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.
Theoretical k Values (ideal end conditions)
These are the textbook values for perfect restraint
| End Condition | Detail | k (Braced) | k (Unbraced) | Note |
|---|
| Fixed | Fixed | 0.50 | 1.00 | Both ends fully restrained |
| Fixed | Hinged | 0.70 | 2.00 | Pin-fixed |
| Hinged | Hinged | 1.00 | — | Pin-pin (Euler standard) |
| Fixed | Free | — | 2.00 | Cantilever — flagpole condition |
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) |
Slenderness Limits (Cl 25.1.2)
| End Condition | Detail | k (Braced) | k (Unbraced) | Note |
|---|
| Short column | — | λ ≤ 12 | Lex/D and Ley/b ≤ 12 | No additional moments needed |
| Slender column | — | λ > 12 | Lex/D > 12 OR Ley/b > 12 | Add Cl 39.7.1 P-Δ moments |
| Maximum slenderness (Cl 25.3.1) | — | L/D ≤ 60 (braced) | L/D ≤ 60 (unbraced) | Hard upper limit for unsupported length |
| Cantilever max (Cl 25.3.2) | — | L/D ≤ 100·b/D | — | Free-standing column maximum |
Steel Columns — IS 800 Table 11 (k values)
| End Condition | Detail | k (Braced) | k (Unbraced) | Note |
|---|
| Restrained in position and direction at both | Both | 0.65 | — | Equivalent to fixed-fixed |
| Restrained in position both ends, in direction at one | One | 0.80 | — | Pin-fixed |
| Restrained in position both ends, in direction at neither | Neither | 1.00 | — | Pin-pin |
| Restrained in position and direction at one, position at other | — | 1.20 | — | Sway permitted |
| Restrained in position and direction at one, direction at other (no position) | — | 1.50 | — | Less common case |
| Restrained in position and direction at one end, free at other | Free | 2.00 | — | Cantilever (mast) |
Slenderness λ = kL / r — Permissible Limits (IS 800 Table 3)
| End Condition | Detail | k (Braced) | k (Unbraced) | Note |
|---|
| Compression member — main | — | λ ≤ 180 | — | Resisting load other than wind/seismic |
| Compression member — wind/seismic only | — | λ ≤ 250 | — | Lateral load combinations |
| Tension member — main | — | λ ≤ 350 | — | — |
| Tension member — wind/seismic | — | λ ≤ 400 | — | — |
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
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