Column Buckling Calculator
Calculate critical load, slenderness ratio, and factor of safety for axially loaded columns
Calculator
Enter the column properties below to compute the Euler critical load, slenderness ratio, and factor of safety.
About the Column Buckling Calculator
The Column Buckling Calculator allows structural engineers, designers, and students to determine the critical load at which a column will buckle under axial compression, its slenderness ratio, and the applied factor of safety. This calculator uses Euler's theory of buckling and is suitable for a wide range of structural engineering applications.
What You Can Calculate
- Slenderness Ratio (λ = L / r): Measures the column’s propensity to buckle based on its length and radius of gyration.
- Euler Critical Load (Pcr): Maximum axial load a column can withstand before buckling.
- Factor of Safety (FoS): Ratio of critical load to applied load, allowing safe design verification.
Formulas Used in the Calculator
- Slenderness Ratio: λ = L / r
- Euler Critical Load: Pcr = (π² × E × I) / L², where I = r² × A is the area moment of inertia.
- Factor of Safety: FoS = Pcr / Papplied (if applied load is provided)
Where:
- L = Column length (m)
- r = Radius of gyration (m)
- E = Modulus of elasticity (Pa)
- I = Area moment of inertia (m²·m²)
- Pcr = Euler critical load (N)
- Papplied = Applied axial load (N, optional)
- FoS = Factor of safety (dimensionless)
How to Use the Calculator
- Enter the column length (L) and select the unit (m, cm, mm).
- Enter the radius of gyration (r) and select the unit (m, cm, mm).
- Input the modulus of elasticity (E) of the column material and select the appropriate unit (Pa, MPa, GPa).
- Optionally, enter a factor of safety (FoS). Default is 1 if left blank.
- The calculator will automatically compute the slenderness ratio (λ), Euler critical load (Pcr), and factor of safety (FoS).
- Adjust the inputs as needed to explore different column sizes, materials, or safety factors.
Applications of Column Buckling Analysis
- Structural Columns: Design and verify beams, pillars, and columns for safe load-carrying capacity.
- Building & Bridge Engineering: Evaluate stability under axial compressive loads.
- Machine Components: Ensure vertical rods, shafts, or supports resist buckling.
- Educational & Research: Learn Euler buckling theory and slenderness ratio concepts for structural mechanics studies.
- Design Safety Checks: Compare calculated critical load with expected service loads to ensure safety and compliance with engineering standards.