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Design of Foundations
Introduction
The function of a footing or a foundation is to safely and effectively
transmit the load from the columns and walls to the underlying soil.
Reinforced concrete (RC) is admirably suitable for footings and RC
footings in turn are used in RC, structural steel, or wooden buildings,
bridges, towers, and other structures.
In addition to providing foundations that will carry the loads without
excessive or uneven settlements and rotations, it is also necessary to
check whether they provide sufficient resistance to sliding and
overturning or pull-out in case of tensile loads.
Foundation structures may be categorized as follows:
1. Shallow foundations
2. Deep foundations
3. Special foundations
The choice of a suitable type of foundation depends on the following:
1. Depth at which the bearing strata lies
2. Soil condition
3. Type of superstructure
4. Magnitude and type of reaction at the base of the
superstructure
Introduction
RC foundations are mainly classified as shallow foundations and deep
foundations.
There are five types of shallow foundations as follows:
1. Strip or continuous wall footings
2. Isolated or spread footings (pad and sloped)
3. Combined footings
4. Raft or mat foundations
5. Floating rafts
Types of RC Foundations
Types of Footings
Strip or continuous wall footings behave as cantilevers on each side
of the wall and spread the wall load over a large soil area.
Isolated or spread footings may be of uniform thickness; stepped or
sloped; or have pedestals to save materials (see Fig. 15.1). Depending on
the shape of the column, isolated footings may be square, rectangular,
or circular in shape.
Combined footings transmit load from two or more columns to the
soil and may have rectangular, trapezoidal, or other shapes (see Fig.
15.2). Such combined footings are used when one column is near the
property line or when the footings of two columns overlap.
Types of Isolated Footings
Fig. 15.1 Types of isolated footings (a) Strip or wall footing (b) Spread footing
(c) Stepped footing (d) Sloped footing
Combined Footings for Two Columns
Fig. 15.2 Combined footings for two columns (a) Combined rectangular
(b) Combined trapezoidal (c) Combined T-shaped (d) Combined strap
Mat and Pile Foundation
A mat or raft foundation transfers loads from all the columns in the
building to the soil beneath; it is used in soils of low bearing capacity or
where the areas of individual footings overlap (Fig. 15.3a).
Mat foundations may also be used to reduce differential settlements
when the loads in adjacent columns vary considerably or when there
are variable soils within the same building.
Piles and caissons are the common types of deep foundations and
transmit loads from columns through the upper layers of poor soil to a
strong soil layer at some depth below the surface.
Mat and Pile Foundation
Fig. 15.3 Mat and pile foundation (a) Mat foundation (b) Pile foundation
Pile Foundation
Piles are small diameter shafts driven or cast in bored holes in the
ground and are usually provided in groups connected by a pile cap (see
Fig. 15.3b). A pile cap transmits the column load to a series of piles,
which, in turn, transmit the load to the soil.
Concrete piles are classified into following:
1. Driven cast in situ piles
2. Bored cast in situ piles
3. Driven precast piles
4. Precast piles in pre-bored holes
5. Under-reamed piles
Caissons and Floating Raft Foundation
Caissons, also called well foundations, are about 0.6–1.5 m in
diameter and are sometimes used instead of piles, especially in bridges.
Three types of caissons are used— open, box, or pneumatic (see Figs
15.4a–c).
A floating raft foundation is a special type of foundation that is used
where deep deposits of compressible cohesive soils exist.
The floating raft is so designed that the net foundation pressure is
zero. This condition is achieved by excavating the soil to such a depth
that the weight of soil removed is equal to the weight of the building
including that of the substructure (see Fig. 15.4d).
Caissons and Floating Raft Foundation
Fig. 15.4 Caissons and floating raft (a) Open caisson (b) Box caisson (c) Pneumatic caisson
(d) Floating raft
Soil Pressure Under Footings
The distribution of soil pressure under a footing is a function of the
type of soil and the relative rigidity of the soil and the footing.
When the load is applied at the centre of gravity (C.G.) of the footing,
the actual soil pressure distribution under the base resting on
cohesionless soil (e.g., sand) and cohesive soil (e.g., clay) will diifer
Fig. 15.5 Pressure distribution under footings (a) Cohesionless soil
(b) Cohesive soil (c) Assumed uniform pressure
Soil Pressure Under Footings
When the footing is loaded, the sand near the edges of the footing
will try to displace laterally, causing a decrease in soil pressure near the
edges, as shown in Fig. 15.5(a).
When the footing is loaded, the clayey soil under the footing deflects
in the shape of a bowl, relieving the pressure near the middle of footing,
as shown in Fig. 15.5(b).
The design of footings considering such a non-uniform soil pressure is
complex. Hence, an idealized uniform pressure distribution as shown in
Fig. 15.5(c) is commonly adopted in the structural design.
Soil Pressure under Footings Subjected to
Lateral Moments
Walls and columns often transfer moments along with axial force to
their footings.
These moments may be due to wind, earthquake, or lateral earth
pressure. The effect of these moments will produce uniformly varying
soil pressure as shown in Fig. 15.6(a).
Fig. 15.6 Non-uniform soil pressure under the base of footing (a) Resultant load within the kern
(b) Plan view showing kern dimensions (c) Eccentricity ex = L/6 (d) Resultant load outside the
kern (ex > L/6)
Settlement of Foundation
In the design of footings, the settlement analysis should be given
more importance than the calculation of bearing capacity.
When foundation failure does occur, it is usually the result of
differential settlement or heaving of the soil that supports the
foundation.
Soils of high bearing capacity tend to settle less than soils of low
bearing capacity. Hence, it is advisable to carefully check the settlement
of structures founded on weak soils.
Where settlement criteria dominate, the bearing pressure is restricted
to a suitable value below that of the SBC, known as the allowable
bearing pressure.
Settlement of Foundation
Type of Soil Type of Settlement Isolated
Footing
Raft
Foundation
Sand and hard clay Maximum (mm) 50 75
Differential (mm) 0.0015L 0.0021L
Angular distortion 1/666 1/500
Plastic clay Maximum (mm) 75 100
Differential (mm) 0.0015L 0.002L
Angular distortion 1/666 1/500
Table 15.1 Allowable maximum and differential settlements of RC buildings
Note: L is the length of the deflected part of raft or the centre-to-centre distance between columns.
Safe Bearing Capacity
Fig. 15.7 Shear failure of soil due to bearing (a) General shear (large heave—dense
sand) (b) Local shear (small heave) (c) Punching shear (no heave) (d) Load settlement
curves for (a), (b), and (c) (e) Allowable pressure qa taken as the lesser of qu/FS or q25
Approximate Safe Bearing Capacity
See Table A.5
of the book
for more
details
Thumb rule:
SBC = N t/m2
Depth of Foundation
The depth of foundation is fixed based on the following:
1. The depth is usually based on the availability of soil of adequate
bearing capacity. Strata of varying thickness, even at appreciable
depth, may increase differential settlement.
2. Due to seasonal changes of alternate wetting and drying, clayey soils
will undergo shrinkage and swelling, resulting in appreciable
movements.
3. In regions where the temperature goes down below freezing point,
the base of the footing should be kept at a depth that is not affected
by frost action, especially in fine sand and silt.
Depth of Foundation
Fig. 15.8 Footing depth in sloping ground or when they are at different levels (a) Footing on sloping
ground (b) Footing in granular or clayey soil (c) Footing at two levels
Depth of Foundation
4. When the ground surface slopes downwards adjacent to a footing,
the sloping surface shall not intersect a frustum of bearing material
under the footing, having sides that make an angle of 30° with the
horizontal for soil.
