Beam theory: Buckling

Engineering Fundamentals


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:


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.

Load caseLbLoad caseLb
Beam theory Buckling case 12LBeam theory Buckling case 41L
Beam theory Buckling case 22LBeam theory Buckling case 50.7L
Beam theory Buckling case 31LBeam theory Buckling case 60.5L

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