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About This Presentation
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Slide Content
CE
-
632
CE
632
Foundation Analysis and Design Design
ShallowFoundations ShallowFoundations Shallow
Foundations Shallow
Foundations
1
-
632
CE
632
Foundation Analysis and Design Design
ShallowFoundations ShallowFoundations Shallow
Foundations Shallow
Foundations
1
Foundation Analysis and Design: Dr. Amit Prashant
SUMMARYofTerminology SUMMARYofTerminology SUMMARY
of
Terminology SUMMARY
of
Terminology
Gross Loading Intensity
Ttl tth l l ff dti
QQQ
++
T
o
t
a
l pressure a
t
th
e
leve
l o
f
f
oun
d
a
ti
on
including the weight of superstructure,
foundation, and the soil above foundation.
superstructure Foundation soil
Foundation
gQQQ
q
A
++
=
Net Loading Intensity
Pressure at the level of foundation causing actual
settlement due to stress increase. This includes
ng f
qq D
γ
=
−
the weight of superstructure and foundation only.
Ultimate Bearing capacity:
ng f
Maximum gross intensity of loading that the
soil can support against shear failure is
called ultimate bearing capacity.
from
Bearing capacity calculation
u
q
Net Ultimate Bearing Capacity:
Maximum net intensity of loading that the
D
γ
2
Maximum
net
intensity
of
loading
that
the
soil can support at the level of foundation.
nu u f
qq
D
γ
=
−
SUMMARYofTerminology SUMMARYofTerminology SUMMARY
of
Terminology SUMMARY
of
Terminology
Gross Loading Intensity
Ttl tth l l ff dti
QQQ
++
T
o
t
a
l pressure a
t
th
e
leve
l o
f
f
oun
d
a
ti
on
including the weight of superstructure,
foundation, and the soil above foundation.
superstructure Foundation soil
Foundation
gQQQ
q
A
++
=
Net Loading Intensity
Pressure at the level of foundation causing actual
settlement due to stress increase. This includes
ng f
qq D
γ
=
−
the weight of superstructure and foundation only.
Ultimate Bearing capacity:
ng f
Maximum gross intensity of loading that the
soil can support against shear failure is
called ultimate bearing capacity.
from
Bearing capacity calculation
u
q
Net Ultimate Bearing Capacity:
Maximum net intensity of loading that the
D
γ
2
Maximum
net
intensity
of
loading
that
the
soil can support at the level of foundation.
nu u f
D
γ
=
−
Foundation Analysis and Design: Dr. Amit Prashant
SUMMARYofTerminology SUMMARYofTerminology SUMMARY
of
Terminology SUMMARY
of
Terminology
Net Safe Bearing capacity:
Maximum net intensity of loading that the soil can
q
Maximum
net
intensity
of
loading
that
the
soil
can
safely support without the risk of shear failure.
nu
nsq
q
FOS
=
Gross Safe Bearing capacity:
Maximum gross intensity of loading that the soil
can safely support without the risk of shear failure.
gs ns f
qq D
γ
=
+
Safe Bearing Pressure:
Maximum net intensity of loading that can be
f ttl t l i
allowed on the soil without settlement
exceeding the permissible limit.
f
rom se
ttl
emen
t
ana
l
ys
i
s
s
q
ρ
Allowable Bearing Pressure:
Maximum net intensity of loading that can
be allowed on the soil with no possibility of
Minimum of bearingcapacityand
anet
q
−
3
shear failure or settlement exceeding the permissible limit.
bearing
capacity
and
settlement analysis
SUMMARYofTerminology SUMMARYofTerminology SUMMARY
of
Terminology SUMMARY
of
Terminology
Net Safe Bearing capacity:
Maximum net intensity of loading that the soil can
q
Maximum
net
intensity
of
loading
that
the
soil
can
safely support without the risk of shear failure.
nu
nsq
q
FOS
=
Gross Safe Bearing capacity:
Maximum gross intensity of loading that the soil
can safely support without the risk of shear failure.
gs ns f
qq D
γ
=
+
Safe Bearing Pressure:
Maximum net intensity of loading that can be
f ttl t l i
allowed on the soil without settlement
exceeding the permissible limit.
f
rom se
ttl
emen
t
ana
l
ys
i
s
s
q
ρ
Allowable Bearing Pressure:
Maximum net intensity of loading that can
be allowed on the soil with no possibility of
Minimum of bearingcapacityand
anet
q
−
3
shear failure or settlement exceeding the permissible limit.
bearing
capacity
and
settlement analysis
Foundation Analysis and Design: Dr. Amit Prashant
CommonTypesofFooting CommonTypesofFooting Common
Types
of
Footing Common
Types
of
Footing
„
Strip footing
„
SpreadFooting
„
Spread
Footing
4
CommonTypesofFooting CommonTypesofFooting Common
Types
of
Footing Common
Types
of
Footing
„
Strip footing
„
SpreadFooting
„
Spread
Footing
4
Foundation Analysis and Design: Dr. Amit Prashant
CommonTypesofFooting CommonTypesofFooting Common
Types
of
Footing Common
Types
of
Footing
„
Combined Footing
„
RaftorMatfooting
„
Raft
or
Mat
footing
5
CommonTypesofFooting CommonTypesofFooting Common
Types
of
Footing Common
Types
of
Footing
„
Combined Footing
„
RaftorMatfooting
„
Raft
or
Mat
footing
5
Foundation Analysis and Design: Dr. Amit Prashant
GeneralRequirementsofFoundation GeneralRequirementsofFoundation General
Requirements
of
Foundation General
Requirements
of
Foundation
„
Location and Depth of Foundation
„
Bearing Capacity of Foundation
DONE DONE
„
Sett
le
m
e
n
t
o
f F
ou
n
dat
io
n
DONE DONE
Sette e to ou dato
DONE DONE
6
GeneralRequirementsofFoundation GeneralRequirementsofFoundation General
Requirements
of
Foundation General
Requirements
of
Foundation
„
Location and Depth of Foundation
„
Bearing Capacity of Foundation
DONE DONE
„
Sett
le
m
e
n
t
o
f F
ou
n
dat
io
n
DONE DONE
Sette e to ou dato
DONE DONE
6
Foundation Analysis and Design: Dr. Amit Prashant
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
„
The following considerations are necessary for deciding the locationanddepthoffoundation location
and
depth
of
foundation
¾
As per IS:1904-1986, minimum depth of foundation shall be 0.50 m.
