Footing_Combined.pdf

DATE

DOCUMENT NO.

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DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

1

1.00 INPUT: Unit Weight of Concrete

=

2.5

t/m3

Unit weight of Soil

=

2.0

t/m3

Unit Weight of water

=

1.0

t/m3

Grade of Concrete

=

M25

Grade of Steel

=

Fe 415

Centre to centre distance of columns

=

5.0

m

Height of pedestal from GL=

0.30

m

Depth of foundation=

6.00

m

Safe bearing capacity of foundation=

45.00

t/m

Load factor Assume Size of Pedestal / Column as

P1

1

P2

Length

=

2.6

1.7 m

Breadth

=

2.6

1.7 m

Height

=

6.30 m

6.3 m

Area of c/s=

2

6.76sq.m

2.89sq.m

Thickness of foundation slab

1.7

m

2.00 Forces at top of Pedestal

P1

P2

Fyt Fzt

pedestal-1Pedestal-2 Fyt

=

t

5000.00

5000.000

Fxt

=

t

0.000

0.000

Fzt

=

t

0.000

0.000

Mxt

=

t-m

0.000

0.000

Myt

=

t-m

0.000

0.000

Mzt

=

t-m

0.000

0.000

Fxt

3.00 DESIGN PEDESTA/COLUMN: 3.01 Moment due to horizontal force in X direction (Mz)

Force acting in X direction ( Fxt) X Height of pedestal / Column

=

Fz1

Fx1

0.30 m

E.G.L Y

Top of Pedestal / Column

E.G.L

P2

P1 4.30 m

4.60 m

Z

1.70 m X

1

6.30 m

DATE

DOCUMENT NO.

PROJEC

DESIGNED

PAGE

CHECKED

DESIGN OF COMBINED FOOTING

TITLE :

Mz

=

0 x 6.3+0

=

2

0 x 6.3+0

0.000

0.000

t-m

0 x 6.3+0

t-m

0.000

t-m

3.02 Moment due to horizontal force in Z direction (Mx)

Force acting in Z direction ( Fzt) X Height of pedestal / Column

=

Mx

=

0 x 6.3+0

=

0.000

3.03 Vertical Force (Fy) =

Vertical force in Top of Column/ Pedestal (Fyt) + Self Weight of Pedestal / Column =

5000 + 2.6 X 2.6 X 6.3 X2.5

3.04 Summary of forces / Moments

=

5106.47

P1

P2

5000 + 1.7 X 1.7 X 6.3 X2.5 5106.47

Fy

=

5106.47

5106.47

Mx

=

0.000

0.000

t-m

Mz

=

0

0

t-m

Load Case:

WIND

STATIC

t

t

SEISMIC

3.05 Design of Column / Pedestal

Size of Column/ Pedestal Breadth

=

2.6

Width

=

2.6

=

40

mm

=

20

mm

If the Effective length is < 3 times the least lateral dimension

=

Pedestal

If the Effective length is > 3 times the least lateral dimension

=

Column

Cover to reinforcement (Cl :26.4.2.1 of IS 456-2000) Diameter of bar

3.06 Check for Pedestal or Column

(Ref : Cl : 26.5.3.1.h. of IS 456-2000)

3.07 Effective Length of Column ( Ref: Table 28 of IS 456-2000 . Effectively held in position and restrained against rotation at one end but not held in position nor restrained against rotation at the other end) Effective Length

=

2 X Unsupported length of Column

Least lateral dimension

Eff. Length / Least Lateral Dimension 4.8

>

3

Hence Use

Column

=

2 X 6.3

=

12.6

=

2.6

=

4.85

design

3.08 Check for biaxial bending Column has to be designed for combibed axial load & biaxial bending Mux Mux1

n +

Muy Muy1

n

0.8

n =

2

n =

Linearly varying

=

0.45 X 25 X 2888555 + 0.75

77266800

32946000

N

7726.68

3294.6

t

5106.47 / 7726.68

=

0.66

n

=

5106.47 / 3294.6

1.55

If Pu / Puz is b/n 0.2 to 0.8

Factored Loads & Moments

Pu

=

Mux

Muz

1.77

2.00

P1

P2

1x5106.47

1x5106.47

t

5106.47

5106.47

t

=

1x0

1x0

t-m

=

0

0

t-m

=

1x0

1x0

t-m

=

0.00000

0

t-m

Calculation of Mux1 & Muz1 d' / D Where

d'

