Buckling Calculator
Calculate critical buckling load for columns using Euler's and Johnson's formulas
Column Properties
K-factor depends on how the column ends are supported
Second moment of area about the axis of bending
Total area of the column cross-section
Actual length of the column
E = 200 GPa, σy = 250 MPa
Calculated Properties
Column Type: Short Column (Johnson's Formula)
Formula: F = σy·A·[1 - (σy/(4π²E))·(Le/R)²]
Critical Buckling Load
Safety Analysis
Example Calculation
Steel Column Example
Column: Steel beam, 3m length
Boundary: Both ends pinned (K = 1.0)
Moment of Inertia: 8.36 × 10⁶ mm⁴
Cross-sectional Area: 2,340 mm²
Material: Mild Steel (E = 200 GPa, σy = 250 MPa)
Calculation Steps
1. R = √(I/A) = √(8.36×10⁶/2,340) = 59.8 mm = 0.0598 m
2. Le = K × L = 1.0 × 3 = 3 m
3. S = Le/R = 3/0.0598 = 50.2
4. Scrit = 2π√(2E/σy) = 128 (Long column, use Euler's formula)
5. F = π²EI/Le² = π² × 200×10⁹ × 8.36×10⁻⁶ / 3² = 1,833 kN
Boundary Conditions
Fixed
No displacement or rotation
Pinned
No displacement, free rotation
Guided
Free displacement, no rotation
Free
Free displacement and rotation
Design Tips
Use safety factors of 2-4 for structural design
Slender columns (S > 200) are very prone to buckling
Increase moment of inertia to improve buckling resistance
Reduce effective length with intermediate supports
Fixed ends provide better buckling resistance than pinned
Understanding Column Buckling
What is Buckling?
Buckling is a structural instability phenomenon where a column suddenly fails under compressive loading, even when the applied stress is below the material's yield strength. It occurs due to the column's geometry and stiffness rather than material strength limitations.
Types of Buckling Failure
- •Flexural Buckling: Column bends laterally
- •Torsional Buckling: Column twists about its axis
- •Flexural-Torsional: Combined bending and twisting
Formulas Used
Euler's Formula (Long Columns)
F = π²EI/Le²
Used when S > Scrit (slender columns)
Johnson's Formula (Short Columns)
F = σy·A·[1 - (σy/(4π²E))·(Le/R)²]
Used when S ≤ Scrit (intermediate columns)
F: Critical buckling load
E: Young's modulus
I: Area moment of inertia
Le: Effective length (K × L)
A: Cross-sectional area
R: Radius of gyration
σy: Yield stress