footing_combined.pdf

1

PROJEC DOCUMENT NO.

DESIGNED CHECKED

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/m2

Load factor 1

Assume Size of Pedestal / Column as P1 P2

Length = 2.6 1.7 m

Breadth = 2.6 1.7 m

Height = 6.30 m 6.3 m

Area of c/s= 6.76sq.m 2.89sq.m

Thickness of foundation slab 1.7 m

2.00 Forces at top of Pedestal

P1 P2 Fyt

pedestal-1Pedestal-2 Fzt

Fyt = t 5000.00 5000.000

Fxt = t 0.000 0.000

Fzt = t 0.000 0.000 Fxt

Mxt = t-m 0.000 0.000

Myt = t-m 0.000 0.000

Mzt = t-m 0.000 0.000

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 Top of Pedestal / Column

E.G.L 0.30 m E.G.L

4.30 m 4.60 m 6.30 m

1.70 m

DATE

PAGETITLE : DESIGN OF COMBINED FOOTING

Y

Z

X

P2P1

1

2

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


Mz = 0 x 6.3+0 0 x 6.3+0

= 0.000 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 x 6.3+0 t-m

= 0.000 0.000 t-m

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 5000 + 1.7 X 1.7 X 6.3 X2.5

= 5106.47 5106.47 t

3.04 Summary of forces / Moments P1 P2Fy = 5106.47 5106.47 t

Mx = 0.000 0.000 t-m

Mz = 0 0 t-m

Load Case:

3.05 Design of Column / Pedestal

Size of Column/ Pedestal

Breadth = 2.6

Width = 2.6

Cover to reinforcement = 40 mm

(Cl :26.4.2.1 of IS 456-2000)

Diameter of bar = 20 mm

3.06 Check for Pedestal or Column

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

If the Effective length is > 3 times the least lateral dimension = 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 = 2 X 6.3 2 X 6.3

= 12.6 12.6 m

Least lateral dimension = 2.6 m

Eff. Length / Least Lateral Dimension = 4.85

4.8 > 3

Hence Use Column design

3.08 Check for biaxial bending

Column has to be designed for combibed axial load & biaxial bending

Mux Muy

Mux1 Muy1 (Refer 39.6 of IS 456-2000)+ <= 1.0

nn

STATIC WIND SEISMIC

2

3

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


Assume % of steel reinforcement (p) = 0.06 0.05

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

Puz = 0.45 fck Ac + 0.75 fy As (Ref : Cl-39.6 of IS 456-2000)

