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IN THE NAME OF ALLAH, THE MOST BENEFICENT,
THE MOST MERCIFUL
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General
The foundation or sub-structure is that part of a
structure which is usually placed below ground level
and which transmits the load to the underlying soil. All
soils compresswhen loaded and cause the supportedstructure to settle. Two essential requirements in the
design of a foundation are:
Total settlement of the structure should be limitedto tolerable limits.
Differential settlement of the various parts of astructure should be eliminated as far as possible.
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To limit the settlement, it is necessary to: -
Transmit the load to a soil of sufficient
strength.
Spread the load over a sufficiently large areato minimize the bearing pressure.
If suitable soil is not found, it is necessary to use
deep foundation such as piles or caissons. Ifsatisfactory soil is found underneath, it is merely
necessary to spread the load of the footing and such
a footing is called Spreadfooting.
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Types of Footings Different types of footing are: - Wall footing
Isolated column footing
Combined footing
Strap footing
Pile foundation
Raft foundation
Grid foundation
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LOAD, BEARING PRESSURE & FOOTING SIZE
Load, Bearing Pressure and Footing SizeAllowable soil pressure is determined from the
principles of Soil Mechanics. FOS 2.5 to 3.0
Effective soil pressure = qe= qa- wt of footing - wt
of soil on top of footing
For concentrically loaded footing
Area of footing required = (D+L)/qe
Most codes permit 33% increase in allowable soilpressure when effect of wind or earthquake is
included
Area of footing required =( D+L+E)/1.33 qe
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LOAD, BEARING PRESSURE &
FOOTING SIZE
Area of footing provided is larger of paras above.
Loads are un factored and values are taken at the
base of footing.
For eccentrically loaded footing
q max min= P/A My/I
if eccentricity falls outside the kern, one value of q is
negative
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LOAD, BEARING PRESSURE &
FOOTING SIZE
Notations
a = Width of wall in inches
c = Width of column in inches
B = Width of footing in ft
L = Length of footing in ft
D = Dead load
L = Live load
qa = Allowable bearing pressure / capacity
qe = Effective bearing pressure / capacity
qu = Design soil pressure ( Factored )
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PROVISIONS OF ACI CODE (CH-15)
Provisions of ACI Code (Chap. 15 ) Size of footing. Size of footing shall be determined
from un factored loads and moments. (ACI 15.2.2)
Design of Footing. Footing shall be designed toresist factored loads and induced reactions.
(ACI 15.2.1).
Shear in Footings. Critical section for one way
shear or beam shear shall be taken at a distance d
from the face of column or wall. (ACI 15.5.2 and
11.1.3.1).
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PROVISIONS OF ACI CODE (CH-15)
Moments in Footing (ACI 15.4)
External moment at any section of a footing shall
be determined by passing a vertical plane through
the footing and computing the moment of the
forces acting on one side of that vertical plane.
Critical section for B.M. shall be taken at the face
of the concrete column, pedestal or concrete wall.
Critical section for moment in footings supporting
a masonry wall shall be taken at half way
between middle and edge of the wall.
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PROVISIONS OF ACI CODE (CH-15)
Minimum Footing Depth (ACI 15.7) 6 for footingresting on soil
Distribution of reinforcement in footing
In one way footing and two way square footing,reinforcement shall be distributed uniformly
across entire width of footing. ACI 15.4.3
In rectangular footing, reinforcement in long
direction shall be distributed uniformly. In shortdirection, a portion of total reinforcement given
by equation below, shall be placed in band width
equal to width of short side. ACI Code 15.4.4
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Rft in band width = [2/(+1)]xTotal rft in short direction
where is ratio of long side to short side of footing.
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WALL FOOTING DESIGN
PROCEDUREWall Footing
Design Procedure.
Design of wall footing is based on the analysis of a
typical 1 foot slice cut by transverse planes normalto the longitudinal axis of the wall.