¾
Foundation shall be placed below the zone of
¾
The frost heave
¾
Excessive volume change due to moisture variation (usually exists
within 1.5 to 3.5 m depth of soil from the top surface)
¾
Topsoil or organic material
¾
Peat and Muck
¾
Unconsolidated material such as waste dump
¾
Unconsolidated
material
such
as
waste
dump
¾
Foundations adjacent to flowing water (flood water, rivers, etc.) shall be protected against scouring. The follo wing steps to be taken for design in such conditions in
such
conditions
¾
Determine foundation type
¾
Estimate probable depth of scour, effects, etc.
7
¾
Estimate cost of foundation for normal and various scour conditions
¾
Determine the scour versus risk, and revise the design accordingly
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
„
The following considerations are necessary for deciding the locationanddepthoffoundation location
and
depth
of
foundation
¾
As per IS:1904-1986, minimum depth of foundation shall be 0.50 m.
¾
Foundation shall be placed below the zone of
¾
The frost heave
¾
Excessive volume change due to moisture variation (usually exists
within 1.5 to 3.5 m depth of soil from the top surface)
¾
Topsoil or organic material
¾
Peat and Muck
¾
Unconsolidated material such as waste dump
¾
Unconsolidated
material
such
as
waste
dump
¾
Foundations adjacent to flowing water (flood water, rivers, etc.) shall be protected against scouring. The follo wing steps to be taken for design in such conditions in
such
conditions
¾
Determine foundation type
¾
Estimate probable depth of scour, effects, etc.
7
¾
Estimate cost of foundation for normal and various scour conditions
¾
Determine the scour versus risk, and revise the design accordingly
Foundation Analysis and Design: Dr. Amit Prashant
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
¾
IS:1904-1986 recommendations for foundations adjacent to
slopes and existing structures
¾
When the ground surface slopes
¾
When
the
ground
surface
slopes
downward adjacent to footing, the
sloping surface should not cut the
line of distribution of the load
1V
2H
line
of
distribution
of
the
load
(2H:1V).
¾
In granular soils, the line joining the
ldjtdf d lower a
dj
acen
t
e
d
ges o
f
upper an
d
lower footings shall not have a
slope steeper than 2H:1V.
¾
In clayey soil, the line joining the lower adjacent edge of the upper footin
g
and the u
pp
er ad
jacent
1V
2H
8
gppj
edge of the lower footing should not
be steeper than 2H:1V.
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
¾
IS:1904-1986 recommendations for foundations adjacent to
slopes and existing structures
¾
When the ground surface slopes
¾
When
the
ground
surface
slopes
downward adjacent to footing, the
sloping surface should not cut the
line of distribution of the load
1V
2H
line
of
distribution
of
the
load
(2H:1V).
¾
In granular soils, the line joining the
ldjtdf d lower a
dj
acen
t
e
d
ges o
f
upper an
d
lower footings shall not have a
slope steeper than 2H:1V.
¾
In clayey soil, the line joining the lower adjacent edge of the upper footin
g
and the u
pp
er ad
jacent
1V
2H
8
gppj
edge of the lower footing should not
be steeper than 2H:1V.
Foundation Analysis and Design: Dr. Amit Prashant
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
¾
Other recommendations for footing adjacent to existing
structures
¾
Minimum horizontal distance between the foundations shall not
be less than the width of larger footing to avoid damage to
existing structure existing
structure
¾
If the distance is limited, the principal of 2H:1V distribution should be used so as to minimize the influence to old structure
¾
Proper care is needed during excavation phase of foundation
construction beyond merely depending on the 2H:1V criteria for
old foundations. Excavation may cause settlement to old foundation due to lateral bulging in the excavation and/or shear failure due to reduction in overburden stress in the surrounding of old foundation
9
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
¾
Other recommendations for footing adjacent to existing
structures
¾
Minimum horizontal distance between the foundations shall not
be less than the width of larger footing to avoid damage to
existing structure existing
structure
¾
If the distance is limited, the principal of 2H:1V distribution should be used so as to minimize the influence to old structure
¾
Proper care is needed during excavation phase of foundation
construction beyond merely depending on the 2H:1V criteria for
old foundations. Excavation may cause settlement to old foundation due to lateral bulging in the excavation and/or shear failure due to reduction in overburden stress in the surrounding of old foundation
9
Foundation Analysis and Design: Dr. Amit Prashant
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
¾
Footings
onsurfacerockorslopingrockfaces
¾
Footings
on
surface
rock
or
sloping
rock
faces
¾
For the locations with shallow rock beds, the foundation can be
laid on the rock surface after chipping the top surface.
¾
If the rock bed has some slope, it may be advisable to provide
dowel bars of minimum 16 mm diameter and 225 mm embedment
into the rock at 1 m s
p
acin
g
.
pg
¾
A raised water table may cause damage to the foundation
by
¾
Floating the structure
¾
Reducing the effective stress beneath the foundation
Water logging around the building may also cause wet basements. In
such cases, proper drainage system around the foundation may be
10
required so that water does not accumulate.
LocationanddepthofFoundation LocationanddepthofFoundation Location
and
depth
of
Foundation Location
and
depth
of
Foundation
¾
Footings
onsurfacerockorslopingrockfaces
¾
Footings
on
surface
rock
or
sloping
rock
faces
¾
For the locations with shallow rock beds, the foundation can be
laid on the rock surface after chipping the top surface.
¾
If the rock bed has some slope, it may be advisable to provide
dowel bars of minimum 16 mm diameter and 225 mm embedment
into the rock at 1 m s
p
acin
g
.
pg
¾
A raised water table may cause damage to the foundation
by
¾
Floating the structure
¾
Reducing the effective stress beneath the foundation
Water logging around the building may also cause wet basements. In
such cases, proper drainage system around the foundation may be
10
required so that water does not accumulate.
Foundation Analysis and Design: Dr. Amit Prashant
LoadsonFoundation LoadsonFoundation Loads
on
Foundation Loads
on
Foundation
„
Permanent Load:This is actual service load/sustained loads of a structure which give rise stresses and deformations in the soil below
the foundation causing its settlement.
TitLd
Thi t dd l d i t d t
„
T
rans
i
en
t
L
oa
d
:
Thi
s momen
t
ary or su
dd
en
loa
d
impar
t
e
d
t
o a
structure due to wind or seismic vibrations. Due to its transitory
nature, the stresses in the soil below the foundation carried by such
loads are allowed certain percentage increase over the allowable loads
are
allowed
certain
percentage
increase
over
the
allowable
safe values.
„
Dead Load:It includes the weight of the column/wall, footings,
foundations, the overlaying fill but excludes the weight of the
dis
p
laced soil
p
„
Live Load:This is taken as per the specifications of IS:875 (pt-2) –
1987.
