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Euler Buckling Critical Load Calculator — result sheet
Estimate the ideal Euler critical load for a slender column from length, stiffness, end-condition factor, and second moment of area.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Critical load=π²×elastic modulus×second moment/(K×length)².
The ideal Euler model estimates the load at which an initially straight, slender, elastic column becomes unstable in a selected buckling mode.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Elastic modulus — Pa; minimum 1.0E-6; maximum 1.0E+15
- Second moment of area — m⁴; minimum 1.0E-12; maximum 1000000000000
- Effective column length — m; minimum 1.0E-6; maximum 1000000000
- Effective-length factor K — minimum 1.0E-6; maximum 10
Worked example
| Input | Value |
|---|---|
| Elastic modulus | 200000000000 |
| Second moment of area | 8.0E-6 |
| Effective column length | 2 |
| Effective-length factor K | 1 |
Critical load ≈3,947,842 N.
Assumptions and limits
- The column is slender, straight, elastic, and centered in compression.
- K represents the idealized end restraints and the selected effective buckling length.
- Initial crookedness, residual stress, material yielding, shear deformation, connection flexibility, and code safety factors are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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