Footing on the sloping ground should have adequate edge
distance from the sloping ground for protection against erosion, as
shown in Fig. 15.8(a).
Depth of Foundation
5. In the case of footings in granular soil, a line drawn between the
lower adjacent edges of adjacent footings should not have a steeper
slope than one vertical to two horizontal (see Fig. 15.8b).
In the case of footing on clayey soils, a line drawn
between the lower adjacent edge of the upper footing and the
upper adjacent edge of lower footing shall not have a steeper slope
than one vertical to two horizontal.
Depth of Foundation
6. The adjacent excavation or foundation that is very close to the
current foundation should be carefully evaluated. If the new
foundation is deeper and closer to the existing one, the damage will
be greater. The minimum horizontal spacing between the existing
and new footings should be equal to the width of the wider one (see
also Fig. 15.8c).
7. Depth of ground water table plays an important role in the depth of
foundation.
8. The approximate depth of foundation Df may be determined by
using the following Rankine’s formula
Gross and Net Soil Pressures
The soil pressure may be expressed in terms of gross or net pressure
at the foundation level.
The gross soil pressure is the total soil pressure produced by all loads
above the foundation level. Thus, it consists of the following:
(a) The column load
(b) The weight of the footing
(c) The weight of the soil from the foundation level to the ground
level
The net soil pressure does not include either the weight of the soil
above the base of the footing or the weight of the footing.
Fig. 15.9 Gross and net bearing pressure (a) Self-weight and soil weight (b) Gross soil pressure
(c) Net soil pressure
Case Study
Design Considerations
Design of foundations consists of two phases—soil design and
structural design.
Due to the complex nature of soils and their behaviour, a hybrid
approach to foundation design is adopted in most of the codes in which
bearing pressures are checked based on the working stress method and
members of foundation are designed using the limit state method.
Both ultimate limit state and serviceability limit state checks are to be
satisfied.
Design Considerations
The following are the ultimate limit states to be checked for soil design:
1. Bearing resistance failure caused by shear failure of the
supporting soil
2. Serviceability failure in which excessive differential settlement
between adjacent footings cause structural damage
3. Excessive settlement and resulting excessive angular distortion
(settlement may be of two types: immediate settlement as in
sands and long-term settlement called consolidation as in clays)
Design Considerations
4. Stability under lateral loads due to sliding
5. Stability against overturning, in case of slender tall structures
6. Failure due to soil liquefaction (soil liquefaction describes a
phenomenon whereby a saturated soil substantially loses
strength and stiffness during earthquakes, causing it to behave
like a liquid)
Design Considerations
Bearing failures of the soil supporting the footing can be prevented by
limiting the service load stresses under the footing to that of the SBC.
The resistance against sliding is provided by the friction between the
base of the footing and the soil below and by the passive resistance of
the soil in contact with the vertical faces of the footing.
The factor of safety against sliding is checked by(Clause 20 of IS 456)
Where P is the compressive load on footing, μ is the coefficient of friction, Ph is
the lateral force, and Ppi is the sum of passive pressure components of the soil
Design Considerations
If the required factor of safety against sliding cannot be achieved by
the provided footing, it is usual to provide a shear key below the base of
footing, especially in the case of retaining walls, as shown in Fig.
15.10(b).
If a construction joint has to be provided at the interface of wall or
column and the footing, then a kind of ‘shear key’ is provided at this
interface, as shown in Fig. 15.10(c), to transfer the horizontal shear
forces due to lateral forces to the footing.
Stability Against Sliding
Fig. 15.10 Stability against sliding (a) Forces resisting sliding (b) Concept of shear key (c) Shear key
at the footing–column or footing–wall interface
Design Considerations
When lateral loads act on the structure, the stability of the structure
as a whole should be ensured at the foundation level. Such overturning
checks are also necessary for footings supporting large cantilevered
beams or slabs (see fig. 15.11).
In general, the problems of overturning and sliding are rare in RC
buildings but common in retaining walls.
When the column it is supporting is subjected to tension (due to wind
or earthquake load, especially in the case of tall towers), footing has to
be designed for uprooting or pull-out.
Stability Against Overturning
Fig. 15.11 Stability against overturning
Design Considerations
The following are the ultimate limit states that apply to the structural
design:
1. Flexural failure of the footing
2. One-way or two-way (punching) shear failure of the footing
3. Inadequate anchorage of the flexural reinforcement in the
footing
4. Bearing failure at column–footing interface
Structural Design of Individual Footings
1. Calculate loads from structure due to various loading casesand
surcharge.
2. Obtain soil properties from soil report provided by a geotechnical
expert.
3. Based on the soil report, determine the footing location and depth;
shallow footings are less expensive, but usually the geotechnical
report will determine the type of footing to be adopted.
Structural Design of Individual Footings
4. Determine footing size.
5. Calculate contact pressure and check stability if required.
6. Estimate settlements.
7. Design the footing based on limit state design.
Structural Design of Individual Footings
Control of crack width is an important serviceability consideration,
especially for footing subjected to aggressive environments. The
following are the requirements as per IS 456:
1. The minimum cover to reinforcement is 50 mm under normal
exposure and the corresponding minimum grade of concrete is M20;
under extreme exposure conditions, it is 75 mm and M25 concrete
(Clause 26.4.2.2 and Table 16).
2. Clause 8.2.2.4 and Table 4 give guidance regarding the type of
cement, minimum free water to cement ratio, and minimum cement
content for situations in which chlorides are encountered along with
sulphates in soil or ground water.
3. Footings are considered to be in moderate category of exposure as
they are buried in soil, and hence it is sufficient to restrict the crack
width to 0.3 mm (SP 24:1980).
However, for severe and above categories, the assessed
surface crack width should not exceed 0.004 times the nominal
cover to main steel (SP 24:1980).
Structural Design of Individual Footings
Structural Design of Individual Footings
4. Minimum reinforcement and spacing should be as per the
requirement of solid slabs (clause 34.5.1). Hence, minimum
percentage in each direction is 0.12 % of the total cross-sectional
area for high-strength deformed bars or welded wire fabric and
0.15 % for Fe 250 grade steel.
Moreover, spacing of main bars should not exceed three times
the effective depth or 300 mm, whichever is smaller (clause
26.3.3b).
Clause 34.5.2 also stipulates a nominal reinforcement of 360 mm2
per meter length in each direction on each face for thick foundations
with thickness greater than 1 m.
Structural Design of Individual Footings
5. In reinforced or plain concrete footings, the thickness at the edge
should be greater than 150 mm (and 300 mm in the case of pile
caps). This ensures that the footing will have enough rigidity to
support the bearing pressures acting on them.
6. Usually, a levelling course of lean cement concrete of thickness 80–
100 mm is provided below the footing base, which serves as a
separating layer between the natural soil and the footing so that any
harmful chemical present in the soil will not react with the footing
concrete.
Shear Design Considerations
One-way Shear
One-way shear in footing is considered similar to that of slabs.
Considering the footing as a wide beam, the critical section is taken
along a vertical plane extending the full width of the footing, located at
a distance equal to the effective depth of footing from the face of the
column, pedestal, or wall, as shown in Fig. 15.12(a).
Two-way Shear
The behaviour of footing in two-way (punching) shear is identical to that
of two-way flat slabs supported on columns. However, punching shear in
footing is not as critical as in flat slabs, since the footing is supported by
the soil below. Hence, it is desirable to check the tendency of the
column punching through the footing, along the surface of a truncated
pyramid around the column, called the critical perimeter.
