Project Name : Design of Isolated Footing F 1001 - 1 for Date : 9/9/2009

Residential Building

DESIGN OF ISOLATED FOOTING :

Working Load P = 1000.0 kN P = 1000.0 kN

x - e = 1150 dx = 695
D= b=

d1 = 532
e = 50 600 dx-e = 645 dx/2= 230

d2 = 358
347.5

Df - Df_min
dx = 695

600

dy = 685
B1 = 915
Df = 750

L2 = 1970 B2 = 1620

=
d2 = 358
Df_min
= 150
Bf = 2500
Lf = 3000

B1 = b+dy = 915
y = 1135

x = 1200
D = 600
L1 = D + dy = 1285
Bf = 2500

Lf = 3000
b+2e = 330

b= 230

D = 600
D+2e = 700
dx = 695
B = 230

1. Area Calculation :

Working Load on the Column : P= 1000 kN

Factored Load = P x 1.5 = Pu = 1500 kN
Safe Bearing Capacity σbs = 175 kN/m²

1.1 · ( Pu / 1.5 )
Area of Footing required Af = = 6.2857 m²
σbs

Width of Column b= 230 mm

Depth of Column D= 600 mm 1/2
2
(D-b) (D-b)
Required length of Footing Lf = ± + Af = 2699 mm
2 2

Width of Footing Bf = Af / Lf = 2329 mm

Provided Size of Footing Lf = 3000 mm

Bf = 2500 mm ( Area Provided = 7.500 m² )

Grade of Concrete Fck = 20 N/mm²

Grade of Steel Fy = 415 N/mm²
2 . Depth Calculation

Upward Soil Reaction wu = Pu / ( Lf · Bf ) = 200 kN/m²

Projextion of Footing x = ( Lf - D ) / 2 = 1200 mm

y = ( Bf - b ) / 2 = 1135 mm

Mux = wu · Bf · x² / 2 = 360.00 kN-m

Muy = wu · Lf · y² / 2 = 386.47 kN-m

e is the projection at the top of footing in order to facilitate form work = 50 mm

Width at the top of Footing b' = b + 2e = 330 mm

Depth at the Top of Footing D' = D + 2e = 700 mm

Ru_max = 0.138 x Fck = 2.76 N / mm²

Dia of Bar proposed Φ = 10 mm

Effective Cover in X- Dir. d'x = 50 + Φ/2 = 55 mm
Effective Cover in Y- Dir. d'y = 50+ Φ/2 +Φ = 65 mm

Required total depth of Footing

Mux 1/2
Dfx = + d'x = 684 mm
Ru_max · b'

Muy 1/2
Dfy = + d'y = 512 mm
Ru_max · D'

Depth of Footing provided ( ≥ 700 mm ) Df = 750 mm

Effective Depth provided dx =Df - 50 - Φ/2 = 695 mm

dy =Df - 50 - Φ/2 - Φ = 685 mm

3 . Check for Two Way Shear

Critical section at distance dy / 2 from the face of the column

( a ) Calculation of Design Shear Vud

Size of Critical Section L1 = D + dy = 1285 mm

B1 = B + dy = 915 mm

Assuming Df_min = 150 mm

dy
- 50
Effective depth at distance dy / 2 = d1 = dy - 2 · ( Df - Df_min )
x - 50

d1 = 532.39 mm

Design Shear = Vud = wu · ( Lf · Bf - L1 · B1 ) = ### kN

 ( b) Calculation of Shear Resistance Vuc

Shear Stress τuc = 0.25 · Fck1/2 = 1.118 N / mm²

Ks = 0.5 + ( b / D ) = 0.88 ≤ 1 ==> Ks = 0.883

Area Resisting Shaear = 2 · ( L1 + B1 ) · d1 = 2342521.7 mm²

Shear Resistance = Vuc = Ks · τuc · Area Resisting Shear = 2313.5 kN

Here , Vuc ≥ Vud SECTION IS SAFE IN TWO WAY SHEAR

4 . Reinforcement Calculation

1/2
0.5 x Fck 4.6 · Mux
Ast_ x =
Fy · 1 - 1 -
Fck · b' · dx² · b' x dx

1/2
= 0.024 · 1 - 1 - 0.51945363265 · 229350

= 1695 mm² ( Pt_x = 0.7392 )

Required 10 # bars at 116 mm c/c

Provide 10 # bars at 200 mm c/c ( Nos. = 14 ) ( Ast = 1100 )

1/2
0.5 · Fck 4.6 · Muy
Ast_ y =
Fy · 1 - 1 -
Fck · D' · dy² · D' · dy

1/2
= 0.024 · 1 - 1 - 0.27062108492 · 479500

= 1686 mm² ( Pt_y = 0.3517 )

Required 10 # bars at 140 mm c/c

Provide 10 # bars at 200 mm c/c ( Nos. = 16 ) ( Ast = 1257 )

5 . Check for Development Length

0.87 · Fy · Φ Value of τbd from IS 456 for Fck = 20 = 1.2

Ld =
4 · τbd

= 752 mm

≤ x = 1200
≤ y = 1135
6 . Check for One Way Shear

Note : If the Effective Depth dx ≥ Projection of footing x, the check is not necessary.

