# 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 _{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)

**J:** Torsional constant, in.^{4} (mm^{4})

**K** : Effective length factor

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

**L _{cz} :** Effective length of member around the z-axis (= KL)

**I _{x} , I_{y} :** Moment of inertia about the principal axes, in.

^{4}(mm

^{4})

**r:** Radius of inertia

### Torsional Buckling Limit State

Buckling occurs when the element rotates around its longitudinal axis. The limit state of torsional buckling is applicable to axially loaded columns with doubly symmetric open sections with very slender cross-sectional elements consisting of 4 corners placed back to back.

### 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.

In the torsional buckling boundary case where buckling occurs by the rotation of the element around its longitudinal axis (+ shaped cross-section or open cross-section elements consisting of 4 corners placed back to back), the elastic buckling stress F

_{e}is calculated for doubly symmetric members by equation E4.2.

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