Column Buckling Calculator (Euler & J.B. Johnson)
Structural analysis for determining the critical axial load at which columns will buckle, utilizing Euler (elastic) and Engesser/J.B. Johnson (inelastic) theories.
Formula
\lambda_c = \sqrt{\frac{2 \cdot \pi^2 \cdot C \cdot E}{S_y}}
E= Modulus of Elasticity (MPa)
Sy= Yield Strength (MPa)
L= Unsupported Length (mm)
I= Least Moment of Inertia (mm^4)
A= Cross-Sectional Area (mm^2)
C= End Condition Constant
Quick Calculation Result
\lambda_c = \sqrt{\frac{2 \cdot \pi^2 \cdot C \cdot E}{S_y}}
Interactive Calculator:
Modulus of Elasticity (MPa)
Yield Strength (MPa)
Unsupported Length (mm)
Least Moment of Inertia (mm^4)
Cross-Sectional Area (mm^2)
End Condition Constant
-- waiting for inputs --
Result
How to Calculate Column Buckling Calculator (Euler & J.B. Johnson) (Step-by-Step)
- 1
Calculate radius of gyration (r) from Area and Inertia.
- 2
Find Slenderness Ratio (λ) = L / r.
- 3
Determine the Transition Ratio (λ_c).
- 4
If λ > λ_c, apply Euler formula. If λ <= λ_c, apply J.B. Johnson formula.
- 5
Calculate Critical Load and Safe Working Load.
Why This Matters
In Civil and Structural applications, accurately predicting buckling prevents catastrophic column collapse.
End Conditions (C)
| Condition | C |
|---|---|
| Pinned-Pinned | 1.0 |
| Fixed-Fixed | 4.0 (Theor.), 1.2 (Rec.) |
| Fixed-Pinned | 2.0 (Theor.), 1.2 (Rec.) |
| Fixed-Free | 0.25 |
✓ Design Checklist
- • Verify Least Moment of Inertia (Weakest Axis)
- • Check Elastic vs Inelastic range (λ vs λ_c)
⚠ Common Pitfalls
- • Using strong axis inertia instead of weakest axis
- • Assuming fixed ends are truly fixed in real-world structures