Column Buckling Calculator

Column Buckling – Definition

Column buckling refers to the sudden sideways deflection of a structural column when subjected to an axial compressive load. It is a stability failure, not a material failure, and typically governs the design of long, slender compression members in steel, concrete, wood, and composite structures.

Background Theory

1. Euler’s Buckling Load

For long, slender columns that behave elastically, the critical load causing instability is given by Euler’s formula:

Where:

• EEE = Modulus of elasticity

• III = Minimum moment of inertia

• LLL = Unsupported column length

• KKK = Effective length factor

2. Effective Length Factor (K)

The end condition of a column affects its buckling strength by changing its effective length:

Smaller K → shorter effective length → higher buckling capacity.

3. Moment of Inertia (I)

Buckling always occurs about the weaker axis, so the minimum moment of inertia (Imin) must be used.
A column with a larger I is more resistant to buckling.

4. Slenderness Ratio

Where r=(I/A)^0.5r is the radius of gyration.

High slenderness → buckling dominates.
Low slenderness → material yielding may govern.

How the Calculator Works

Step 1 – User Inputs

• Column length

• Elastic modulus

• Cross-section moment of inertia

• End condition (pinned, fixed, free combinations)

Step 2 – Convert Units

All values are converted into consistent units (N, mm, mm⁴).

Step 3 – Compute Effective Length

Step 4 – Compute Euler Critical Load

The output is displayed in kN for practical engineering use.

Step 5 – Output

The calculator provides:

• Critical buckling load (Pcr)

• Interpretation as the Euler elastic buckling capacity

This allows engineers to size compression members quickly, screen preliminary designs, and check slenderness-controlled failures.