11
LoadsonFoundation LoadsonFoundation Loads
on
Foundation Loads
on
Foundation
„
Permanent Load:This is actual service load/sustained loads of a structure which give rise stresses and deformations in the soil below
the foundation causing its settlement.
TitLd
Thi t dd l d i t d t
„
T
rans
i
en
t
L
oa
d
:
Thi
s momen
t
ary or su
dd
en
loa
d
impar
t
e
d
t
o a
structure due to wind or seismic vibrations. Due to its transitory
nature, the stresses in the soil below the foundation carried by such
loads are allowed certain percentage increase over the allowable loads
are
allowed
certain
percentage
increase
over
the
allowable
safe values.
„
Dead Load:It includes the weight of the column/wall, footings,
foundations, the overlaying fill but excludes the weight of the
dis
p
laced soil
p
„
Live Load:This is taken as per the specifications of IS:875 (pt-2) –
1987.
11
Foundation Analysis and Design: Dr. Amit Prashant
Loads for Proportioning and Design of Foundation Loads for Proportioning and Design of Foundation IS:1904 IS:1904 --19861986
„
Followingcombinationsshallbeused Following
combinations
shall
be
used
¾
Dead load + Live load
¾
Dead Load + Live load + Wind/Seismic load
„
For cohesive soils only 50% of actual live load is considered
for design
(Due to settlement being time dependent)
„
For wind/seismic load < 25% of Dead + Live load
¾
Wind/seismic load is neglected and first combination is used to compare with safe bearing load to satisfy allowable bearing pressure compare
with
safe
bearing
load
to
satisfy
allowable
bearing
pressure
„
For wind/seismic load ≥25% of Dead + Live load
¾
It becomes necessar
y
to ensure that
p
ressure due to second
yp
combination of load does not exceed the safe bearing capacity by
more than 25%. When seismic forces are considered, the safe
bearin
g
capacit
y
shall be increased as specified in IS: 1893
(
Part-1
)
-
12
gy (
)
2002 (see next slide). In non-cohesive soils, analysis for liquefaction and settlement under earthquake shall also be made.
Loads for Proportioning and Design of Foundation Loads for Proportioning and Design of Foundation IS:1904 IS:1904 --19861986
„
Followingcombinationsshallbeused Following
combinations
shall
be
used
¾
Dead load + Live load
¾
Dead Load + Live load + Wind/Seismic load
„
For cohesive soils only 50% of actual live load is considered
for design
(Due to settlement being time dependent)
„
For wind/seismic load < 25% of Dead + Live load
¾
Wind/seismic load is neglected and first combination is used to compare with safe bearing load to satisfy allowable bearing pressure compare
with
safe
bearing
load
to
satisfy
allowable
bearing
pressure
„
For wind/seismic load ≥25% of Dead + Live load
¾
It becomes necessar
y
to ensure that
p
ressure due to second
yp
combination of load does not exceed the safe bearing capacity by
more than 25%. When seismic forces are considered, the safe
bearin
g
capacit
y
shall be increased as specified in IS: 1893
(
Part-1
)
-
12
gy (
)
2002 (see next slide). In non-cohesive soils, analysis for liquefaction and settlement under earthquake shall also be made.
Foundation Analysis and Design: Dr. Amit Prashant
13
13
Foundation Analysis and Design: Dr. Amit Prashant
Safe Bearing Capacity: National Building Code of Safe Bearing Capacity: National Building Code of India (1983) India (1983)
14
Safe Bearing Capacity: National Building Code of Safe Bearing Capacity: National Building Code of India (1983) India (1983)
14
Foundation Analysis and Design: Dr. Amit Prashant
Safe Bearin
g
Safe Bearin
g
g g
Capacity: National Capacity: National
Building Code of Building Code of
India (1983) India (1983)
15
Safe Bearin
g
Safe Bearin
g
g g
Capacity: National Capacity: National
Building Code of Building Code of
India (1983) India (1983)
15
Foundation Analysis and Design: Dr. Amit Prashant
OtherconsiderationsforShallowFoundationDesign OtherconsiderationsforShallowFoundationDesign Other
considerations
for
Shallow
Foundation
Design Other
considerations
for
Shallow
Foundation
Design
„
For economical design, it is preferr ed to have square footing for vertical
loads and rectangular footing for the columns carrying moment
„
Allowable bearing pressure should not be very high in comparison to the net loading intensity leading to an uneconomical design.
„
It is preferred to use SPT or Plate load test for cohesion less soils and
„
It
is
preferred
to
use
SPT
or
Plate
load
test
for
cohesion
less
soils
and
undrained shear strength test for cohesive soils.
„
In case of lateral loads or moments, the foundation should also be
checked to be safe against sliding and overturning The FOS shall not be checked
to
be
safe
against
sliding
and
overturning
.
The
FOS
shall
not
be
less than 1.75 against sliding and 2.0 against overturning. When
wind/seismic loads are considered the FOS is taken as 1.5 for both the
cases.
„
Wall foundation width shall not be less than [wall thickness + 30 cm].
„
Unreinforced foundation should have angular spread of load from the supported column with the following criteria supported
column
with
the
following
criteria
¾
2V:1H for masonry foundation
¾
3V:2H for lime concrete
16
¾
1V:1H for cement concrete foundation
The bottom most layer should have a thickness of atleast 150 mm.
OtherconsiderationsforShallowFoundationDesign OtherconsiderationsforShallowFoundationDesign Other
considerations
for
Shallow
Foundation
Design Other
considerations
for
Shallow
Foundation
Design
„
For economical design, it is preferr ed to have square footing for vertical
loads and rectangular footing for the columns carrying moment
„
Allowable bearing pressure should not be very high in comparison to the net loading intensity leading to an uneconomical design.
„
It is preferred to use SPT or Plate load test for cohesion less soils and
„
It
is
preferred
to
use
SPT
or
Plate
load
test
for
cohesion
less
soils
and
undrained shear strength test for cohesive soils.
„
In case of lateral loads or moments, the foundation should also be
checked to be safe against sliding and overturning The FOS shall not be checked
to
be
safe
against
sliding
and
overturning
.
The
FOS
shall
not
be
less than 1.75 against sliding and 2.0 against overturning. When
wind/seismic loads are considered the FOS is taken as 1.5 for both the
cases.
„
Wall foundation width shall not be less than [wall thickness + 30 cm].
„
Unreinforced foundation should have angular spread of load from the supported column with the following criteria supported
column
with
the
following
criteria
¾
2V:1H for masonry foundation
¾
3V:2H for lime concrete
16
¾
1V:1H for cement concrete foundation
The bottom most layer should have a thickness of atleast 150 mm.