Where fck = Characteristic cube comp. Strength of concrete

= M25 N/mm2

fy = Characteristic Strength of steel

= Fe 415 N/mm2

As = Area of Steel 4056 1445 mm2

Ac = Area of Concrete 2600 X 2600 - As

= 6755944 2888555 mm2

=

Puz = 0.45 X 25 X 6755944 + 0.75 X 415 X 4056 0.45 X 25 X 2888555 + 0.75

= 77266800 32946000 N

= 7726.68 3294.6 t

Pu / Puz = 5106.47 / 7726.68 5106.47 / 3294.6

= 0.66 1.55

If Pu / Puz < 0.2 n = 1

If Pu / Puz > 0.8 n = 2

If Pu / Puz is b/n 0.2 to 0.8

n = Linearly varying

n = 1.77 2.00

P1 P2

Factored Loads & Moments Pu = 1x5106.47 1x5106.47 t

5106.47 5106.47 t

Mux = 1x0 1x0 t-m

= 0 0 t-m

Muz = 1x0 1x0 t-m

= 0.00000 0 t-m

Calculation of Mux1 & Muz1

d' / D

Where d' = Cover + 1/2 of dia of bar

D = 50 mm

D = Overall Width/ Breadth

= 2600 mm

d' / D = 0.01923

For P1 For P2

Pu/fck b D = 5106.47 X 10^4 / 25 X 2600 X 2600 5106.47 X 10^4 / 25 X 1700 X 1700

= 0.302 0.302 t

² p/fck = 0.06 / 25 0.05 / 25

= 0.0024 0.0020

Referring from Chart 48 of SP16

3

4

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


For p/fck = 0.0024 0.002

Pu/fck b D = 0.3022 0.30216

Mux1 / fck b D2 = 0.26233 0.262

Mux1 = 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

= 1.15268E+11 32221825727 N-mm

= 11526.7802 3222.18 t-m

For p/fck = 0.0024

Pu/fck b D = 0.30

Muz1 / fck b D2 = 0.26233 0.262

Muz1 = 0.26233 X fck X b X D^2

= 0.26233 X 25 X 2600 X 2600² 0.262 X 25 X 1700 X 1700²

= 1.15268E+11 32221825727 N-mm

= 11526.7802 t-m

Mux / Mux1 = 0 / 11526.7802 3222.18 / 11526.7802

= 0 0

Muz / Muz1 = 0 / 11526.7802 0 / 3222.182

0 0

Mux Muz 0.00000 0.00000

Mux1 Muz1

0.00 < 1

Hence the assumed % of reinforcement is SAFE

3.09 Reinforcement

Area of Steel required = 4056 mm2

Hence Provide

8 Nos 25 mm dia mars = 3925 mm2

8 Nos 25 mm dia mars = 3925 mm2

Area of steel Provided = 7850 mm2

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 Y8 @300C/C

1.00m 5.0m 1.0m

+

nn

4

5

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


7.65m

8# Y25 dia bars

8# Y25 dia bars

4.00 Design of Combined footing offsets on L/S 1.0m

Assume Size of footing 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

c.g. OF RAFT= 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

z

x

5

6

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


Weight of L/s Pedestal 77.74 t

Weight of R/s Pedestal 33.235 t

Weight of footing 227.5875 t

Weight of soil 377.54 t

Total Weight 10716.10 t

= 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 0 X (4.6 + 1.7)+0

= 0 0 t-m

Net Moment about Z axis at footing bottom from both column = Mz X 2 Columns

= 0 t-m

Moment about X axis at footing bottom Mx = Fz X Lever Arm

= 0 X (4.6 + 1.7)+0 0 X (4.6 + 1.7)+0

= 0 0 t-m

Net Moment about x axis at footing bottom from both column = Mx X 2 Columns

= 0 t-m

4.01 Stresses at the bottom of footing

D 5.00 m C

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

= 200.11 t/m2

Stress at point B = P/A - Mx/Zx + Mz/Zz

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

= 200.11 t/m2

Stress at point C = P/A + Mx/Zx - Mz/Zz

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

= 200.11 t/m2

Stress at point D = P/A - Mx/Zx - Mz/Zz

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

= 200.11 t/m2

4.02 Summary of Stresses (t/m2)

Permissible bearing capacity=(q+yd) x Factor= 53.60 t/m2

200.110 t/m2

200.110 t/m2 Not safe

200.110 t/m2

200.110 t/m2D

Width (m)

Stress at Point

A

B

C

6

7

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


4.03 Bending Moment calculation

D C

P 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/m2

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

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 = 32.5125 t/m along Z axis

Weight of soil on footing = 7 x 7.65 - [(2.6 x2.6)+(1.7 x 1.7 )] x4.3 x 2= 377.54 t 53.934 t/m along Z axis

Total UDL acting on Slab = 86.44678571 t/m along Z axis

Point Loads

Vertical Point Loads Fy = 5106.47 t

Moments

Moment in X direction Mx = 0 t-m

4.05 Loading Diagram

Column-A Column-B

P1= 5106.47 t 86.45t/m P2= 5106.47 t

Mx Mx ########

0.00t-m

1.00 m 5.00 m 1.00 m (w2-w1)/L= 0.00t/sq.m

1530.84t/sq.m

w1=1530.8t/sq.m 0.00t-m

w2=1530.84t/sq.m

Width (m)

7

8

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


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 = 0.00

Maximum (-ve) Bending Moment -51531.45 t-m

Maximum Bending Moment = 0.00 t-m

8

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PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


4.07 Moment Calculation for Bottom Reinforcement at the face of the column

Moment about X-axis

D S C

7.65m N M

m

B 2.53m A

7.00m

0.15m

Stress acting along P&O

Avearge Pressure = 1530.8 t/m2

Net UDL acting on Slab (Self Weight + Soil Load) = 1530.841 - 86.446 t/m

= 1444.40 t/m

Taking Moment about face of Column B (section RS) = 1444.395X7.65X0.15X0.15/2

= 124.31 t-m

Moment/m width = 16.25 t-m /m

4.08 Moment about X-axis (Moment will be maximum near Column B)

Consider Section M-N

Stress acting at section - A = 200.110 t/m2

Stress acting at section - B = 200.110 t/m2

Average Pressure = 200.11 t/m2

Total UDL on the Slab = 1.615 t/m2

Net Pressure = 198.495 t/m2

Taking Moment about face of column (Section MN) = 198.495 X 7 X 2.525 X 2.525/2

= 4429.354 / 7m length

= 632.765 t-m/m

Bottom reinforcemnt has to be designed for a bending moment of = 632.765 t-m

4.09 Design of Slab

Grade of Concrete = M25

Grade of Steel = Fe415

Cover to reinforcement = 50 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