Critical Section for one way shear occurs at distance dx ( or dy ) from face of column

( a) For Bending about x - x axis

Width at top of Footing at critical Section B2 = b + 2 dx = 1620 mm

dx - 50
Effective Depth at critical Section d2 = dx - ( Df - Df_min )
x - 50

= 358 mm

( Bf - B2 )
Area resisting Shear = Bf · d2 - · ( d2 - ( Df_min - d'x ) )
2

= 854395.7 mm²

Percentage of Steel Provided Pt_x = 0.20 ( Ast_x / Area resisting Shear )

Permissible Shear Stress τc = 0.344 N/mm²

Shear Resistance = Vuc = τc · Area resisting Shear = 293.49 kN

Enhenced Shear Resistance ( IS 456 , cl: 40.5.1 ) = 2 · Vuc = 586.97 kN

Design Shear = Vud = wu · Bf · ( x - dx ) = 252.5 kN

Here, Vuc ≥ Vud , SECTION IS SAFE IN ONE WAY SHEAR

( b) For Bending about y - y axis

Width at top of Footing at critical Section L2 = D + 2 dy = 1970 mm

dy - 50
Effective Depth at critical Section d2 = dy - ( Df - Df_min )
y - 50

= 334 mm

( Lf - L2 )
Area resisting Shear = Lf · d2 - · ( d2 - ( Df_min - d'y ) )
2

= 873387.1 mm²

Percentage of Steel Provided Pt_y = 0.14 ( Ast_y / Area resisting Shear )

Permissible Shear Stress τc = 0.326 N/mm²

Shear Resistance = Vuc = τc · Area resisting Shear = 284.76 kN

Enhenced Shear Resistance ( IS 456 , cl: 40.5.1 ) = 2 · Vuc = 569.52 kN

Design Shear = Vud = wu · Lf · ( y - dy ) = 270 kN

Here, Vuc ≥ Vud , SECTION IS SAFE IN ONE WAY SHEAR

Project Name : Design of Combined Footing F 1001 - 1 for Date : 10/17/2009 -1 1 1
Residential Building -1 -1 1

DESIGN of Combined FOOTING : ( Safe Bearing Capacity = 150 kN / m² ) Fck = 25 Mpa

X Y Dead Load Live Load EQx Eqz

Column
ID.
Co.Ord. Co.Ord Py Mx Mz Py Mx Mz Py Mx Mz Py Mx Mz
.
C65 0 0 525.77 -12.14 -0.24 106.9818 1.15 -1.36 133.37 -5.79 90.86 -297.5 -298 2.06

TOTAL 525.77 -12.14 -0.24 106.9818 1.15 -1.36 133.37 -5.79 90.86 -297.5 -298 2.06

Area of Footing Required for DL+LL= 4.6402 m² 2000 0 2000

150
CG of ( DL + LL ) = ( ### , -2.529 ) 141 934 B
Live Load Reduction for EQ = 1

1250
1075

x1 x2
Pressure Calculation 2

y2
2500
758

0
Load Case A B C D

y1
808 267

Dead 56.0 59.6 59.7 56.1 1

1250
1075

Live 10.5 10.2 10.9 11.2

Live for EQ 10.5 10.2 10.9 11.2 450 C 4000
Eqx 34.3 36.0 -7.6 -9.3 450
Eqz -74.0 15.4 14.5 -74.9 1625 -750 1625
484 47
1.5(DL+LL) 66.50 69.8 70.57 67.3
450

1.5(DL+Eqx) 90.2 95.6 52.1 46.7 150 Cover = 20 mm

1.5(DL-Eqx) 21.7 23.6 67.3 65.4 .
1.5(DL+Eqz) -18.0 75.0 74.2 -18.9 Col. Size X Size Z Area of Footing Provided A = 10 m²
GEOMETRICAL
PROPERTIES

1.5(DL-Eqz) 129.9 44.2 45.3 131.0 Id mm mm

Moment of Inertia @ CG Ixx = 13.333 m4
1.2(DL+LL+Eqx) 100.8 105.8 63.0 57.9 C65 750 350 Moment of Inertia @ CG Izz = 5.2083 m4
1.2(DL+LL-Eqx) 32.2 33.8 78.2 76.6 Section Modulus @ CG Zxx = 6.6667 m3
1.2(DL+LL+Eqz) -7.5 85.2 85.0 -7.7 Section Modulus @ CG Zzz = 4.1667 m3
1.2(DL+LL-Eqz) 140.5 54.4 56.1 142.2
0.9DL+1.5Eqx 101.8 107.7 42.3 36.5 Moment of inertia Section Modulus
Column
0.9DL-1.5Eqx -1.1 -0.4 65.1 64.5 Ixx Izz ZL ZR ZT ZB
0.9DL+1.5Eqz -60.6 76.8 75.4 -62.0 C65 13.333 5.2083 6.6667 6.6667 4.1667 4.166667
0.9DL-1.5Eqz 161.3 30.5 32.1 162.9 0 13.333 5.2083 6.6667 6.6667 4.1667 4.166667
Min. -60.57 -0.38 32.06 -61.95 0 13.333 5.2083 6.6667 6.6667 4.1667 4.166667
Max. 161.30 107.66 85.02 162.88 0 13.333 5.2083 6.6667 6.6667 4.1667 4.166667
0 13.333 5.2083 6.6667 6.6667 4.1667 4.166667