Foundation Analysis and Design: Dr. Amit Prashant
CbidFti CbidFti C
om
bi
ne
d
F
oo
ti
ngs
C
om
bi
ne
d
F
oo
ti
ngs
„
Combined footin
g
is
p
referred when
gp
¾
The columns are spaced too closely that if isolated footing is
provided the soil beneath may have a part of common influence
zone.
¾
The bearing capacity of soil is su ch that isolated footing design
will require extent of the column foundation to go beyond the
propert
y
line.
y
„
Types of combined footings
¾
Rectangular combined footing Tidlbidfti
17
¾
T
rapezo
id
a
l com
bi
ne
d
f
oo
ti
ng
¾
Strap beam combined footing
CbidFti CbidFti C
om
bi
ne
d
F
oo
ti
ngs
C
om
bi
ne
d
F
oo
ti
ngs
„
Combined footin
g
is
p
referred when
gp
¾
The columns are spaced too closely that if isolated footing is
provided the soil beneath may have a part of common influence
zone.
¾
The bearing capacity of soil is su ch that isolated footing design
will require extent of the column foundation to go beyond the
propert
y
line.
y
„
Types of combined footings
¾
Rectangular combined footing Tidlbidfti
17
¾
T
rapezo
id
a
l com
bi
ne
d
f
oo
ti
ng
¾
Strap beam combined footing
Foundation Analysis and Design: Dr. Amit Prashant
RectangularCombinedFooting RectangularCombinedFooting
Q
1
+Q
2
x
Rectangular
Combined
Footing Rectangular
Combined
Footing
„
If two or more columns are carrying almostequalloads rectangular
Q
1
Q
2
almost
equal
loads
,
rectangular
combined footing is provided
„
Pro
p
ortionin
g
of foundation will
L
1
SL
2
pg
involve the following steps
¾
Area of foundation
12
QQ
A
+
=
¾
Location of the resultant force
anet
A
q
−
2
QS
xQQ
=
+
¾
For uniform distribution of pressure under the foundation, the
resultant load should
p
ass throu
g
h the center of foundation base.
12
QQ
+
pg
L
ength of foundation,
O
ffset on the other side,
(
)
1
2 LLS
=
+
21
0 LLSL
=
−−>
18
¾
The width of foundation,
BAL
=
RectangularCombinedFooting RectangularCombinedFooting
Q
1
+Q
2
x
Rectangular
Combined
Footing Rectangular
Combined
Footing
„
If two or more columns are carrying almostequalloads rectangular
Q
1
Q
2
almost
equal
loads
,
rectangular
combined footing is provided
„
Pro
p
ortionin
g
of foundation will
L
1
SL
2
pg
involve the following steps
¾
Area of foundation
12
A
+
=
¾
Location of the resultant force
anet
A
q
−
2
QS
xQQ
=
+
¾
For uniform distribution of pressure under the foundation, the
resultant load should
p
ass throu
g
h the center of foundation base.
12
+
pg
L
ength of foundation,
O
ffset on the other side,
(
)
1
2 LLS
=
+
21
0 LLSL
=
−−>
18
¾
The width of foundation,
BAL
=
Foundation Analysis and Design: Dr. Amit Prashant
TrapezoidalCombinedFooting TrapezoidalCombinedFooting
Q
1
+Q
2
x
Trapezoidal
Combined
Footing Trapezoidal
Combined
Footing
„
If one of the columns is carrying much larger load than the other one
Q
1
Q
2
L
S
L
larger
load
than
the
other
one
,
trapezoidal combined footing is provided
„
Proportioning of foundation will involve
the following steps if L and L
are known
L
1
S
L
2
the
following
steps
if
L
,
and
L
1
are
known
¾
Area of foundation
12
QQ
A
q
+
=
¾
Location of the resultant force
anet
q
−
2
12QS
xQQ
=
+
B
1
B
2
¾
For uniform distribution of pressure under the foundation, the
resultant load should pass through the center of foundation base.
Thi i th l ti hi
12
QQ
Thi
s g
ives
th
e re
la
ti
ons
hi
p,
12
1
12
2
3
BBL
xL
BB
⎛⎞+
+=⎜⎟
+
⎝⎠
Slti fth
19
¾
Area of the footing,
12
⎝⎠
12
2
B
B
LA +
=
S
o
lu
ti
on o
f
th
ese
two equations
gives B
1
and B
2
TrapezoidalCombinedFooting TrapezoidalCombinedFooting
Q
1
+Q
2
x
Trapezoidal
Combined
Footing Trapezoidal
Combined
Footing
„
If one of the columns is carrying much larger load than the other one
Q
1
Q
2
L
S
L
larger
load
than
the
other
one
,
trapezoidal combined footing is provided
„
Proportioning of foundation will involve
the following steps if L and L
are known
L
1
S
L
2
the
following
steps
if
L
,
and
L
1
are
known
¾
Area of foundation
12
A
q
+
=
¾
Location of the resultant force
anet
q
−
2
12QS
xQQ
=
+
B
1
B
2
¾
For uniform distribution of pressure under the foundation, the
resultant load should pass through the center of foundation base.
Thi i th l ti hi
12
Thi
s g
ives
th
e re
la
ti
ons
hi
p,
12
1
12
2
3
BBL
xL
BB
⎛⎞+
+=⎜⎟
+
⎝⎠
Slti fth
19
¾
Area of the footing,
12
⎝⎠
12
2
B
B
LA +
=
S
o
lu
ti
on o
f
th
ese
two equations
gives B
1
and B
2
Foundation Analysis and Design: Dr. Amit Prashant
StrapCombinedFooting StrapCombinedFooting
M
2
Strap
Combined
Footing Strap
Combined
Footing
„
Strap footing is used to connect an eccentrically loaded
Q
1
Q
2
2
connect
an
eccentrically
loaded
column footing to an interior
column so that the moment can
be transferred throu
g
h the
g
beam and have uniform stress distribution beneath both the foundations.
„
This type of footing is preferred over the rectangular or tra
p
ezoidal footin
g
if distance
pg
between the columns is relatively large.
„
Some design considerations:
„
Some
design
considerations:
¾
Strap must be rigid: I
strap
/I
footing
> 2.
¾
Footings should be proportioned to have approximately equal soil
i d t id diff ti l ttl t
20
pressure
in or
d
er
t
o avo
id
diff
eren
ti
a
l se
ttl
emen
t
¾
Strap beam should not have contact with soil to avoid soil reaction to it.
