# Flexural - Torsional Buckling

**Symbols**

**A _{g} :** Gross cross-sectional area of member

**C _{w} : **Warping constant, in.

^{6}(mm

^{6})

**E: **Structural steel modulus of elasticity

**F _{cr} : **Critical stress

**F _{e} : **Elastic buckling stress determined according to Equation E3-4

**F _{ey} **: Elastic buckling stress in buckling limit state with bending around y-axis

**F _{ez} **: Elastic buckling stress in torsional buckling limit state z-axis

**F _{y} :** Specified minimum yield stress of the type of steel being used

**G:** Shear modulus of elasticity of steel = 11,200 ksi (77 200 MPa)

**H:** Flexural constant

**K** : Effective length factor

**L:** Laterally unbraced length of the member

**r:** Radius of inertia

### Flexural - Torsional Buckling Limit State

The buckling deformations consist of a combination of twisting and bending about two flexural axes of the member.

The symmetry axis is the y-axis, where the buckling around the y-axis is caused by the tilting and rotation of the element around its longitudinal axis. The limit state of flexural-torsional buckling is applicable to columns with singly symmetric shapes, such as double angle, T- and U-shapes and asymmetric cross-sections.

### Design with AISC 360-16

The compressive strength of the elements is determined according to the axial force acting from the section center of gravity.

With the symmetry axis being the y-axis, the elastic buckling stress F

_{e}in the flexural-torsional buckling limit state where buckling around the y-axis occurs by tilting and rotating around the longitudinal axis, F_{e}equation E4-3 is calculated.

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