=

D

= D

=

d' / D For P1 Pu/fck b D

²

=

50

mm

Overall Width/ Breadth

=

2600

=

0.01923

mm

For P2

5106.47 X 10^4 / 25 X 2600 X 2600

p/fck

Cover + 1/2 of dia of bar

5106.47 X 10^4 / 25 X 1700 X 1700

=

0.302

=

0.06 / 25

0.05 / 25

=

0.0024

0.0020

Referring from Chart 48 of SP16 3

0.302

t

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

For

Mux1 / fck b D

=

0.0024

Pu/fck b D

=

0.3022

=

0.26233

=

0.2623 X fck X b X D^2

0.2623 X fck X b X D^2

=

0.26233 X 25 X 2600 X 2600²

0.262 X 25 X 1700 X 1700²

2

Mux1

For

p/fck

=

0.0024

Pu/fck b D

=

0.30 Muz1 / fck b D

2

Muz1

32221825727

=

11526.7802

3222.18

=

0.26233

n

<

Muz

0.26233 X 25 X 2600 X 2600²

=

11526.7802

0.262 X 25 X 1700 X 1700²

32221825727

0 / 11526.7802

3222.18 / 11526.7802

0

0

0 / 11526.7802

n

0 / 3222.182

0

0

0.00000

0.00000

1 SAFE

3.09 Reinforcement Area of Steel required

=

4056

mm

2

Hence Provide 2

8

Nos

25

mm dia mars

=

3925

mm

8

Nos

25

mm dia mars

=

3925

mm2

=

7850

mm

Area of steel Provided 7850

>

4056

Hence it is SAFE 3.11 Lateral Reinforcement (Ref : Cl 26.5.3.2-IS 456-2000) Least of (1)

Least lateral dimension

=

2600

mm

(2)

16 X Smallest dia of longitudinal bar

=

400

mm

(3)

300 mm

=

300

mm

Hence provide 8mm dia bars @ 300 c/c

8# Y25 dia bars 8# Y25 dia bars Y8 @300C/C

1.00m

Y8 @300C/C

5.0m

4

N-mm t-m

Muz1

Hence the assumed % of reinforcement is

t-m

0.26233 X fck X b X D^2

1.15268E+11

=

N-mm

0.262

=

=

Muz / Muz1

0.00

0.262

1.15268E+11

=

Mux1

0.30216

=

Mux / Mux1

+

0.002

=

=

Mux

4

p/fck

1.0m

2

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

5 z

7.65m x 8# Y25 dia bars 8# Y25 dia bars

4.00

Design of Combined footing Assume Size of footing

c.g. OF RAFT=

offsets on L/S

1.0m

sets on R/S

1.0m

Length

=

7.00

m

Breadth

=

7.65

m

Depth

=

1.7

m

Area

=

53.55

sq.m

Ixx=

=

261.16

m4

Iyy=

=

218.66

m4

Zxx=

=

68.28

m3

zyy=

=

62.48

m3

3.50 m FROM L/S EDGE

Total vertical load acting at C.G. of footing =

Fy X 2 Columns + Self Weight of footing + Weight of soil on footing

=

5106.47+5106.47+ 7 X 7.65 X 1.7 X 2.5 + ((7 X 7.65) - 2 (2.6 X 2.6)) X 4.3 X 2+2 (2.6 X 2.6)) X 4.6 X 2.5 Reaction Left side

5000.00

t

Reaction Right Side

5000.000

t

5

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

Weight of L/s Pedestal

77.74

t

Weight of R/s Pedestal

33.235

t

227.5875

t

Weight of soil

377.54

t

Total Weight

10716.10

t

Weight of footing

=

6

10716.10 t

Moment about Z axis at footing bottom from one column Mz

=

Fx X Lever Arm

=

0 X (4.6+1.7)+0

= Net Moment about Z axis at footing bottom from both column

0 = =

Moment about X axis at footing bottom

Mx

=

Fz X Lever Arm

=

0 X (4.6 + 1.7)+0

= Net Moment about x axis at footing bottom from both column

0 X (4.6 + 1.7)+0 0 Mz X 2 Columns 0

t-m

0 X (4.6 + 1.7)+0

0 = =

0 Mx X 2 Columns 0

t-m

4.01 Stresses at the bottom of footing D

5.00 m

C

Width (m) 7.65

B

Length (m)

