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					DESIGN OF FOOTINGS




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Detailing of Steel in Footings
Footings

The function of a footing or a foundation is to transmit the
load form the structure to the underlying soil.


The choice of suitable type of footing depends on the depth at
which the bearing strata lies, the soil condition and the type of
superstructure.

                                                              19
Types of footing

Following are the different types of footing used for concrete
 structure

• Isolated footing
• Combined footings
• Strap footing
• Mat or raft foundation
• Pile foundation


                                                             20
Isolated footings

Isolated footings are provided under each column and may
be square, rectangular, or circular in plan. Footing may be
flat or tapered.




                                                        21
Combined footings

       PROPERTY LINE




        COMBINED            COMBINED
        FOOTING             FOOTING


        RECTANGULAR AND TRAPEZOIDAL TYPES



                                            22
 Combined footings

• Combined footings are provided to support two or more column
  loads. These may be continuous with rectangular or trapezoidal
  in plan as shown. Combined footings become necessary under
  the following circumstances:
• when the isolated footings overlap.
• when    the   exterior   column   is   close   to   the   property
  line/BOUNDARY LINE with the result symmetrical isolated
  footing can not be provided.




                                                               23
Strap footing
• Strap footing is one of the types of combined types of
  combined. It consists of an isolated footing of two
  columns connected by a beam called strap beam. The
  strap beam does not remain in contact with the soil and
  thus does not transfer any load to the soil. This is
  provided when one of the columns is on the property
  line.


                    PROPERTY LINE



                         STRAP
                         BEAM

                    STRAP FOOTING

                                                            24
Mat foundation

• The is provided when the soil is having
  very low bearing capacity and or when
  columns loads are heavy, the required
  footing area becomes very large and
  uneconomical.



                      MAT FOUNDATION

                                            25
Detailing
• Size of footing
                                       BM1
• Depth at footing                           OWS
• Depth of footing edge
• Nominal and effective cover          d/2       BM2
• Development length
• Minimum and maximum steel
                                 TWS
• Spacing of bars and stirrups               d
                                   PLAN
                                                  26
Detailing of steel in rectangular
footing as per IS:456-2000
Reinforcement
Long and short direction
In short direction larger steel area is needed in the central portion and is given
by


         Ast ,central −band                   2
                                      =
     Ast ,total , short − direction     ( L / B) + 1
Reminder of the steel in end bands
                                      f s .φ s
Development length= Ldt=
                                      4τ
                                           bd
Ldt = 47φs for M20 concrete and Fe 415 steel



                                                                              27
    CODE PROVISIONS FOR FOOTING
 CLAUSE :34 PAGE NO.63 OF IS 456-2000



THICKNESS AT THE EDGE OF THE FOOTING : 150 MM
BENDING MOMENT
SHEAR AND BOND : CLAUSE 31.6, 34.2.6,25.2.3
TENSILE REINFORCEMENT




                                                28
PROBLEM
Design a footing of uniform thickness to carry an axial load of
1200 kN. Size of column is 400 mm x 400 mm. SBC = 150
kN/m2. Use M20 Concrete and Fe 415 steel.

Solution:

Axial load =1200 kN
Ultimate load = 1200 x 1.5 = 1800 KN
Safe bearing capacity of soil = 150 kN/m2
Ultimate bearing capacity of soil = SBC x Factor of safety
                               = 150 x 2 (assumed)=300 kN/m2
Ultimate load on footing       = 1800 kN
Add 10% for self wt of footing = 180kN
                    Total     = 1980 kN
                                                                  29
Area of footing required = Total load/UBC of soil
                         = 1980/300 = 6.6 m2
Since column size is square, let us provide footing also in
  square shape.
Length of footing = Г6.6 = 2.56 say 2.6 m
Size of footing = 2600 mm x 2600 mm
Upward soil pressure q
  = Load on footing without its self weight /Area of footing
 = 1800 / 2.6 x 2.6 = 266.272 kN/m2
Factored moment (Mud):As per clause 34.2.3.2, maximum bending
  moment occurs at the face of the column. For design purpose,
  consider any one overhang.
Max. moment at face of column,
Mud = Upward soil pressure x hatched area x
                                                          30
      (distance between CG of force and face of column)
          qu= 266.27kN/m2
           1100


