Effective length factor (k) for compression members, used to compute slenderness ratio λ = kL/r. Values depend on end restraint conditions: braced frames (no sway) have k ≤ 1.0; unbraced frames (sway permitted) have k ≥ 1.0. For RCC columns in buildings, use Table 28 directly; for steel, use IS 800 Table 11.
IS 456 Table 28 — Recommended k (for practical RCC columns)
Larger than theoretical to account for partial restraint at concrete joints
| End Condition | Detail | k (Braced) | k (Unbraced) | Note |
|---|
| Both ends restrained against rotation and translation | — | 0.65 | 1.20 | Fixed-fixed practical |
| One end restrained, other partially restrained | — | 0.80 | 1.50 | Common interior column |
| Both ends partially restrained | — | 0.85 | 1.80 | — |
| One end free, other fixed | — | — | 2.00 | Cantilever column (water tank, flagpole) |
Notes
• Effective length Le = k × L, where L is the unsupported length
• Slenderness ratio λ = Le / r, where r = √(I/A) is the radius of gyration
• For RCC columns, IS 456 uses Lex/D and Ley/b instead of λ — easier to apply
• A 'braced' column means the frame has shear walls, lift cores, or X-bracing carrying lateral loads
• An 'unbraced' (sway) column resists lateral loads itself — much higher k
• When in doubt, use the higher k — slenderness errors are dangerous
• For very slender columns (λ > 60), additional P-δ moments must be applied per Cl 39.7.1
• Always check both axes (x and y) — the larger slenderness governs