Short & Long Columns Notes

Last reviewed 16 Sept 2026 · 6 min read

Definitions and classification

Column — a compression member whose effective length exceeds three times its least lateral dimension.
Pedestal — a compression member whose effective length does not exceed three times its least lateral dimension (designed as plain or nominally reinforced concrete).
Short column — both $\frac{l _{e x}}{D} < 12$ and $\frac{l _{ey}}{b} < 12$ .
Slender (long) column — either ratio ≥ 12. Slender columns carry additional moments from lateral deflection.
Braced column — lateral loads resisted by walls or bracing; no significant sway.
Unbraced column — the frame itself resists sway; effective lengths are larger.

Classification by loading: axially loaded, uniaxially eccentric, biaxially eccentric. By ties: tied (lateral ties) and spiral / helically reinforced.

Effective length

Code ProvisionIS 456 Table 28 — effective length of compression members (selected)

End condition	Theoretical	Recommended design value
Effectively held in position and restrained against rotation at both ends	$0.50 l$	$0.65 l$
Held in position at both ends, restrained against rotation at one end	$0.70 l$	$0.80 l$
Held in position at both ends, not restrained against rotation	$1.00 l$	$1.00 l$
Held in position and restrained against rotation at one end, other end restrained against rotation but not held in position	$1.00 l$	$1.20 l$
Held in position and restrained against rotation at one end, other end free	$2.00 l$	$2.00 l$

$l$ = unsupported length.

Minimum eccentricity

No column is perfectly axially loaded. IS 456 requires every column to be designed for a minimum eccentricity:

e_{min} = \frac{l}{500} + \frac{D}{30} \geq 20 mm

( $l$ = unsupported length, $D$ = lateral dimension in the direction considered.)

Axially loaded short columns

When $e_{min}$ does not exceed $0.05 D$ , the IS 456 simplified formula (which already includes the effect of minimum eccentricity) applies:

FormulaShort axially loaded column (IS 456 cl. 39.3)

P_{u} = 0.4 f_{c k} A_{c} + 0.67 f_{y} A_{sc}

$A_{c}$ = area of concrete ( $A_{g} - A_{sc}$ ); $A_{sc}$ = area of longitudinal steel.

The coefficients 0.4 and 0.67 are lower than the pure axial values ( $0.45 f_{c k}$ and $0.75 f_{y}$ ) to allow for $e_{min}$ .

Helically reinforced columns

Closely spaced helical (spiral) reinforcement confines the core, improving ductility and strength. IS 456 allows the load capacity to be taken as 1.05 times that of a tied column when

\frac{volume of helical reinforcement}{volume of core} \geq 0.36 (\frac{A _{g}}{A _{k}} - 1) \frac{f _{c k}}{f _{y}}

$A_{k}$ = area of core measured to the outside of the helix.

Detailing requirements

Code ProvisionIS 456 — longitudinal reinforcement in columns

Minimum 0.8% and maximum 6% of gross area (4% is the practical maximum recommended to allow proper placing and compaction; laps count in this).
Minimum number of bars: 4 in rectangular columns, 6 in circular columns.
Minimum bar diameter 12 mm.
Spacing of longitudinal bars along the periphery not more than 300 mm.
Nominal cover to longitudinal bars ≥ 40 mm or bar diameter (see Concrete & Reinforcement).

Code ProvisionIS 456 — transverse reinforcement (ties)

Diameter of lateral ties: not less than one-fourth of the largest longitudinal bar diameter, and not less than 6 mm.
Pitch of ties: not more than the least of
- the least lateral dimension of the column,
- 16 times the smallest longitudinal bar diameter,
- 300 mm.
Every corner bar and alternate bars must be held by the corner of a tie with an included angle not more than 135°; a bar more than 75 mm from a restrained bar needs its own tie.

Helical reinforcement: pitch not more than 75 mm or one-sixth of the core diameter, and not less than 25 mm or three times the helix bar diameter.

Columns with uniaxial bending

For a short column with $P_{u}$ and $M_{u}$ (the larger of the applied moment and $P_{u} e_{min}$ ), design uses interaction diagrams (SP 16 charts) built from strain compatibility: for each neutral-axis position, compute the axial force and moment capacity. Parameters:

\frac{P _{u}}{f _{c k} b D}, \frac{M _{u}}{f _{c k} b D ^{2}} \to \frac{p}{f _{c k}} from the chart

The interaction curve shows that a moderate axial compression can increase moment capacity (up to the balanced point) — compression delays tension yielding.

Columns with biaxial bending

FormulaIS 456 interaction formula (cl. 39.6)

(\frac{M _{ux}}{M _{ux 1}})^{α_{n}} + (\frac{M _{u y}}{M _{u y 1}})^{α_{n}} \leq 1.0

$M_{ux 1}$ , $M_{u y 1}$ = uniaxial moment capacities under $P_{u}$ ; $α_{n}$ depends on $P_{u} / P_{u z}$ : 1.0 for $P_{u} / P_{u z} \leq 0.2$ , 2.0 for $P_{u} / P_{u z} \geq 0.8$ , linear in between.

P_{u z} = 0.45 f_{c k} A_{c} + 0.75 f_{y} A_{sc}

Downloaded from civilgyantests.com · Not for resale. Verify every code clause and date against the official source.

Short & Long Columns