CVL-243

Reinforced Concrete Design

Semester 1, 2020-21

Sahil Bansal, IIT Delhi 1

Design of Footings

Sahil Bansal, IIT Delhi 2

INTRODUCTION
• In a typical structure built on ground, that part of the structure which is located above ground is generally referred to as
the superstructure, and the part which lies below ground is referred to as the substructure or the ‘foundation structure’
(or simply, foundation).
• The purpose of the foundation is to effectively support the superstructure by:
• transmitting the applied load effects (reactions in the form of vertical and horizontal forces and moments) to the
soil below
• ensuring that the settlement of the structure is within tolerable limits, and as nearly uniform as possible.

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Types of footings
The choice of the type of foundation depends on the type of the superstructure and the magnitudes and types of reactions
induced, and the nature of the soil strata.

Shallow foundations
When soil of sufficient
strength is available within
a relatively short depth
below the ground surface

Deep foundations
Carry loads from structure
through weak shallow soils
to rocks/soil at a large
depth

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Types of footings
Shallow foundations
When soil of sufficient strength is
available within a relatively short depth
below the ground surface

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Shallow foundations (Isolated Footing)
• Pad footing/individual footing provided to support an individual column.
• Circular, square or rectangular slab.
• It may be stepped or haunched to spread the load over a large area.

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Shallow foundations (Combined Footing)
• Supports two columns.
• It is used when the two columns are so close to each other that their individual footings would overlap.
• A combined footing is also provided when the property line is so close to one column that a spread footing would be
eccentrically loaded when kept entirely within the property line. By combining it with that of an interior column, the
load is evenly distributed. A combined footing may be rectangular or trapezoidal in plan.

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Shallow foundations (Strap Footing)
• A strap footing consists of two isolated footings connected with a structural strap or a lever.
• The strap connects the two footings such that they behave as one unit.
• The strap is designed as a rigid beam.
• The individual footings are so designed that their combined line of action passes through the resultant of the total load.
• A strap footing is more economical than a combined footing when the allowable soil pressure is relatively high and/or
the distance between the columns is large.

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Shallow foundations (Continuous Footing)
• A strip footing is also provided for a row of columns which are so closely spaced that their spread footings overlap or
nearly touch each other.
• It is more economical to provide a strip footing than to provide a number of spread footings in one line.
• A strip footing is also known as continuous footing.

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Shallow foundations (Raft Footing)
• A mat or raft foundation is a large slab supporting a number of columns and walls under the entire structure or a large
part of the structure.
• A mat is required when the allowable soil pressure is low or where the columns and walls are so close that individual
footings would overlap or nearly touch each other.
• Raft foundation may be used when the areas of isolated footings exceeds 50% of the plan area of building
• Mat foundations are useful in reducing the differential settlements on non-homogeneous soils or where there is a large
variation in the loads on individual columns.

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Types of footings
Deep foundations
Carry loads from structure
through weak shallow soils
to rocks/soil at a large
depth

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Isolated Footing Design

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Shallow Footing
The shallow foundation (footing or raft) has a large plan area in
comparison with the cross-sectional area of the column(s) it supports:
• The loads from the columns are transmitted by the footing/raft to a
relatively weak supporting soil by bearing pressures.
• The ‘safe bearing capacity’ of the soil is very low (100 - 400 kPa)
in comparison with the permissible compressive stresses in
concrete (5 - 15 MPa) and steel (130 -190 MPa) under service
loads.

The soil bearing capacity, according to soil mechanics theory, depends on the
size of the footing, and this is to be accounted for (approximately) in the
recommendation made in the Soil Report

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Allowable Soil Pressure UNDER ISOLATED FOOTINGS
• The main considerations in determining the allowable soil pressure, as well as fixing the depth of foundation, are

• that the soil does not fail under the applied loads

• that the settlements, both overall and differential, are within the limits permissible for the structure

• The soil safety factor lies in the range 2 – 6, and depends on the type of soil.