Critical Sections for Shear
Fig. 15.12 Critical sections for shear (a) One-way shear (b) Two-way punching shear
For the purposes of computing stresses in footings that support a round
or octagonal column or pedestal, Clause 34.2.2 of IS 456 recommends
the use of an equivalent inscribed square column which will result in
conservative design.
Equivalent Square Column
Fig. 15.13 Equivalent square column (a) For round column
(b) For octagonal column
Bending Moment Considerations
The bending moment at any section of a footing is determined by
considering a vertical plane at this section, which extends completely
across the footing, and then computing the moment due to soil pressure
acting over the entire area of the footing on one side of this plane.
The maximum bending moment to be used in the design of an
isolated footing that supports a column, pedestal, or wall occurs at the
following locations:
1. For footings supporting a wall, column, or pedestal, the
maximum bending moment occurs at the face of the wall,
column, or pedestal, as shown in Figs 15.14(a) and (b).
2. Since brick walls are generally less rigid than concrete walls, the
maximum bending moment location is assumed at halfway
between the centre line and the edge of the wall for footings
supporting masonry walls, as shown in Fig. 15.14(c).
3. For footings supporting steel columns, the critical section is
taken at halfway between the face of the column or pedestal and
the edge of the base plate, as shown in Fig. 15.14(d).
Bending Moment Considerations
Fig. 15.14 Critical section for moment (a) Concrete column or wall
(b) Pedestal footing (b) Masonry wall (c) Column with steel base plate
Bending Moment Considerations
The total tensile reinforcement, calculated to resist the maximum
bending moment, has to be distributed as follows:
1. In one-way reinforced footing: The total reinforcement is
distributed evenly across the full width of the footing.
2. In two-way square footing: The calculated reinforcement is
distributed evenly across the width in both directions.
3. In two-way rectangular footing: The calculated reinforcement in the
long direction is distributed evenly across the full width of the
footing, whereas in the short span direction, it is distributed in
different proportions in the central zone and the edge zones (see
Fig. 15.15).
Zones for Reinforcement in a
Rectangular Footing
Fig. 15.15 Zones for reinforcement in a rectangular footing
Providing Development Length
The design bond strength and development length in footing is the
same as that in beams and slabs.
The critical section for checking the development length in footing
should be the same planes where the maximum bending moment
occurs.
In addition, it should be checked at all other vertical planes where
abrupt changes of sections occur.
In locations where the reinforcement is curtailed, anchorage
requirements must be satisfied as in the case of beams.
Transfer of Load at Base of Column
The axial load, moments, and shear acting at the base of a column or
pedestal are transferred to the footing by any one of the following
means:
1. Compressive forces by bearing on concrete surface as well as by
reinforcement
2. Tensile forces due to moment by reinforcement bars, which are
properly anchored into column as well as footing, with adequate
development length
3. Lateral forces by shear friction or shear keys
Fig. 15.16 Bearing area in a stepped or sloped footing
Transfer of Load at Base of Column
If the permissible bearing stress is exceeded either in the base of the
column or in the footing, reinforcement must be provided for
developing the excess force.
The reinforcement may be provided either by extending the
longitudinal bars of column into the footing or by providing dowels as
follows:
1. Minimum area of extended longitudinal bars or dowels must be
0.5 per cent of the cross-sectional area of the supported column
or pedestal.
2. A minimum of four bars must be provided.
Transfer of Load at Base of Column
3. If dowels are used, their diameter should not exceed the diameter of
the column bars by more than 3 mm.
4. Enough development length should be provided to transfer the
compression or tension to the supporting member.
5. Only column bars of diameter larger than 36 mm in compression can
be doweled into the footings with bars of smaller diameter of
necessary area. The dowel must extend into the column a distance
equal to the development length of the column bar and also it must
extend vertically into the footing up to a distance equal to the
development length as shown in Fig. 15.17.
Development Length Requirement
Fig. 15.17 Development length requirement (a) Column
in compression (b) Column in tension
Design of Wall Footings
The design principles used for beam actions also apply to the wall
footings with minor modifications.
As a result of the very large rigidity of the wall, the footing below the
wall behaves like a cantilever on both sides of the wall, as shown in Fig.
15.18.
The soil pressure causes the cantilevers to bend upwards, and as a
result, reinforcement is required at the bottom of the footing, as shown
in Fig. 15.18.
Behaviour of Wall Footing
Fig. 15.18 Behaviour of wall footing
Design of Square Column Footings
The various steps involved in the design of footings are as follows:
1. Determine the plan size of footing.
2. Calculate upward soil pressure.
3. Determine the depth of footing based on one-way shear
considerations.
4. Check for punching shear.
Fig. 15.19 Design of square footing
Design of Square Column Footings
5. Calculate the area of steel. Check for minimum percentage of steel
and bar spacing for crack control.
6. Check for development length.
7. Check for transfer of force at the base of column.
8. Check for development length of column bars. the column bars
should project into the footing for a length equal to the
development length in compression.
Detailing of Reinforcement in Footing
Fig. 15.20 Detailing of reinforcement in footing
Design of Rectangular Footing
The expressions are derived in this section for a rectangular pad-type
footing as shown in Fig. 15.21.
The design procedure is similar to that of square footings, except that
the reinforcements are calculated in two directions and the check for
one-way shear is to be made in both directions at a distance d from the
face of the footing.
All other checks are similar.
In addition, the distribution of reinforcement should be made.
Fig. 15.21 Design of rectangular footing (a) Plan and elevation (b) Critical sections for bending moment
Design of Sloped Footings
In India, sloped footings are used when the thickness of footing
exceeds about 300–350 mm and they have a sloped top surface as
shown in Fig. 15.22.
This type of footing may require more depth but lesser reinforcement
than uniform pad-type footing and hence may be economical.
Moreover, the projection of the footing beyond the column face
bends as a cantilever, and hence, the required flexibility is obtained by
reducing the depth towards the free end, as is usually done in cantilever
beams or slabs.
Fig. 15.22 Sloped rectangular footing (a) Sloped footing (b) Critical sections for bending
(c) Trapezoidal section
Design of Sloped Footings
There are three approaches to the calculation of bending moment and
determination of depth of sloped footing as follows:
1. Determine the bending moment and corresponding depth.
2. Check for one-way shear.
3. Check for two-way shear.
The other checks for development length (in both directions), transfer
of force at the base of column, and development length of column bars
have to be done as for square pad-type footing.
Design of Combined Footings
When the distance between two columns is small, the individual
footings of these columns will overlap and hence it may be necessary to
provide a combined footing. Such combined footings are also adopted
when one of the columns is very close to the property line.
The footing of this edge column will have to be combined with that of
another column in the same line.
When one column is near the property line and the next column in
that row is far away, connecting these columns by a combined footing
may be expensive. In such cases, counterweights called ‘dead man’ may
be provided for the edge column to take care of the eccentric loading.
Design of Combined Footings
Combined footing can be divided into two categories:
1. Those supporting only two columns
2. Those supporting multiple columns (more than two columns)
 When the SBC of the soil is low, the footings of individual columns
merge, and hence, individual footings are combined to form a strip
column footing that supports more than two columns that are
placed in rows (see Fig. 15.23).
Fig. 15.23 Strip column footing (a) With equal column spacings and loads
(b) With unequal column spacings and loads
Design of Combined Footings
The longitudinal bending moment on the base at any section is the
sum of the anticlockwise moments of each load to the left of the section
minus the clockwise moment of the upward pressure between the
section and the left-hand end of the base.
The shearing force at any section is the algebraic sum of the vertical
forces on one side of the section. In the transverse direction, the
moment due to the cantilevering slab from the face of the column has
to be considered.
