Design of Shallow Foundation (Isolated Footings)

Steps involved in Footing design

1. Calculation of gross soil pressure for footing area
2. Calcultion of net soil pressure for flexural and shear design
3. Initial depth of footing calculation
4. Flexural reinforcement cakculation
5. One way shear check
6. Two way shear check

1.Gross soil presuure and footing area

• Unfactored load with surcharge +Self wt of footing /Allowable soil pressure

=(2000/1.5x1.1)/150

=9.82m^2

Assuming we have squre footing

=3.12m side footing

Consider 3.2m sided isolated footing

2.Net soil pressure and initial footing depth

• Factored load /Actual area of footing

=2000X1000 (LXB)

=2000X1000 (3.2X3.2)

Pn=195.3kN/mm^2

• Assume depth of footing 500mm and checking it for bearing stress as per IS-456-2000 clause 3.4.4

` squre root`(Footing base bearing area/Loaded area)<2

• Permissible besring stress =0.45Xfck=11.25N/mm^2
• Permissible neaeing stress multiplied with area factor

=11.25X2

=22.5 N/mm^2

• Actual bearing stress at column base

(2000X1000)/(400X400)=12.5N/mm^2

12.5N/mm^2 actual stress is less than permissible stress 22.5N/mm^2 hence ok

• We can proceed with 500mm depth footing further design check
• If we assume 500mm cover for footing , the effective depth (d) shall be taken as 450mm

D=500mm

d'=50mm

d=D-d'=450mm

3.Felxural reinforcement

• Conversion of net pressure into UDL

=195.3X3.2=625kN/m

• Bending moment due to UDL over cantiliver section =wl^2/2

M=625X1.6x1.6/2

M=800kN-m

• Reinforcement calculation as per IS-456:2000 Annuex G

Mu=800kN-m

d=450mm

fy=500 N/mm^2

b=400mm

fck=20 N/mm^2

Ast=4350mm^2

• If we provide 16mm dia rebar at 125mm spacing actual rebar provided =3200/125 X201

Ast provided =5146mm^2

4.One way shear stress check

• Shear force in the one way shaded area

V =0.95X3.2X195.3

V=593.7kN

• Design shear stress at one way cut face

Tc=593.7 X1000/(3200X450)

Tc =0.412 N/mm^2

• Shear stress capacity at section as per IS 450:2000 T-19 (include rebar)

= 0.425N/mm^2

• Design shear stress is less than shear capacity

Hence okay

5.Two way shear stress check

• Shear firce in two way shaded area

V =(3.2X3.2)-(0.85X0.85) X195.6

=1895 kN

• Design shear stress at two way cut face

Tv=1859 X 1000 /(3400X450)

=1859 x1000

=1.215 N/mm^2

• Shear stress capacity of section as per IS 456:2000 Clause 31.6.3.1

=0.25 X `square root`(fck)=1.25N/mm^

• Design shear stress is less tan shear capacity

Hence ok

Reinforcement details