Design of Shallow Foundation (Isolated Footings)

Gross Soil Pressure

Factored Load=2000 KN

Unfactored Load=2000/1.5=1333.33 KN

For the Gross Soil Pressure,we do use only the unfactored load along with the self weight of the column and the surcharge load on the footing.

But,as here we don't have any information related to the surcharge weight and the self weight of the footing,we just add 10% of the unfactored load for the area of footing calculation.

Allowable Soil Pressure=150 KN/(sq m)

Area of Footing

Area of Footing=Sum of [Unfactored Load and Surcharge Weight and Self Weight of Footing]/Allowable Soil Pressure

Area of Footing=(1333.33X1.1)/150=9.78 sq m

We assume the footing is of square shape.

Then,one side of the square=sqrt(9.78)=3.12 m=>3.2 m

So,we take the size of the square footing as 3.2 mX3.2 m.

Net Soil Pressure

For the net soil pressure,we use the factored load but here we don't consider the surcharge weight of the soil as well as the self weight of the footing.

Net Soil Pressure=2000/(3.2X3.2)=195.31 KN/sq m

Depth of Footing

We assume the depth of the footing as 500 mm where the effective depth of the footing be 450 mm.

Then,

Permissible bearing stress=0.45XfckXarea factor=0.45X25X2=22.5 N/ sq mm

Actual bearing stress at column base=(2000X1000)/(400X400)=12.5 N /sq mm<22.5 N/sq mm

Hence,OK!

Flexural Reinforcement

Conversion of net pressure in to UDL=195.31X3.2=625 KN/m

Bending Moment due to the Cantilever action of the footing be,

M=W(LXL)/2=625(1.6X1.6)/2=800 kNm

As per the IS 456:2000,

Mu=0.87(fy)(Ast)d{1-(Ast/bd)(fy/fck)}

8000X1000X1000=0.87X415XAstX450{1-(Ast/3200X450)(415/25)}

4923.91=Ast[1-0.000115Ast]

4923.91=Ast-0.000115(AstXAst)

0.000115(AstXAst)-Ast+4923.91=0

(AstXAst)-8695.65Ast+42816608.7=0

Ast= 4347.825 sq mm

So,we provide 16 mm dia bars@125 mm c/c.

Then,3200/125=>26+1=27 bars

So,the steel provided=3.14X8X8=5425.92 sq mm>4347.825 sq mm

One Way Shear Check

Here,we consider the shear force acting only on one side where the section is at a distance of effective depth from the column face.

Shear Force=0.95X3.2X195.31=593.74 KN

Where we use the Net Soil Pressure for the calculation.

Design Shear Stress=(593.74X1000)/(3200X450)=0.412 N/sq mm

We then calculate the Capacity Design Shear using Table 19 of IS 456:2000.

100Ast/bd=(100X5425.92)/(3200X450)=0.3768

For 0.3768,from table,Capacity Design Shear=0.49 N/sq mm>0.412N/sq mm

Hence,OK!

Two Way Shear Check

Here,we consider the shear force acting on all sides where the section is at a distance of half of the effective depth from the column face.

Shear Force=[(3.2X3.2)-(0.84X0.85)]X195.31=1858.86 KN

Design Shear Stress=(1858.86X1000)/(3400X450)=1.214 N/sq mm