             CG             2600




= 266.272 x 2.6 x 1.1 x 1.1/2
= 418.846 KNm
Mud = Qu bd2

d = √ Mud/Qub = √ 418.846x106 /2.76 x 2600
                                             31
d = 241 mm
Assuming 50 mm effective cover,
D=241 + 50 =291say300mm
To resist the factored moment at face of column a overall
thickness of 300 mm is sufficient for a balanced section. But
practically it is observed that this depth may not be sufficient
to take care off shear. So to make the footing safe against
shear it is suggested to increase the depth by two to three
times. Safe and economical section can be arrived by trial
and error method. As first trial, let us increase the depth
double.
Final D = 300 x 2 =600 mm and d = 600-50 = 550 mm. Since
the depth is revised it is no more a balanced section (but this
increase in depth is not necessary for footing of varying
thickness( sloped footing)
Mu(lim) = Qubd2 = 2.76 x 2600 x 5502 = 2170 kNm
Mud = 418.846< Mu(lim) – under reinforced                  32
418.846 x 106 = 0.87x 415x Astx550 (1- 415Ast/20x2600x550)
Ast= 2178 mm2


No of 12 mm dia bars = Ast/ast = 2178/113.1 = 19.25
                                      say 20 numbers
Actual Ast = 113.1 x 20 = 2262 mm2
Provide same dia in both direction.
Length of the bar from face of the column should be < Ld
as per clause 26.2.1
Development length= Ld =   f s .φ s
                           4τ                          33
                                bd
Ld = 0.87x415x12/4x1.2x1.6
   =564 mm
Length of bar available from face of column
          =overhang of footing-cover
          = 1100-50 =1050mm>564mm ok
Check for shear (clause 34.2.4-IS456-2000)
The potential cracks may occurs
a) in a plane across the entire width at a
   distance equal to effective depth from face
   of column
b) In a plane around the periphery of column
   at a distance equal to d/2.
                                           34
    a) Check for shear at d from face of column
    Shear force at plane xx = q x hatched area
    Vu= 266.27x2.6x0.55=380.796kN
    Area of resisting shear=2600mm x 550 mm
                                  x
τv= Vu/bd=380.796x 106
                 2600 x 550                       600

                         2           x
                =0.27N/mm       qu= 266.27kN/m2
                                        2600
Permissible shear stress, kTc

                                                  2600

                                 1100
                                                         35
                                550
% Ast at plane xx = 100 Ast/bd
                = 100 x 2262
                  2600 x 550
                = 0.16
Tc up to 0.25% = 0.36 MPa
K for 600 mm thick slab = 1.0
kTc= 1.0x0.36 = 0.36MPa
Since Tv < kTc, safe against shear.


                                      36
b) Check for shear at d/2 around face of column:
One side of critical plane = size of column + d/2 +d/2
                     = 400 + 550/2 +550/2 = 950 mm
Periphery of critical plane
Around column at d/2, b = 950x4 = 3800mm
Area of resisting shear = bd = 3800 x 550
Shear force, Vu = q x hatched area
=266.272(2.62 – 0.952)=1559.688KN

Nominal shear stress, τv= Vu/bd
                              = 1559.688x103
                                3800 x 550
                              = 0.75Mpa
                                                         37
Permissible shear stress= ksTc (clause 31.6.3.1)
Ks=0.5 +ßc
ßc =Short side of column /long side of the column
=400/400 = 1.0
Ks=0.5 +ßc= 0.5+1.0 =1.5 but restricted to 1.0
Tc= 0.25√fck =0.25√20 =1.12MPa
Perm. shear stress= ksTc= 1 x1.12=1.12MPa
Since Tv< ksTc, safe against shear