Depth Calc. at Critical Sec. at d/2 at d

Two Way Shear Calculation Critical Depth at TOP = 427 363
Depth of Footing = 450 mm Critical Depth at BOT = 450 396
Effective Depth in X-Dir = 424 mm Critical Depth at LEFT = 450 450
Effective Depth in Y-Dir = 412 mm Critical Depth at RIGHT = 419 378
Critical Length = 1174 mm
Critical Width = 774 mm
Design Shear = 1481 kN
Shear Stress ( τc ) = 1.25 N/mm²
Area Resisting Shear = 1.7021 m²
Co-efficient Ks = 0.9 ---
Shear Resistance = 1915 kN
1
-1

D
Project Name : Design of Combined Footing F 1001 - 1 for Date : -1 1 1 1
Residential Building -1 -1 1 -1

DESIGN of Combined FOOTING : ( Safe Bearing Capacity = 150 kN / m² ) Fck = 25 Mpa

X Y Dead Load Live Load EQx Eqz

Column
ID.
Co.Ord. Co.Ord Py Mx Mz Py Mx Mz Py Mx Mz Py Mx Mz
.
C1 0 0 298.08 0.6 -41.04 4.68 -0.06 -0.78 184.85 36.17 4.8 7.85 -0.37 -71.678
C4 2 0 432.33 4.68 -139 19.81 -0.55 -15.85 -76.97 239.35 -2.08 11.8 -1.89 -153.3

TOTAL 730.41 5.28 -180 24.49 -0.61 -16.63 107.88 275.52 2.72 19.65 -2.26 -224.978

Area of Footing Required for DL+LL= 5.5359 m² 1125 2000 1125

150
CG of ( DL + LL ) = ( 1204 , -260.5 ) B A

950
Live Load Reduction for EQ = 0.5

1375
1000
50

x1 x2
Pressure Calculation 2

y2
2750
850

0
Load Case A B C D

y1
Dead 52.0 18.3 85.5 119.2 1

1375
50
1000

950

Live 0.7 -2.8 3.4 7.0

Live for EQ 0.4 -1.4 1.7 3.5 150 C 4250 D
Eqx 11.4 8.1 7.1 10.4 450
Eqz -40.1 -40.5 43.5 43.9 750 1250 750
50 50
1.5(DL+LL) 52.73 15.5 88.9 126.2
450

1.5(DL+Eqx) 63.4 26.4 92.6 129.6 150 Cover = 20 mm

1.5(DL-Eqx) 40.6 10.2 78.4 108.8 .
1.5(DL+Eqz) 11.9 -22.2 129.0 163.1 Col. Size X Size Z Area of Footing Provided A = 11.688 m²
GEOMETRICAL
PROPERTIES

1.5(DL-Eqz) 92.1 58.8 42.0 75.3 Id mm mm

Moment of Inertia @ CG Ixx = 17.592 m4
1.2(DL+LL+Eqx) 63.8 25.0 94.3 133.1 C1 750 350 Moment of Inertia @ CG Izz = 7.3656 m4
1.2(DL+LL-Eqx) 41.0 8.8 80.2 112.3 C4 750 350 Section Modulus @ CG Zxx = 8.2786 m3
1.2(DL+LL+Eqz) 12.2 -23.6 130.7 166.6 Section Modulus @ CG Zzz = 5.3568 m3
1.2(DL+LL-Eqz) 92.5 57.4 43.7 78.8
0.9DL+1.5Eqx 63.9 28.6 87.6 122.9 Moment of inertia Section Modulus
Column
0.9DL-1.5Eqx 29.7 4.3 66.4 91.7 Ixx Izz ZL ZR ZT ZB
0.9DL+1.5Eqz -13.4 -44.3 142.2 173.1 C1 29.28 7.3656 8.2786 8.2786 5.3568 5.357
0.9DL-1.5Eqz 107.0 77.2 11.7 41.5 C4 29.28 7.3656 8.2786 8.2786 5.3568 5.357
Min. -13.38 -44.33 11.74 41.46 0 29.28 7.3656 8.2786 8.2786 5.3568 5.357
Max. 106.96 77.23 142.17 173.12 0 29.28 7.3656 8.2786 8.2786 5.3568 5.357
0 29.28 7.3656 8.2786 8.2786 5.3568 5.357

Depth Calc. at Critical Sec. at d/2 at d

Two Way Shear Calculation Critical Depth at TOP = 399 150
Depth of Footing = 450 mm Critical Depth at BOT = 399 150
Effective Depth in X-Dir = 424 mm Critical Depth at LEFT = 381 290
Effective Depth in Y-Dir = 412 mm Critical Depth at RIGHT = 381 290
Critical Length = 3174 mm
Critical Width = 1174 mm
Design Shear = 1378 kN
Shear Stress ( τc ) = 1.25 N/mm²
Area Resisting Shear = 3.4254 m²
Co-efficient Ks = 0.9 ---
Shear Resistance = 3854 kN
COMBINED FOOTING C65 + C68

COLUMN LOADS : ( Safe Bearing Capacity = 150 kN / m² ) Fck = 25 Mpa

Column X Y Dead Load Live Load EQx Eqz

ID. Co.Ord. Co.Ord. Py Mx Mz Py Mx Mz Py Mx Mz Py Mx Mz
C1 0 0 298.08 0.6 -41.04 4.68 -0.06 -0.78 184.85 36.17 4.8 7.85 -0.37 -71.68
C4 2 0 432.33 4.68 -139 19.81 -0.55 -15.85 -76.97 239.35 -2.08 11.8 -1.89 -153.3

TOTAL 730.41 5.28 -180 24.49 -0.61 -16.63 107.88 275.52 2.72 19.65 -2.26 -225
kN/m²
75.5