StrapCombinedFooting StrapCombinedFooting
M
2
Strap
Combined
Footing Strap
Combined
Footing
„
Strap footing is used to connect an eccentrically loaded
Q
1
Q
2
2
connect
an
eccentrically
loaded
column footing to an interior
column so that the moment can
be transferred throu
g
h the
g
beam and have uniform stress distribution beneath both the foundations.
„
This type of footing is preferred over the rectangular or tra
p
ezoidal footin
g
if distance
pg
between the columns is relatively large.
„
Some design considerations:
„
Some
design
considerations:
¾
Strap must be rigid: I
strap
/I
footing
> 2.
¾
Footings should be proportioned to have approximately equal soil
i d t id diff ti l ttl t
20
pressure
in or
d
er
t
o avo
id
diff
eren
ti
a
l se
ttl
emen
t
¾
Strap beam should not have contact with soil to avoid soil reaction to it.
Foundation Analysis and Design: Dr. Amit Prashant
Example:StrapFooting Example:StrapFooting Example:
Strap
Footing Example:
Strap
Footing
S
Q
1
Q
2
1
2
R
1
R
2
B
1
B
2
L
d
c1
21
Example:StrapFooting Example:StrapFooting Example:
Strap
Footing Example:
Strap
Footing
S
Q
1
Q
2
1
2
R
1
R
2
B
1
B
2
L
d
c1
21
Foundation Analysis and Design: Dr. Amit Prashant
Rft MtF dti Rft MtF dti R
a
ft
or
M
a
t
F
oun
d
a
ti
ons
R
a
ft
or
M
a
t
F
oun
d
a
ti
ons
„
Whereisitneeded?
„
Where
is
it
needed?
¾
Structures like chimneys, silos, cooling towers, buildings
with basements where continuous water proofing is
needed needed
¾
For foundations where differential settlement can be a major concern
¾
For soft soils strata or site with pockets of weak soil
¾
In situations where individual footings may touch or overla
p
each other.
22
p
Rft MtF dti Rft MtF dti R
a
ft
or
M
a
t
F
oun
d
a
ti
ons
R
a
ft
or
M
a
t
F
oun
d
a
ti
ons
„
Whereisitneeded?
„
Where
is
it
needed?
¾
Structures like chimneys, silos, cooling towers, buildings
with basements where continuous water proofing is
needed needed
¾
For foundations where differential settlement can be a major concern
¾
For soft soils strata or site with pockets of weak soil
¾
In situations where individual footings may touch or overla
p
each other.
22
p
Foundation Analysis and Design: Dr. Amit Prashant
TypesofRaftFoundation TypesofRaftFoundation Types
of
Raft
Foundation Types
of
Raft
Foundation
Pl Sl b R f
Ffil lldif i fl
„
Pl
ane
Sl
a
b
R
a
f
ts:
F
or
f
a
ir
ly sma
ll
an
d
un
if
orm spac
ing o
f
co
lumns
and when the supporting soil is not too compressible.
„
Beam and Slab:
For large column spacing and unequal column
„
Beam
and
Slab:
For
large
column
spacing
and
unequal
column
loads.
„
Slab with Column Pedestals:For columns with heav
y
loads which
y
may require large shear strength or flexural strength of slab.
„
Cellular Rafts:For compensated foundations to avoid differential settlements in weak soils.
„
Piled Rafts:For heavy structures on soft soils in order to share the loads with piles loads
with
piles
.
„
Strip Rafts or Grid Rafts:For economical design where a complete slab may be avoided.
23
slab
may
be
avoided.
TypesofRaftFoundation TypesofRaftFoundation Types
of
Raft
Foundation Types
of
Raft
Foundation
Pl Sl b R f
Ffil lldif i fl
„
Pl
ane
Sl
a
b
R
a
f
ts:
F
or
f
a
ir
ly sma
ll
an
d
un
if
orm spac
ing o
f
co
lumns
and when the supporting soil is not too compressible.
„
Beam and Slab:
For large column spacing and unequal column
„
Beam
and
Slab:
For
large
column
spacing
and
unequal
column
loads.
„
Slab with Column Pedestals:For columns with heav
y
loads which
y
may require large shear strength or flexural strength of slab.
„
Cellular Rafts:For compensated foundations to avoid differential settlements in weak soils.
„
Piled Rafts:For heavy structures on soft soils in order to share the loads with piles loads
with
piles
.
„
Strip Rafts or Grid Rafts:For economical design where a complete slab may be avoided.
23
slab
may
be
avoided.
Foundation Analysis and Design: Dr. Amit Prashant
GeneralConsiderationsforRaftFoundation GeneralConsiderationsforRaftFoundation General
Considerations
for
Raft
Foundation General
Considerations
for
Raft
Foundation
„
The depth of foundation shall not be less than 1.0 m.
„
Punching shear failure for raft foundation on cohesionless
soils is not an option so it shall not be considered for
analysis Thedesignismostlygovernedbysettlement analysis
.
The
design
is
mostly
governed
by
settlement
criteria.
„
Forraftfoundationsoncohesivesoils stabilityagainst
„
For
raft
foundations
on
cohesive
soils
,
stability
against
deep seated failure shall be analyzed. The effect of long
term settlement due to consolidation shall also be
id d
cons
id
ere
d
.
„
The uplift due to sub-soil water shall be considered in di Th t ti bl ttblhllb d
es
ign.
Th
e cons
t
ruc
ti
on
b
e
low wa
t
er
t
a
bl
e s
h
a
ll
b
e
checked for floatation
„
Foundationssubjectedtoheavyvibratoryloadingshould
24
„
Foundations
subjected
to
heavy
vibratory
loading
should
preferably be isolated
GeneralConsiderationsforRaftFoundation GeneralConsiderationsforRaftFoundation General
Considerations
for
Raft
Foundation General
Considerations
for
Raft
Foundation
„
The depth of foundation shall not be less than 1.0 m.
„
Punching shear failure for raft foundation on cohesionless
soils is not an option so it shall not be considered for
analysis Thedesignismostlygovernedbysettlement analysis
.
The
design
is
mostly
governed
by
settlement
criteria.
„
Forraftfoundationsoncohesivesoils stabilityagainst
„
For
raft
foundations
on
cohesive
soils
,
stability
against
deep seated failure shall be analyzed. The effect of long
term settlement due to consolidation shall also be
id d
cons
id
ere
d
.
„
The uplift due to sub-soil water shall be considered in di Th t ti bl ttblhllb d
es
ign.
