# Beam theory: Buckling

## Engineering Fundamentals

#### Introduction

For slender structures there is a risk that buckling can occur when they are loaded on axial compression. This sheet gives an overview of the force at which buckling occurs ($F_b$) for beams constrained in various ways.
The buckling force is given by:

$$F_b=\frac{\pi^2EI_x}{L_b^2}$$

With $L_b$ the buckling length of the beam given by the buckling length table, $E$ the Young’s modulus of the material and $I_x$ the area moment of inertia. For more information on, and calculations of the area moment of inertia $I$, see sheet: Area moment of inertia.

#### Buckling length

The buckling length of a beam is the buckling coefficient times the length of the beam. The buckling coefficient is dependent on the load case. A lower buckling coefficient means that the load case is more resistant to buckling.