• The value of the safe soil bearing capacity (qa :allowable soil pressure) given to the structural designer by the

geotechnical consultant, is applicable for service load conditions. Hence, the calculation for the required area of a

footing must be based on allowable soil pressure and the service load effects.

• The ‘partial load factors’ to be used for different load combinations (DL, LL, WL/EL) should, therefore, be those

applicable for the serviceability limit state and not the ‘ultimate limit state’

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Soil pressures under isolated footing: Gross/Net pressure
• Gross pressure : Pressure due to the overburden (P+ΔP)/A.
• Net pressure : Pressure in excess of the existing overburden P/A.
• Allowable soil pressure at a given depth is generally the gross pressure.
• Hence, the total load to be considered in calculating the maximum soil pressure must include the weight of the footing
itself and that of the backfill.
• In preliminary calculations existing overburden weights are assumed equal to 10-15% of the axial load on the column
(this assumption should be verified)

Load of footing + soil backfill

Shall be less than allowable

soil pressure

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Area of Footing Required?

Where qa is the safe bearing capacity

of the soil. Note that qa is applicable
for service load conditions.

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Eccentrically loaded footings
Fixedity moment at the base of the column

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Distribution of Base Pressure
• The distribution of the soil reaction at the base of the footing depends on the rigidity of the footing as well as the soil
properties.
• The distribution of soil pressure is generally non-uniform.
• For convenience, a linear distribution of soil pressure is assumed in normal design practice.

Bowles (1996)
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General Design Considerations
• The major design considerations in the structural design of a footing relate to:
• One-way shear
Determine depth of footing
• Two-way shear
• Flexure
• Bearing
• Bond (development length)
• Deflection control is not a consideration in the design of footings.
• Control of crack-width and protection of reinforcement by adequate cover are important serviceability considerations,
particularly in aggressive environments.
• The minimum cover prescribed in the Code (Cl. 26.4.2.2) is 50 mm, it is desirable to provide a clear cover of 75 mm to
the flexural reinforcement in all footings
• Code (Cl. 34.1.2) restricts the minimum thickness at the edge of the footing to 150 mm for footings in general (and to
300 mm in the case of pile caps)
• A ‘levelling course’ of lean concrete (about 100 mm thick) is usually provided below the footing base.

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Levelling course of lean concrete

Levelling course of lean concrete

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Factored Soil Pressure at Ultimate Limit State
• Area of a footing is fixed on the basis of the allowable bearing pressure qa and the applied loads and moments under
service load conditions.
• The subsequent structural design of the footing is done for the factored loads, using the partial load factors applicable
for the ‘ultimate limit state’.
• In order to compute the factored moments, shears, etc., acting at critical sections of the footing, a fictitious factored
(net) soil pressure qu, corresponding to the factored loads, should be considered.

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Design for Shear
• The thickness (depth) of the footing base slab is most often dictated by the need to check shear stress, and for this
reason, the design for shear usually precedes the design for flexure
• Both one-way shear and two-way shear (‘punching shear’) need to be considered in general [Cl. 34.2.4.1 of IS:456]
• Shear reinforcement is generally avoided in footing slabs by providing the necessary depth such that the:
• factored one way shear force Vu1 is below the shear resistance of the concrete Vc1
• factored two-way shear force Vu2 is below the two-way shear resistance of the concrete Vc2
• Where, for some reason, there is a restriction on the depth of the footing base slab on account of which Vu1 > Vc1,
appropriate shear reinforcement should be designed and provided, to resist the excess shear Vu1 – Vc1

Vc1 =  cbd
Vc 2 = k s 0.25 f ck b0 d

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Critical Sections for One way shear
Critical sections for checking vertical one way shear is located at a distance equal to effective depth from the face of the
column (in case footing is in compression)

Critical section
L

d
B Loaded are
for calculating
one-way shear

𝑽
For one-way shear, nominal shear stress is calculated as follows: 𝝉𝒗 = 𝑩𝒅𝒖

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Punching Shear Failure (Two-way shear)

