a) Material Proerties

fcu : 20 MPa (28 days compressive cube strength of concrete)

fy : 415 MPa (Characteristic steel strength)

wc : 25 kN/m3

(unit wt. of concrete)

Soil qallow : 600 kN/m2

(Safe bearing capacity of soil)

: 18 kN/m3

(unit wt. of soil)

: 30 deg (angle of internal friction of soil)

: 0.5 (Conc. friction factor)

b) Section Proerties Footing - Type-5 - Eccentric Footing with Irregular Geometry

Footing

Length L : 1.80 m Clear cover C : 50 mm

Width B : 1.50 m effective depth of footing

Thickness H : 0.45 m d : 388 mm

Column

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Design of Footing - F1

Pamml House

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Column

column width b : 300 mm

column depth h : 230 mm

c) Load Evaluation

Embedment of column inside footing : 500 mm

Ht. of soil fill on external side above nib : 1200 mm

Ht. of soil fill on internal side above nib : 1200 mm

Pocket details

Nib thickness of pocket at top : 120 mm

Nib thickness of pocket at bottom : 205 mm

ht of nib from top of footing pad : 0 mm

Gap b/w nib and column at top of nib : 25 mm

eccentricity of column position ex : 555 mm

ez : 150 mm

Surcharge on

Internal side : 0.0 kPa

External side : 0.0 kPa

Fx Fz Mz

1.6 1.9 -0.8

-1.0 0.1 0.2

-0.1 -0.3 0.1

Dead Load(DL) 294.2

Mx

0.7

Column Reactions

Primary Load

Type

vertical Horizontal Moment

kN kNm

Fy

0.0

Seismic (EQ) -42.3

Live load (LL) 24.4

-0.3

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Design of Footing - F1

Pamml House

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Volume occupied by concrete nib

Volnib : [(0.555x2)+(0.485x2)]x0.163x0

: 0.000 m3

wt. of nib wnib : 0.00 kN

wt. of footing wfoot : 30.38 kN

Vol. occupied by soil :

Volsoil : (1.2x1.8x1.5)+(1.2x1.455x1.5)-0-0

: 5.859 m3

wt. of soil wsoil : 105.46 kN : 39.06 kPa

Total unfactored vertical load without eccentricity

P1 : 30.38 kN

vol of soil - vol of nib - vol

of column

ZZ

XX

1800

45

0

ex=555

Footing Elevation

P1 : 30.38 kN

Fx Fz Mz

1.6 1.9 163.2

-1.0 0.1 13.3

-0.1 -0.3 -23.4

Fx Fz Mz

Service Load

1 1.0 DL 0.6 2.0 176.5

2 1.0 DL + 1.0 EQ 0.5 1.7 153.1

3 0.9 DL + 1.0 EQ 1.3 1.4 123.5

4 0.9 DL - 1.0 EQ 1.3 1.4 170.3

Ultimate Load

5 1.4 DL 0.9 2.7 247.1

6 1.4 DL + 1.4 EQ 2.1 2.3 195.7

7 1.2 DL + 1.2 EQ 0.6 2.1 183.7

8 1.0 DL + 1.4 EQ 1.5 1.5 130.4

9 1.0 DL - 1.4 EQ 1.5 1.5 196.0

10 1.4 DL - 1.4 EQ 2.1 2.3 261.3

55.0

454.5 49.4

Horizontal

73.3

412.2

+ 1.2 LL

Horizontal

+ 1.0 LL

494.6

-42.3

kN

+ 1.0 LL

Dead Load(DL)

Live load (LL)

kN kNm

Fy

430.0

24.4

636.3

42.7

69.1

344.7 34.4

kNm

Moment

47.8

Vertical

Fy

Load

Case -

(LC)

370.8

542.8

vertical

Seismic (EQ)

Load Combinations

45.6

3.7

-6.7

370.8

Design Loads on Footing

+ 1.4 LL

Additional moments develop due to vertical and horizontal

reactions from column eccentricity.

Moment

Mx

Primary Load

Type

36.2

Mx

51.2

542.8 54.5

344.7

XX

1800

15

00

ex=555

ez=

15

0

Footing Plan

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Design of Footing - F1

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e) Stability Check

Check for overturning 4

OTMx : 47.78 kNm (Overturning moment about x- axis)

OTMz : 170.32 kNm (Overturning moment about z- axis)

The restoring moment is

RMx : [430.04+105.462+0]x(0.75) RMz : 535.5x(0.9)

: 401.63 kNm : 482 kNm

FOS : RMx/OTMx : 8.406 > 1.5 Hence the footing is safe against overturning in 'x'.

