Chapter 13 of 22

Columns & Footings

In the NCRTC Supervisor Civil syllabus under RCC Design · 2 parts

Short & Long Columns · Design of Footings

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📑 Contents (17 sections)

Part 1 of 2

Short & Long Columns

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}

Part 2 of 2

Design of Footings

Last reviewed 16 Sept 2026 · 6 min read

Purpose and types

A footing spreads the concentrated column or wall load over a larger area of soil so that the soil pressure stays within the safe bearing capacity (SBC) and settlement is acceptable.

Footing	Use
Wall (strip) footing	Continuous strip under a load-bearing wall
Isolated (pad) footing	Single column; square, rectangular or circular; flat, stepped or sloped top
Combined footing	Two or more columns close together, or a column near the property line
Strap (cantilever) footing	Two isolated footings joined by a stiff strap beam to balance an eccentric boundary column
Strip footing under columns	A row of columns on a continuous footing
Raft (mat) foundation	Whole building on one slab; for weak soils or heavy loads where footings would cover > about 50% of the plan
Pile cap	Transfers column load to a group of piles

Sizing

Area required uses service (unfactored) loads:

A_{r e q} = \frac{P + self-weight of footing and backfill}{q _{s a f e}}

Self-weight is commonly taken as 10% of the column load for a first estimate. Choose convenient dimensions ≥ $A_{r e q}$ .

For structural design use factored loads and the net upward pressure (self-weight of the footing does not bend the footing since it is supported directly by the soil beneath):

q_{u} = \frac{P _{u}}{A _{p r o v i d e d}}

IS 456 provisions for footings

Code ProvisionIS 456 — critical sections and minimum requirements

Thickness at the edge: not less than 150 mm for footings on soil (300 mm above the tops of piles for pile caps).
Bending moment is taken at the face of the column, pedestal or wall (for a masonry wall: halfway between the centre line and the edge of the wall; for a steel column with base plate: halfway between the column face and the edge of the plate).
One-way (beam) shear: at a distance $d$ from the face of the column.
Two-way (punching) shear: on a perimeter at $d /2$ from the column face; $τ_{v} \leq k_{s} τ_{c}$ with $τ_{c} = 0.25 f_{c k}$ and $k_{s} = 0.5 + β_{c} \leq 1$ .
Development length of bars must be available from the critical section for moment.
Minimum cover: 50 mm.
Minimum steel: 0.12% (HYSD) as in slabs.

Distribution of steel in rectangular footings

Long direction: spread uniformly across the full width.
Short direction: a central band of width equal to the short side of the footing gets

\frac{steel in central band}{total steel in short direction} = \frac{2}{β + 1}, β = \frac{long side}{short side}

The rest is spread uniformly in the outer portions.

Transfer of load at the base of the column

Compressive stress at the column–footing interface must not exceed the permissible bearing stress:

f_{b r} = 0.45 f_{c k} \frac{A _{1}}{A _{2}}, \frac{A _{1}}{A _{2}} \leq 2

$A_{1}$ = supporting area (largest area of the footing geometrically similar to the column and concentric with it, within the footing); $A_{2}$ = loaded area (column). If exceeded, provide dowels (starter bars) or extend column bars into the footing; dowel area at least 0.5% of the column cross-section and at least four bars, extending the development length into both members.

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