Th
e cons
t
ruc
ti
on
b
e
low wa
t
er
t
a
bl
e s
h
a
ll
b
e
checked for floatation
„
Foundationssubjectedtoheavyvibratoryloadingshould
24
„
Foundations
subjected
to
heavy
vibratory
loading
should
preferably be isolated
Foundation Analysis and Design: Dr. Amit Prashant
RigidityofSoil RigidityofSoil
--
StructureSystem StructureSystem
Rigidity
of
Soil Rigidity
of
Soil
--
Structure
System Structure
System
„
Performance of raft depends on the relative rigidity of its threecomponents three
components
¾
Super structure
¾
Raft
¾
Soil
„
Distribution of contact pressures depends on the relative
i idit fth f d ti ith tt il
r
ig
idit
y o
f
th
e
f
oun
d
a
ti
on w
ith
respec
t
t
o so
il
„
It is important that the rigidity of superstructure also matches withtherigidityoffoundation with
the
rigidity
of
foundation
¾
Rigid Superstructure with Rigid Foundation:Does not allow
differential settlement so it is good
Ri id S i h Fl ibl F d i
Ldf ii
¾
Ri
g
id
S
uperstructure w
it
h
Fl
ex
ibl
e
F
oun
d
at
ion:
L
arge
d
e
f
ormat
ions
in
the foundation which is not suitable for superstructure
¾
Flexible Superstructure with Ri
g
id Foundation:It ma
y
acceptable but
25
g
y
not necessary
¾
Flexible Superstructure with Flexible Foundation: This is also good
RigidityofSoil RigidityofSoil
--
StructureSystem StructureSystem
Rigidity
of
Soil Rigidity
of
Soil
--
Structure
System Structure
System
„
Performance of raft depends on the relative rigidity of its threecomponents three
components
¾
Super structure
¾
Raft
¾
Soil
„
Distribution of contact pressures depends on the relative
i idit fth f d ti ith tt il
r
ig
idit
y o
f
th
e
f
oun
d
a
ti
on w
ith
respec
t
t
o so
il
„
It is important that the rigidity of superstructure also matches withtherigidityoffoundation with
the
rigidity
of
foundation
¾
Rigid Superstructure with Rigid Foundation:Does not allow
differential settlement so it is good
Ri id S i h Fl ibl F d i
Ldf ii
¾
Ri
g
id
S
uperstructure w
it
h
Fl
ex
ibl
e
F
oun
d
at
ion:
L
arge
d
e
f
ormat
ions
in
the foundation which is not suitable for superstructure
¾
Flexible Superstructure with Ri
g
id Foundation:It ma
y
acceptable but
25
g
y
not necessary
¾
Flexible Superstructure with Flexible Foundation: This is also good
Foundation Analysis and Design: Dr. Amit Prashant
FlexuralRigidityofStructure FlexuralRigidityofStructure
EIEI
Flexural
Rigidity
of
Structure
,
Flexural
Rigidity
of
Structure
,
EIEI
(
)
2 2
''
1
ul
ll
I
Ib EIb
EI EI
⎡
⎤
+
⎢⎥
∑
(
)
()
2 22
1
2'''
ul
ll
b
bu f
EI EI
H
I
IIl
⎢⎥
=+ +
++
⎢
⎥
⎣
⎦
∑
ÆÆTerms on next slide Terms on next slide
„
The summation is to be
done over all the floors,
includin
g
foundation
g
beam of raft.
„
For top layer I
u
'
becomes zero becomes
zero
.
„
For foundation beams
I
f' re
p
laces I
b
‘ and I
l
26
f
p
b
l
becomes zero
FlexuralRigidityofStructure FlexuralRigidityofStructure
EIEI
Flexural
Rigidity
of
Structure
,
Flexural
Rigidity
of
Structure
,
EIEI
(
)
2 2
''
1
ul
ll
I
Ib EIb
EI EI
⎡
⎤
+
⎢⎥
∑
(
)
()
2 22
1
2'''
ul
ll
b
bu f
EI EI
H
I
IIl
⎢⎥
=+ +
++
⎢
⎥
⎣
⎦
∑
ÆÆTerms on next slide Terms on next slide
„
The summation is to be
done over all the floors,
includin
g
foundation
g
beam of raft.
„
For top layer I
u
'
becomes zero becomes
zero
.
„
For foundation beams
I
f' re
p
laces I
b
‘ and I
l
26
f
p
b
l
becomes zero
Foundation Analysis and Design: Dr. Amit Prashant
27
27
Foundation Analysis and Design: Dr. Amit Prashant
R
e
l
at
iv
e
St
iffn
ess
o
f
St
r
uctu
r
e
a
n
d
F
ou
n
dat
i
o
n
So
il R
e
l
at
iv
e
St
iffn
ess
o
f
St
r
uctu
r
e
a
n
d
F
ou
n
dat
i
o
n
So
il
eat eSt esso St uctu ea d ou dato So eat eSt esso St uctu ea d ou dato So
Relative Stiffness Factor:
„
For K > 0.5, the foundation may be considered as rigid with the ratio of differential to total settlement (
δ
) being equal to zero
28
differential
to
total
settlement
(
δ
)
being
equal
to
zero
.
„
For K = 0, ratio δmay be taken as 0.1, and for K < 0.5, it can be taken as
0.35 for square and 0.5 for long mat foundations.
R
e
l
at
iv
e
St
iffn
ess
o
f
St
r
uctu
r
e
a
n
d
F
ou
n
dat
i
o
n
So
il R
e
l
at
iv
e
St
iffn
ess
o
f
St
r
uctu
r
e
a
n
d
F
ou
n
dat
i
o
n
So
il
eat eSt esso St uctu ea d ou dato So eat eSt esso St uctu ea d ou dato So
Relative Stiffness Factor:
„
For K > 0.5, the foundation may be considered as rigid with the ratio of differential to total settlement (
δ
) being equal to zero
28
differential
to
total
settlement
(
δ
)
being
equal
to
zero
.
„
For K = 0, ratio δmay be taken as 0.1, and for K < 0.5, it can be taken as
0.35 for square and 0.5 for long mat foundations.