: RMz/OTMz : 2.83 > 1.5 Hence the footing is safe against overturning in 'z'.

Check for Sliding 4

DFx : 1.34 kN (Disturbing force along x- axis)

DFz : 1.42 kN (Disturbing force along z- axis)

The resisting force is

(Load case)

(Load case)

The resisting force is

RF : x (total vertical force)

RF : 344.73x0.5

: 172.4 kN

FOS : RF/DFx : 128.82 > 1.5 Hence the footing is safe against sliding in 'x'.

: RF/DFz : 121 > 1.5 Hence the footing is safe against sliding in 'z'.

e) Design of Footing

Check footing 4

Mx : 47.78 kNm Ps : 344.73 kN

Mz : 170.32 kNm

eccentricity due to moment

ez : Mx/P B/6 : 0.25 m

: 0.139 m e < L/6, therefore the pressure is trapezoidal.

ex : Mz/P L/6 : 0.3 m

: 0.494 m e > L/6, therefore the pressure is triangular.

The trapezoidal pressure along z direction is given by,

qmax : (P/A) + (6 M/LB^2) qmin : (P/A) - (6 M/LB^2)

: 198.47 kPa : 56.89 kPa

The triangular pressure along x direction is given by,

qmax : 2P/[3B(L/2-e)] qmin : no tension = 0

: 377.43 kPa : 0 kPa

Check the adequacy of footing

Due to the wind load case, the allowable bearing pressure can be increased by 25% as per

BS 8004:1986, sec- 2.3.2.4.3.

qa,enh : 1.25 x 600 : 750 kPa

(Load case)

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Design of Footing - F1

Pamml House

PRC

qmax : 586.69 - 39.06 (Maximum pressure - pressure due to wt. of soil above the footing)

: 547.6 kPa < 750 kPa, Hence the footing is safe.

Check for Shear and BM

The governing ultimate load combinations is

5

Pu : 636.27 kN

Mux : 69.119 kNm ezu : 0.109 m

Muz : 247.09 kNm exu : 0.388 m

The trapezoidal pressure along z direction is given by,

qumax,z : (P/A) + (6 M/LB^2)

: 338.1 kPa

qumin,z : (P/A) - (6 M/LB^2)

: 133.3 kPa

(Load case)

: 133.3 kPa

The triangular pressure along x direction is given by,

qumax,x : 2P/[3B(L/2-e)]

: 552.7 kPa

qumin,x : no tension = 0

: 0 kPa

Z

D C

1800

A B

X

The pressure calculation is made cosidereing an equivalent area available against the length and width of

footing. Additional eccentricity is considered in the design for arriving at the size of footing.

LC-1 LC-2 LC-3 LC-4 LC-5 LC-6 LC-7 LC-8 LC-9 LC-10

P kN 454.5 412.18 344.7 344.7 636.3 542.8 494.6 370.8 370.8 542.8

Mx kNm 49.37 42.664 34.37 47.78 69.1 54.5 51.2 36.25 55.03 73.28

Mz kNm 176.5 153.06 123.5 170.3 247.1 195.7 183.7 130.4 196 261.3

ez m 0.109 0.1035 0.1 0.139 0.109 0.1 0.104 0.098 0.148 0.135

ex m 0.388 0.3713 0.358 0.494 0.388 0.361 0.371 0.352 0.529 0.481

P/A kPa 168.3 152.66 127.7 127.7 235.7 201 183.2 137.3 137.3 201

15

00

DescriptionService Load Combination (kPa) Ultimate Load Combination (kPa)

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LC-1 LC-2 LC-3 LC-4 LC-5 LC-6 LC-7 LC-8 LC-9 LC-10

A kPa 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

B kPa 223.2 203.1 170.0 168.2 312.5 267.6 243.7 183 180.3 265.1

C kPa 566.3 490.0 395.5 586.7 792.8 626.8 588.0 418 707.1 887.5

D kPa 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

586.7 kPa < allowable = 750 kPa, hence footing is safe.

The ultimate pressure across 'x' and 'z' direction are, (Load case) 5

X - direction Z - direction

AD qAD : 0 kN/m AB qAB : 239.9 kN/m

BC qBC : 829.03 kN/m CD qCD : 608.5 kN/m

The acting length 'a' of pressure along length of footing from qmax

ax : 1.535 m az : 1.5 m

Status

Corner

Pressure

Service Load Combination (kPa) Ultimate Load Combination (kPa)

ax : 1.535 m az : 1.5 m

Considering the direction of wind from both the sides, the footing is checked for shear and BM.