                                             38
                A1=bxD



                    Loaded
                    frustum of
                    pyramid


d                        1:2




    2d    400       2d

         400 + 4d              39
Check for transfer of load at base of column:
(clause 34.4)
Nominal bearing stress = Axial load on footing
                          Top area of frustum
=1800x 103
 400x400
=11.25 MPa
Permissible bearing stress = 0.45 fck√A1/A2
A1=bottom area of frustum = 400+4d=400+4x550
                            =2600mm
 A2=top area of frustum =400x400
                                               40
√A1/A2= √2600/160000 =6.5 but limited to 2.
Permissible bearing stress =0.45x20x2=18MPa
Since
nominal bearing stress<
                    Permissible bearing stress
It is safe.                          400 mm

                  20-12mmΦ

                                       600mm

             20-12mmΦ




                                       2600mm


                                       20-12mmΦ
                                             41
                             2600 mm
Number of bars in footing = 11 Numbers at 200 mm c/c with a
side cover of 100 mm.

Width of footing= 10 x 250 + 100 x 2 =2700 mm

Follow all specification of SP 34 and prepare the drawing




                                                            42
Square footing
                                400
                                             400
  CROSS SECTION                                           4- #16



                                                                        27
         3000 mm                                                        00
                                                   GROUND LEVEL

                                              4- #16
  DEPTH OF
 FOUNDATION                                  #6@220
   ≥ 500 mm
                                                         #20@250                  27
                                                                                  00
                          Ldt         L dc
                                                             150 min.

   75                                 300 min.
                   Ldt                              LEVELLING COURSE
        75                                                              PL
                         SECTIONAL ELEVATION
                                                                        AN

                                                                             43
Rectangular footing
                            400


                                         300

                      CROSS SECTION




                                             GROUND LEVEL

    DEPTH OF                             6- #20
   FOUNDATION                            #8@200
     ≥ 500 mm
                                                    #16@200


                      Ldt         L dc


   75
     75                           300 min.
                Ldt                            LEVELLING COURSE   PLAN
          75
                  SECTIONAL ELEVATION

                                                                                44

                                                                         PLAN
Rectangular footing

                                      300


                      CROSS SECTION


                                                                     320
                                                                     0
                                          GROUND LEVEL

    DEPTH OF                          6- #20
   FOUNDATION                         #8@200
     ≥ 500 mm                                     #16@200
                                                                                      220
                      Ldt      L dc                                                   0


  75
    75                         300 min.
                Ldt                         LEVELLING COURSE
         75                                                    EB   CB=     EB
                  SECTIONAL ELEVATION
                                                                    2200
                                                                     PLAN

                                                                                 45
Column steel detailing

                         ≤ 48φtr




                ≤ 75     > 75



                                   46
Column steel detailing

    > 48φtr    ≤ 48φtr   > 48φtr


                                   > 75



                 > 75      > 75
     > 75



                                          47
Column steel detailing
                         > 48φtr




                  φtr



        ≤ 48φtr         ≤ 75




                                   48
Detailing with dowel bars
                                       A1=bxD
Pu/bD < 0.45fck √A1/A2


                                          2Df


                   Df                            2:1



                         A2= [b+4Df] x [D+4Df}


                                                       49
 Detailing with
  dowel bars
                                             Dowel bars
                                             or starter
                                             bars
  DEPTH OF
 FOUNDATION
                                     LAP
   ≥ 500 mm                                  #16@200

                    Ldt       L dc
75
  75                         300 min.
              Ldt                       LEVELLING COURSE
       75
               SECTIONAL ELEVATION
                                                           50
  Bar bending schedule
    For exercise problem
    For footing only
                                              Total
                                  Length    length in
              No. of   Diameter
Member Mark                         in         m      Bar details    Remarks
              bars      in mm
                                  m/piece
                                              #20

          A    11        20        2.55     28.05                   #20@250
Footing
          B    11        20        2.55     28.05                   #20@250
     Total length in m/diameter             56.10
          Weight in kg/m                     2.45
    Total weight in kg/diameter             137.45
                                                                          51
Estimation of quantity of concrete

 Volume of concrete = L x B x D

    L= length in m
    B=Breadth in m
    D=Thickness in m
    Apply for rectangular and trapezoidal part

    Weight of concrete, kg = Volume x density


                                                 52
Combined Footings


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