Euler Buckling Load

\[P_{cr}=\frac{\pi^{2}EI}{(KL)^{2}}\]

Variables

Pcrcritical buckling load (N)

EYoung's modulus (Pa)

Isecond moment of area (m⁴)

Keffective length factor

Lunsupported column length (m)

Description

What is this formula?

The Euler Buckling Load formula calculates the theoretical critical axial load at which a slender column becomes unstable and buckles.

It is one of the fundamental equations in structural engineering and is widely used for the design and verification of compression members.

When to use it

Use this formula when analyzing:

- Steel columns

- Structural compression members

- Towers and masts

- Truss members in compression

- Slender structural elements

Example

A steel column has the following properties:

E = 200 GPa

I = 8×10⁻⁶ m⁴

K = 1.0

L = 3.0 m

Formula:

Pcr = (π²EI)/(KL)²

Substitution:

Pcr = (π² × 200,000,000,000 × 8×10⁻⁶)/(3²)

Pcr = 1,754,596 N

Result:

Pcr ≈ 1.75 MN

Applications

- Column design

- Structural stability analysis

- Steel structures

- Industrial buildings

- Towers and transmission structures

- Bridge engineering

Note

Euler's equation is valid primarily for slender columns that fail by elastic buckling before yielding. Short columns and intermediate columns may require more advanced design methods and code-specific buckling formulations.