Design of Shallow Foundation (Isolated Footings)
A. Gross soil pressure & Footing area
unfactored load with surcharge + self weight of footing / allowable soil pressure = ( 2000/1.5x1.1)/150 = 9.78 m2
`sqrt9.78`= 3.12 m side footing , consider 3.2 m isolated footing
net soil pressure & initial Footing depth
= 2000x1000/(3.2x3.2), pn =195.3 kN/m2
Assume depth of footing 500mm and checking it for bearing stress as per IS 456 -2000 clause 34.4
`sqrt`(footing base bearing area / loaded area)` <=2
Permissible bearing stress 0.45xfck= 0.45x25= 11.25 N/mm2
Permissible bearing stress multipied with area factor 11.25x2=22.5N/mm2
Actual bearing stress at column base
(2000x1000)/(400x400)=12.5N/mm2
12.5N/mm2 actual stress is less than permissible 22.5N/mm2 . hence ok
We proceed with 500mm depth footing for furthur design checks
if we assume 50mm cover for footing , the effective depth (d) shall be taken as 450mm
Flexural reinforcement
Conversion of net pressure into udl= 195.3x 3.2=625KN/m
BM due to UDl over cantilever section = Wl2/2= 625x1.6x1.6/2 , M=800KNm
Reinforcement calculation as per Is 456 -2000 annex-G
Mu=o.87 Fy Ast d (1-Ast fy/ bd fck)
Assume Fy=500N/mm2 , Ast = 4350mm2
If we provide 16mm dia rebar at 125mm spacing , the actual rebar provided = 3200/125x201
Ast=5146 mm2.
One way shear stress check :
Shear force in one way shaded area = 0.95 x3.2 x195.3= 593.7 KN
Design Shear stress at One way cut face
`tauv`= 593.7x1000(3200x450)= 0.412N/mm2
Shear stress capacity of section as per Is 456-2000 Table 19 = 0.425 N/mm2
Design shear stress is less than shear capacity , hence ok
Two way shear stress check:
Shear force in two way shaded area =(3.2x3.2)- (0.85x0.85) x 195.3= 1859 KN
Design Shear stress at two way cut face
`tauv`=1859x1000/ ( 3400x450)= 1.215 N/mm2
Shear stress capacity of section as per Is 456-2000 clause 31.6.3.1
=`0.25xsqrt Fck= 1.25 N/mm2
Design shear stress is less than shear capacity , hence ok