Design of Shallow Foundation (Isolated Footings)

Aim: To design a square footing for a column size of 400x400 and sketch the footing.

Introduction: Footings and other foundation units transfer loads from the structure to the soil or rock supporting the structure. Because the soil is generally much weaker than the concrete columns and walls that must be supported, the contact area between the soil and the footing is much larger than that between the supported member and the footing.

Most common types of footings used are:

• Strip or wall footing
• Spread footing
• Pile cap 
• Combined footing
• Mat or raft footing

Procedure:

Steps involved in design of square footing :

• Determine the size of footing
• Depth of footing on the basis of BM
• Area of R/F
• Check for one way shear
• Check for two way shear

a) Calculation of pressure for footing area

• Gross soil pressure = (2000/1.5 x 1.1)/150 = 9.78 m2 (Assuming square footing)
• Side footing = √9.78 = 3.12 m 
• Consider, 3.2 m sided isolated footing

b) Calculation of pressure for flexure and shear design

• Net soil pressure = Factored load/actual area of footing
• Pn = 2000x1000/ (3.2x3.2)
• Pn = 195.3 kN/m2

c) Initial depth of footing

• Assume depth of footing 500 mm and checking it for bearing stress as per 1S-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 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. (Okay). We can proceed with 500mm depth footing for further design checks. If we assume 50mm cover for footing, the effective depth (d) shall be taken as 450 mm.

d) Flexural reinforcement calculation

• Bending moment due to UDL over a cantilever section, M = wL2/2 = 625x1.6x1.6/2 = 800 kNm
• Reinforcement calculation as per IS-456-2000 Annex-G

fy = 500 N/mm2 (Assume) Ast req= 4350 mm2 (In result) If we provide 16 mm dia. rebar at 125 mm spacing, Ast  provided = 3200/125 x 201 Ast  provided = 5146 mm2

e) One way shear check

• Shear force in the one way shaded area = 0.95 x 3.2 x 195.3 = 593.7 kN
• Design shear stress at One way cut face, τv = 593.7x1000/ (3200x450) = 0.412 N/mm2
• Shear stress capacity of section as per IS-456-2000 Table-19 (include rebar) = 0.425 N/mm2 

Design shear stress 0.412 N/mm2 is less than shear capacity 0.425 N/mm2. ( Okay )

f) Two way shear check

• Shear force in the two way shaded area = (3.2x3.2) - (0.85x0.85) x 195.3 = 1859 kN
• Design shear stress at Two way cut face, τv = 1859x1000 / (3400x450) = 1.215 N/mm2
• Shear stress capacity of section as per IS-456-2000 clause 31.6.3.1 = 0.25 x √Fck = 1.25 N/mm2

Design shear stress 1.215 N/mm2 is less than shear capacity 1.25 N/mm2. ( Okay )

g) Sketch the footing 

Result: Using the given details the square footing has been designed successfully.

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