When there is irregular column spacing or there are varying column
loads, a slab with upstanding T-beam may be used.
Design of Combined Footings
The degree of rigidity that must be given to the foundation beam is
governed by the limiting differential movements that can be tolerated
by the superstructure and by economies in the size and amount of
reinforcement in the beams.
Too great a rigidity should be avoided since it will result in high
bending moments and shearing forces and the possibility of forming a
wide crack if moments and shears are underestimated.
When the beam is provided, it is designed as a continuous beam and
the base slab as cantilevering from either side of the beam.
Arrangement of Strips
When the strips are arranged in both directions, a grid foundation is
formed as shown in Fig. 15.24(a).
In many cases, especially when the SBC is very low, the strips may
merge resulting in a mat foundation or raft foundation, as shown in Fig.
15.24(b).
Strip or mat foundations may also be provided with column pedestals,
as shown in Fig. 15.24(a), in order to provide the required shear
strength or development length for dowels.
The strip and mat foundations, due to their continuity and rigidity,
reduce the differential settlement of individual columns relative to each
other.
Arrangement of Strips
Fig. 15.24 Arrangement of strips (a) Grid foundation (b) Mat foundation
Two-column Footings
The first step in the design of combined footings is to make the
centroid of the footing area coincide with the resultant of the two-
column loads.
This produces uniform bearing pressure over the entire area and
avoids tilting of the footing.
In plan, the footing may be rectangular, trapezoidal, or T-shaped (see
Fig. 15.25).
The simple relationships as shown in Fig. 15.25 may be used to
determine the shape of the bearing area, so that the centroid of the
footing and the resultant of loads coincide.
Two-column Footings
Fig. 15.25 Two-column footings (a) Rectangular (b) Trapezoidal (c) T-shaped
As in isolated footings, the factored net soil pressure is computed as
the resultant factored load divided by the selected base area.
This pressure is assumed to act as uniformly distributed load. It has to
be noted that when there are moments in addition to loads, the
pressure distribution will be non-uniform.
There will be a predominant flexural behaviour in the longitudinal
direction (as shown in longitudinal beam strips A–B–C of Figs 15.26a and
b), and the two-way action will be limited and present only in the
transverse strips in the neighbourhood of columns (as shown by strips
A–D and B–E in Fig. 15.26a).
Behaviour of Combined Two-column
Footing
Fig. 15.26 Behaviour of two-column footing (a) Load distribution (b) Behaviour of longitudinal beam
strips (c) Behaviour of transverse beam strips
Behaviour of Combined Two-column
Footing
Design Considerations of
Combined Footing
The following are the various steps of one such approach:
1. Determine the size of footing.
2. Calculate the bending moment and shear at various locations.
The loads are then multiplied by the appropriate load
factors, and the shear and bending moments are calculated from
statics for these loads, considering the footing slab as simply
supported on the two-column strips, with overhangs (if any) beyond
each column strip, and assuming the supports at the column centre
lines, as shown in Fig. 15.27.
Fig. 15.27 Bending moment and shear force in two-column footing (a) Rectangular combined footing
(b) Bending of footing and loading (c) Bending moment diagram (d) Shear force diagram
3. Determine the thickness of the footing. The thickness of the footing
will usually be governed by shear considerations.
4. Check for punching shear. Check the calculated depth for safety of
punching shear.
5. Determine the reinforcement in the long direction. Find the bending
moment where shear V = 0 and determine reinforcement in the long
direction for the chosen depth.
Check whether minimum steel requirements and the
reinforcement required for resisting shear are satisfied. Provide
minimum steel in the remaining parts of the footing.
Design Considerations of
Combined Footing
Design Considerations of
Combined Footing
6. Check for development length for the chosen diameter of steel.
7. Determine the reinforcement in the short direction. Provide
minimum steel in the remaining parts of the footing in the
transverse direction.
8. Check for development length in the transverse direction as well for
the chosen diameter of steel.
9. Check for shear in the transverse direction as well at a distance d
from the face of the column.
Fig. 15.28 Typical detailing of combined rectangular footing
Design Considerations of
Combined footing
10. Check for transfer of force at the column face. If the limiting bearing
resistance is less than the column load, dowels must be provided.
11. Detail the reinforcement as per design and provide nominal
reinforcement wherever necessary. Typical detailing for combined
rectangular footing is shown in Fig. 15.28.
In order to prevent shear failure along the inclined plane in footing,
where a column is placed on the edge, SP 34:1987 suggests
providing horizontal U-bars around the vertical starter bars, as
shown in Fig. 15.29.
Column at the Edge of Footing
Fig. 15.29 Column at the edge of footing
Design Considerations of
Combined Footing
The design of trapezoidal combined footing is similar to that
of rectangular combined footing.
However, in such footings the longitudinal bars are usually
arranged in a fan shape with alternate bars cut off at some
distance away from the narrow end (typical detailing is shown
in Fig. 15.30).
Fig. 15.30 Detailing of trapezoidal footing
Design of Combined Slab and
Beam Footing
When the depth required for slab footing is large based on shear
considerations, it will become uneconomical. In such cases, a combined
slab and beam footing may be provided as shown in Fig. 15.31, in which
a central longitudinal beam connects the two columns.
The base slab bends transversely under the action of uniform soil
pressure from below and behaves like a one-way cantilevered slab.
The loads transferred from the slab are resisted by the longitudinal
beam.
Combined Slab and Beam Footing
Fig. 15.31 Combined slab and beam footing
The beam will be subjected to high shear forces, which may be
resisted by providing multi-legged stirrups, as shown in Fig. 15.31.
The flexural reinforcement in the slab, designed for the cantilever
moment at the face of the beam, should be provided at the bottom of
the slab, as shown in Fig. 15.31.
Punching shear will not govern such beam and slab footings. The
reinforcements should be checked for development length
requirements.
Design of Combined Slab and
Beam Footing
Design of Combined Footing with
Strap Beam
When the distance between the two columns is large, it is economical
to provide strap footings, in which a beam connecting the two-column
footings is provided, as shown in Fig. 15.2(d).
It is assumed that the strap beam is rigid and that it transfers the load
from the columns to the footings and not directly to the soil.
The column loads are transferred to the soil only through the
independent footings. The areas of independent footings are so chosen
that the soil pressure acting on the footings is uniform and the resultant
soil pressure on the footing areas coincide with the C.G. of the column
loads.
Design of Combined Footing with
Strap Beam
Fig. 15.32 Bending moment and shear force in strap beam (a) Plan (b) Loading on strap beam
(c) Bending moment diagram (d) Shear force diagram
The width of strap beam is generally equal to or greater than the sides
of columns at a right angle to the strap beam.
The strap beam is designed as a rectangular beam by assuming that
the loads are acting uniformly on it from (a) columns in the downward
direction and (b) footings of columns C1 and C2 in the upward direction,
as shown in Fig. 15.32.
The depth of the strap beam is decided based on bending moment
and shear force considerations.
Longitudinal reinforcements are provided based on bending moment
considerations and transverse stirrups based on shear considerations.
Design of Combined Footing with
Strap Beam
Design of Plain Concrete Footings
Occasionally, plain concrete footings are used to support light loads,
especially when the supporting soil has good SBC. Such footings are also
called pedestal footings.
The footing will be in the form of a solid rectangular unreinforced
concrete block.
The depth of the plain concrete pedestal can be determined based on
the angle of dispersion of the load.
When the depth to transfer the load to the ground bearing is less than
the permissible angle of spread, the foundations should be reinforced.
