-34):
    M n = M cr ≤ M p M n M cr M p (7)

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