B A
1200

1375
750 750
kN/m²
107

2750

350

350
kN/m²

C1 C4
117

1375

1125 2000 1125

1200

C D
kN/m²
148.6

450 4250

750 1250 750

Footing Longitudional
Sectiomn
450

335.8
B,C A,D

Base Pressure

84.72 92 98.4
59.6 66.48 73.32 kN/m² kN/m² kN/m²
kN/m² kN/m² kN/m²

375.0 kN 382.3 kN 360.0 kN 378.4 kN

Shear Force
380.0 kN
396.4 kN 358.8 kN 345.0 kN

18.95 kN-m
Bending moment

210.9 kN-m 196.7 kN-m

 Area of Footing Provided A = 11.688 m² Concrete grade = M 25
GEOMETRICAL
PROPERTIES
Moment of Inertia @ CG Ixx = 17.59 m4 Steel Grade = Fe 415
Moment of Inertia @ CG Izz = 7.37 m4
M.O.R
Section Modulus @ CG Zxx = 8.28 m3 = 0.138Fck = 3.45
Section Modulus @ CG Zzz = 5.36 m3

Calculating Load Eccentricity :

Load Case CG_X of Load Ecc_x CG_z of Load Ecc_z

Dead Load 864.66 / 730.41 = 2.31 m 0.184 m 0 / 730.41 = 1.38 m 0.000 m
Live Load 39.62 / 24.49 = 2.74 m 0.618 m 0 / 24.49 = 1.38 m 0.000 m
Eqx -153.9 / 107.88 = -0.30 m -2.427 m 0 / 107.88 = 1.38 m 0.000 m
Eqz 23.6 / 19.65 = 2.33 m 0.201 m 0 / 19.65 = 1.38 m 0.000 m

Pressure Calculation ( UNIT : kN / m² ) Avg. Pressure Avg. Pressure

Load Case A B C D BC AD AB CD
Dead 52.0 18.3 85.5 119.2 51.9 85.6 35.1 102.4
Live 0.7 -2.8 3.4 7.0 0.3 3.8 -1.0 5.2
Live for EQ 0.4 -1.4 1.7 3.5 0.2 1.9 -0.5 2.6
Eqx 11.4 8.1 7.1 10.4 7.6 10.9 9.7 8.7
Eqz -40.1 -40.5 43.5 43.9 1.5 1.9 -40.3 43.7

(DL+LL) 53 16 89 126 52.2 89.4 34.1 107.6

(DL+Eqx) 63 26 93 130 59.5 96.5 44.9 111.1
(DL-Eqx) 41 10 78 109 44.3 74.7 25.4 93.6
(DL+Eqz) 12 -22 129 163 53.4 87.5 -5.2 146.0
(DL-Eqz) 92 59 42 75 50.4 83.7 75.5 58.7
(DL+LL+Eqx) 64 25 94 133 59.6 98.4 44.4 113.7
(DL+LL-Eqx) 41 9 80 112 44.5 76.6 24.9 96.2
(DL+LL+Eqz) 12 -24 131 167 53.5 89.4 -5.7 148.6
(DL+LL-Eqz) 92 57 44 79 50.6 85.6 74.9 61.3

Min. 11.87 -23.6 42.0 75.33 44.3 74.71 -5.69 58.68

Max. 92.5 58.8 130.7 166.6 59.6 98.4 75.5 148.6

Sample Calculation of base pressure for Dead Load Case at Corner A :

Pressure due to Column Load C1

P P ex Mx Mz where ex = 1125 - 4250 / 2 = -1000 mm

= + + +
A Zx Zx Zz = -1 m

= 298.1 x 1.1 298.1 x -1 0.6 -41.04

+ + +
11.69 8.28 8.28 5.36

= 28.05 + -36 + 0.072 + -7.661

= -15.54 kN / m²

Pressure due to Column Load C4

P P ex Mx Mz where ex = 4250 / 2 - 1125 = 1000 mm

= + + +
A Zx Zx Zz = 1m

= 432.3 x 1.1 432.3 x 1 4.68 -139

+ + +
11.69 8.28 8.28 5.36

= 40.69 + 52.22 + 0.565 + -26

= 67.53 kN / m²
Total Pressure at Corner A = -15.54 + 67.53 = 51.99 kN/m²

Depth Calculation : ( Moment Criteria )

Max. working moment = 210.9 kN-m

Factored moment = 1.5 x 210.9 = 316.4 kN - m

Width of Footing = 2750 mm

Cover Provided = 50 mm

Reinforcement Dia = 20 mm

Mu
Depth Required = √ R x b
+ Cover + Reinf. Dia / 2

316.4 x 1000 x 1000

=
√ 0.138 x 25 x 2750
+ 50 + 10

= 242.6 mm
Depth Provided = 450 mm --------------------------------- SAFE

Effective Depth = 450 - 50 - 10 = 390 mm

Two Way Shear Check :

Column C1 Column C4
Load Combinations : DL + LL = 302.76 452.14 kN
DL + LL+ Eqx = 487.61 375.17 kN
DL + LL- Eqx = 117.91 529.11 kN
DL + LL+ Eqz = 310.61 463.94 kN
DL + LL- Eqz = 294.91 440.34 kN