7

A

Earthquake forces are not considered in this case.Hence moment in X direction (Mx) is zero. Stress at point A

=

P/A + Mx/Zx + Mz/Zz

=

10716.1025/(7X7.65) + 0/(7.65X7^2)/6 + 0/(7X7.65^2)/6 =

Stress at point B

=

P/A - Mx/Zx + Mz/Zz

=

10716.1025/(7X7.65) - 0/(7.65X7^2)/6 + 0/(7X7.65^2)/6 =

Stress at point C

=

P/A + Mx/Zx - Mz/Zz

=

10716.1025/(7X7.65)+ 0/(7.65X7^2)/6 - 0/(7X7.65^2)/6 =

Stress at point D

=

P/A - Mx/Zx - Mz/Zz

=

10716.1025/(7X7.65)- 0/(7.65X7^2)/6 - 0/(7X7.65^2)/6 =

2

200.11

t/m

200.11

t/m2

200.11

t/m

2

200.11

t/m

2

4.02 Summary of Stresses (t/m2) 53.60 t/m2

Permissible bearing capacity=(q+yd) x Factor= Stress at Point A

200.110

t/m2

B

200.110

t/m2

C

200.110

t/m2

D

200.110

t/m2

Not safe

6

t-m

t-m

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

7

4.03 Bending Moment calculation

D

C

P Width (m)

Q

7.65m B

A Length =

7.00m

Average Stress acting along PQ Average of A & C at Point Q

=

200.11

t/m2

Average of B & D at Point P

=

200.11

t/m

Reactions along the width /m length of footing at Point Q

=

1530.8415

t/m

Reactions along the width /m length of footing at Point P

=

1530.8415

t/m

=

32.5125

t/m along Z axis

377.54 t

53.934

t/m along Z axis

2

4.04 Loads acting on slab Uniformly Distributed Load/m (U.D.L) ((7X7.65)-(2.6X2.6X2))X4.3X2/7

Self Weight of footing =

7.65X 7 X 1.7 X 2.5/7

Weight of soil on footing =

7 x 7.65 - [(2.6 x2.6)+(1.7 x 1.7 )] x4.3 x 2=

Total UDL acting on Slab

=

86.44678571 t/m along Z axis

Point Loads Vertical Point Loads

Fy

=

5106.47

Mx

=

0

t

Moments Moment in X direction

t-m

4.05 Loading Diagram Column-A

Column-B

P1= 5106.47 t

86.45t/m

Mx w1=1530.8t/sq.m

P2= 5106.47 t Mx

0.00t-m

########

0.00t-m w2=1530.84t/sq.m

1530.84t/sq.m

1.00 m

5.00 m

1.00 m

7

(w2-w1)/L= 0.00t/sq.m

DATE

DOCUMENT NO.

PROJEC

DESIGNED

PAGE

CHECKED

DESIGN OF COMBINED FOOTING

TITLE :

8

4.06 Moment Calculation for Top Reinforcement M ( top pressure)

M (rect. base pressure)

M (∆. base pressure)

