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Flexural-Torsional Buckling

Module by: Michael Terk

Summary: (Blank Abstract)

Definitions

There are three ways a compression member can buckle, or become unstable. These are flexural buckling, torsional buckling, and flexural-torsional buckling.

Definition 1: Flexural buckling
This type of buckling can occur in any compression member that experiences a deflection caused by bending or flexure. Flexural buckling occurs about the axis with the largest slenderness ratio, and the smallest radius of gyration.
Definition 2: Torsional buckling
This type of buckling only occurs in compression members that are doubly-symmetric and have very slender cross-sectional elements. It is caused by a turning about the longitudinal axis. Torsional buckling occurs mostly in built-up sections, and almost never in rolled sections.
Definition 3: Flexural-torsional buckling
This type of buckling only occurs in compression members that have unsymmetrical cross-section with one axis of symmetry. Flexural-torsional buckling is the simultaneous bending and twisting of a member. This mostly occurs in channels, structural tees, double-angle shapes, and equal-leg single angles.

Where to find information for flexural-torsional information

The Manual provides specifications for flexural-torsional buckling in the Specification section, Section E3 (p. 16.1-28), and Appendix E3 (p. 16.1-94. Section E3 is specifically for double-angles and tee-shaped compression member whose elements have width-thickness ratios less than λ r λ r .

Torsional variables can be found in the Dimensions and Properties section of the Manual in the first section. Torsional properties start on page 1-89 and Flexural-torsional properties on page 1-96.

Center of Gravity and Shear Center

Definition 4: Shear center
"The shear center is that point through which the loads must act if there is to be no twisting, or torsion, of the beam." LRFD Steel Design Second Edition -- William T. Segui

The shear center is always located on the axis of symmetry, therefore, if a member has two axes of symmetry, the shear center will be the intersection of the two axes. Channels have a shear center that is not located on the member; the value, e 0 e 0 , tabulated in the Manual is the distance from the channel to the shear center.

Definition 5: Center of gravity
The center of gravity is the point at which all moments generated from the mass of the element equal zero.

For members like an I-shaped member, the center of gravity and the shear center are the exact same point where the two axes of symmetry intersect. for channels, the shear center and the center of gravity are different, which creates a couple and makes the twisting that causes torsional buckling.

Design strength for double-angle and tee-shaped compression members

Double-angles and tee-shaped members with a width-thickness ratio less than λ r λ r should use the formula:

φ c =0.85 φ c 0.85 (1)
P n = A g F crft P n A g F crft (2)

where the "ft" of F crft F crft stands for "flexural-torsional," and is expressed as:

F crft = F cry + F crz 2H1-1-4 F cry F crz H F cry + F crz 2 F crft F cry F crz 2 H 1 1 4 F cry F crz H F cry F crz 2 (3)

Here, F crz F crz is expressed as:

F crz =GJA r 0 ¯2 F crz G J A r 0 2 (4)

where

  • r 0 ¯ r 0 = the polar radius of gyration about the shear center, in.
  • G=E21+ϑ G E 2 1 ϑ
  • J J = torsional stiffness
  • H=1- y 0 2 r 0 ¯2 H 1 y 0 2 r 0 2
  • y 0 y 0 = distance between shear center and centroid, in.
  • F cry F cry = equation given in Section E2 for flexural buckling about the y-axis of symmetry.

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