Structural Mechanics
Euler Buckling Simulator
Examine elastic column buckling limits under compressive loads. Toggle boundary conditions to see physical mode shapes, slenderness effects, and load capacities.
Class
Long Column
λ = 400
Critical Load
24.2 kN
Elastic threshold
Output
CSV
Export ready
Parameters
Boundary Conditions
Length Sweep Sweep
Structural Equations
Euler Critical Buckling Load (Pcr)
Pcr = (π² * E * I) / (K * L)²
Moment of Inertia (Circular Section)
I = (π * d⁴) / 64
Slenderness Ratio (λ)
λ = Le / r where r = sqrt(I/A)
Column diameter: 50 mm (Area = 19.63 cm²).
Effective Length Le = K * L = 5.00 m (Boundary factor K = 1).
Buckling Response & Support Model
Critical Load (Pcr)
24.2kN
Slenderness Ratio
400.0
Effective Length (Le)
5.00m
Moment of Inertia (I)
30.68cm⁴
Critical Load (Pcr) vs Column Length
Buckling Stability Profile
| Length L (m) | Slenderness Ratio | Critical Load (kN) |
|---|---|---|
| 1.00 | 80.0 | 605.6 |
| 1.50 | 120.0 | 269.1 |
| 2.00 | 160.0 | 151.4 |
| 2.50 | 200.0 | 96.9 |
| 3.00 | 240.0 | 67.3 |
| 3.50 | 280.0 | 49.4 |
| 4.00 | 320.0 | 37.9 |
| 4.50 | 360.0 | 29.9 |
| 5.00 | 400.0 | 24.2 |
| 5.50 | 440.0 | 20.0 |
| 6.00 | 480.0 | 16.8 |
| 6.50 | 520.0 | 14.3 |
| 7.00 | 560.0 | 12.4 |
| 7.50 | 600.0 | 10.8 |
| 8.00 | 640.0 | 9.5 |
| 8.50 | 680.0 | 8.4 |
| 9.00 | 720.0 | 7.5 |