KEVOS® MAKEOS · Strength
Column Formula Comparison (Rankine, Euler and Classic Safe Load)
How do the Rankine, Euler and classic working-stress column formulas compare for this strut, and does it carry my load by each?
Comparison of column formulas for a concentrically loaded strut: slenderness ratio, Euler buckling load, Rankine–Gordon crippling load and safety factor (as the Rankine column tool), and the classic working-stress safe unit stress and safe load for a main or secondary member (as the classic column safe stress tool), with checks of the Rankine factor and the classic safe load.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Cross-section area | mm² | Area of the strut section. |
| Least radius of gyration | mm | Least radius of gyration of the section. |
| Length | mm | Length between end restraints. |
| Effective length factor | Effective length factor for the end conditions. | |
| Crushing (compressive) strength | MPa | Crushing strength of the material (for the Rankine formula). |
| Elastic modulus | GPa | Elastic modulus. |
| Rankine constant (0 = theoretical) | Empirical Rankine constant; 0 uses S_c ÷ π²E. | |
| Member type (classic formula) | choice | Whether the strut is a main member or bracing (classic formula). |
| Applied concentric load | kN | Concentric load on the strut. |
| Required Rankine safety factor | Safety factor you need by the Rankine formula. |
Method and formulas
- Slenderness = K L ÷ r; Euler load = π² E A ÷ (K L ÷ r)².
- Rankine crippling load = S_c A ÷ [1 + a (K L ÷ r)²] (as the Rankine column tool).
- Classic safe unit stress from the slenderness by the working-stress formulas, × area for the safe load (as the classic column safe stress tool).
- Example: KL/r = 100; Euler 296.09 kN, Rankine 183.13 kN (factor 3.0521), classic safe load 125.66 kN.
Limitations
- Concentric load and straight member; eccentric loads need the secant formula.
- The classic formula is a historic working-stress method; use the current steel code for new designs.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an existing strut by more than one method
- Teach how column formulas compare
- Check old steelwork designed by working stress
Who it is for
- Structural designers
- Maintenance engineers
- Students
What you get
- Slenderness ratio
- Euler and Rankine loads and factors
- Classic safe stress and load
Interpreting the result
- Euler overestimates short columns; Rankine blends crushing and buckling, so it is lower than both at every length.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 281–287. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Column Formula Comparison (Rankine, Euler and Classic Safe Load) calculator