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Critical Sections for Two-way shear
Critical sections for checking vertical two way shear is located at a distance equal to half effective depth from the
periphery of the column

d/2
Critical section
a
b d/2

Loaded are
for calculating
two-way shear

𝑽
For two-way shear, nominal shear stress is calculated as follows: 𝝉𝒗 = 𝒖
𝒃𝟎𝒅
where b0= periphery of the critical section = 2(a+d)+2(b+d)
a
Allowable two-way shear stress in Cl-31.6.3 of
IS 456:2000 is given by 𝒔𝒉𝒐𝒓𝒕 𝒔𝒊𝒅𝒆
b βc = = b/a
𝒍𝒐𝒏𝒈 𝒔𝒊𝒅𝒆

Column Section

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Critical Sections for BM
The critical section for computing maximum bending moment for design of an isolated concrete footing is at the face of
column, pedestal or wall for footings supporting a concrete column, pedestal or wall.

Critical section

Loaded area
for calculating
moment at column
face

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Design for Flexure
• Total tensile reinforcement at any section should ensure the moment of resistance greater than the bending moment due
to factored forces.
• Reinforcement should not be less than the minimum prescribed for slabs unless the footing is designed as a plain
concrete (pedestal) footing.
• It is advisable to select small bar diameters with small spacings, in order to reduce crack widths and development
length requirements.
• Development length requirements for flexural reinforcement in a footing should be satisfied.
• Longitudinal reinforcement in the column/pedestal must also have the required development length, measured from the
interface between the column/pedestal and the footing.

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Design for Flexure
Tensile reinforcement should be provided in accordance with the following:
• in one-way footing (such as wall footings) reinforcement must be distributed uniformly
• in two-way square footing - reinforcement in each direction must be distributed uniformly
• in two-way rectangular footing with varying depth
• reinforcement in the shorter and longer direction should be distributed uniformly
• in two-way rectangular footing with uniform depth
• reinforcement in the longer direction should be distributed uniformly
• reinforcement in the short direction should be provided by dividing the length in three bands

• Reinforcement in central band should be

uniformly distributed and provided in
accordance with the following equation:
𝟐𝑨𝒔𝒕, 𝒔𝒉𝒐𝒓𝒕
𝑨𝒄𝒆𝒏𝒕𝒓𝒂𝒍 𝒃𝒂𝒏𝒅 =
𝟏 + 𝑳𝒚Τ𝑳𝒙
• Remainder reinforcement is to be uniformly
distributed within in the outer portions of the
footing

This is done to account (approximately) for the observed variation of

the transverse bending moment along the length of the footing.

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Design for Flexure

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Transfer of load at base of column
All forces (axial force, moment) acting at the base of the column must be transferred to the footing
either by compression in concrete or by tension/compression in reinforcing steel

In case transfer of forces from column/pedestal to footing by bearing alone

• The force transfer achieved through compression in concrete at the interface is
limited by the bearing resistance of concrete (the column reinforcement can not be
considered effective near the column base)
• If the compression forces can be transferred to footing by bearing alone, technically
there is no need to extend column bars inside the footing, but as a standard practice
the column bars are extended up to a certain distance inside the footing.

In case bearing alone is insufficient

• Transfer of forces from column to footing by bearing + reinforcement
• Development length of the reinforcement shall be sufficient to transfer the
compression or tension to the footing.

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 Transfer of load at base of column and footing
• Incase column rebars are not extended to footing: Strength in the lower part of the column should be checked since
the column reinforcement can not be considered effective near the column base because the force in the reinforcement
is not developed for some distance above the base.
• Incase bearing stress is exceeded: Find out the force in excess of force transferred by bearing action. This excess force
should be transferred to the footing by providing rebars with adequate development length. Min requirement 0.5% of
gross cross-sectional area of column, 4 bars, .. (Cl-34 of IS:456)

fbr, max = 0.45fck

bearing strength should fbr, max = 0.45fck√(A1/A2)

be checked at the Increase in bearing
base of the column and capacity because of
top of footing confinement (tri-axial
state of compressive
stresses)