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Figure. Basis of wall footing design
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Effective Soil Pressure. Assume thickness of footing
and density of soil
Effective soil pressure = qe = qa - wt of concrete - wt
of soil
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WALL FOOTING DESIGN PROCEDURE
Width of Footing
width of footing=B= ( D+L ) /qe
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Design Soil PressureDesign soil pressure=qu=(1.2D+1.6L)/Area provided
= (1.2D+1.6L) / Bx1
Thickness of Footing. Critical section for shear in a
footing supporting a R.C.C or a masonry wall lies at a
distance dfrom face of wall (ACI 11.1.3.1)
Vu = qu [(B - a)/2 d)] .(i)
and Vc= 2fc.b.d/1000 ..(ii)
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WALL FOOTING DESIGN PROCEDURE
Equate (i) and (ii) to find value of d
Thickness of footing = h = d+3+db/2
Compare the thickness of footing with assumed
value in step -1 (Assume 3concrete cover)
d actual = h3 db/2
Design Moment
R.C.C Wall. Critical section for B.M lies at theface of the wall (ACI 15.4.2)
Mu= qu(B - a)/2 x (B - a)/2
= qu/8 (B - a/12)2
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WALL FOOTING DESIGN PROCEDURE
Masonry Wall. Critical section for B.M is at mid
point between centre line of wall and face of thewall (ACI 15.4.2)
Distance of Critical section from edge of footing
= (B _ a/2 + a/4) = (2B-a)/4
Mu=qu(2B-a)/4 x (2B-a)/4 = qu(2B-a/12)2 /32
Area of Steel. Find the steel ratio by flexural eqn
As = xbxd
check As > Asmin= 3 fc/fy b.d 200/fy bd
(ACI Code 10.5.1)
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WALL FOOTING DESIGN PROCEDURE
Development Length. ACI Code 12.2.3
ld/db=3/40xfy / [fc(c+Ktr)/db] or 12
The term (c+Ktr)/db shall not be taken greater
than 2.5
ld aval=distance between critical section and edge
of the footing _ cover
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WALL FOOTING DESIGN PROCEDURE
Temp and Shrinkage Reinforcement. ACI 7.12.1
As(sh) =0.002bxh (for grade 40 or 50 steel)
= 0.0018bxh (for grade 60 steel)
Sketch. Draw sketch showing the depth of footing
dimension of wall, footing, clear concrete cover and
steel reinforcement.
DESIGN EXAMPLES - WALL FOOTINGS
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COLUMN FOOTINGS
Types of Column Footings.
Single Slab. In the simplest form, they consist of a
single slab. Single column footings are usually
square in plan. Rectangular footings are used if
space restrictions dictate this choice or the supportedcolumns are of strongly elongated cross section.
Stepped Footing. In stepped footing, a pedestal or
cap is interposed between column and footing slab.Pedestal provides for a favourable transfer of load
and is required to provide necessary development
length of dowels. All parts must be cast monolithically
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Slopped Footings. They require less concrete than
stepped or single slab but require additional labour.
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Shear and Flexural Behaviour of Footings
To simplify design, footings are assumed to be
rigid and the supporting soil elastic. Consequently,
uniform or uniformly varying soil distribution can be
assumed.
Column footing can be considered as an
inverted floorwhere the soil pressure is acting asa load on the slab causing bending and shear in a
similar manner to a floor slab subjected to gravity
loads.
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COLUMN FOOTINGS
When heavy loads are involved, it has been found
that shear controls the thickness of footing rather
than bending.
The mechanism of shear failure in a footing is
similar to that in supported floor slabs. (Flat Plate)
Shear capacity is considerably higher than that of
a beam.
Footings in most cases, bend in double curvature;
shear and bending about both principle axes have
to be considered for column footing.
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Design of Column FootingThe required bearing area is obtained by dividing
the total service load by effective soil pressure.
In computing B.M and shear force, only the upwardsoil pressure that is caused by factored column loads
is considered.
Column footing behaves as a cantilever projectingout in both directions from the edge of the column. It
is designed to resist the bending moment and shear
force produced by the upward soil pressure.
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Footing is checked for punching shear (two wayshear) and beam shear (one way shear). No shear
reinforcement is provided in footings.
Reinforcement for flexure is provided in both
directions at the bottom, perpendicular to each other
and parallel to the edges. Effective depth d is taken
for upper layer and the same is used for other
direction.
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Shear in Column Footings
The thickness of footings is mostly governed by
SHEAR.Since column footings are subjected to two
way action i.e. bend in both major direction, their
performance in shear is much like that of flat plate inthe vicinity of column.
It is NOT economical and practical to use shear
reinforcement in footing and shear is carried only by
the concrete.
Two different types of shear strengths are
distinguished in footings: Two way shear or punching
shear and one way shear or beam shear.
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A column supported by footing slab tends to
punch through it because of the shear stresses that
act in the footing slab around the perimeter of the
column. At the same time, the concentrated
compressive stresses from the column spread out
into the footing so that the concrete adjacent to the
column is in vertical or slightly inclined compression,
in addition to shear. In consequence, if failureoccurs, the fracture takes the form of the truncated
pyramid (as shown in fig) with sides sloping outwards
at an angle approaching 450
.
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The average shear stress in concrete that fails in
this manner can be taken as that acting on a vertical
plane through the footing, around the column, on a
perimeter, at a dist d/2from the face of the column.
ACI Code 11.12.1.2&3.
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The concrete subjected to shear stress is also
subjected to vertical compression from the stresses
spreading out from the column and in horizontal
compression in both major directions because of
biaxial B.M. in the footing. This triaxiality of stresses
increase the shear strength of concrete.
