Stability Check
Acier Column Slenderness Calculatrice
Use this page to see how unsupported length, weak-axis inertia, et area combine into the slenderness ratio that drives elastic column buckling.
Enter length in meters, E in GPa, inertia in cm^4, area in cm^2, et applied axial charge in kN.
Buckling Entrees
End condition
Member data
Use the end condition that best matches the expected rotational restraint.
Use the weaker-axis inertia when buckling can occur about multiple axes.
Area is used to calculate the radius of gyration et slenderness.
Applied charge is compared directly avec the ideal Charge critique d'Euler.
Buckling Diagram
Stability Summary
| End condition | Pinned-Pinned |
| Longueur efficace factor K | 1,000 |
| Radius of gyration r | 7,13 cm |
| Euler stress Fe | 597,97 MPa |
| Reserve de charge Pcr - P | 1 789,17 kN |
Buckling Formule
Longueur efficace
Forme generale
L_e = K L
Avec actuel values
L_e = 1.000 * 4.20
Resultat calcule
L_e = 4.20 m
Charge critique d'Euler
Forme generale
P_cr = pi^2 E I / L_e^2
Avec actuel values
P_cr = pi^2 * 210 * 1,710 / 4.20^2
Resultat calcule
P_cr = 2,009.17 kN
Rapport de slenderness
Forme generale
lambda = L_e / r, r = sqrt(I / A)
Avec actuel values
lambda = 4.20 / sqrt(1,710 / 34)
Resultat calcule
lambda = 58.87
This screen applies classical Euler elastic buckling et is most reliable pour slender columns before inelastic or code-specific checks.
Hypotheses du modele
- The column is straight, prismatic, et loaded concentrically.
- Material behavior is linear elastic up to the predicted buckling charge.
- Only ideal Euler global buckling is screened here; local buckling et imperfections are excluded.
Lecture technique
Calculation Basis
Assumptions & Limits
- The model screens ideal global Euler buckling only et does not include local buckling or material nonlinearity.
- Imperfections, eccentricity, et frame sway effects need separate ingenierie revue.
- K-factors are modeling hypotheses about end restraint et should be treated as a sensitivity study when restraint is uncertain.
Reference Basis
- Documentation: Methodology
- Documentation: Engineering Review
- Roark's Formulas for Stress and Strain
- Mechanics of Materiaux references
- Euler buckling et column-stability references
Slenderness Reference Setup
| Member basis | Steel compression member under concentric axial load |
| Actuel end condition | Pinned-pinned |
| Actuel unsupported length | 4.2 m |
| Main driver | Effective length divided by radius of gyration |
| Use case | Early weak-axis stability check |
Notes techniques
- This page is strongest when the design question is not the exact code resistance yet, but whether the member is drifting into a slender-column regime too early.
- Slenderness usually changes faster avec unsupported length et weak-axis rigidite than avec small shifts in acier grade, so geometry et restraint should be checked before material upgrades are assumed to solve the problem.
- If the column is part of a braced frame or has realistic partial rotational restraint, continue into the effective-length page et update the end condition hypotheses before trusting the final ratio.
Pages associees