Foundation Analysis and Design: Dr. Amit Prashant
CharacteristicLength andCriticalColumnSpacing CharacteristicLength andCriticalColumnSpacing Characteristic
Length
and
Critical
Column
Spacing Characteristic
Length
and
Critical
Column
Spacing
„
The characteristic coefficient
λ
as used in classical solution of beams
„
The
characteristic
coefficient
λ
,
as
used
in
classical
solution
of
beams
on elastic foundation, can be obtained as
1
Characteristic Length Parameter,
e
L
λ
=
29
CharacteristicLength andCriticalColumnSpacing CharacteristicLength andCriticalColumnSpacing Characteristic
Length
and
Critical
Column
Spacing Characteristic
Length
and
Critical
Column
Spacing
„
The characteristic coefficient
λ
as used in classical solution of beams
„
The
characteristic
coefficient
λ
,
as
used
in
classical
solution
of
beams
on elastic foundation, can be obtained as
1
Characteristic Length Parameter,
e
L
λ
=
29
Foundation Analysis and Design: Dr. Amit Prashant
CharacteristicLength andCriticalColumnSpacing CharacteristicLength andCriticalColumnSpacing Characteristic
Length
and
Critical
Column
Spacing Characteristic
Length
and
Critical
Column
Spacing
„
Rigidity of foundation can be defined by the spacing
1.75
LL
<
×
⇒
Foundations ma
y
be treated as short beam, hence ri
g
id
between columns, L
()1.75
32
e
e
LL LL
π
<⇒ >×⇒
yg
Foundations may be treated as long beam, hence flexible
(
)
1.75 3 2
ee
L
LL
π
×
<< ×⇒
Foundations may be treated as finite beam
with intermediate rigidity
08
LL
<×⇒
„
Hetenyi’s(1946) recommendations
Rigid Fo ndation
0
.8
3
e
e
LL LL
<×⇒ >× ⇒
Rigid
Fo
u
ndation
Flexible Foundation
30
0.8 3
ee
LL L
×
<>×⇒
Intermediate Flexibility of Foundation
CharacteristicLength andCriticalColumnSpacing CharacteristicLength andCriticalColumnSpacing Characteristic
Length
and
Critical
Column
Spacing Characteristic
Length
and
Critical
Column
Spacing
„
Rigidity of foundation can be defined by the spacing
1.75
LL
<
×
⇒
Foundations ma
y
be treated as short beam, hence ri
g
id
between columns, L
()1.75
32
e
e
LL LL
π
<⇒ >×⇒
yg
Foundations may be treated as long beam, hence flexible
(
)
1.75 3 2
ee
L
LL
π
×
<< ×⇒
Foundations may be treated as finite beam
with intermediate rigidity
08
LL
<×⇒
„
Hetenyi’s(1946) recommendations
Rigid Fo ndation
0
.8
3
e
e
LL LL
<×⇒ >× ⇒
Rigid
Fo
u
ndation
Flexible Foundation
30
0.8 3
ee
LL L
×
<>×⇒
Intermediate Flexibility of Foundation
Foundation Analysis and Design: Dr. Amit Prashant
Determination of Modulus of Elasticit
y
from Plate Determination of Modulus of Elasticit
y
from Plate
y y
Load Test Load Test
2
1
ν
1
s
f
EqB I
s
ν
−
=
intensity of contact pressure
Platewidth
q B
=
Posson's ratio
Influencefactor
Iν
=
Plate
width
settlement
Bs
==
Influence
factor
f
I
=
Elastic Modulus of granular soil below
foundation considering scale effects:
2
ffp
sf sP
BBB
EE
⎛⎞+
=
⎜⎟⎜⎟
31
2
sf sP
Pf
BB
⎜⎟⎜⎟⎝⎠
Determination of Modulus of Elasticit
y
from Plate Determination of Modulus of Elasticit
y
from Plate
y y
Load Test Load Test
2
1
ν
1
s
f
EqB I
s
ν
−
=
intensity of contact pressure
Platewidth
q B
=
Posson's ratio
Influencefactor
Iν
=
Plate
width
settlement
Bs
==
Influence
factor
f
I
=
Elastic Modulus of granular soil below
foundation considering scale effects:
2
ffp
sf sP
BBB
EE
⎛⎞+
=
⎜⎟⎜⎟
31
2
sf sP
Pf
BB
⎜⎟⎜⎟⎝⎠
Foundation Analysis and Design: Dr. Amit Prashant
Modulus of Modulus of Subgrade SubgradeReaction from Plate Load Test Reaction from Plate Load Test ss sionle
Soil
Cohes
S
esive
oil
Cohe
So
32
Modulus of Modulus of Subgrade SubgradeReaction from Plate Load Test Reaction from Plate Load Test ss sionle
Soil
Cohes
S
esive
oil
Cohe
So
32
Foundation Analysis and Design: Dr. Amit Prashant
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
gy gy
„
Assumptions
¾
Foundation is ri
g
id relative to soil and com
p
ressible la
y
er is relativel
y
gpyy
shallow.
¾
The contact pressure is planar such that centroid of the contact p
ressure coincides with the line of action of resultant force.
p
„
The above conditions are satisfied if
¾
Relative stiffness factor
>
0.5
¾
Relative
stiffness
factor
0.5
¾
Spacing between the columns is
less than 1.75xL
e
„
Types of Analysis
¾
Flat Slab Analysis: Flat
plate with regular layout of
Flat
plate
with
regular
layout
of
vertical loads can be analyzed
assuming beam with the width of
distance between mid
-
span width
33
distance
between
mid
span
width
when ground settlement due to
structural loads are not large.
Strip
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
gy gy
„
Assumptions
¾
Foundation is ri
g
id relative to soil and com
p
ressible la
y
er is relativel
y
gpyy
shallow.
¾
The contact pressure is planar such that centroid of the contact p
ressure coincides with the line of action of resultant force.
p
„
The above conditions are satisfied if
¾
Relative stiffness factor
>
0.5
¾
Relative
stiffness
factor
0.5
¾
Spacing between the columns is
less than 1.75xL
e
„
Types of Analysis
¾
Flat Slab Analysis: Flat
plate with regular layout of
Flat
plate
with
regular
layout
of
vertical loads can be analyzed
assuming beam with the width of
distance between mid
-
span width
33
distance
between
mid
span
width
when ground settlement due to
structural loads are not large.
Strip
Foundation Analysis and Design: Dr. Amit Prashant
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
„
Types of Analysis (Continued…)
gy gy
¾
Equivalent Frame Analysis:
If adjacent loads or column
spacing exceed 20% of their higher value, the perpendicular beams as defined above may be treated as part of a frame structure
dth l i i f df
an
d
th
e ana
lys
is
is per
f
orme
d
f
or
this equivalent frame.
¾
Beam
and SlabAnalysis:
¾
Beam
and
Slab
Analysis:
For the raft with added perpendicular beams to increase rigidity of foundation an elemental rigidity
of
foundation
,
an
elemental
analysis may be performed by
cutting it into pieces as beams and
slabs Slab is designed as two way
34
slabs
.