P1x

P2x

M1

M2

NET MOME

M @ -1.00 m from Col. A

0.00

0.00

0.00

0.00

0.00

0.00

0.00

=

0.00

M @ -0.88 m from Col. A

0.68

-11.96

0.00

0.00

0.00

0.00

0.00

= -11.28

M @ -0.75 m from Col. A

2.70

-47.84

0.00

0.00

0.00

0.00

0.00

= -45.14

M @ -0.63 m from Col. A

6.08

-107.64

0.00

0.00

0.00

0.00

0.00

= -101.56

M @ -0.50 m from Col. A

10.81

-191.36

0.00

0.00

0.00

0.00

0.00

= -180.55

M @ -0.38 m from Col. A

16.88

-298.99

0.00

0.00

0.00

0.00

0.00

= -282.11

M @ -0.25 m from Col. A

24.31

-430.55

0.00

0.00

0.00

0.00

0.00

= -406.24

M @ -0.13 m from Col. A

33.09

-586.03

0.00

0.00

0.00

0.00

0.00

= -552.93

M @ 0.00 m from Col. A

43.22

-765.42

0.00

0.00

0.00

0.00

0.00

= -722.20

M @ 0.42 m from Col. A

86.75 -1536.16

0.00

-2127.70

0.00

0.00

0.00

= ####

M @ 0.83 m from Col. A

145.28 -2572.66

0.00

-4255.39

0.00

0.00

0.00

= ####

M @ 1.25 m from Col. A

218.82 -3874.94

0.00

-6383.09

0.00

0.00

0.00

= ####

M @ 1.67 m from Col. A

307.37 -5442.99

0.00

-8510.78

0.00

0.00

0.00

= ####

M @ 2.08 m from Col. A

410.92 -7276.81

0.00

-10638.48

0.00

0.00

0.00

= ####

M @ 2.50 m from Col. A

529.49 -9376.40

0.00

-12766.18

0.00

0.00

0.00

= ####

M @ 2.92 m from Col. A

663.06 -11741.77

0.00

-14893.87

0.00

0.00

0.00

= ####

M @ 3.33 m from Col. A

811.64 -14372.90

0.00

-17021.57

0.00

0.00

0.00

= ####

M @ 3.75 m from Col. A

975.23 -17269.81

0.00

-19149.26

0.00

0.00

0.00

= ####

M @ 4.17 m from Col. A

1153.82 -20432.48

0.00

-21276.96

0.00

0.00

0.00

= ####

M @ 4.58 m from Col. A

1347.43 -23860.93

0.00

-23404.65

0.00

0.00

0.00

= ####

M @ 5.00 m from Col. A

1556.04 -27555.15

0.00

-25532.35

0.00

0.00

0.00

= ####

M @ 5.13 m from Col. A

33.09

-586.03

0.00

= -552.93

M @ 5.25 m from Col. A

24.31

-430.55

0.00

= -406.24

M @ 5.38 m from Col. A

16.88

-298.99

0.00

= -282.11

M @ 5.50 m from Col. A

10.81

-191.36

0.00

= -180.55

M @ 5.63 m from Col. A

6.08

-107.64

0.00

= -101.56

M @ 5.75 m from Col. A

2.70

-47.84

0.00

= -45.14

M @ 5.88 m from Col. A

0.68

-11.96

0.00

= -11.28

M @ 6.00 m from Col. A

0.00

0.00

0.00

=

Maximum (-ve) Bending Moment Maximum Bending Moment

=

8

-51531.45

t-m

0.00

t-m

0.00

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

9

4.07 Moment Calculation for Bottom Reinforcement at the face of the column Moment about X-axis D

S

C

Width (m)

7.65m

N

Column

Column

A

B

M m

2.53m

B

A

7.00m 0.15m R

Stress acting along P&O Avearge Pressure

=

Net UDL acting on Slab (Self Weight + Soil Load)

= =

Taking Moment about face of Column B (section RS)

=

1530.8

t/m

2

1530.841 - 86.446 1444.40

t/m

1444.395X7.65X0.15X0.15/2

=

124.31

t-m

=

16.25

t-m /m

Stress acting at section - A

=

200.110

t/m2

Stress acting at section - B

=

200.110

t/m

2

Average Pressure

=

200.11

t/m

2

Total UDL on the Slab

=

1.615

t/m2

Net Pressure

=

198.495

t/m2

Taking Moment about face of column (Section MN)

=

Moment/m width 4.08 Moment about X-axis (Moment will be maximum near Column B) Consider Section M-N

