Design Footings

5/28/2018 Design Footings

1/66

IN THE NAME OF ALLAH, THE MOST BENEFICENT,

THE MOST MERCIFUL


2/66

FOOTINGS


3/66

FOOTINGS

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.


4/66

FOOTINGS

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.

FOOTINGS


5/66

FOOTINGS

Types of Footings Different types of footing are: - Wall footing

Isolated column footing

Combined footing

Strap footing

Pile foundation

Raft foundation

Grid foundation

FOOTINGS


6/66


7/66


8/66


9/66

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

FOOTINGS


10/66


11/66

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

FOOTINGS


12/66

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 )

FOOTINGS


13/66

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).

FOOTINGS


14/66

FOOTINGS


15/66


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.

FOOTINGS


16/66

FOOTINGS


17/66

FOOTINGS


18/66

FOOTINGS


19/66


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

FOOTINGS


20/66

Rft in band width = [2/(+1)]xTotal rft in short direction

where is ratio of long side to short side of footing.

FOOTINGS


21/66

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.

FOOTINGS


22/66

Figure. Basis of wall footing design


23/66

FOOTINGS

Effective Soil Pressure. Assume thickness of footing

and density of soil

Effective soil pressure = qe = qa - wt of concrete - wt

of soil


24/66


25/66

WALL FOOTING DESIGN PROCEDURE

Width of Footing

width of footing=B= ( D+L ) /qe

FOOTINGS


26/66

FOOTINGS

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)


27/66

FOOTINGS


28/66


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

FOOTINGS


29/66

FOOTINGS


30/66


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)

FOOTINGS


31/66

FOOTINGS


32/66


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

FOOTINGS


33/66


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

FOOTINGS


34/66

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

FOOTINGS


35/66

COLUMN FOOTINGS

Slopped Footings. They require less concrete than

stepped or single slab but require additional labour.

FOOTINGS


36/66

FOOTINGS

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.


37/66

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.

FOOTINGS


38/66

FOOTINGS


39/66

COLUMN FOOTINGS

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.

FOOTINGS


40/66

COLUMN FOOTINGS

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.

FOOTINGS


41/66

FOOTINGS

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.

FOOTINGS


42/66

COLUMN FOOTINGS

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

.

FOOTINGS


43/66

COLUMN FOOTINGSFOOTINGS


44/66

COLUMN FOOTINGS

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.

FOOTINGS

FOOTINGS


45/66

FOOTINGS


46/66

FOOTINGS

COLUMN FOOTINGSOO GS


47/66

COLUMN FOOTINGS

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.

FOOTINGS



48/66

COLUMN FOOTINGS

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.

FOOTINGS



49/66

COLUMN FOOTINGS

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.

FOOTINGS

FOOTINGS


50/66

FOOTINGS



51/66

COLUMN FOOTINGS

DESIGN PROCEDURE- COLUMN FOOTING

Effective Soil Pressure. Assume thickness ofconcrete footing and soil density.

qe = qa - wt of concrete footing - wt of soil

FOOTINGS



52/66

COLUMN FOOTINGS

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.

FOOTINGS

FOOTINGS


53/66

FOOTINGS



54/66

COLUMN FOOTINGS

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

FOOTINGS

FOOTINGS


55/66

FOOTINGS



56/66

COLUMN FOOTINGS

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]

FOOTINGS



57/66




58/66

COLUMN FOOTINGS

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

FOOTINGS



59/66

COLUMN FOOTINGS

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

FOOTINGS



60/66

COLUMN FOOTINGS

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.

FOOTINGS



61/66

COLUMN FOOTINGS

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

FOOTINGS



62/66

COLUMN FOOTINGS

Sketch. Draw sketch showing footing size concrete

cover and steel arrangement.

FOOTINGS

FOOTINGS


63/66

FOOTINGS

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



64/66

COLUMN FOOTINGS

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.

FOOTINGS

FOOTINGS


65/66

FOOTINGS

DESIGN EXAMPLES

COLUMN FOOTING

DESIGN EXAMPLE - TWO COLUMN FOOTING


66/66

ANY QUESTION ?

Design Footings

Documents

Transcript of Design Footings