Max. Column Load 487.61 529.11 kN

Two Way Shear Check For Column C1

max. Axial Load = 487.61 kN

Factored Load = 487.61 x 1.5 = 731.42 kN

Area Resisting Shear = 2( 750 + 390 + 350 + 390 ) x 390

= 1466400 mm²

731.42 x 1000
Shear Stress = = 0.499 N/mm²
1466400
Ks = 0.5 + ß
τc = 0.25 √ Fck = 0.5 + 0.467
= 0.25 x √ 25 = 0.967
= 1.25
b 350
ß = = = 0.467
 ß = = = 0.467
Permissible Shear Stress = Ks · τc D 750
= 0.967 x 1.25
= 1.208 N/mm² --------------------------------------------------------------------- SAFE

Two Way Shear Check For Column C4

max. Axial Load = 529.11 kN

Factored Load = 529.11 x 1.5 = 793.67 kN

Area Resisting Shear = 2( 750 + 390 + 350 + 390 ) x 390

= 1466400 mm²

793.67 x 1000
Shear Stress = = 0.541 N/mm²
1466400
Ks = 0.5 + ß
τc = 0.25 √ Fck = 0.5 + 0.467
= 0.25 x √ 25 = 0.967
= 1.25
b 350
ß = = = 0.467
Permissible Shear Stress = Ks · τc D 750
= 0.967 x 1.25
= 1.208 N/mm² --------------------------------------------------------------------- SAFE

Reinforcement Calculation :

Longitudional Reinforcement :

Bottom Reinforcement :

max. Bending Moment = 210.9 kN

Factored bending Moment = 1.50 x 210.9 = 316.4 kN / m²

Considering Effective Width of Footing = 2750 mm

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 316.4 x 1000 x 1000

415 [ 1 - √ 1 -
25 x 2750 x 390 x 390 ]
x 2750 x 390

= 2332 mm²

Minimum Reinforcement = 0.12 %

= 0.12 x 2750 x 390 / 100

= 1287 mm²

Provide 16 Dia 16 No Reinforcement Provided = 3217 mm²

Spacing Provided = 168.8 mm

Providing 16 Dia 165 mm c/c --------------------- SAFE

Top Reinforcement :
max. Bending Moment = 18.95 kN

Factored bending Moment = 1.50 x 18.95 = 28.43 kN / m²

Considering Effective Width of Footing = 2750 mm

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 28.43 x 1000 x 1000

415 [ 1 - √ 1 -
25 x 2750 x 390 x 390 ]
x 2750 x 390

= 203 mm²

Minimum Reinforcement = 0.12 %

= 0.12 x 2750 x 390 / 100

= 1287 mm²

Provide 16 Dia 16 No Reinforcement Provided = 3217 mm²

Spacing Provided = 168.8 mm

Providing 16 Dia 165 mm c/c --------------------- SAFE

Transverse Reinforcement :

Bottom Reinforcement :

Effective Width of Footing = 1000 mm

Max. Bending moment at face of Column from AB side =

= (75.45+107.39)/2x(1200/1000)x(2x75.45+107.39)/(75.45+107.39)*(1200/3000)

= 61.99 kN - m ------------------------------------------------ (a)

Max. Bending moment at face of Column from CD side =

= (148.64+116.7)/2x(1200/1000)x(2x148.64+116.7)/(148.64+116.7)*(1200/3000)

= 99.35 kN - m ------------------------------------------------ (b)

Local Distribution of Forces from each Column

band Width of Footing = b+ 2 d = 750 + 2x 390 = 1530 mm

Max. Axial Force In Column = 529.11 kN

529.11 x 1000
Upward Pressure = = 192.40 kN/m
2750

Cantilever Projection = 1200 mm

2
192.40 x 1.2
Max. Moment at Face of Column = = 138.53 kN- m
2

This moment is acting along width of 1530 mm

Hence, moment per meter width = 138.53 / 1.53 = 90.54 kN -m ---------------------------- ( c )

Considering maximum moment from ( a ) , ( b ) and ( c )

Max. bending moment = 99.4 kN-m

Factored Moment = 99.4 x 1.5 = 149.0 kN - m

Mu
Depth Required = √ R x b
+ Cover + Reinf. Dia / 2

149.0 x 1000 x 1000

=
√ 0.138 x 25 x 1000
+ 50 + 10

= 267.8 mm
Depth Provided = 450 mm ------------------------------------------------- SAFE

Reinforcement in transverse Direction =

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 149.0 x 1000 x 1000

415 [ 1 - √ 1 -
25 x 1000 x 390 x 390 ]
x 1000 x 390

= 1111 mm²

Minimum Reinforcement = 0.12 %

= 0.12 x 1000 x 390 / 100

= 468 mm²

Providing 16 Dia 100 mm c/c ( Ast provided = 2011 mm² )

------------------------------------------------------ SAFE

Top Reinforcement :

Providing minimum reinforcement

Minimum Reinforcement = 0.12 %

= 0.12 x 1000 x 390 / 100

= 468 mm²

Providing 16 Dia 175 mm c/c ( Ast provided = 1149 mm² )

------------------------------------------------------ SAFE

Summary of Reinforcement :

Longitudional Direction Top 16 Dia 165 c/c = 1219 mm² 0.31 %

Bottom 16 Dia 165 c/c = 1219 mm² 0.31 %

Transverse Direction Top. 16 Dia 175 c/c = 1149 mm² 0.29 %

Bottom 16 Dia 100 c/c = 2011 mm² 0.52 %

Check for one way shear :

