KEVOS® MAKEOS · Strength
Column Buckling (Euler and Johnson)
What load will buckle this column or strut, and is the safety factor enough?
Critical buckling load of a straight, centrally loaded column using Euler’s formula for slender members and the J.B. Johnson parabola for intermediate ones, with the safety factor against an applied load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Elastic modulus | GPa | Elastic modulus from the material data sheet or an approved materials database (steel is typically about 200 GPa). |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification, not a typical value. |
| Cross-section area | mm² | Area of the section, from a section table or the section properties calculator. |
| Least second moment of area | mm⁴ | Smallest second moment of area of the section (the weak axis). |
| Unsupported length | mm | Length between points that are held against sideways movement. |
| Effective length factor K | Theoretical values: 1.0 pinned–pinned, 0.5 fixed–fixed, 0.7 fixed–pinned, 2.0 fixed–free. Design codes often use larger values for real end conditions. | |
| Applied axial load | N | Largest compressive load on the member. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
Method and formulas
- r = √(I ÷ A); slenderness λ = K L ÷ r; transition C_c = π√(2E ÷ S_y).
- Euler (λ ≥ C_c): σ_cr = π²E ÷ λ².
- Johnson (λ < C_c): σ_cr = S_y − (S_y λ ÷ 2π)² ÷ E.
- P_cr = σ_cr × A; safety factor = P_cr ÷ P.
- Example: the default strut has λ = 100, below C_c = 125.66, so Johnson gives P_cr = 170.84 kN and a factor of 3.4169.
Limitations
- Straight, centrally loaded, prismatic members; eccentricity and initial crookedness reduce capacity (see the eccentric column method or your code).
- Local buckling of thin walls and lateral-torsional buckling are not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check push rods, cylinder rods, props and frame members in compression
- Choose a section to resist buckling
- Compare end fixity options
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Slenderness ratio and transition slenderness
- Method used (Euler or Johnson)
- Critical load
- Safety factor
Interpreting the result
- Structural steelwork must also be checked to the applicable code (e.g. AS 4100), which includes imperfection factors.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 281–287. Topic reference; no source tables or recommended settings are reproduced.
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