Column Buckling Calculator Formula
Understand the math behind the column buckling calculator. Each variable explained with a worked example.
Formulas Used
Euler Critical Load (Pcr)
critical_load = pow(pi, 2) * e_pa * i_m4 / pow(le, 2) / 1000Effective Length
slenderness = leVariables
| Variable | Description | Default |
|---|---|---|
modulus | Elastic Modulus (E)(GPa) | 200 |
inertia | Moment of Inertia (I)(cm^4) | 1000 |
length | Column Length (L)(m) | 4 |
k_factor | Effective Length Factor (K) | 1 |
e_pa | Derived value= modulus * 1e9 | calculated |
i_m4 | Derived value= inertia * 1e-8 | calculated |
le | Derived value= k_factor * length | calculated |
How It Works
Euler Column Buckling
A slender column under axial compression can buckle laterally before the material yields.
Formula
Pcr = pi^2 E I / (K L)^2
K is the effective length factor that accounts for end conditions: K = 1.0 for pinned-pinned, K = 0.7 for fixed-pinned, K = 0.5 for fixed-fixed, and K = 2.0 for fixed-free (cantilever). The formula assumes perfectly straight, elastic behaviour.
Worked Example
A 4 m pinned-pinned steel column with I = 1000 cm^4 and E = 200 GPa.
modulus = 200inertia = 1000length = 4k_factor = 1
- 01Effective length Le = 1.0 x 4 = 4 m
- 02E = 200 x 10^9 Pa, I = 1000 x 10^-8 m^4 = 1 x 10^-5 m^4
- 03Pcr = pi^2 x 200 x 10^9 x 1 x 10^-5 / 4^2
- 04Pcr = 9.8696 x 2 x 10^6 / 16 = 1,233,700 N = 1233.7 kN
Ready to run the numbers?
Open Column Buckling Calculator