Longitudional Direction

Max. Shear Force = 380.0 kN

Factored Shear Force = 380.0 x 1.5 = 570 kN

Width of Footing = 2.75 m

Eff. Depth of Footing = 390 mm

570 x 1000
Shear Stress = = 0.531 N/mm²
2750 x 390

% Reinforcement Provided = 0.31 %

Permissible Shear Stress = 0.392 N/mm² < 0.531 ------------------ Providing Stuirrups

Design shear Stress = 0.531 - 0.392 = 0.139 N/mm²

Design Shear Force = 0.139 x 2750 x 390 / 1000 = 149.1 kN

Providing Stirrups Dia = 10 mm Legged = 6

Asv = 471.2 mm²

0.87 x Fy x Asv x d
Spacing provided =
Vu

0.87 x 415 x 471.2 x 390

=
149.0713 x 1000

= 445.1 mm

Min. Shear Reinforcement 0.87 x Fy x Asv

=
Spacing 0.4 x b

0.87 x 415 x 471.2

=
0.4 x 2750

= 154.67 mm

Providing 10 Dia 6 Legged Stirrups at Spacing of 150 mm c/c

----------------------------- SAFE

Transverse Direction :

Upward Pressure = 192.40 kN / m

Cantilever Projection = 1200 mm

Effective Depth = 390 mm

Max. Shear Force at 'd' distance from face of Column = 192.40 x ( 1200 - 390 ) / 1000
= 155.85 kN

Factored Shear Force = 155.85 x 1.5 = 233.8 kN

Width of Footing = 1530 mm

233.8 x 1000
Shear Stress = = 0.39 N/mm²
1530 x 390
% Reinforcement Provided = 0.52 %

Permissible Shear Stress = 0.495 N/mm² < 0.39 ----------------------------- SAFE

 Depth 0.6 m

A = 28
Zx = 32.6667 C1 C3
Zz = 18.6667

1.9 2 1.8

C
7

P Mx Mz ez Mx_add ex Mz_add P_s.w P

C1 DL 504 -10 52 -1.6 806.4 0 0 1024.8 1528.8
LL 88 0 0 -1.6 140.8 0 0 0 88

C2 DL 273 -40 0 2.2 -600.6 0 0 0 273

LL 51 0 0 2.2 -112.2 0 0 0 51

C3 DL 168 0 -67 0.4 -67.2 -0.55 -92.4 0 168

LL 204 0 -422 0.4 -81.6 -0.55 -112.2 0 204
WL1 -99 0 260 0.4 39.6 -0.55 54.45 0 -99
WL2 -64 0 87 0.4 25.6 -0.55 35.2 0 -64

DL+LL 2313
DL+LL+WL1 2214
p_ADD = 604.8 Kn DL+LL+WL2 2249
DL+WL1 1871
DL+WL2 1906
 A

C2
4 z

1.3

pressure at
A B C D
P Mx Mz
1528.8 796.4 52 27 76 82 33
88 140.8 0 -1 7 7 -1

273 -640.6 0 29 -10 -10 29

51 -112.2 0 5 -2 -2 5

168 -67.2 -159.4 17 12 -5 0

204 -81.6 -534.2 38 33 -24 -19
-99 39.6 314.45 -22 -19 15 12
-64 25.6 122.2 -10 -8 5 3

2313 36 -642 116 118 49 47

2214 75 -327 94 99 64 59
2249 61 -519 106 110 54 51
1871 128 207 52 60 82 74
1906 114 15 64 71 72 65
COMBINED FOOTING C65 + C68

COLUMN LOADS : ( Safe Bearing Capacity = 150 kN / m² ) Fck = 25 Mpa

X Y Dead Load Live Load EQx Eqz

Column Co.Ord. Co.Ord.
ID. Py Mx Mz Py Mx Mz Py Mx Mz Py Mx Mz
C1 0 0 298.08 0.6 -41.04 4.68 -0.06 -0.78 184.85 36.17 4.8 7.85 -0.37 -71.68
C4 2 0 432.33 4.68 -139 19.81 -0.55 -15.85 -76.97 239.35 -2.08 11.8 -1.89 -153.3

TOTAL 730.41 5.28 -180 24.49 -0.61 -16.63 107.88 275.52 2.72 19.65 -2.26 -225
kN/m²
75.5

B A
750 750
1200

1375
kN/m²
107

2750

350

350
450
kN/m²

C1 C4
117

1125 2000 1125

1200

1375

C D
kN/m²
148.6

450 4250

750 1250 750

Footing Longitudional
Sectiomn
450

B,C A,D

Base Pressure

84.72 92 98.4
59.6 66.48 73.32 kN/m² kN/m² kN/m²
kN/m² kN/m² kN/m²
 Area of Footing Provided A = 11.688 m² Concrete grade = M 25
GEOMETRICAL
PROPERTIES
Moment of Inertia @ CG Ixx = 17.59 m4 Steel Grade = Fe 415
Moment of Inertia @ CG Izz = 7.37 m4
M.O.R
Section Modulus @ CG Zxx = 8.28 m3 = 0.138Fck = 3.45
Section Modulus @ CG Zzz = 5.36 m3
Cover = 50 mm

Calculating Load Eccentricity :

Load Case CG_X of Load Ecc_x CG_z of Load Ecc_z

Dead Load 864.66 / 730.41 = 2.31 m 0.184 m 0 / 730.41 = 1.38 m 0.000 m
Live Load 39.62 / 24.49 = 2.74 m 0.618 m 0 / 24.49 = 1.38 m 0.000 m
Eqx -153.9 / 107.88 = -0.30 m -2.427 m 0 / 107.88 = 1.38 m 0.000 m
Eqz 23.6 / 19.65 = 2.33 m 0.201 m 0 / 19.65 = 1.38 m 0.000 m