Plain Concrete Footings
Fig. 15.33 Thickness of plain concrete footing

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3.4 Foundations.pptx

  • 2. Introduction The function of a footing or a foundation is to safely and effectively transmit the load from the columns and walls to the underlying soil. Reinforced concrete (RC) is admirably suitable for footings and RC footings in turn are used in RC, structural steel, or wooden buildings, bridges, towers, and other structures. In addition to providing foundations that will carry the loads without excessive or uneven settlements and rotations, it is also necessary to check whether they provide sufficient resistance to sliding and overturning or pull-out in case of tensile loads.
  • 3. Foundation structures may be categorized as follows: 1. Shallow foundations 2. Deep foundations 3. Special foundations The choice of a suitable type of foundation depends on the following: 1. Depth at which the bearing strata lies 2. Soil condition 3. Type of superstructure 4. Magnitude and type of reaction at the base of the superstructure Introduction
  • 4. RC foundations are mainly classified as shallow foundations and deep foundations. There are five types of shallow foundations as follows: 1. Strip or continuous wall footings 2. Isolated or spread footings (pad and sloped) 3. Combined footings 4. Raft or mat foundations 5. Floating rafts Types of RC Foundations
  • 5. Types of Footings Strip or continuous wall footings behave as cantilevers on each side of the wall and spread the wall load over a large soil area. Isolated or spread footings may be of uniform thickness; stepped or sloped; or have pedestals to save materials (see Fig. 15.1). Depending on the shape of the column, isolated footings may be square, rectangular, or circular in shape. Combined footings transmit load from two or more columns to the soil and may have rectangular, trapezoidal, or other shapes (see Fig. 15.2). Such combined footings are used when one column is near the property line or when the footings of two columns overlap.
  • 6. Types of Isolated Footings Fig. 15.1 Types of isolated footings (a) Strip or wall footing (b) Spread footing (c) Stepped footing (d) Sloped footing
  • 7. Combined Footings for Two Columns Fig. 15.2 Combined footings for two columns (a) Combined rectangular (b) Combined trapezoidal (c) Combined T-shaped (d) Combined strap
  • 8. Mat and Pile Foundation A mat or raft foundation transfers loads from all the columns in the building to the soil beneath; it is used in soils of low bearing capacity or where the areas of individual footings overlap (Fig. 15.3a). Mat foundations may also be used to reduce differential settlements when the loads in adjacent columns vary considerably or when there are variable soils within the same building. Piles and caissons are the common types of deep foundations and transmit loads from columns through the upper layers of poor soil to a strong soil layer at some depth below the surface.
  • 9. Mat and Pile Foundation Fig. 15.3 Mat and pile foundation (a) Mat foundation (b) Pile foundation
  • 10. Pile Foundation Piles are small diameter shafts driven or cast in bored holes in the ground and are usually provided in groups connected by a pile cap (see Fig. 15.3b). A pile cap transmits the column load to a series of piles, which, in turn, transmit the load to the soil. Concrete piles are classified into following: 1. Driven cast in situ piles 2. Bored cast in situ piles 3. Driven precast piles 4. Precast piles in pre-bored holes 5. Under-reamed piles
  • 11. Caissons and Floating Raft Foundation Caissons, also called well foundations, are about 0.6–1.5 m in diameter and are sometimes used instead of piles, especially in bridges. Three types of caissons are used— open, box, or pneumatic (see Figs 15.4a–c). A floating raft foundation is a special type of foundation that is used where deep deposits of compressible cohesive soils exist. The floating raft is so designed that the net foundation pressure is zero. This condition is achieved by excavating the soil to such a depth that the weight of soil removed is equal to the weight of the building including that of the substructure (see Fig. 15.4d).
  • 12. Caissons and Floating Raft Foundation Fig. 15.4 Caissons and floating raft (a) Open caisson (b) Box caisson (c) Pneumatic caisson (d) Floating raft
  • 13. Soil Pressure Under Footings The distribution of soil pressure under a footing is a function of the type of soil and the relative rigidity of the soil and the footing. When the load is applied at the centre of gravity (C.G.) of the footing, the actual soil pressure distribution under the base resting on cohesionless soil (e.g., sand) and cohesive soil (e.g., clay) will diifer Fig. 15.5 Pressure distribution under footings (a) Cohesionless soil (b) Cohesive soil (c) Assumed uniform pressure
  • 14. Soil Pressure Under Footings When the footing is loaded, the sand near the edges of the footing will try to displace laterally, causing a decrease in soil pressure near the edges, as shown in Fig. 15.5(a). When the footing is loaded, the clayey soil under the footing deflects in the shape of a bowl, relieving the pressure near the middle of footing, as shown in Fig. 15.5(b). The design of footings considering such a non-uniform soil pressure is complex. Hence, an idealized uniform pressure distribution as shown in Fig. 15.5(c) is commonly adopted in the structural design.
  • 15. Soil Pressure under Footings Subjected to Lateral Moments Walls and columns often transfer moments along with axial force to their footings. These moments may be due to wind, earthquake, or lateral earth pressure. The effect of these moments will produce uniformly varying soil pressure as shown in Fig. 15.6(a).
  • 16. Fig. 15.6 Non-uniform soil pressure under the base of footing (a) Resultant load within the kern (b) Plan view showing kern dimensions (c) Eccentricity ex = L/6 (d) Resultant load outside the kern (ex > L/6)
  • 17. Settlement of Foundation In the design of footings, the settlement analysis should be given more importance than the calculation of bearing capacity. When foundation failure does occur, it is usually the result of differential settlement or heaving of the soil that supports the foundation. Soils of high bearing capacity tend to settle less than soils of low bearing capacity. Hence, it is advisable to carefully check the settlement of structures founded on weak soils. Where settlement criteria dominate, the bearing pressure is restricted to a suitable value below that of the SBC, known as the allowable bearing pressure.
  • 18. Settlement of Foundation Type of Soil Type of Settlement Isolated Footing Raft Foundation Sand and hard clay Maximum (mm) 50 75 Differential (mm) 0.0015L 0.0021L Angular distortion 1/666 1/500 Plastic clay Maximum (mm) 75 100 Differential (mm) 0.0015L 0.002L Angular distortion 1/666 1/500 Table 15.1 Allowable maximum and differential settlements of RC buildings Note: L is the length of the deflected part of raft or the centre-to-centre distance between columns.
  • 19. Safe Bearing Capacity Fig. 15.7 Shear failure of soil due to bearing (a) General shear (large heave—dense sand) (b) Local shear (small heave) (c) Punching shear (no heave) (d) Load settlement curves for (a), (b), and (c) (e) Allowable pressure qa taken as the lesser of qu/FS or q25
  • 20. Approximate Safe Bearing Capacity See Table A.5 of the book for more details Thumb rule: SBC = N t/m2
  • 21. Depth of Foundation The depth of foundation is fixed based on the following: 1. The depth is usually based on the availability of soil of adequate bearing capacity. Strata of varying thickness, even at appreciable depth, may increase differential settlement. 2. Due to seasonal changes of alternate wetting and drying, clayey soils will undergo shrinkage and swelling, resulting in appreciable movements. 3. In regions where the temperature goes down below freezing point, the base of the footing should be kept at a depth that is not affected by frost action, especially in fine sand and silt.
  • 22. Depth of Foundation Fig. 15.8 Footing depth in sloping ground or when they are at different levels (a) Footing on sloping ground (b) Footing in granular or clayey soil (c) Footing at two levels
  • 23. Depth of Foundation 4. When the ground surface slopes downwards adjacent to a footing, the sloping surface shall not intersect a frustum of bearing material under the footing, having sides that make an angle of 30° with the horizontal for soil. Footing on the sloping ground should have adequate edge distance from the sloping ground for protection against erosion, as shown in Fig. 15.8(a).
