Design of Shallow Foundation (Isolated Footings)

Area of Footing

Unfactored load with surcharge+ self weight of footing / allowable bearing capacity

= ( 2000/1.5 * 1.1)/ 150 = 9.78m ²

√9.78 m ² = 3.12 m Side footing

Hence, 3.2 m side isolated footing.

Net Soil Pressure & Initial footing depth.

Factored Load / actual area of Footing

2000/(3.2*3.2)

Pn = 195.3 KN/m²

Assuming depth of Footing 500mm and checking it for bearing stress IS 456: 2000 clauses 34.4

√ Footing base bearing area / Loaded area <= 2

√ 5.76/0.16 = 6

Which is greater then 2 so we consider 2

Permissible bearing stress 0.45fck = 11.25 N/mm²

Permissible bearing stress multiplied with area factores = 11.25*2 = 22.5 N/mm²

Actual area stress at column Base

Load / area = (2000*1000)/(400*400)= 12.5N/mm²

12.5 N/mm² is less then permissible stress i.e. 22.5 N/mm²

Henck Ok

Flexural Reinforcement

Conversions of net Pressure into UDL

= 195.3*3.2 = 625 KN/m

Bending Moment due to UDL over cantilever section

Wl²/2 = 625*1.6*1.6/2

M= 800 KNm

Reinforcement Calculation as per IS 456: 2000

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

Assume Fy = 500 N/mm²

In result, Ast = 4350 m²

If we provide 16mm dia rebar 125 mm spacing

Therefore actual rebar provided

= 3200/125* 201 = 5146 mm ²

One Way shear Check

Shear force in the one way cut face

Tv= 593.7*1000/3200*450 = 0.412 N/mm²

Shear stress Capacity of S/c as per IS code 456:2000 Table 19

=0.425 N/mm²

Hence shear is ok

Two way shear stress

Shear Force in the two way shaded area

=(3.2*3.2)-(0.85*0.85)*195.3 = 1859KN

Design Shear stress at Two way cut face

Tv= 1859*1000/(3400*450) = 1.215 N/mm²

shear stress Capacity of s/c as per Is codes 456:2000 clauses 31.6.3.1

=0.25√fck = 1.25 N/mm²

Design shear stress is less then permissible shear capacity Hence Ok.