Slenderness Ratio Reference
Reference for slenderness ratio, radius of gyration, transition slenderness and column behaviour regimes.
Buckling & Stability4 min read
bucklingreferenceslendernessradius of gyrationtransition
Slenderness ratio
lambda = L_e / r
where:
L_e = effective length (m)
r = radius of gyration = sqrt(I / A) (m)
Radius of gyration for common sections
| Section | r (weak axis) |
|---|
| Solid circle (diameter d) | d / 4 |
| Solid square (side b) | b / sqrt(12) ≈ 0.289 * b |
| Rectangular (b x h, b < h) | b / sqrt(12) ≈ 0.289 * b |
| I-section (flange width b_f) | ≈ 0.25 * b_f (approximate) |
| Thin tube (diameter D, t << D) | D / (2 * sqrt(2)) |
Transition slenderness
lambda_t = pi * sqrt(E / sigma_y)
lambda > lambda_t: elastic (Euler) buckling
lambda < lambda_t: inelastic buckling or yielding
Typical transition values
| Material | E (GPa) | sigma_y (MPa) | lambda_t |
|---|
| Structural steel | 200 | 250 | 89 |
| High-strength steel | 200 | 500 | 63 |
| Aluminium 2024-T3 | 73 | 345 | 46 |
| Aluminium 6061-T6 | 69 | 270 | 50 |
| Titanium Ti-6Al-4V | 114 | 880 | 36 |
Column behaviour regimes
- Slender (lambda > lambda_t): Euler elastic buckling governs
- Intermediate (lambda ≈ lambda_t): transition — inelastic buckling
- Stocky (lambda << lambda_t): yielding governs, no buckling