Pressure Calculation ( UNIT : kN / m² ) Avg. Pressure Avg. Pressure

Load Case A B C D BC AD AB CD
Dead 52.0 18.3 85.5 119.2 51.9 85.6 35.1 102.4
Live 0.7 -2.8 3.4 7.0 0.3 3.8 -1.0 5.2
Live for EQ 0.4 -1.4 1.7 3.5 0.2 1.9 -0.5 2.6
Eqx 11.4 8.1 7.1 10.4 7.6 10.9 9.7 8.7
Eqz -40.1 -40.5 43.5 43.9 1.5 1.9 -40.3 43.7

(DL+LL) 53 16 89 126 52.2 89.4 34.1 107.6

(DL+Eqx) 63 26 93 130 59.5 96.5 44.9 111.1
(DL-Eqx) 41 10 78 109 44.3 74.7 25.4 93.6
(DL+Eqz) 12 -22 129 163 53.4 87.5 -5.2 146.0
(DL-Eqz) 92 59 42 75 50.4 83.7 75.5 58.7
(DL+LL+Eqx) 64 25 94 133 59.6 98.4 44.4 113.7
(DL+LL-Eqx) 41 9 80 112 44.5 76.6 24.9 96.2
(DL+LL+Eqz) 12 -24 131 167 53.5 89.4 -5.7 148.6
(DL+LL-Eqz) 92 57 44 79 50.6 85.6 74.9 61.3

Min. 11.87 -23.6 42.0 75.33 44.3 74.71 -5.69 58.68

Max. 92.5 58.8 130.7 167 59.6 98.4 75.5 148.6

Sample Calculation of base pressure for Dead Load Case at Corner A :

Pressure due to Column Load C1

P P ex Mx Mz where ex = 1125 - 4250 / 2 = -1000 mm

= + + +
A Zx Zx Zz = -1.00 m

= 298.1 x 1.1 298.1 x -1.00 0.6 -41.0

+ + +
11.69 8.28 8.28 5.36

= 28.05 + -36.01 + 0.072 + -7.661

= -15.54 kN / m²

Pressure due to Column Load C4

P P ex Mx Mz where ex = 4250 / 2 - 1125 = 1000 mm

= + + +
A Zx Zx Zz = 1.00 m

= 432.3 x 1.1 432.3 x 1.00 4.68 -139

+ + +
11.69 8.28 8.28 5.36

= 40.69 + 52.22 + 0.565 + -25.95

= 67.53 kN / m²
Total Pressure at Corner A = -15.54 + 67.53 = 51.99 kN/m²

Transverse Analysis :
350
148.6 + 75.5
Max. Average pressure = = 112.0 kN/m²
2
1100
Cantilever projection = 1.10 m 450

Width considering = 1000 m

75.5
Bending moment = 112.0 x 1.10 148.6 kN/m²
= 123.2 kN - m kN/m²

Factored moment = 123.2 x 1.5 = 184.9 kN - m

Mu
Depth Required = √ R x b
+ Cover + Reinf. Dia / 2

184.9 x 1000 x 1000

=
√ 0.138 x 25 x 1000
+ 50 + 8

= 289.5 mm
Depth Provided = 450 mm --------------------------------- SAFE

Effective Depth = 450 - 50 - 8 = 392 mm

Reinforcement Calculation :

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 184.9 x 1000 x 1000

415 [ 1 - √ 1 -
25 x 1000 x 392 x 392 ]
x 1000 x 392

= 1389 mm²

Minimum Reinforcement = 0.12 %

= 0.12 x 1000 x 392 / 100

= 470.4 mm²

Providing 16 Dia 125 mm c/c Reinforcement Provided = 1608 mm²

--------------------- SAFE

Longitudional Analysis :

66.5 + 91.6
Max. Average pressure = = 79.0 kN/m²
2

Width of Footing = 2.75 m

UDL of Beam = 79.0 x 2.75 = 217.3 kN / m

Span of Beam = 2.00 m

 2
217.3 x 2.00
Bending Moment = = 108.7 kN - m
8

Factored Moment = 108.7 x 1.5 = 163.0 kN - m

Width of Beam = 450 mm

Mu
Depth Required = √ R x b
+ Cover + Reinf. Dia / 2

163.0 x 1000 x 1000

=
√ 0.138 x 25 x 450
+ 50 + 8

= 382.0 mm
Depth Provided = 600 mm ------------------------------------------------- SAFE

Effective Depth = 600 - 50 - 8 = 542 mm

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 163.0 x 1000 x 1000

415 [ 1 - √ 1 -
25 x 450 x 542 x 542 ]
x 450 x 542

= 887 mm²

Provide 16 Dia 5 No Reinforcement Provided = 1005 mm²

Two Way Shear Check :
Column C1 Column C4
Load Combinations : DL + LL = 302.76 452.14 kN
DL + LL+ Eqx = 487.61 375.17 kN
DL + LL- Eqx = 117.91 529.11 kN
DL + LL+ Eqz = 310.61 463.94 kN
DL + LL- Eqz = 294.91 440.34 kN