Tests conducted on footing and slabs have shown
that for punching type failure, the shear stress
computed on critical perimeter (area) is larger than
one way shear.
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ACI Code 11.12.2.1 gives nominal punching shear
strength on the perimeter.
Vc = 4 fcbo.d
where bo is the shear perimeter around the
column at a distance d/2 from its face.
For column of elongated cross section,
Vc = (2+4/c) fcbo.d
where c is ratio of long side to short side of
column.
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For the case in which ratio of critical perimeter
to slab depth, bo/d is very large,
Vc = (s.d /bo+ 2) fc bo.d
The lowest of the three values governs.
Shear failure can also occur, as in beam or one
way slab, at a section located at a distance dfrom
the face of the column and shear strength given by
equation in ACI Code 11.3.1.1
Vc = 2 fcb.d
where bis the width of slab subjected to shear.
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DESIGN PROCEDURE- COLUMN FOOTING
Effective Soil Pressure. Assume thickness ofconcrete footing and soil density.
qe = qa - wt of concrete footing - wt of soil
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Area of Footing Required.
Area of footing req=(D+L)/qe
(Loads are un factored).
Determine the dimensions of footingShear. Thickness of column footing is generally
controlled by shear and effective depth is taken for
upper layerEffective depth = d = h _ 3_ 1.5 db
Punching Shear. Critical section for shear is at a
distance d/2from the face of column.
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Vu1= qu [B2-{(c+d)/12}2]
Vcis smallest of the following ( ACI 11.12.2.1)
Vc1 = (2+4/c) fcbod
Vc1
= (s.d/bo
+2) fcb
o
.d and
Vc1 = 4 fcbod
where bo= shear perimeter = 4(c+d)
(For sq column)
Vc1> Vu1 If not, increase d
One-way Shear. Critical section for one wayshear lies at a distance dfrom face of column
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Vu2
= qu [(B-c/12)/ 2d/12].B
Vc2 = 2fcx Bx12xd /1000
Vc2 > Vc2 O.K.
Bending Moment. Critical section for B.M. lies at
the face of the column.
Mu= qu/8 [(B-c/12)2x B]
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Steel Ratio and Area of Steel
max= 0.75x0.85 1fc/fy 87/(87+fy)
Find from formula
Mu= bd2fy (1 0.59fy/fc), where, b = Bx12
As= x b .d.
As > Asmin
= 200/fy b.d 3fc/fy b.d
Detailing (No of bars)
No of bars = As / Ab
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Development Length.
ld= 3/40.fc/fy. . /(c + Ktr / db)..ACI 12.2.3
Apply M.F. if applicable
Compare ldwith ldavailable
ld aval = ( Bx12 - c) / 2 - 3
If ldis not available, Provide hooks.
ldh= (0.02 fy / fc) db but not less than 8 dbor 6
ACI 12.5.2. Apply M.F. if applicableACI 12.5.3
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Check For Transfer of Load.
Pu =1.4D+1.7L
Pb= 0.85 fcA1(A2/A1) < 0.85 fcA1x2
If Pb < Pu, provide dowel for extra load otherwiseprovide minimum area of dowel.
Minimum Area of dowels = 0.5% of column cross
section area. (ACI 15.8.2.1).
Use minimum 4 bars as dowel in square and
rectangular column.
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Check For Development Length of Dowel.
Into Footing. Bars must extend for a distance
equal to development length of bar in
compression
ldb= 0.02 dbfy/fcbut not less than 0.0003dbfy
Into Column. Dowel must extend into column
equal to development length of larger bar orsplice length of smaller bar (splice
length=0.0005 dbfy) whichever is larger .
ACI Code 12.16.1
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Sketch. Draw sketch showing footing size concrete
cover and steel arrangement.
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Distribution of Reinforcement in Rectangular Footing.
Reinforcement in the long direction is uniformly
distributed over the entire width.
In short direction, the support provided by the
footing to the column is concentrated near the
middle and consequently the curvature of the footing
is sharpest i.e. moment / ft is largest under the
column. Moment decreases with increasing distance
from the column and thus a larger area of steel per
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longitudinal / ft is needed in the central portion than
the far ends of the footing.
According to ACI 15.4.4, for reinforcement in the
short direction, a portion of the total reinforcement
(Given by eqn below) shall be distributed uniformlyover a band width equal to length of short side of
the footing. The remainder of the reinforcement
required in short direction shall be distributed
uniformly outside the centre band width of footing.Reinforcement in band width/Total reinforcement =
= 2/(+1)
where is ratio of long side to short side of footing.
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DESIGN EXAMPLES
COLUMN FOOTING
DESIGN EXAMPLE - TWO COLUMN FOOTING
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ANY QUESTION ?