  • 24. Depth of Foundation 5. In the case of footings in granular soil, a line drawn between the lower adjacent edges of adjacent footings should not have a steeper slope than one vertical to two horizontal (see Fig. 15.8b). In the case of footing on clayey soils, a line drawn between the lower adjacent edge of the upper footing and the upper adjacent edge of lower footing shall not have a steeper slope than one vertical to two horizontal.
  • 25. Depth of Foundation 6. The adjacent excavation or foundation that is very close to the current foundation should be carefully evaluated. If the new foundation is deeper and closer to the existing one, the damage will be greater. The minimum horizontal spacing between the existing and new footings should be equal to the width of the wider one (see also Fig. 15.8c). 7. Depth of ground water table plays an important role in the depth of foundation. 8. The approximate depth of foundation Df may be determined by using the following Rankine’s formula
  • 26. Gross and Net Soil Pressures The soil pressure may be expressed in terms of gross or net pressure at the foundation level. The gross soil pressure is the total soil pressure produced by all loads above the foundation level. Thus, it consists of the following: (a) The column load (b) The weight of the footing (c) The weight of the soil from the foundation level to the ground level The net soil pressure does not include either the weight of the soil above the base of the footing or the weight of the footing.
  • 27. Fig. 15.9 Gross and net bearing pressure (a) Self-weight and soil weight (b) Gross soil pressure (c) Net soil pressure
  • 29. Design Considerations Design of foundations consists of two phases—soil design and structural design. Due to the complex nature of soils and their behaviour, a hybrid approach to foundation design is adopted in most of the codes in which bearing pressures are checked based on the working stress method and members of foundation are designed using the limit state method. Both ultimate limit state and serviceability limit state checks are to be satisfied.
  • 30. Design Considerations The following are the ultimate limit states to be checked for soil design: 1. Bearing resistance failure caused by shear failure of the supporting soil 2. Serviceability failure in which excessive differential settlement between adjacent footings cause structural damage 3. Excessive settlement and resulting excessive angular distortion (settlement may be of two types: immediate settlement as in sands and long-term settlement called consolidation as in clays)
  • 31. Design Considerations 4. Stability under lateral loads due to sliding 5. Stability against overturning, in case of slender tall structures 6. Failure due to soil liquefaction (soil liquefaction describes a phenomenon whereby a saturated soil substantially loses strength and stiffness during earthquakes, causing it to behave like a liquid)
  • 32. Design Considerations Bearing failures of the soil supporting the footing can be prevented by limiting the service load stresses under the footing to that of the SBC. The resistance against sliding is provided by the friction between the base of the footing and the soil below and by the passive resistance of the soil in contact with the vertical faces of the footing. The factor of safety against sliding is checked by(Clause 20 of IS 456) Where P is the compressive load on footing, μ is the coefficient of friction, Ph is the lateral force, and Ppi is the sum of passive pressure components of the soil
  • 33. Design Considerations If the required factor of safety against sliding cannot be achieved by the provided footing, it is usual to provide a shear key below the base of footing, especially in the case of retaining walls, as shown in Fig. 15.10(b). If a construction joint has to be provided at the interface of wall or column and the footing, then a kind of ‘shear key’ is provided at this interface, as shown in Fig. 15.10(c), to transfer the horizontal shear forces due to lateral forces to the footing.
  • 34. Stability Against Sliding Fig. 15.10 Stability against sliding (a) Forces resisting sliding (b) Concept of shear key (c) Shear key at the footing–column or footing–wall interface
  • 35. Design Considerations When lateral loads act on the structure, the stability of the structure as a whole should be ensured at the foundation level. Such overturning checks are also necessary for footings supporting large cantilevered beams or slabs (see fig. 15.11). In general, the problems of overturning and sliding are rare in RC buildings but common in retaining walls. When the column it is supporting is subjected to tension (due to wind or earthquake load, especially in the case of tall towers), footing has to be designed for uprooting or pull-out.
  • 36. Stability Against Overturning Fig. 15.11 Stability against overturning
  • 37. Design Considerations The following are the ultimate limit states that apply to the structural design: 1. Flexural failure of the footing 2. One-way or two-way (punching) shear failure of the footing 3. Inadequate anchorage of the flexural reinforcement in the footing 4. Bearing failure at column–footing interface
  • 38. Structural Design of Individual Footings 1. Calculate loads from structure due to various loading casesand surcharge. 2. Obtain soil properties from soil report provided by a geotechnical expert. 3. Based on the soil report, determine the footing location and depth; shallow footings are less expensive, but usually the geotechnical report will determine the type of footing to be adopted.
  • 39. Structural Design of Individual Footings 4. Determine footing size. 5. Calculate contact pressure and check stability if required. 6. Estimate settlements. 7. Design the footing based on limit state design.
  • 40. Structural Design of Individual Footings Control of crack width is an important serviceability consideration, especially for footing subjected to aggressive environments. The following are the requirements as per IS 456: 1. The minimum cover to reinforcement is 50 mm under normal exposure and the corresponding minimum grade of concrete is M20; under extreme exposure conditions, it is 75 mm and M25 concrete (Clause 26.4.2.2 and Table 16). 2. Clause 8.2.2.4 and Table 4 give guidance regarding the type of cement, minimum free water to cement ratio, and minimum cement content for situations in which chlorides are encountered along with sulphates in soil or ground water.
  • 41. 3. Footings are considered to be in moderate category of exposure as they are buried in soil, and hence it is sufficient to restrict the crack width to 0.3 mm (SP 24:1980). However, for severe and above categories, the assessed surface crack width should not exceed 0.004 times the nominal cover to main steel (SP 24:1980). Structural Design of Individual Footings
  • 42. Structural Design of Individual Footings 4. Minimum reinforcement and spacing should be as per the requirement of solid slabs (clause 34.5.1). Hence, minimum percentage in each direction is 0.12 % of the total cross-sectional area for high-strength deformed bars or welded wire fabric and 0.15 % for Fe 250 grade steel. Moreover, spacing of main bars should not exceed three times the effective depth or 300 mm, whichever is smaller (clause 26.3.3b). Clause 34.5.2 also stipulates a nominal reinforcement of 360 mm2 per meter length in each direction on each face for thick foundations with thickness greater than 1 m.
  • 43. Structural Design of Individual Footings 5. In reinforced or plain concrete footings, the thickness at the edge should be greater than 150 mm (and 300 mm in the case of pile caps). This ensures that the footing will have enough rigidity to support the bearing pressures acting on them. 6. Usually, a levelling course of lean cement concrete of thickness 80– 100 mm is provided below the footing base, which serves as a separating layer between the natural soil and the footing so that any harmful chemical present in the soil will not react with the footing concrete.
  • 44. Shear Design Considerations One-way Shear One-way shear in footing is considered similar to that of slabs. Considering the footing as a wide beam, the critical section is taken along a vertical plane extending the full width of the footing, located at a distance equal to the effective depth of footing from the face of the column, pedestal, or wall, as shown in Fig. 15.12(a). Two-way Shear The behaviour of footing in two-way (punching) shear is identical to that of two-way flat slabs supported on columns. However, punching shear in footing is not as critical as in flat slabs, since the footing is supported by the soil below. Hence, it is desirable to check the tendency of the column punching through the footing, along the surface of a truncated pyramid around the column, called the critical perimeter.