198.495 X 7 X 2.525 X 2.525/2

=

4429.354

=

632.765

t-m/m

=

632.765

t-m

Grade of Concrete

=

M25

Grade of Steel

=

Fe415

Cover to reinforcement

=

50

mm

Diameter of bar

=

16

mm

Overall deprh of slab

=

1700

mm

Effective depth of slab

=

1642

mm

Bottom reinforcement B.M

=

632.76

t-m

Top reinforcement B.M

=

0.00

t-m

=

949.15

t-m

=

0.46

Bottom reinforcemnt has to be designed for a bending moment of

/ 7m length

4.09 Design of Slab

4.10 Reinforcement for Bottom of slab(shorter direction) Factored moment Mu/bD

2

Refering from Table 2 of SP-16 For

Mu/bD2 =

0.46

&

Fe415 9

t/m

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

pt req

=

1.1930

%

Min. reinforcement

=

0.12

%

pt adopted

=

1.1930

As

=

pt X b x d / 10

=

19589.06

Diameter of bar

=

25

area

=

490.87

mm

Spacing

=

25.06

mm

=

20

=

24543.69

=

0.00

=

0.000

pt req

=

0.00

%

Min. reinforcement

=

0.12

%

pt adopted

=

0.12

%

As

=

Provide

Y-25 at

Area privided=

mm

10

2

mm C/C mm

2

4.11 Reinforcement for Top of slab(at centre) Factored moment Mu/bD

2

t-m/7.65m length

Refering from Table 2 of SP-16 2 Mu/bD =

For

0

& for

Fe415

0.12 X b x D / 100 2

=

1970.4

mm

Diameter of bar

=

32

mm

area

=

804.25

mm2

Spacing

=

408.16

mm

=

405.00

mm c/c

=

1985.80

mm2

=

24.37

=

1.085

pt req

=

0.02

%

Min. reinforcement

=

0.12

%

pt adopted

=

0.12

%

As

=

Provide

Y-32 at

(as per Cl: 26.3.3.b(1) of IS 456-2000)

Area privided= 4.11 Reinforcement for Bottom of slab(longer direction) Factored moment Mu/bD

2

t-m/7.65m length

Refering from Table 2 of SP-16 For

2 Mu/bD =

1.085

& for

Fe415

0.12 X b x D / 100

=

1970.400

mm

Diameter of bar

=

20

mm

area

=

314.16

mm

Spacing of

=

159.44

mm

=

155

=

2026.83

Factored moment

=

0.00

Mu/bD2

=

0.000

Provide

Y-20 at

(as per Cl: 26.3.3.b(1) of IS 456-2000)

Area privided=

2

2

mm c/c mm

2

4.11 Reinforcement for Top of slab(at sides)

Refering from Table 2 of SP-16 For

Mu/bD2 =

0

& for

Fe415 10

t-m/Consider Section M-N

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

pt req

=

0.00

%

Min. reinforcement

=

0.12

%

pt adopted

=

0.12

%

As

=

0.12 X b x D / 100

=

2040.000

mm

Diameter of bar

=

20

mm

area

=

314.16

mm

Spacing of

=

154.00

mm

=

150

=

2094.40

Provide

Y-20 at

(as per Cl: 26.3.3.b(1) of IS 456-2000)

Area privided=

-0.30 m 2.53 m

11

2

2

mm c/c mm

2

#20@150 C/C 0.15 m

2.53 m

#20@155 C/C #25@20 C/C

11

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

4.12 Check for oneway Shear

Width (m)

12

d

Column

Column

A

B

7.65

Length (m) =

7 0.15 m

m

One way shear has to be checked from "d" m from face of the column

Average stress at "d" from face of column

=

200.11

t/m

2

Factored stress at "d" from face of column

=

200.11

t/m

2

Shear load acting at the strip which is "d" from face of column Vu

=

Factored stress x width x ( 0.15 - eff.depth)

=

200.11 x 7.65 x (0.15 - 1.642)

=

2284.02

t v

Shear Stress

Hence provided depth is

Vu / b x d

=

2284.02 / 7.65 x (1642 /1000)

=

181.83

t/m2

=

1.82

N/mm

=

0.26

N/mm2

4242

mm

c

Permissible shear stress (Table 1 of IS 456-2000) v

=

>

c

UNSAFE

4.13 Check for two way shear Bo =

Width (m)

Column

Column

A

B

Length(m)

12

2

DATE

DOCUMENT NO.

PROJEC

DESIGNED

CHECKED

PAGE

DESIGN OF COMBINED FOOTING

TITLE :

13

Two way shear has to be checked at "d/2" m from face of column Punching load on the column

Total vertical load on column

=

5106.47

= v

Punching stress at "d/2" m from base

Permissible shear stress (Cl: 31.6.3.1 of IS 456-2000) Where

Ks

=

t

=

Punching load / 4 x Bo x d

=

5106.47x10^4 / (4 x 4242 x 1642)

v

=

1.83

c

=

ks xc

N/mm2

(0.5+c) but no greater than 1, c being the ratio of short side to long side of column

c

=

1

Ks

=

1

c

=

0.25 x Sqrt(fck) 1.25

=

v

(for limit state design)

N/mm

2

ks xc

=

1 x 1.25

c

=

1.25

c

>

Hence Provided depth is

UNSAFE

1000.00 500.00

-1000.00 -1500.00 -2000.00 -2500.00 -3000.00 -3500.00 -4000.00

1

-4500.00

13

6.82

6.46

6.10

5.74

5.38

5.03

4.67

4.31

3.95

3.59

3.23

2.87

2.51

2.15

1.79

1.44

1.08

0.72

-500.00

0.36

0

0.00

N/mm2