Analysis & loading · Sections & mechanics
Euler buckling (end conditions) calculator
Critical buckling load and stress for the four classic end conditions.
Standard: Elastic stability (Euler)
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| End condition | Pinned–pinned (K 1.0) | |
| Length | 4 | m |
| E | 200000 | MPa |
| I | 8000000 | mm⁴ |
| A | 3000 | mm² |
| Applied load | 300 | kN |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Pcr = π²EI/(KL)² | 987.0 | kN |
| σcr | 329.0 | MPa |
| Slenderness KL/r | 77.46 |
- ✓ Load ≤ Pcr
Method, formulas and assumptions
- Pcr = π²EI/(KL)² = PI()^2*2.000e+5*8.000e+6/(1*4*1000)^2/1000 = 986.96 kN
- σcr = 986.96*1000/3000 = 328.99 MPa
- Slenderness KL/r = 1*4*1000/SQRT(8.000e+6/3000) = 77.46
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.