Slab
is
designed
as
two
way
slab and beam as T-beam.
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
„
Types of Analysis (Continued…)
gy gy
¾
Equivalent Frame Analysis:
If adjacent loads or column
spacing exceed 20% of their higher value, the perpendicular beams as defined above may be treated as part of a frame structure
dth l i i f df
an
d
th
e ana
lys
is
is per
f
orme
d
f
or
this equivalent frame.
¾
Beam
and SlabAnalysis:
¾
Beam
and
Slab
Analysis:
For the raft with added perpendicular beams to increase rigidity of foundation an elemental rigidity
of
foundation
,
an
elemental
analysis may be performed by
cutting it into pieces as beams and
slabs Slab is designed as two way
34
slabs
.
Slab
is
designed
as
two
way
slab and beam as T-beam.
Foundation Analysis and Design: Dr. Amit Prashant
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
„
T
yp
es of Anal
y
sis
(
Continued…
)
gy gy
yp y (
)
¾
Deep Cellular Raft:This involves raft slab with beams and
structural walls. Cross walls act as beam between the columns
with net loading from soil pressure minus the self weight of wall and slab section beneath. A simple elemental analysis may be performed as in the previous case. An arbitrary value of ±wL
2
/10
for positive and negative moment can give reasonable results.
35
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
„
T
yp
es of Anal
y
sis
(
Continued…
)
gy gy
yp y (
)
¾
Deep Cellular Raft:This involves raft slab with beams and
structural walls. Cross walls act as beam between the columns
with net loading from soil pressure minus the self weight of wall and slab section beneath. A simple elemental analysis may be performed as in the previous case. An arbitrary value of ±wL
2
/10
for positive and negative moment can give reasonable results.
35
Foundation Analysis and Design: Dr. Amit Prashant
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
Pressure distribution:
gy gy
36
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
Pressure distribution:
gy gy
36
Foundation Analysis and Design: Dr. Amit Prashant
Raft Foundation: Raft Foundation:
Modification Factor for Column
e
Q
Rigid Rigid Beam Analysis Beam Analysis
Loads and Soil Reaction :
e
y
e
x
BL
The total soil reaction =
Q
1
Q
2
Q
3
Q
4
1
..
av
q
BL
Total load from columns
=
L
Total
load
from
columns
1234
QQQQ+++
Q
1
Q
2
Q
3
Q
4
1
B
Total load from columns is slightly
different than the total soil reaction
due to the fact that no consideration
av
q
due
to
the
fact
that
no
consideration
has been given to the shear
between adjacent strips. Therefore
llddilti d
37
co
lumn
loa
d
s an
d
so
il
reac
ti
on nee
d
to adjusted.
Raft Foundation: Raft Foundation:
Modification Factor for Column
e
Q
Rigid Rigid Beam Analysis Beam Analysis
Loads and Soil Reaction :
e
y
e
x
BL
The total soil reaction =
Q
1
Q
2
Q
3
Q
4
1
..
av
q
BL
Total load from columns
=
L
Total
load
from
columns
1234
QQQQ+++
Q
1
Q
2
Q
3
Q
4
1
B
Total load from columns is slightly
different than the total soil reaction
due to the fact that no consideration
av
q
due
to
the
fact
that
no
consideration
has been given to the shear
between adjacent strips. Therefore
llddilti d
37
co
lumn
loa
d
s an
d
so
il
reac
ti
on nee
d
to adjusted.
Foundation Analysis and Design: Dr. Amit Prashant
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
Modification Factor for Column Loads and Soil Reaction :
gy gy
Average Load =
(
)
11234
..
2
av
qBL QQ Q Q++++
2
Modified Soil Reaction
(
)
Average Load
qq
⎛⎞
=
⎜⎟
Modified
Soil
Reaction
(
)
modified
1
..
av av
av
qq
qBL
=
⎜⎟⎝⎠
Column load modification factor
1234Average Load
F
QQQQ
=
+++
Modified Column Loads:
(
)
iim
QFQ=
38
Raft Foundation: Ri
g
id Beam Anal
y
sis Raft Foundation: Ri
g
id Beam Anal
y
sis
Modification Factor for Column Loads and Soil Reaction :
gy gy
Average Load =
(
)
11234
..
2
av
qBL QQ Q Q++++
2
Modified Soil Reaction
(
)
Average Load
⎛⎞
=
⎜⎟
Modified
Soil
Reaction
(
)
modified
1
..
av av
av
qBL
=
⎜⎟⎝⎠
Column load modification factor
1234Average Load
F
QQQQ
=
+++
Modified Column Loads:
(
)
iim
QFQ=
38
Foundation Analysis and Design: Dr. Amit Prashant
RaftFoundation:RigidBeam RaftFoundation:RigidBeam
Analysis Analysis
--
Example Example
Raft
Foundation:
Rigid
Beam
Raft
Foundation:
Rigid
Beam
Analysis
Analysis
Example Example
1
200
Q
kN =
4
230
Q
kN
=
2
370
Q
kN
=
3
420
Q
kN
=
1.0m
1
Q
5
370
QkN
=
4
Q
8
420
QkN
=
2
Q
3
Q
740
QkN
=
7
900
QkN
=
6.0m
5
370
QkN
8
420
QkN
6
740
QkN
=
7
900
QkN
e
x
e
6.0m
y
e
9
370 QkN=
12
370 QkN
=
10
740 QkN
=
11
740 QkN
=
6.0
m
13
200 QkN=
16
200 QkN
=
14
370 QkN
=
15
370 QkN
=
6.0
m
10
m
39
1
.0
m
1.0m
1.0m
6.0m 6.0m 6.0m
RaftFoundation:RigidBeam RaftFoundation:RigidBeam
Analysis Analysis
--
Example Example
Raft
Foundation:
Rigid
Beam
Raft
Foundation:
Rigid
Beam
Analysis
Analysis
Example Example
1
200
Q
kN =
4
230
Q
kN
=
2
370
Q
kN
=
3
420
Q
kN
=
1.0m
1
Q
5
370
QkN
=
4
Q
8
420
QkN
=
2
Q
3
Q
740
QkN
=
7
900
QkN
=
6.0m
5
370
QkN
8
420
QkN
6
740
QkN
=
7
900
QkN
e
x
e
6.0m
y
e
9
370 QkN=
12
370 QkN
=
10
740 QkN
=
11
740 QkN
=
6.0
m
13
200 QkN=
16
200 QkN
=
14
370 QkN
=
15
370 QkN
=
6.0
m
10
m
39
1
.0
m
1.0m
1.0m
6.0m 6.0m 6.0m
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