  • 45. Critical Sections for Shear Fig. 15.12 Critical sections for shear (a) One-way shear (b) Two-way punching shear
  • 46. For the purposes of computing stresses in footings that support a round or octagonal column or pedestal, Clause 34.2.2 of IS 456 recommends the use of an equivalent inscribed square column which will result in conservative design. Equivalent Square Column Fig. 15.13 Equivalent square column (a) For round column (b) For octagonal column
  • 47. Bending Moment Considerations The bending moment at any section of a footing is determined by considering a vertical plane at this section, which extends completely across the footing, and then computing the moment due to soil pressure acting over the entire area of the footing on one side of this plane. The maximum bending moment to be used in the design of an isolated footing that supports a column, pedestal, or wall occurs at the following locations: 1. For footings supporting a wall, column, or pedestal, the maximum bending moment occurs at the face of the wall, column, or pedestal, as shown in Figs 15.14(a) and (b).
  • 48. 2. Since brick walls are generally less rigid than concrete walls, the maximum bending moment location is assumed at halfway between the centre line and the edge of the wall for footings supporting masonry walls, as shown in Fig. 15.14(c). 3. For footings supporting steel columns, the critical section is taken at halfway between the face of the column or pedestal and the edge of the base plate, as shown in Fig. 15.14(d). Bending Moment Considerations
  • 49. Fig. 15.14 Critical section for moment (a) Concrete column or wall (b) Pedestal footing (b) Masonry wall (c) Column with steel base plate
  • 50. Bending Moment Considerations The total tensile reinforcement, calculated to resist the maximum bending moment, has to be distributed as follows: 1. In one-way reinforced footing: The total reinforcement is distributed evenly across the full width of the footing. 2. In two-way square footing: The calculated reinforcement is distributed evenly across the width in both directions. 3. In two-way rectangular footing: The calculated reinforcement in the long direction is distributed evenly across the full width of the footing, whereas in the short span direction, it is distributed in different proportions in the central zone and the edge zones (see Fig. 15.15).
  • 51. Zones for Reinforcement in a Rectangular Footing Fig. 15.15 Zones for reinforcement in a rectangular footing
  • 52. Providing Development Length The design bond strength and development length in footing is the same as that in beams and slabs. The critical section for checking the development length in footing should be the same planes where the maximum bending moment occurs. In addition, it should be checked at all other vertical planes where abrupt changes of sections occur. In locations where the reinforcement is curtailed, anchorage requirements must be satisfied as in the case of beams.
  • 53. Transfer of Load at Base of Column The axial load, moments, and shear acting at the base of a column or pedestal are transferred to the footing by any one of the following means: 1. Compressive forces by bearing on concrete surface as well as by reinforcement 2. Tensile forces due to moment by reinforcement bars, which are properly anchored into column as well as footing, with adequate development length 3. Lateral forces by shear friction or shear keys
  • 54. Fig. 15.16 Bearing area in a stepped or sloped footing
  • 55. Transfer of Load at Base of Column If the permissible bearing stress is exceeded either in the base of the column or in the footing, reinforcement must be provided for developing the excess force. The reinforcement may be provided either by extending the longitudinal bars of column into the footing or by providing dowels as follows: 1. Minimum area of extended longitudinal bars or dowels must be 0.5 per cent of the cross-sectional area of the supported column or pedestal. 2. A minimum of four bars must be provided.
  • 56. Transfer of Load at Base of Column 3. If dowels are used, their diameter should not exceed the diameter of the column bars by more than 3 mm. 4. Enough development length should be provided to transfer the compression or tension to the supporting member. 5. Only column bars of diameter larger than 36 mm in compression can be doweled into the footings with bars of smaller diameter of necessary area. The dowel must extend into the column a distance equal to the development length of the column bar and also it must extend vertically into the footing up to a distance equal to the development length as shown in Fig. 15.17.
  • 57. Development Length Requirement Fig. 15.17 Development length requirement (a) Column in compression (b) Column in tension
  • 58. Design of Wall Footings The design principles used for beam actions also apply to the wall footings with minor modifications. As a result of the very large rigidity of the wall, the footing below the wall behaves like a cantilever on both sides of the wall, as shown in Fig. 15.18. The soil pressure causes the cantilevers to bend upwards, and as a result, reinforcement is required at the bottom of the footing, as shown in Fig. 15.18.
  • 59. Behaviour of Wall Footing Fig. 15.18 Behaviour of wall footing
  • 60. Design of Square Column Footings The various steps involved in the design of footings are as follows: 1. Determine the plan size of footing. 2. Calculate upward soil pressure. 3. Determine the depth of footing based on one-way shear considerations. 4. Check for punching shear.
  • 61. Fig. 15.19 Design of square footing
  • 62. Design of Square Column Footings 5. Calculate the area of steel. Check for minimum percentage of steel and bar spacing for crack control. 6. Check for development length. 7. Check for transfer of force at the base of column. 8. Check for development length of column bars. the column bars should project into the footing for a length equal to the development length in compression.
  • 63. Detailing of Reinforcement in Footing Fig. 15.20 Detailing of reinforcement in footing
  • 64. Design of Rectangular Footing The expressions are derived in this section for a rectangular pad-type footing as shown in Fig. 15.21. The design procedure is similar to that of square footings, except that the reinforcements are calculated in two directions and the check for one-way shear is to be made in both directions at a distance d from the face of the footing. All other checks are similar. In addition, the distribution of reinforcement should be made.
  • 65. Fig. 15.21 Design of rectangular footing (a) Plan and elevation (b) Critical sections for bending moment
  • 66. Design of Sloped Footings In India, sloped footings are used when the thickness of footing exceeds about 300–350 mm and they have a sloped top surface as shown in Fig. 15.22. This type of footing may require more depth but lesser reinforcement than uniform pad-type footing and hence may be economical. Moreover, the projection of the footing beyond the column face bends as a cantilever, and hence, the required flexibility is obtained by reducing the depth towards the free end, as is usually done in cantilever beams or slabs.
  • 67. Fig. 15.22 Sloped rectangular footing (a) Sloped footing (b) Critical sections for bending (c) Trapezoidal section
  • 68. Design of Sloped Footings There are three approaches to the calculation of bending moment and determination of depth of sloped footing as follows: 1. Determine the bending moment and corresponding depth. 2. Check for one-way shear. 3. Check for two-way shear. The other checks for development length (in both directions), transfer of force at the base of column, and development length of column bars have to be done as for square pad-type footing.
  • 69. Design of Combined Footings When the distance between two columns is small, the individual footings of these columns will overlap and hence it may be necessary to provide a combined footing. Such combined footings are also adopted when one of the columns is very close to the property line. The footing of this edge column will have to be combined with that of another column in the same line. When one column is near the property line and the next column in that row is far away, connecting these columns by a combined footing may be expensive. In such cases, counterweights called ‘dead man’ may be provided for the edge column to take care of the eccentric loading.
  • 70. Design of Combined Footings Combined footing can be divided into two categories: 1. Those supporting only two columns 2. Those supporting multiple columns (more than two columns)  When the SBC of the soil is low, the footings of individual columns merge, and hence, individual footings are combined to form a strip column footing that supports more than two columns that are placed in rows (see Fig. 15.23).
  • 71. Fig. 15.23 Strip column footing (a) With equal column spacings and loads (b) With unequal column spacings and loads
  • 72. Design of Combined Footings The longitudinal bending moment on the base at any section is the sum of the anticlockwise moments of each load to the left of the section minus the clockwise moment of the upward pressure between the section and the left-hand end of the base. The shearing force at any section is the algebraic sum of the vertical forces on one side of the section. In the transverse direction, the moment due to the cantilevering slab from the face of the column has to be considered. When there is irregular column spacing or there are varying column loads, a slab with upstanding T-beam may be used.
