KEVOS® MAKEOS · Strength
Column Strength by Rankine–Gordon
What load will this column carry by the Rankine–Gordon formula?
Crippling load of a column by the Rankine–Gordon formula, which blends crushing and Euler buckling, with the theoretical or an empirical Rankine constant and the safety factor.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Crushing (compressive) strength | MPa | Crushing or compressive yield strength of the material. |
| Elastic modulus | GPa | Elastic modulus from the material data sheet (steel is typically about 200 GPa). |
| Area | mm² | Cross-section area. |
| Least second moment of area | mm⁴ | Least second moment of area. |
| Length | mm | Unsupported length. |
| Effective length factor | Effective length factor for the end conditions (1.0 pinned–pinned). | |
| Rankine constant a (0 = theoretical Sc ÷ π²E) | Empirical Rankine constant for pinned ends from your reference (e.g. about 1/7500 for mild steel); 0 uses the theoretical Sc ÷ π²E. | |
| Applied load | N | Applied compressive load. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
Method and formulas
- r = √(I/A); slenderness λ = KL/r.
- P_cr = Sc A ÷ (1 + a λ²), with a = Sc ÷ π²E (theoretical) or an empirical value.
- Safety factor = P_cr ÷ P.
- Example: the default strut has λ = 100 and a Rankine load of 122.08 kN.
Limitations
- Empirical blend of crushing and buckling; codes (e.g. AS 4100) use other column curves.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check columns and struts of any slenderness with one formula
- Compare with Euler and Johnson results
- Use published Rankine constants for cast iron or timber
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Slenderness ratio
- Rankine constant used
- Crippling load and safety factor
Interpreting the result
- Compare with the Euler and Johnson tool; the Rankine result lies below both limits.
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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