Design of Shallow Foundation (Isolated Footings)

Steps involved in Footing design

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

Gross soil pressure and footing area first trophy

Unfactored load with surcharge + self weight of footing / allowable soil pressure

= (2000/1.5x1.1)/150 = 9.76 m²

Assuming we have square footing

√9.78 = 3.12 meter side footing

Consider, 3.2 meter sided isolated footing

Net soil pressure & initial footing depth

• Factored load / actual area of footing

2000x1000 / (3.2x3.2)

P_n = 195.3 Kn/m²

• Assume depth of footing 500 mm 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 F_ck= 11.25 N/mm²

Permissible bearing stress multiplied with area factor 11.25 x 2 = 22.5 N/mm²

• Actual bearing stress at column base

(2000x1000) / (400x400) = 12.5 N/mm²

12.5 N/mm² actual stress is less than permissible 22.5 N/mm² .Hence Okay

We can proceed with 500mm depth footing for further design check.

If we assume 50mm cover for footing, the effective depth (d) shall be taken 450mm.

Flexural reinforcement:

• Conversation 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 1.6x 1.6/2

M= 800 Knm

• Reinforcement calculation as per IS - 456-2000 Annex-G

M_u =0.87 f_y A_st d (1- A_st f_y / bd f_ck)

Assume Fy = 500N/mm², In result Ast Required = 4350 mm²

If we Provide 16mm dia rebar at 125 mm spacing, the actual rebar provided = 3200/125 x 201

Ast provided = 5146 mm²

One way shear stress check:

• Shear force in the one way shaded area = 0.95 x 3.2 x 195 = 593.7 Kn

• Design shear stress at one way cut face Ʈ_v = 593.7 x 1000 / (3200x450) = 412 N/mm²

• Shear stress capacity of section as per IS-456-2000 Table -19 (Included rebar) = 425 N/mm²

• Design shear stress is less than shear capacity hence okay.

Two way shear stress check:

• Shear force in the two way shaded area = (3.2x3.2) - 195 = (0.85x0.85) x 195.3 = 1859 Kn

• Design shear stress at two way cut face Ʈ_v = 1859 x 1000 / (3400x450) = 215 N/mm²

• Shear stress capacity of section as per IS-456-2000 clause 31.6.3.1 = 0.25 x √F_ck= 25 N/mm²

• Design shear stress is less than shear capacity hence okay.