  • 73. Design of Combined Footings The degree of rigidity that must be given to the foundation beam is governed by the limiting differential movements that can be tolerated by the superstructure and by economies in the size and amount of reinforcement in the beams. Too great a rigidity should be avoided since it will result in high bending moments and shearing forces and the possibility of forming a wide crack if moments and shears are underestimated. When the beam is provided, it is designed as a continuous beam and the base slab as cantilevering from either side of the beam.
  • 74. Arrangement of Strips When the strips are arranged in both directions, a grid foundation is formed as shown in Fig. 15.24(a). In many cases, especially when the SBC is very low, the strips may merge resulting in a mat foundation or raft foundation, as shown in Fig. 15.24(b). Strip or mat foundations may also be provided with column pedestals, as shown in Fig. 15.24(a), in order to provide the required shear strength or development length for dowels. The strip and mat foundations, due to their continuity and rigidity, reduce the differential settlement of individual columns relative to each other.
  • 75. Arrangement of Strips Fig. 15.24 Arrangement of strips (a) Grid foundation (b) Mat foundation
  • 76. Two-column Footings The first step in the design of combined footings is to make the centroid of the footing area coincide with the resultant of the two- column loads. This produces uniform bearing pressure over the entire area and avoids tilting of the footing. In plan, the footing may be rectangular, trapezoidal, or T-shaped (see Fig. 15.25). The simple relationships as shown in Fig. 15.25 may be used to determine the shape of the bearing area, so that the centroid of the footing and the resultant of loads coincide.
  • 77. Two-column Footings Fig. 15.25 Two-column footings (a) Rectangular (b) Trapezoidal (c) T-shaped
  • 78. As in isolated footings, the factored net soil pressure is computed as the resultant factored load divided by the selected base area. This pressure is assumed to act as uniformly distributed load. It has to be noted that when there are moments in addition to loads, the pressure distribution will be non-uniform. There will be a predominant flexural behaviour in the longitudinal direction (as shown in longitudinal beam strips A–B–C of Figs 15.26a and b), and the two-way action will be limited and present only in the transverse strips in the neighbourhood of columns (as shown by strips A–D and B–E in Fig. 15.26a). Behaviour of Combined Two-column Footing
  • 79. Fig. 15.26 Behaviour of two-column footing (a) Load distribution (b) Behaviour of longitudinal beam strips (c) Behaviour of transverse beam strips Behaviour of Combined Two-column Footing
  • 80. Design Considerations of Combined Footing The following are the various steps of one such approach: 1. Determine the size of footing. 2. Calculate the bending moment and shear at various locations. The loads are then multiplied by the appropriate load factors, and the shear and bending moments are calculated from statics for these loads, considering the footing slab as simply supported on the two-column strips, with overhangs (if any) beyond each column strip, and assuming the supports at the column centre lines, as shown in Fig. 15.27.
  • 81. Fig. 15.27 Bending moment and shear force in two-column footing (a) Rectangular combined footing (b) Bending of footing and loading (c) Bending moment diagram (d) Shear force diagram
  • 82. 3. Determine the thickness of the footing. The thickness of the footing will usually be governed by shear considerations. 4. Check for punching shear. Check the calculated depth for safety of punching shear. 5. Determine the reinforcement in the long direction. Find the bending moment where shear V = 0 and determine reinforcement in the long direction for the chosen depth. Check whether minimum steel requirements and the reinforcement required for resisting shear are satisfied. Provide minimum steel in the remaining parts of the footing. Design Considerations of Combined Footing
  • 83. Design Considerations of Combined Footing 6. Check for development length for the chosen diameter of steel. 7. Determine the reinforcement in the short direction. Provide minimum steel in the remaining parts of the footing in the transverse direction. 8. Check for development length in the transverse direction as well for the chosen diameter of steel. 9. Check for shear in the transverse direction as well at a distance d from the face of the column.
  • 84. Fig. 15.28 Typical detailing of combined rectangular footing
  • 85. Design Considerations of Combined footing 10. Check for transfer of force at the column face. If the limiting bearing resistance is less than the column load, dowels must be provided. 11. Detail the reinforcement as per design and provide nominal reinforcement wherever necessary. Typical detailing for combined rectangular footing is shown in Fig. 15.28. In order to prevent shear failure along the inclined plane in footing, where a column is placed on the edge, SP 34:1987 suggests providing horizontal U-bars around the vertical starter bars, as shown in Fig. 15.29.
  • 86. Column at the Edge of Footing Fig. 15.29 Column at the edge of footing
  • 87. Design Considerations of Combined Footing The design of trapezoidal combined footing is similar to that of rectangular combined footing. However, in such footings the longitudinal bars are usually arranged in a fan shape with alternate bars cut off at some distance away from the narrow end (typical detailing is shown in Fig. 15.30).
  • 88. Fig. 15.30 Detailing of trapezoidal footing
  • 89. Design of Combined Slab and Beam Footing When the depth required for slab footing is large based on shear considerations, it will become uneconomical. In such cases, a combined slab and beam footing may be provided as shown in Fig. 15.31, in which a central longitudinal beam connects the two columns. The base slab bends transversely under the action of uniform soil pressure from below and behaves like a one-way cantilevered slab. The loads transferred from the slab are resisted by the longitudinal beam.
  • 90. Combined Slab and Beam Footing Fig. 15.31 Combined slab and beam footing
  • 91. The beam will be subjected to high shear forces, which may be resisted by providing multi-legged stirrups, as shown in Fig. 15.31. The flexural reinforcement in the slab, designed for the cantilever moment at the face of the beam, should be provided at the bottom of the slab, as shown in Fig. 15.31. Punching shear will not govern such beam and slab footings. The reinforcements should be checked for development length requirements. Design of Combined Slab and Beam Footing
  • 92. Design of Combined Footing with Strap Beam When the distance between the two columns is large, it is economical to provide strap footings, in which a beam connecting the two-column footings is provided, as shown in Fig. 15.2(d). It is assumed that the strap beam is rigid and that it transfers the load from the columns to the footings and not directly to the soil. The column loads are transferred to the soil only through the independent footings. The areas of independent footings are so chosen that the soil pressure acting on the footings is uniform and the resultant soil pressure on the footing areas coincide with the C.G. of the column loads.
  • 93. Design of Combined Footing with Strap Beam Fig. 15.32 Bending moment and shear force in strap beam (a) Plan (b) Loading on strap beam (c) Bending moment diagram (d) Shear force diagram
  • 94. The width of strap beam is generally equal to or greater than the sides of columns at a right angle to the strap beam. The strap beam is designed as a rectangular beam by assuming that the loads are acting uniformly on it from (a) columns in the downward direction and (b) footings of columns C1 and C2 in the upward direction, as shown in Fig. 15.32. The depth of the strap beam is decided based on bending moment and shear force considerations. Longitudinal reinforcements are provided based on bending moment considerations and transverse stirrups based on shear considerations. Design of Combined Footing with Strap Beam
  • 95. Design of Plain Concrete Footings Occasionally, plain concrete footings are used to support light loads, especially when the supporting soil has good SBC. Such footings are also called pedestal footings. The footing will be in the form of a solid rectangular unreinforced concrete block. The depth of the plain concrete pedestal can be determined based on the angle of dispersion of the load. When the depth to transfer the load to the ground bearing is less than the permissible angle of spread, the foundations should be reinforced.
  • 96. Plain Concrete Footings Fig. 15.33 Thickness of plain concrete footing