Design of Shallow Foundation (Isolated Footings)
Gross soil pressure and footing area:
Unfactored load with surcharge + self weight of footing / allowable soil pressure
=(2000/1.5 x 1.1) /150 = 9.78 m2
Assuming we have sqaure footing √9.78=3.12 meter side footing consider, 3.2 meter sided isolate footing.
Net soil pressure and initial footing depth:
Factored Load/Actual Area footing= 2000 x 1000/ (3.2 x 3.2)
ρn = 195.3 Kn/m2
Assuming depth of footing 500mm and checking it for bearing stress as per IS-456-2000 clause 34.4-
√(footing base bearing area / loaded area)≤ 2
Permissible bearing stress 0.45 x fck=11.25 N/mm2
Permissible bearing stress multiply with area factor= 11.25 x 2 = 22.5N/mm2
Actual bearing stress at column = (2000 x 1000) / (400 x 400) = 12.5 N/mm2
12.5 N/mm2 actual stress is less than permissible 22.5N/mm2. Hence Okay.
We can proceed with 500mm depth footing for further design.
If we assume 50mm cover for footing the effective depth(d) shall be taken as 450mm
Flenural reinforcement=
Conversion of net pressure into Uniformly Distributed Load = 195.3 x 3.2 = 625 KN/m
Bending moment due to UDL over a cantilever section = WL2/2 = 625 x 1.6 x 1.6 /2 = 800 KN/m
Reinforcement calculation as per IS-456-2000 Annexure-G
μu= 0.87 fy Ast d (1-Ast.fy/bd.fck)
Assume fy=500 N/mm2
In result Ast required= 4350mm2
If we provide 16mm Dia rebar at 125mm spacing,the actual rebar provided= 3200/125 x 201
Ast provided= 5146 mm2
One way shear stress check:
Shear force in the one way area= 0.95 x 3.2 x 195.3 = 593.7 KN
Design shear stress at one way cut face τv =593.7 x 1000/ (3200 x 450) = 0.412 N/mm2
Shear stress capacity of section as per IS -456-2000 table-19 = 0.425N/mm2
Design shear stress is less than shear capacity-HENCE OKAY
Two way shear stress check:
Shear force in the two way shadded area = (3.2 x 3.2) - (0.85 x 0.85) x 195.3 = 1859 KN
Design shear stress at TWO WAY cut force τv = 1859 x 1000 / (3400 x 450) = 1.215N/mm2
Shear Stress capacity at section as per IS- 456-2000 clause 31.6.3.1
= 0.25 x √ Fck = 1.25 N/mm2
Design shear stress is less than shear capacity - HENCE OK