# Slenderness for Flexural Buckling per EN 1993-1-1

**Notations**

* A : *Gross cross-sectional area of member

* A_{eff} :* Effective area

* N_{cr} : *the elastic critical force for the relevant buckling mode

* E :* Modulus of Elastisity,

* f_{y} :* Specified minimum yield stress of the type of steel being used,

* K :* Effective length factor

* L:* Laterally unbraced length of the member

* L_{cr} *: the buckling length in the buckling plane considered

* i:* Radius of gyration

### Flexural Buckling Limit State

The buckling deformations (deflections) all lie in one of the principal planes of cross section. No twisting of the cross section occurs for flexural buckling.

The limit state of flexural buckling is applicable for axially loaded columns with, doubly symmetric sections such as bars, HSS and round HSS, and I-shapes and singly symmetric sections, such as T- and U-shapes. Flexural buckling is the simplest type of buckling.

There are two different equations depending on classification of cross sections. Eq. 6.47 is for class 1,2, and 3 and Eq. 6.48 is for class 4. The non-dimensional slenderness of flexural buckling is determined according to Eq. 6.50 and Eq. 6.51.

for Class 1,2 and 3 cross-sections

for Class 4 cross-sections

For the calculation of reduction factor, the imperfection factor should be determined depending on buckling curve according to Table 6.1. There are five different buckling curve in EN 1993-1-1 Figure 6.4. To select buckling curve of the cross section is determined according to Table 6.2.