Euler Column Buckling
Critical load, buckling modes, and post-buckling deformation
Parameters
Applied load P:
1.0
kN
Column length L:
3.0
m
Moment of inertia I:
1.0
×10⁻⁶ m⁴
Elastic modulus E:
200
GPa
Mode 1
Mode 2
Mode 3
Animate
Euler's formula
:
P_cr = n²π²EI / (KL)²
n = mode number (1,2,3...)
K = effective length factor
(K=1 for pin-pin, K=0.5 for fixed-fixed)
Mode shapes
: y(x) = A·sin(nπx/L)
Below P_cr: stable straight column.
Above P_cr: bifurcation — column deflects into sinusoidal shape. Post-buckling: deflection grows as √(P−P_cr).