The critical BM at the face of the column along XX direction

Left MxL : [0x1.34^(2)/2]+[1/2x580.58x1.075x0.36]

: 112.34 kNm

Right MxR : [704.81x0.23^(2)/2]+[1/2x124.22x0.23x0.15]

: 20.785 kNm Muxx : 112.3 kNm

The critical BM at the face of the column along ZZ direction

Left MzL : [239.86x0.75^(2)/2]+[1/2x184.32x0.75x0.25]

: 84.741 kNm

Right MzR : [497.91x0.45^(2)/2]+[1/2x110.59x0.45x0.3]

: 57.878 kNm Muzz : 84.74 kNm

XX

0 kN/m

1535

L=1800

829 kN/m

1340230

Ultimate Base Pressure along Length

(kN/m)

Load Case - 5

A B

ZZ

240 kN/m

1500

B=1500

609 kN/m

750 450

Ultimate Base Pressure along Width

(kN/m)

Load Case - 5

A D

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Design of Footing - F1

Pamml House

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For beam shear, the critical location is at 'd' from col. Face. Therefore distance from edge of fooring is

XL : 0.952 m ZL : 0.362 m

XR : 1.8 m ZR : 1.438 m

Shear force from left is

V1XL : (0 + 371.03)/2 x 0.687 V1ZL : (239.86 + 328.82)/2 x 0.362

: 127.45 kN : 102.9 kN

Shear force from right is

V1XR : (829.03 + 829.03)/2 x 0 V1ZR : (608.5 + 593.26)/2 x 0.062

: 0.0 kN : 37.3 kN

V1X : 127.4 kN V1X : 102.9 kN

For Punching shear, the critical location is at 1.5d from face of col.

L1 : 1042.0 mm PrL : 4.75 m (shear perimeter)

B1 : 1332.0 mm A2s : 1.39 sqm (Shear area)

Total load under footing Ptot : 636.27 kN

Average pressure under shear area : {[(266.25 + 829.03)/2/1.5]+[(281.15 + 608.5)/2/1.8]}/2

: 306.1 kPa

load under shear area A2s : 306.11 x 1.042 x 1.332

: 425 kN

Punching shear : Total load - Load under shear area

V2 : 636.27 - 424.86

V2 : 211.40 kN

Check for Flexure

Effective depth of footing d : 388 mm

Along Length Along Width

bx : 1500 mm bz : 1800 mm

Mux : 112.3 kNm Muz : 84.7 kNm

Here, k : Mu/bd2fcu (BS-8110-1:1997- Sec.3.4.4.4)

: 0.025 : 0.016

< 0.156, hence comp. reinf. is not required. < 0.156, hence comp. reinf. is not required.

zx : 376.96 mm zz : 381.1 mm

but not greater than, 0.95d 0.95d : 368.6 mm

z : lesser of {376.96, 0.95 d}

zx : 368.6 mm zz : 368.6 mm

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Design of Footing - F1

Pamml House

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Required reinforcement for the BM,

As,req : Mu/0.95Fyz

Asx,req : 773.05 mm2

Asz,req : 583.1 mm2

Minimum reinforcement required for slab as per Table 3.25 of BS-8110-1:1997 is

: (for slab) As,min : 1053 mm2

Provide reinforcement along x direction as

@ 150 mm c/c. no. of bars : 10 nos.

Asx,prov : 1,131 mm2

> 1053 sqmm, Hence o.k.

Along z direction,

@ 150 mm c/c. no. of bars : 12 nos.

Asz,prov : 1,357 mm2

> 1053 sqmm, Hence o.k.

Check for shear

12 mm

0.13%

12 mm

Check for shear

One way Shear

c1x : 127450 / (1500 x 388) c1Z : 102930 / (1800 x 388)

: 0.22 N/mm2

: 0.15 N/mm2

Shear strength of concrete is given by

vc :

Along X direction Along Z direction

100 Asx/(bx d) : 0.19 100 Asz/(bz d) : 0.19

(400/d)1/4

: 1.01

(Fcu/25)1/3

: 0.93

vc,X : 0.34 N/mm2

vc,Z : 0.342 N/mm2

> 0.22 MPa, Hence o.k. > 0.15 MPa, Hence o.k.

Vc,X : 199.29 kN Vc,Z : 239.1 kN

Punching Shear

c2x : 211400 / (4748 x 388)

: 0.11 N/mm2

Shear strength of concrete is given by

vc :

Here,

100 Asx/(bx d) : (0.194 + 0.194) /2

: 0.194

vc,X : 0.34 N/mm2

> 0.11 MPa, Hence o.k.

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Design of Footing - F1

Pamml House

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