Max. Column Load 487.61 529.11 kN

Two Way Shear Check For Column C1

max. Axial Load = 487.61 kN

Factored Load = 487.61 x 1.5 = 731.42 kN

Area Resisting Shear = 2( 750 + 392 + 350 + 392 ) x 392

= 1477056 mm²

731.42 x 1000
Shear Stress = = 0.495 N/mm²
1477056
Ks = 0.5 + ß
τc = 0.25 √ Fck = 0.5 + 0.467
= 0.25 x √ 25 = 0.967
= 1.25
b 350
ß = = = 0.467
Permissible Shear Stress = Ks · τc D 750
= 0.967 x 1.25
= 1.208 N/mm² --------------------------------------------------------------------- SAFE

Two Way Shear Check For Column C4

max. Axial Load = 529.11 kN

Factored Load = 529.11 x 1.5 = 793.67 kN

Area Resisting Shear = 2( 750 + 392 + 350 + 392 ) x 392

= 1477056 mm²

793.67 x 1000
Shear Stress = = 0.537 N/mm²
1477056
Ks = 0.5 + ß
τc = 0.25 √ Fck = 0.5 + 0.467
= 0.25 x √ 25 = 0.967
= 1.25
b 350
ß = = = 0.467
Permissible Shear Stress = Ks · τc D 750
= 0.967 x 1.25
= 1.208 N/mm² --------------------------------------------------------------------- SAFE
Reinforcement Calculation :

Longitudional Reinforcement :

Bottom Reinforcement :

max. Bending Moment = 0.0 kN

Factored bending Moment = 1.50 x 0.0 = 0 kN / m²

Considering Effective Width of Footing = 2750 mm

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 0 x 1000 x 1000

415 [ 1 - √ 1 -
25 x 2750 x 392 x 392 ]
x 2750 x 392

= 0 mm²

Minimum Reinforcement = 0.12 %

= 0.12 x 2750 x 392 / 100

= 1294 mm²

Provide 16 Dia 16 No Reinforcement Provided = 3217 mm²

Spacing Provided = 168.8 mm

Providing 16 Dia 165 mm c/c --------------------- SAFE

Top Reinforcement :

max. Bending Moment = 0.00 kN

Factored bending Moment = 1.50 x 0.00 = 0 kN / m²

Considering Effective Width of Footing = 2750 mm

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 0 x 1000 x 1000

415 [ 1 - √ 1 -
25 x 2750 x 392 x 392 ]
x 2750 x 392

= 0 mm²

Minimum Reinforcement = 0.12 %

= 0.12 x 2750 x 392 / 100

= 1294 mm²
Provide 16 Dia 16 No Reinforcement Provided = 3217 mm²
Spacing Provided = 168.8 mm

Providing 16 Dia 165 mm c/c --------------------- SAFE

Transverse Reinforcement :

Bottom Reinforcement :

Effective Width of Footing = 1000 mm

Max. Bending moment at face of Column from AB side =

= (75.45+107.39)/2x(1200/1000)x(2x75.45+107.39)/(75.45+107.39)*(1200/3000)

= 61.99 kN - m ------------------------------------------------ (a)

Max. Bending moment at face of Column from CD side =

= (148.64+116.7)/2x(1200/1000)x(2x148.64+116.7)/(148.64+116.7)*(1200/3000)

= 99.35 kN - m ------------------------------------------------ (b)

Local Distribution of Forces from each Column

band Width of Footing = b+ 2 d = 750 + 2x 392 = 1534 mm

Max. Axial Force In Column = 529.11 kN

529.11 x 1000
Upward Pressure = = 192.40 kN/m
2750

Cantilever Projection = 1200 mm

2
192.40 x 1.2
Max. Moment at Face of Column = = 138.53 kN- m
2

This moment is acting along width of 1534 mm

Hence, moment per meter width = 138.53 / 1.534 = 90.31 kN -m ---------------------------- ( c )

Considering maximum moment from ( a ) , ( b ) and ( c )

Max. bending moment = 99.4 kN-m

Factored Moment = 99.4 x 1.5 = 149.0 kN - m

Mu
Depth Required = √ R x b
+ Cover + Reinf. Dia / 2

149.0 x 1000 x 1000

=
√ 0.138 x 25 x 1000
+ 0 + 0

= 207.8 mm
Depth Provided = 0 mm ------------------------------------------------- UNSAFE

Reinforcement in transverse Direction =

0.5 x Fck 4.6 Mu

Ast =
Fy [ 1 - √ 1 -
Fck b d² ] bd

= 0.5 x 25 4.6 x 149.0 x 1000 x 1000

[ 1 - √ 1 - ]
 415 [ 1 - √ 1 -
25 x 1000 x 392 x 392 ]
x 1000 x 392

= 1105 mm²

Minimum Reinforcement = 0.12 %

= 0.12 x 1000 x 392 / 100

= 470.4 mm²

Providing 16 Dia 100 mm c/c ( Ast provided = 2011 mm² )

------------------------------------------------------ SAFE

Top Reinforcement :

Providing minimum reinforcement

Minimum Reinforcement = 0.12 %

= 0.12 x 1000 x 392 / 100

= 470.4 mm²

Providing 16 Dia 175 mm c/c ( Ast provided = 1149 mm² )

------------------------------------------------------ SAFE

Summary of Reinforcement :

Longitudional Direction Top 16 Dia 165 c/c = 1219 mm² 0.31 %

Bottom 16 Dia 165 c/c = 1219 mm² 0.31 %

Transverse Direction Top. 16 Dia 175 c/c = 1149 mm² 0.29 %

Bottom 16 Dia 100 c/c = 2011 mm² 0.51 %