What's the difference between elastic and inelastic buckling?
Euler buckling applies to slender members staying elastic. Johnson buckling describes stockier members failing inelastically.
Engineering
Simple Beam Buckling Calculator
Compute Euler's critical load for a simply supported slender beam ignoring advanced constraints.
Structural Buckling Analysis
Helps approximate the load at which a beam may fail by buckling.
What this calculator does
The Simple Beam Buckling Calculator predicts the critical load at which a slender beam will suddenly bend sideways under compression. Buckling is a stability failure distinct from material crushing—a thin rod can buckle at far less load than needed to crush it.
How it works
The calculator applies Euler's buckling formula, modeling how resistance to bending depends on material stiffness (Young's modulus), geometric properties (moment of inertia), and length. The effective length factor accounts for end support conditions.
Formula
Euler Critical Load = π² × E × I ÷ (K × L)². Slenderness Ratio = (K × L) ÷ r. Allowable Load = Critical Load ÷ Safety Factor (typically 2.5).
Tips for using this calculator
- Verify Young's modulus for specific material and temperature
- End conditions affect buckling load dramatically: fixed-fixed allows 4× higher load than pinned-pinned
- Use accurate section properties for reliable predictions
- Compare to published buckling tables as sanity check
- Always apply safety factor of at least 2.5
Frequently asked questions
How do I determine effective length factor?
K=1.0 for pinned-pinned, K=0.5 for fixed-fixed, K=0.7 for fixed-pinned, K=2.0 for cantilever. When uncertain, use K=1.0.
Why does longer beam buckle at lower load?
Longer beams are more slender with less lateral stiffness. Buckling load decreases with the square of length.