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Transfer of load at base of column
A1= maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the
loaded area
A2 = loaded area at the column base
√(A1/A2) is limited to 2.0. (empirical factor)

A2 A1

Footing slab

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Design of Plain Footing (Pedestal Footing)
• For lightly loaded columns/without any longitudinal reinforcement.
• The entire column force is transmitted to the footing base by compression (strut action), and the soil pressure does not
induce any bending in the footing If (Cl. 34.1.3)

• To carry the tie forces and to avoid possible cracking of concrete due to the resulting tensile forces, provide minimum
reinforcement.

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Typical details
of a column
footing (SP:34) • Development length
to compression bars
can not be provided
by the means of
bend/hook.
• Where the depth of
the footing or footing
and pedestal
combined is less than
the minimum
development length in
compression required,
the size of dowels
(starter bars) may be
suitably decreased,
and the number of
dowels increased to
satisfy the required
area and development
length.

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Examples, Pillai & Menon
✓ EXAMPLE 14.1: Plain Concrete Footing

✓ EXAMPLE 14.2: Square Isolated Footing, Concentrically Loaded

✓ EXAMPLE 14.3: Rectangular Isolated Footing, Concentrically Loaded

✓ EXAMPLE 14.5: Isolated footing, eccentrically loaded

• EXAMPLE 14.6: Isolated footing, eccentrically loaded (study yourself)

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EXAMPLE 14.1: Design of a Plain Concrete Footing
Design a plain concrete footing for a column, 300 mm × 300 mm, carrying an axial load of 330 kN (under service loads,
due to dead and live loads). Assume an allowable soil bearing pressure of 360 kN/m2 at a depth of 1.0 m below ground.
Assume M 20 concrete and Fe 415 steel.

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EXAMPLE 14.1: Design of a Plain Concrete Footing

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EXAMPLE 14.1: Design of a Plain Concrete Footing

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EXAMPLE 14.2
Design an isolated footing for a square column, 450 mm × 450 mm, reinforced with 8–25 φ bars, and carrying a service
load of 2300 kN. Assume soil with a safe bearing capacity of 300 kN/m2 at a depth of 1.5 m below ground. Assume M20
grade concrete and Fe415 grade steel for the footing, and M25 concrete and Fe415 steel for the column.

3m

3m

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 1275

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Check on soil pressures below the footing

Weight of 750 mm thick soil backfill on footing

Weight of 750 mm thick concrete in footing

Available development length

1275-75

Critical section for moment

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Force to be transferred by each longitudinal bar to footing = 1172/8 = 147 kN
Corresponding stress in concrete = 147000/( 252 /4)=299 MPa
This force has to be developed in the bar through adequate embedment
f 25  299
Ld = s = = 778 mm
4 bd 4  (1.2  1.6  1.25)
Available vertical embedment length in footing = d = 659 mm
Solution:
Provide 2 extra dowel bars
Embedment length required = 788  8/10=622 can be provided
or
Provide pedestal of height 788-659  130 mm Sahil Bansal, IIT Delhi 42
 At least 3 ties of the column shall extend into
the footing

300

Pedestal 130 mm thick

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 75 mm cover block

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EXAMPLE 14.5
Design an isolated footing for a column, 300 mm × 500 mm, reinforced with 6–25 φ bars with Fe 415 steel and M 25
concrete, subject to a factored axial load Pu = 1000 kN and a factored uniaxial moment Mux = 120 kNm (with respect to
the major axis) at the column base. Assume that the moment is reversible. The safe soil bearing capacity may be taken as
200 kN/m2 at a depth of 1.25 m. Assume M 20 concrete and Fe 415 steel for the footing.

Using a factored soil pressure with ultimate loads is

equivalent to considering allowable pressure with the service
loads. (*factors should be same)

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Development length for reinforcement in compression should also be checked.
Stresses in longitudinal reinforcement are available from column design.

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