4.10 Reinforcement for Bottom of slab(shorter direction)

Factored moment = 949.15 t-m

Mu/bD2 = 0.46

Refering from Table 2 of SP-16

For Mu/bD2 = 0.46 & Fe415

Width (m)

Column

AColumn

B

R

9

10

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


pt req = 1.1930 %

Min. reinforcement = 0.12 %

pt adopted = 1.1930

As = pt X b x d / 10

= 19589.06 mm2

Diameter of bar = 25

area = 490.87 mm

Spacing = 25.06 mm

Provide Y-25 at = 20 mm C/C

Area privided= = 24543.69 mm2

4.11 Reinforcement for Top of slab(at centre)

Factored moment = 0.00 t-m/7.65m length

Mu/bD2 = 0.000


For Mu/bD2 = 0 & for Fe415

pt req = 0.00 %


pt adopted = 0.12 %

As = 0.12 X b x D / 100

= 1970.4 mm2


area = 804.25 mm2

Spacing = 408.16 mm

Provide Y-32 at (as per Cl: 26.3.3.b(1) of IS 456-2000) = 405.00 mm c/c


4.11 Reinforcement for Bottom of slab(longer direction)

Factored moment = 24.37 t-m/7.65m length

Mu/bD2 = 1.085


For Mu/bD2 = 1.085 & for Fe415

pt req = 0.02 %


pt adopted = 0.12 %

As = 0.12 X b x D / 100

= 1970.400 mm2


area = 314.16 mm2

Spacing of = 159.44 mm

Provide Y-20 at (as per Cl: 26.3.3.b(1) of IS 456-2000) = 155 mm c/c


4.11 Reinforcement for Top of slab(at sides)

Factored moment = 0.00 t-m/Consider Section M-N

Mu/bD2 = 0.000


For Mu/bD2 = 0 & for Fe415

10

11

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


pt req = 0.00 %


pt adopted = 0.12 %

As = 0.12 X b x D / 100

= 2040.000 mm2


area = 314.16 mm2

Spacing of = 154.00 mm

Provide Y-20 at (as per Cl: 26.3.3.b(1) of IS 456-2000) = 150 mm c/c


-0.30 m #20@150 C/C

2.53 m 2.53 m 0.15 m

#20@155 C/C

#25@20 C/C

11

12

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


4.12 Check for oneway Shear d

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/m2

Factored stress at "d" from face of column = 200.11 t/m2

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

Shear Stress v = Vu / b x d

= 2284.02 / 7.65 x (1642 /1000)

= 181.83 t/m2

= 1.82 N/mm2

Permissible shear stress (Table 1 of IS 456-2000) c = 0.26 N/mm2

v > c

Hence provided depth is UNSAFE

4.13 Check for two way shear

Bo = 4242 mm

Length(m)

Width (m)Column

AColumn

B

Width (m)Column

AColumn

B

12

13

PROJEC DOCUMENT NO.

DESIGNED CHECKED

DATE


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 t

Punching stress at "d/2" m from base v = Punching load / 4 x Bo x d

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

v = 1.83 N/mm2

Permissible shear stress (Cl: 31.6.3.1 of IS 456-2000) c = ks xc

Where Ks = (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) (for limit state design)

= 1.25 N/mm2

ks xc = 1 x 1.25

c = 1.25 N/mm2

v > c

Hence Provided depth is UNSAFE

1-4500.00

-4000.00

-3500.00

-3000.00

-2500.00

-2000.00

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

0

0.3

6

0.7

2

1.0

8

1.4

4

1.7

9

2.1

5

2.5

1

2.8

7

3.2

3

3.5

9

3.9

5

4.3

1

4.6

7

5.0

3

5.3

8

5.7

4

6.1

0

6.4

6

6.8

2

13

footing_combined.pdf

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