Annex E provides the effective length (le) of compression members based on end restraint conditions. The effective length factor determines whether a column is 'short' (le/D ≤ 12) or 'slender'. For braced frames (sway prevented), factors range from 0.65 to 1.0. For unbraced frames (sway permitted), factors range from 1.0 to 2.0.
Key Requirements
•Effective length le = k × L, where k is the effective length factor from Table 28
•For braced frames: k ranges from 0.65 (both ends fixed) to 1.0 (one end fixed, one end free to rotate)
•For unbraced frames: k ranges from 1.0 (both ends fixed but sway allowed) to 2.0 (cantilever)
•Column is short if le/b ≤ 12 AND le/D ≤ 12 in both directions
•If column is slender (le/D > 12), apply additional moment Madd = Pu × D × (le/D)² / 2000 — Clause 39.7
Reference Tables
Table 28 — Effective Length of Compression Members (Annex E)
End Condition 1
End Condition 2
k (Braced)
k (Unbraced)
Fixed
Fixed
0.65
1.2
Fixed
Hinged
0.8
—
Fixed
Rotation fixed, translation free
—
1
Fixed
Free (cantilever)
—
2
Hinged
Hinged
1
—
Rotation fixed, translation free
Rotation fixed, translation free
—
1
In practice, most RCC frame columns have partially restrained ends. Use k = 0.65 for internal columns in braced frames with beams on all four sides. Use k = 1.0 for corner columns or where beam stiffness is much lower than column stiffness.
Formulas
le = k × L
Effective length of column
le = Effective length (mm)k = Effective length factor from Table 28L = Unsupported length of column (mm)
Madd = Pu × D × (le/D)² / 2000
Additional moment due to slenderness (Clause 39.7)
Madd = Additional moment (N·mm)Pu = Factored axial load (N)D = Depth of column in the direction under consideration (mm)le = Effective length in the direction under consideration (mm)
Practical Notes
✓For a typical 3 m floor-to-floor height with 450 mm beams: unsupported length L = 3000 − 450 = 2550 mm. For braced frame (both ends fixed): le = 0.65 × 2550 = 1658 mm. For 230 mm column: le/b = 7.2 — safely short.
✓Most RCC frames in India are 'braced' because of infill masonry. Even without a formal bracing check, infill walls provide significant lateral stiffness. However, for open ground storeys (stilts), use unbraced frame factors.
✓Open ground storey (stilt parking) columns are the most critical — they're effectively unbraced (k = 1.2 to 2.0) and have the longest unsupported length. IS 1893 requires special provisions for soft storeys.
Common Mistakes
⚠Assuming all columns are 'short' without checking — stilt floor columns, tall basement columns, and corner columns may be slender.
⚠Using unsupported length L instead of effective length le — the two are different. le = k × L, and k < 1.0 for braced frames.
⚠Not applying the additional moment (Clause 39.7) for slender columns — this can significantly increase the design moment.